diff --git a/stable b/stable
index 53fb28c2..496bc26d 120000
--- a/stable
+++ b/stable
@@ -1 +1 @@
-v0.15.14
\ No newline at end of file
+v0.15.15
\ No newline at end of file
diff --git a/v0.15 b/v0.15
index 53fb28c2..496bc26d 120000
--- a/v0.15
+++ b/v0.15
@@ -1 +1 @@
-v0.15.14
\ No newline at end of file
+v0.15.15
\ No newline at end of file
diff --git a/v0.15.15/assets/documenter.js b/v0.15.15/assets/documenter.js
new file mode 100644
index 00000000..22f0f9a0
--- /dev/null
+++ b/v0.15.15/assets/documenter.js
@@ -0,0 +1,260 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.15.10/languages/julia.min',
+    'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.10.3/headroom.min',
+    'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.12.1/jquery-ui.min',
+    'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/contrib/auto-render.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min',
+    'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.10.3/jQuery.headroom.min',
+    'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min',
+    'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.15.10/highlight.min',
+    'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/9.15.10/languages/julia-repl.min',
+  },
+  shim: {
+  "highlight-julia": {
+    "deps": [
+      "highlight"
+    ]
+  },
+  "katex-auto-render": {
+    "deps": [
+      "katex"
+    ]
+  },
+  "headroom-jquery": {
+    "deps": [
+      "jquery",
+      "headroom"
+    ]
+  },
+  "highlight-julia-repl": {
+    "deps": [
+      "highlight"
+    ]
+  }
+}
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'katex', 'katex-auto-render'], function($, katex, renderMathInElement) {
+$(document).ready(function() {
+  renderMathInElement(
+    document.body,
+    {
+  "delimiters": [
+    {
+      "left": "$",
+      "right": "$",
+      "display": false
+    },
+    {
+      "left": "$$",
+      "right": "$$",
+      "display": true
+    },
+    {
+      "left": "\\[",
+      "right": "\\]",
+      "display": true
+    }
+  ]
+}
+
+  );
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'highlight', 'highlight-julia', 'highlight-julia-repl'], function($, hljs) {
+$(document).ready(function() {
+    hljs.initHighlighting();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'headroom', 'headroom-jquery'], function($, Headroom) {
+
+// Manages the top navigation bar (hides it when the user starts scrolling down on the
+// mobile).
+window.Headroom = Headroom; // work around buggy module loading?
+$(document).ready(function() {
+  $('#documenter .docs-navbar').headroom({
+    "tolerance": {"up": 10, "down": 10},
+  });
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Modal settings dialog
+$(document).ready(function() {
+  var settings = $('#documenter-settings');
+  $('#documenter-settings-button').click(function(){
+    settings.toggleClass('is-active');
+  });
+  // Close the dialog if X is clicked
+  $('#documenter-settings button.delete').click(function(){
+    settings.removeClass('is-active');
+  });
+  // Close dialog if ESC is pressed
+  $(document).keyup(function(e) {
+    if (e.keyCode == 27) settings.removeClass('is-active');
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Manages the showing and hiding of the sidebar.
+$(document).ready(function() {
+  var sidebar = $("#documenter > .docs-sidebar");
+  var sidebar_button = $("#documenter-sidebar-button")
+  sidebar_button.click(function(ev) {
+    ev.preventDefault();
+    sidebar.toggleClass('visible');
+    if (sidebar.hasClass('visible')) {
+      // Makes sure that the current menu item is visible in the sidebar.
+      $("#documenter .docs-menu a.is-active").focus();
+    }
+  });
+  $("#documenter > .docs-main").bind('click', function(ev) {
+    if ($(ev.target).is(sidebar_button)) {
+      return;
+    }
+    if (sidebar.hasClass('visible')) {
+      sidebar.removeClass('visible');
+    }
+  });
+})
+
+// Resizes the package name / sitename in the sidebar if it is too wide.
+// Inspired by: https://github.com/davatron5000/FitText.js
+$(document).ready(function() {
+  e = $("#documenter .docs-autofit");
+  function resize() {
+    var L = parseInt(e.css('max-width'), 10);
+    var L0 = e.width();
+    if(L0 > L) {
+      var h0 = parseInt(e.css('font-size'), 10);
+      e.css('font-size', L * h0 / L0);
+      // TODO: make sure it survives resizes?
+    }
+  }
+  // call once and then register events
+  resize();
+  $(window).resize(resize);
+  $(window).on('orientationchange', resize);
+});
+
+// Scroll the navigation bar to the currently selected menu item
+$(document).ready(function() {
+  var sidebar = $("#documenter .docs-menu").get(0);
+  var active = $("#documenter .docs-menu .is-active").get(0);
+  if(typeof active !== 'undefined') {
+    sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+  }
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+function set_theme(theme) {
+  var active = null;
+  var disabled = [];
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    var themename = ss.ownerNode.getAttribute("data-theme-name");
+    if(themename === null) continue; // ignore non-theme stylesheets
+    // Find the active theme
+    if(themename === theme) active = ss;
+    else disabled.push(ss);
+  }
+  if(active !== null) {
+    active.disabled = false;
+    if(active.ownerNode.getAttribute("data-theme-primary") === null) {
+      document.getElementsByTagName('html')[0].className = "theme--" + theme;
+    } else {
+      document.getElementsByTagName('html')[0].className = "";
+    }
+    disabled.forEach(function(ss){
+      ss.disabled = true;
+    });
+  }
+
+  // Store the theme in localStorage
+  if(typeof(window.localStorage) !== "undefined") {
+    window.localStorage.setItem("documenter-theme", theme);
+  } else {
+    console.error("Browser does not support window.localStorage");
+  }
+}
+
+// Theme picker setup
+$(document).ready(function() {
+  // onchange callback
+  $('#documenter-themepicker').change(function themepick_callback(ev){
+    var themename = $('#documenter-themepicker option:selected').attr('value');
+    set_theme(themename);
+  });
+
+  // Make sure that the themepicker displays the correct theme when the theme is retrieved
+  // from localStorage
+  if(typeof(window.localStorage) !== "undefined") {
+    var theme =  window.localStorage.getItem("documenter-theme");
+    if(theme !== null) {
+      $('#documenter-themepicker option').each(function(i,e) {
+        e.selected = (e.value === theme);
+      })
+    }
+  }
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// update the version selector with info from the siteinfo.js and ../versions.js files
+$(document).ready(function() {
+  var version_selector = $("#documenter .docs-version-selector");
+  var version_selector_select = $("#documenter .docs-version-selector select");
+
+  version_selector_select.change(function(x) {
+    target_href = version_selector_select.children("option:selected").get(0).value;
+    window.location.href = target_href;
+  });
+
+  // add the current version to the selector based on siteinfo.js, but only if the selector is empty
+  if (typeof DOCUMENTER_CURRENT_VERSION !== 'undefined' && $('#version-selector > option').length == 0) {
+    var option = $("<option value='#' selected='selected'>" + DOCUMENTER_CURRENT_VERSION + "</option>");
+    version_selector_select.append(option);
+  }
+
+  if (typeof DOC_VERSIONS !== 'undefined') {
+    var existing_versions = version_selector_select.children("option");
+    var existing_versions_texts = existing_versions.map(function(i,x){return x.text});
+    DOC_VERSIONS.forEach(function(each) {
+      var version_url = documenterBaseURL + "/../" + each;
+      var existing_id = $.inArray(each, existing_versions_texts);
+      // if not already in the version selector, add it as a new option,
+      // otherwise update the old option with the URL and enable it
+      if (existing_id == -1) {
+        var option = $("<option value='" + version_url + "'>" + each + "</option>");
+        version_selector_select.append(option);
+      } else {
+        var option = existing_versions[existing_id];
+        option.value = version_url;
+        option.disabled = false;
+      }
+    });
+  }
+
+  // only show the version selector if the selector has been populated
+  if (version_selector_select.children("option").length > 0) {
+    version_selector.toggleClass("visible");
+  }
+})
+
+})
diff --git a/v0.15.15/assets/logo.png b/v0.15.15/assets/logo.png
new file mode 100644
index 00000000..86f00ed5
Binary files /dev/null and b/v0.15.15/assets/logo.png differ
diff --git a/v0.15.15/assets/search.js b/v0.15.15/assets/search.js
new file mode 100644
index 00000000..e30e9070
--- /dev/null
+++ b/v0.15.15/assets/search.js
@@ -0,0 +1,247 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'lunr': 'https://cdnjs.cloudflare.com/ajax/libs/lunr.js/2.3.6/lunr.min',
+    'lodash': 'https://cdnjs.cloudflare.com/ajax/libs/lodash.js/4.17.15/lodash.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.4.1/jquery.min',
+  }
+});
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery', 'lunr', 'lodash'], function($, lunr, _) {
+
+$(document).ready(function() {
+  // parseUri 1.2.2
+  // (c) Steven Levithan <stevenlevithan.com>
+  // MIT License
+  function parseUri (str) {
+    var  o   = parseUri.options,
+      m   = o.parser[o.strictMode ? "strict" : "loose"].exec(str),
+      uri = {},
+      i   = 14;
+
+    while (i--) uri[o.key[i]] = m[i] || "";
+
+    uri[o.q.name] = {};
+    uri[o.key[12]].replace(o.q.parser, function ($0, $1, $2) {
+      if ($1) uri[o.q.name][$1] = $2;
+    });
+
+    return uri;
+  };
+  parseUri.options = {
+    strictMode: false,
+    key: ["source","protocol","authority","userInfo","user","password","host","port","relative","path","directory","file","query","anchor"],
+    q:   {
+      name:   "queryKey",
+      parser: /(?:^|&)([^&=]*)=?([^&]*)/g
+    },
+    parser: {
+      strict: /^(?:([^:\/?#]+):)?(?:\/\/((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?))?((((?:[^?#\/]*\/)*)([^?#]*))(?:\?([^#]*))?(?:#(.*))?)/,
+      loose:  /^(?:(?![^:@]+:[^:@\/]*@)([^:\/?#.]+):)?(?:\/\/)?((?:(([^:@]*)(?::([^:@]*))?)?@)?([^:\/?#]*)(?::(\d*))?)(((\/(?:[^?#](?![^?#\/]*\.[^?#\/.]+(?:[?#]|$)))*\/?)?([^?#\/]*))(?:\?([^#]*))?(?:#(.*))?)/
+    }
+  };
+
+  $("#search-form").submit(function(e) {
+    e.preventDefault()
+  })
+
+  // list below is the lunr 2.1.3 list minus the intersect with names(Base)
+  // (all, any, get, in, is, only, which) and (do, else, for, let, where, while, with)
+  // ideally we'd just filter the original list but it's not available as a variable
+  lunr.stopWordFilter = lunr.generateStopWordFilter([
+    'a',
+    'able',
+    'about',
+    'across',
+    'after',
+    'almost',
+    'also',
+    'am',
+    'among',
+    'an',
+    'and',
+    'are',
+    'as',
+    'at',
+    'be',
+    'because',
+    'been',
+    'but',
+    'by',
+    'can',
+    'cannot',
+    'could',
+    'dear',
+    'did',
+    'does',
+    'either',
+    'ever',
+    'every',
+    'from',
+    'got',
+    'had',
+    'has',
+    'have',
+    'he',
+    'her',
+    'hers',
+    'him',
+    'his',
+    'how',
+    'however',
+    'i',
+    'if',
+    'into',
+    'it',
+    'its',
+    'just',
+    'least',
+    'like',
+    'likely',
+    'may',
+    'me',
+    'might',
+    'most',
+    'must',
+    'my',
+    'neither',
+    'no',
+    'nor',
+    'not',
+    'of',
+    'off',
+    'often',
+    'on',
+    'or',
+    'other',
+    'our',
+    'own',
+    'rather',
+    'said',
+    'say',
+    'says',
+    'she',
+    'should',
+    'since',
+    'so',
+    'some',
+    'than',
+    'that',
+    'the',
+    'their',
+    'them',
+    'then',
+    'there',
+    'these',
+    'they',
+    'this',
+    'tis',
+    'to',
+    'too',
+    'twas',
+    'us',
+    'wants',
+    'was',
+    'we',
+    'were',
+    'what',
+    'when',
+    'who',
+    'whom',
+    'why',
+    'will',
+    'would',
+    'yet',
+    'you',
+    'your'
+  ])
+
+  // add . as a separator, because otherwise "title": "Documenter.Anchors.add!"
+  // would not find anything if searching for "add!", only for the entire qualification
+  lunr.tokenizer.separator = /[\s\-\.]+/
+
+  // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+  lunr.trimmer = function (token) {
+    return token.update(function (s) {
+      return s.replace(/^[^a-zA-Z0-9@!]+/, '').replace(/[^a-zA-Z0-9@!]+$/, '')
+    })
+  }
+
+  lunr.Pipeline.registerFunction(lunr.stopWordFilter, 'juliaStopWordFilter')
+  lunr.Pipeline.registerFunction(lunr.trimmer, 'juliaTrimmer')
+
+  var index = lunr(function () {
+    this.ref('location')
+    this.field('title',{boost: 100})
+    this.field('text')
+    documenterSearchIndex['docs'].forEach(function(e) {
+        this.add(e)
+    }, this)
+  })
+  var store = {}
+
+  documenterSearchIndex['docs'].forEach(function(e) {
+      store[e.location] = {title: e.title, category: e.category}
+  })
+
+  $(function(){
+    searchresults = $('#documenter-search-results');
+    searchinfo = $('#documenter-search-info');
+    searchbox = $('#documenter-search-query');
+    function update_search(querystring) {
+      tokens = lunr.tokenizer(querystring)
+      results = index.query(function (q) {
+        tokens.forEach(function (t) {
+          q.term(t.toString(), {
+            fields: ["title"],
+            boost: 100,
+            usePipeline: true,
+            editDistance: 0,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+          q.term(t.toString(), {
+            fields: ["title"],
+            boost: 10,
+            usePipeline: true,
+            editDistance: 2,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+          q.term(t.toString(), {
+            fields: ["text"],
+            boost: 1,
+            usePipeline: true,
+            editDistance: 0,
+            wildcard: lunr.Query.wildcard.NONE
+          })
+        })
+      })
+      searchinfo.text("Number of results: " + results.length)
+      searchresults.empty()
+      results.forEach(function(result) {
+        data = store[result.ref]
+        link = $('<a class="docs-label">'+data.title+'</a>')
+        link.attr('href', documenterBaseURL+'/'+result.ref)
+        cat = $('<span class="docs-category">('+data.category+')</span>')
+        li = $('<li>').append(link).append(" ").append(cat)
+        searchresults.append(li)
+      })
+    }
+
+    function update_search_box() {
+      querystring = searchbox.val()
+      update_search(querystring)
+    }
+
+    searchbox.keyup(_.debounce(update_search_box, 250))
+    searchbox.change(update_search_box)
+
+    search_query_uri = parseUri(window.location).queryKey["q"]
+    if(search_query_uri !== undefined) {
+      search_query = decodeURIComponent(search_query_uri.replace(/\+/g, '%20'))
+      searchbox.val(search_query)
+    }
+    update_search_box();
+  })
+})
+
+})
diff --git a/v0.15.15/assets/themes/documenter-dark.css b/v0.15.15/assets/themes/documenter-dark.css
new file mode 100644
index 00000000..1c370f22
--- /dev/null
+++ b/v0.15.15/assets/themes/documenter-dark.css
@@ -0,0 +1,7628 @@
+@charset "UTF-8";
+/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */
+@keyframes spinAround {
+  from {
+    transform: rotate(0deg); }
+  to {
+    transform: rotate(359deg); } }
+
+html.theme--documenter-dark .delete, html.theme--documenter-dark .modal-close, .is-unselectable, html.theme--documenter-dark .button, html.theme--documenter-dark .file, html.theme--documenter-dark .breadcrumb, html.theme--documenter-dark .pagination-previous,
+html.theme--documenter-dark .pagination-next,
+html.theme--documenter-dark .pagination-link,
+html.theme--documenter-dark .pagination-ellipsis, html.theme--documenter-dark .tabs {
+  -webkit-touch-callout: none;
+  -webkit-user-select: none;
+  -moz-user-select: none;
+  -ms-user-select: none;
+  user-select: none; }
+
+html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after, html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after {
+  border: 3px solid transparent;
+  border-radius: 2px;
+  border-right: 0;
+  border-top: 0;
+  content: " ";
+  display: block;
+  height: 0.625em;
+  margin-top: -0.4375em;
+  pointer-events: none;
+  position: absolute;
+  top: 50%;
+  transform: rotate(-45deg);
+  transform-origin: center;
+  width: 0.625em; }
+
+html.theme--documenter-dark .box:not(:last-child), html.theme--documenter-dark .content:not(:last-child), html.theme--documenter-dark .notification:not(:last-child), html.theme--documenter-dark .progress:not(:last-child), html.theme--documenter-dark .table:not(:last-child), html.theme--documenter-dark .table-container:not(:last-child), html.theme--documenter-dark .title:not(:last-child),
+html.theme--documenter-dark .subtitle:not(:last-child), html.theme--documenter-dark .block:not(:last-child), html.theme--documenter-dark .highlight:not(:last-child), html.theme--documenter-dark .breadcrumb:not(:last-child), html.theme--documenter-dark .level:not(:last-child), html.theme--documenter-dark .list:not(:last-child), html.theme--documenter-dark .message:not(:last-child), html.theme--documenter-dark .tabs:not(:last-child), html.theme--documenter-dark .admonition:not(:last-child) {
+  margin-bottom: 1.5rem; }
+
+html.theme--documenter-dark .delete, html.theme--documenter-dark .modal-close {
+  -moz-appearance: none;
+  -webkit-appearance: none;
+  background-color: rgba(10, 10, 10, 0.2);
+  border: none;
+  border-radius: 290486px;
+  cursor: pointer;
+  pointer-events: auto;
+  display: inline-block;
+  flex-grow: 0;
+  flex-shrink: 0;
+  font-size: 0;
+  height: 20px;
+  max-height: 20px;
+  max-width: 20px;
+  min-height: 20px;
+  min-width: 20px;
+  outline: none;
+  position: relative;
+  vertical-align: top;
+  width: 20px; }
+  html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::before, html.theme--documenter-dark .delete::after, html.theme--documenter-dark .modal-close::after {
+    background-color: white;
+    content: "";
+    display: block;
+    left: 50%;
+    position: absolute;
+    top: 50%;
+    transform: translateX(-50%) translateY(-50%) rotate(45deg);
+    transform-origin: center center; }
+  html.theme--documenter-dark .delete::before, html.theme--documenter-dark .modal-close::before {
+    height: 2px;
+    width: 50%; }
+  html.theme--documenter-dark .delete::after, html.theme--documenter-dark .modal-close::after {
+    height: 50%;
+    width: 2px; }
+  html.theme--documenter-dark .delete:hover, html.theme--documenter-dark .modal-close:hover, html.theme--documenter-dark .delete:focus, html.theme--documenter-dark .modal-close:focus {
+    background-color: rgba(10, 10, 10, 0.3); }
+  html.theme--documenter-dark .delete:active, html.theme--documenter-dark .modal-close:active {
+    background-color: rgba(10, 10, 10, 0.4); }
+  html.theme--documenter-dark .is-small.delete, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.delete, html.theme--documenter-dark .is-small.modal-close, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.modal-close {
+    height: 16px;
+    max-height: 16px;
+    max-width: 16px;
+    min-height: 16px;
+    min-width: 16px;
+    width: 16px; }
+  html.theme--documenter-dark .is-medium.delete, html.theme--documenter-dark .is-medium.modal-close {
+    height: 24px;
+    max-height: 24px;
+    max-width: 24px;
+    min-height: 24px;
+    min-width: 24px;
+    width: 24px; }
+  html.theme--documenter-dark .is-large.delete, html.theme--documenter-dark .is-large.modal-close {
+    height: 32px;
+    max-height: 32px;
+    max-width: 32px;
+    min-height: 32px;
+    min-width: 32px;
+    width: 32px; }
+
+html.theme--documenter-dark .button.is-loading::after, html.theme--documenter-dark .loader, html.theme--documenter-dark .select.is-loading::after, html.theme--documenter-dark .control.is-loading::after {
+  animation: spinAround 500ms infinite linear;
+  border: 2px solid #dbdee0;
+  border-radius: 290486px;
+  border-right-color: transparent;
+  border-top-color: transparent;
+  content: "";
+  display: block;
+  height: 1em;
+  position: relative;
+  width: 1em; }
+
+.is-overlay, html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img,
+html.theme--documenter-dark .image.is-square .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img,
+html.theme--documenter-dark .image.is-1by1 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img,
+html.theme--documenter-dark .image.is-5by4 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img,
+html.theme--documenter-dark .image.is-4by3 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img,
+html.theme--documenter-dark .image.is-3by2 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img,
+html.theme--documenter-dark .image.is-5by3 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img,
+html.theme--documenter-dark .image.is-16by9 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img,
+html.theme--documenter-dark .image.is-2by1 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img,
+html.theme--documenter-dark .image.is-3by1 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img,
+html.theme--documenter-dark .image.is-4by5 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img,
+html.theme--documenter-dark .image.is-3by4 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img,
+html.theme--documenter-dark .image.is-2by3 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img,
+html.theme--documenter-dark .image.is-3by5 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img,
+html.theme--documenter-dark .image.is-9by16 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img,
+html.theme--documenter-dark .image.is-1by2 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img,
+html.theme--documenter-dark .image.is-1by3 .has-ratio,
+html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, html.theme--documenter-dark .modal, html.theme--documenter-dark .modal-background, html.theme--documenter-dark .hero-video {
+  bottom: 0;
+  left: 0;
+  position: absolute;
+  right: 0;
+  top: 0; }
+
+html.theme--documenter-dark .button, html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea, html.theme--documenter-dark .select select, html.theme--documenter-dark .file-cta,
+html.theme--documenter-dark .file-name, html.theme--documenter-dark .pagination-previous,
+html.theme--documenter-dark .pagination-next,
+html.theme--documenter-dark .pagination-link,
+html.theme--documenter-dark .pagination-ellipsis {
+  -moz-appearance: none;
+  -webkit-appearance: none;
+  align-items: center;
+  border: 1px solid transparent;
+  border-radius: 0.4em;
+  box-shadow: none;
+  display: inline-flex;
+  font-size: 15px;
+  height: 2.25em;
+  justify-content: flex-start;
+  line-height: 1.5;
+  padding-bottom: calc(0.375em - 1px);
+  padding-left: calc(0.625em - 1px);
+  padding-right: calc(0.625em - 1px);
+  padding-top: calc(0.375em - 1px);
+  position: relative;
+  vertical-align: top; }
+  html.theme--documenter-dark .button:focus, html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .file-cta:focus,
+  html.theme--documenter-dark .file-name:focus, html.theme--documenter-dark .pagination-previous:focus,
+  html.theme--documenter-dark .pagination-next:focus,
+  html.theme--documenter-dark .pagination-link:focus,
+  html.theme--documenter-dark .pagination-ellipsis:focus, html.theme--documenter-dark .is-focused.button, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .is-focused.file-cta,
+  html.theme--documenter-dark .is-focused.file-name, html.theme--documenter-dark .is-focused.pagination-previous,
+  html.theme--documenter-dark .is-focused.pagination-next,
+  html.theme--documenter-dark .is-focused.pagination-link,
+  html.theme--documenter-dark .is-focused.pagination-ellipsis, html.theme--documenter-dark .button:active, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .file-cta:active,
+  html.theme--documenter-dark .file-name:active, html.theme--documenter-dark .pagination-previous:active,
+  html.theme--documenter-dark .pagination-next:active,
+  html.theme--documenter-dark .pagination-link:active,
+  html.theme--documenter-dark .pagination-ellipsis:active, html.theme--documenter-dark .is-active.button, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .select select.is-active, html.theme--documenter-dark .is-active.file-cta,
+  html.theme--documenter-dark .is-active.file-name, html.theme--documenter-dark .is-active.pagination-previous,
+  html.theme--documenter-dark .is-active.pagination-next,
+  html.theme--documenter-dark .is-active.pagination-link,
+  html.theme--documenter-dark .is-active.pagination-ellipsis {
+    outline: none; }
+  html.theme--documenter-dark .button[disabled], html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .select select[disabled], html.theme--documenter-dark .file-cta[disabled],
+  html.theme--documenter-dark .file-name[disabled], html.theme--documenter-dark .pagination-previous[disabled],
+  html.theme--documenter-dark .pagination-next[disabled],
+  html.theme--documenter-dark .pagination-link[disabled],
+  html.theme--documenter-dark .pagination-ellipsis[disabled],
+  fieldset[disabled] html.theme--documenter-dark .button,
+  html.theme--documenter-dark fieldset[disabled] .button,
+  fieldset[disabled] html.theme--documenter-dark .input,
+  html.theme--documenter-dark fieldset[disabled] .input,
+  fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,
+  html.theme--documenter-dark #documenter .docs-sidebar fieldset[disabled] form.docs-search > input,
+  fieldset[disabled] html.theme--documenter-dark .textarea,
+  html.theme--documenter-dark fieldset[disabled] .textarea,
+  fieldset[disabled] html.theme--documenter-dark .select select,
+  html.theme--documenter-dark .select fieldset[disabled] select,
+  fieldset[disabled] html.theme--documenter-dark .file-cta,
+  html.theme--documenter-dark fieldset[disabled] .file-cta,
+  fieldset[disabled] html.theme--documenter-dark .file-name,
+  html.theme--documenter-dark fieldset[disabled] .file-name,
+  fieldset[disabled] html.theme--documenter-dark .pagination-previous,
+  html.theme--documenter-dark fieldset[disabled] .pagination-previous,
+  fieldset[disabled] html.theme--documenter-dark .pagination-next,
+  html.theme--documenter-dark fieldset[disabled] .pagination-next,
+  fieldset[disabled] html.theme--documenter-dark .pagination-link,
+  html.theme--documenter-dark fieldset[disabled] .pagination-link,
+  fieldset[disabled] html.theme--documenter-dark .pagination-ellipsis,
+  html.theme--documenter-dark fieldset[disabled] .pagination-ellipsis {
+    cursor: not-allowed; }
+
+/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */
+html,
+body,
+p,
+ol,
+ul,
+li,
+dl,
+dt,
+dd,
+blockquote,
+figure,
+fieldset,
+legend,
+textarea,
+pre,
+iframe,
+hr,
+h1,
+h2,
+h3,
+h4,
+h5,
+h6 {
+  margin: 0;
+  padding: 0; }
+
+h1,
+h2,
+h3,
+h4,
+h5,
+h6 {
+  font-size: 100%;
+  font-weight: normal; }
+
+ul {
+  list-style: none; }
+
+button,
+input,
+select,
+textarea {
+  margin: 0; }
+
+html {
+  box-sizing: border-box; }
+
+*, *::before, *::after {
+  box-sizing: inherit; }
+
+img,
+embed,
+iframe,
+object,
+video {
+  height: auto;
+  max-width: 100%; }
+
+audio {
+  max-width: 100%; }
+
+iframe {
+  border: 0; }
+
+table {
+  border-collapse: collapse;
+  border-spacing: 0; }
+
+td,
+th {
+  padding: 0; }
+  td:not([align]),
+  th:not([align]) {
+    text-align: left; }
+
+.is-clearfix::after {
+  clear: both;
+  content: " ";
+  display: table; }
+
+.is-pulled-left {
+  float: left !important; }
+
+.is-pulled-right {
+  float: right !important; }
+
+.is-clipped {
+  overflow: hidden !important; }
+
+.is-size-1 {
+  font-size: 3rem !important; }
+
+.is-size-2 {
+  font-size: 2.5rem !important; }
+
+.is-size-3 {
+  font-size: 2rem !important; }
+
+.is-size-4 {
+  font-size: 1.5rem !important; }
+
+.is-size-5 {
+  font-size: 1.25rem !important; }
+
+.is-size-6 {
+  font-size: 15px !important; }
+
+.is-size-7, html.theme--documenter-dark .docstring > section > a.docs-sourcelink {
+  font-size: 0.85em !important; }
+
+@media screen and (max-width: 768px) {
+  .is-size-1-mobile {
+    font-size: 3rem !important; }
+  .is-size-2-mobile {
+    font-size: 2.5rem !important; }
+  .is-size-3-mobile {
+    font-size: 2rem !important; }
+  .is-size-4-mobile {
+    font-size: 1.5rem !important; }
+  .is-size-5-mobile {
+    font-size: 1.25rem !important; }
+  .is-size-6-mobile {
+    font-size: 15px !important; }
+  .is-size-7-mobile {
+    font-size: 0.85em !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-size-1-tablet {
+    font-size: 3rem !important; }
+  .is-size-2-tablet {
+    font-size: 2.5rem !important; }
+  .is-size-3-tablet {
+    font-size: 2rem !important; }
+  .is-size-4-tablet {
+    font-size: 1.5rem !important; }
+  .is-size-5-tablet {
+    font-size: 1.25rem !important; }
+  .is-size-6-tablet {
+    font-size: 15px !important; }
+  .is-size-7-tablet {
+    font-size: 0.85em !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-size-1-touch {
+    font-size: 3rem !important; }
+  .is-size-2-touch {
+    font-size: 2.5rem !important; }
+  .is-size-3-touch {
+    font-size: 2rem !important; }
+  .is-size-4-touch {
+    font-size: 1.5rem !important; }
+  .is-size-5-touch {
+    font-size: 1.25rem !important; }
+  .is-size-6-touch {
+    font-size: 15px !important; }
+  .is-size-7-touch {
+    font-size: 0.85em !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-size-1-desktop {
+    font-size: 3rem !important; }
+  .is-size-2-desktop {
+    font-size: 2.5rem !important; }
+  .is-size-3-desktop {
+    font-size: 2rem !important; }
+  .is-size-4-desktop {
+    font-size: 1.5rem !important; }
+  .is-size-5-desktop {
+    font-size: 1.25rem !important; }
+  .is-size-6-desktop {
+    font-size: 15px !important; }
+  .is-size-7-desktop {
+    font-size: 0.85em !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-size-1-widescreen {
+    font-size: 3rem !important; }
+  .is-size-2-widescreen {
+    font-size: 2.5rem !important; }
+  .is-size-3-widescreen {
+    font-size: 2rem !important; }
+  .is-size-4-widescreen {
+    font-size: 1.5rem !important; }
+  .is-size-5-widescreen {
+    font-size: 1.25rem !important; }
+  .is-size-6-widescreen {
+    font-size: 15px !important; }
+  .is-size-7-widescreen {
+    font-size: 0.85em !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-size-1-fullhd {
+    font-size: 3rem !important; }
+  .is-size-2-fullhd {
+    font-size: 2.5rem !important; }
+  .is-size-3-fullhd {
+    font-size: 2rem !important; }
+  .is-size-4-fullhd {
+    font-size: 1.5rem !important; }
+  .is-size-5-fullhd {
+    font-size: 1.25rem !important; }
+  .is-size-6-fullhd {
+    font-size: 15px !important; }
+  .is-size-7-fullhd {
+    font-size: 0.85em !important; } }
+
+.has-text-centered {
+  text-align: center !important; }
+
+.has-text-justified {
+  text-align: justify !important; }
+
+.has-text-left {
+  text-align: left !important; }
+
+.has-text-right {
+  text-align: right !important; }
+
+@media screen and (max-width: 768px) {
+  .has-text-centered-mobile {
+    text-align: center !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-centered-tablet {
+    text-align: center !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-centered-tablet-only {
+    text-align: center !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-centered-touch {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-centered-desktop {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-centered-desktop-only {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-centered-widescreen {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-centered-widescreen-only {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-centered-fullhd {
+    text-align: center !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-justified-mobile {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-justified-tablet {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-justified-tablet-only {
+    text-align: justify !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-justified-touch {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-justified-desktop {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-justified-desktop-only {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-justified-widescreen {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-justified-widescreen-only {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-justified-fullhd {
+    text-align: justify !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-left-mobile {
+    text-align: left !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-left-tablet {
+    text-align: left !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-left-tablet-only {
+    text-align: left !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-left-touch {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-left-desktop {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-left-desktop-only {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-left-widescreen {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-left-widescreen-only {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-left-fullhd {
+    text-align: left !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-right-mobile {
+    text-align: right !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-right-tablet {
+    text-align: right !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-right-tablet-only {
+    text-align: right !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-right-touch {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-right-desktop {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-right-desktop-only {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-right-widescreen {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-right-widescreen-only {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-right-fullhd {
+    text-align: right !important; } }
+
+.is-capitalized {
+  text-transform: capitalize !important; }
+
+.is-lowercase {
+  text-transform: lowercase !important; }
+
+.is-uppercase {
+  text-transform: uppercase !important; }
+
+.is-italic {
+  font-style: italic !important; }
+
+.has-text-white {
+  color: white !important; }
+
+a.has-text-white:hover, a.has-text-white:focus {
+  color: #e6e6e6 !important; }
+
+.has-background-white {
+  background-color: white !important; }
+
+.has-text-black {
+  color: #0a0a0a !important; }
+
+a.has-text-black:hover, a.has-text-black:focus {
+  color: black !important; }
+
+.has-background-black {
+  background-color: #0a0a0a !important; }
+
+.has-text-light {
+  color: #ecf0f1 !important; }
+
+a.has-text-light:hover, a.has-text-light:focus {
+  color: #cfd9db !important; }
+
+.has-background-light {
+  background-color: #ecf0f1 !important; }
+
+.has-text-dark {
+  color: #282f2f !important; }
+
+a.has-text-dark:hover, a.has-text-dark:focus {
+  color: #111414 !important; }
+
+.has-background-dark {
+  background-color: #282f2f !important; }
+
+.has-text-primary {
+  color: #375a7f !important; }
+
+a.has-text-primary:hover, a.has-text-primary:focus {
+  color: #28415b !important; }
+
+.has-background-primary {
+  background-color: #375a7f !important; }
+
+.has-text-link {
+  color: #1abc9c !important; }
+
+a.has-text-link:hover, a.has-text-link:focus {
+  color: #148f77 !important; }
+
+.has-background-link {
+  background-color: #1abc9c !important; }
+
+.has-text-info {
+  color: #024c7d !important; }
+
+a.has-text-info:hover, a.has-text-info:focus {
+  color: #012d4b !important; }
+
+.has-background-info {
+  background-color: #024c7d !important; }
+
+.has-text-success {
+  color: #008438 !important; }
+
+a.has-text-success:hover, a.has-text-success:focus {
+  color: #005122 !important; }
+
+.has-background-success {
+  background-color: #008438 !important; }
+
+.has-text-warning {
+  color: #ad8100 !important; }
+
+a.has-text-warning:hover, a.has-text-warning:focus {
+  color: #7a5b00 !important; }
+
+.has-background-warning {
+  background-color: #ad8100 !important; }
+
+.has-text-danger {
+  color: #9e1b0d !important; }
+
+a.has-text-danger:hover, a.has-text-danger:focus {
+  color: #6f1309 !important; }
+
+.has-background-danger {
+  background-color: #9e1b0d !important; }
+
+.has-text-black-bis {
+  color: #121212 !important; }
+
+.has-background-black-bis {
+  background-color: #121212 !important; }
+
+.has-text-black-ter {
+  color: #242424 !important; }
+
+.has-background-black-ter {
+  background-color: #242424 !important; }
+
+.has-text-grey-darker {
+  color: #282f2f !important; }
+
+.has-background-grey-darker {
+  background-color: #282f2f !important; }
+
+.has-text-grey-dark {
+  color: #343c3d !important; }
+
+.has-background-grey-dark {
+  background-color: #343c3d !important; }
+
+.has-text-grey {
+  color: #5e6d6f !important; }
+
+.has-background-grey {
+  background-color: #5e6d6f !important; }
+
+.has-text-grey-light {
+  color: #8c9b9d !important; }
+
+.has-background-grey-light {
+  background-color: #8c9b9d !important; }
+
+.has-text-grey-lighter {
+  color: #dbdee0 !important; }
+
+.has-background-grey-lighter {
+  background-color: #dbdee0 !important; }
+
+.has-text-white-ter {
+  color: #ecf0f1 !important; }
+
+.has-background-white-ter {
+  background-color: #ecf0f1 !important; }
+
+.has-text-white-bis {
+  color: #fafafa !important; }
+
+.has-background-white-bis {
+  background-color: #fafafa !important; }
+
+.has-text-weight-light {
+  font-weight: 300 !important; }
+
+.has-text-weight-normal {
+  font-weight: 400 !important; }
+
+.has-text-weight-medium {
+  font-weight: 500 !important; }
+
+.has-text-weight-semibold {
+  font-weight: 600 !important; }
+
+.has-text-weight-bold {
+  font-weight: 700 !important; }
+
+.is-family-primary {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-secondary {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-sans-serif {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-monospace {
+  font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; }
+
+.is-family-code {
+  font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; }
+
+.is-block {
+  display: block !important; }
+
+@media screen and (max-width: 768px) {
+  .is-block-mobile {
+    display: block !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-block-tablet {
+    display: block !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-block-tablet-only {
+    display: block !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-block-touch {
+    display: block !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-block-desktop {
+    display: block !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-block-desktop-only {
+    display: block !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-block-widescreen {
+    display: block !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-block-widescreen-only {
+    display: block !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-block-fullhd {
+    display: block !important; } }
+
+.is-flex {
+  display: flex !important; }
+
+@media screen and (max-width: 768px) {
+  .is-flex-mobile {
+    display: flex !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-flex-tablet {
+    display: flex !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-flex-tablet-only {
+    display: flex !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-flex-touch {
+    display: flex !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-flex-desktop {
+    display: flex !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-flex-desktop-only {
+    display: flex !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-flex-widescreen {
+    display: flex !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-flex-widescreen-only {
+    display: flex !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-flex-fullhd {
+    display: flex !important; } }
+
+.is-inline {
+  display: inline !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-mobile {
+    display: inline !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-tablet {
+    display: inline !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-tablet-only {
+    display: inline !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-touch {
+    display: inline !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-desktop {
+    display: inline !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-desktop-only {
+    display: inline !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-widescreen {
+    display: inline !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-widescreen-only {
+    display: inline !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-fullhd {
+    display: inline !important; } }
+
+.is-inline-block {
+  display: inline-block !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-block-mobile {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-block-tablet {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-block-tablet-only {
+    display: inline-block !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-block-touch {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-block-desktop {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-block-desktop-only {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-block-widescreen {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-block-widescreen-only {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-block-fullhd {
+    display: inline-block !important; } }
+
+.is-inline-flex {
+  display: inline-flex !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-flex-mobile {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-flex-tablet {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-flex-tablet-only {
+    display: inline-flex !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-flex-touch {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-flex-desktop {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-flex-desktop-only {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-flex-widescreen {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-flex-widescreen-only {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-flex-fullhd {
+    display: inline-flex !important; } }
+
+.is-hidden {
+  display: none !important; }
+
+.is-sr-only {
+  border: none !important;
+  clip: rect(0, 0, 0, 0) !important;
+  height: 0.01em !important;
+  overflow: hidden !important;
+  padding: 0 !important;
+  position: absolute !important;
+  white-space: nowrap !important;
+  width: 0.01em !important; }
+
+@media screen and (max-width: 768px) {
+  .is-hidden-mobile {
+    display: none !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-hidden-tablet {
+    display: none !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-hidden-tablet-only {
+    display: none !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-hidden-touch {
+    display: none !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-hidden-desktop {
+    display: none !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-hidden-desktop-only {
+    display: none !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-hidden-widescreen {
+    display: none !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-hidden-widescreen-only {
+    display: none !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-hidden-fullhd {
+    display: none !important; } }
+
+.is-invisible {
+  visibility: hidden !important; }
+
+@media screen and (max-width: 768px) {
+  .is-invisible-mobile {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-invisible-tablet {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-invisible-tablet-only {
+    visibility: hidden !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-invisible-touch {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-invisible-desktop {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-invisible-desktop-only {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-invisible-widescreen {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-invisible-widescreen-only {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-invisible-fullhd {
+    visibility: hidden !important; } }
+
+.is-marginless {
+  margin: 0 !important; }
+
+.is-paddingless {
+  padding: 0 !important; }
+
+.is-radiusless {
+  border-radius: 0 !important; }
+
+.is-shadowless {
+  box-shadow: none !important; }
+
+.is-relative {
+  position: relative !important; }
+
+html.theme--documenter-dark {
+  /* This file contain the overall layout.
+ *
+ * The main container is <div> that is identified by id #documenter.
+ */
+  /* a11y-dark theme */
+  /* Based on the Tomorrow Night Eighties theme: https://github.com/isagalaev/highlight.js/blob/master/src/styles/tomorrow-night-eighties.css */
+  /* @author: ericwbailey */
+  /* Comment */
+  /* Red */
+  /* Orange */
+  /* Yellow */
+  /* Green */
+  /* Blue */
+  /* Purple */ }
+  html.theme--documenter-dark html {
+    background-color: #1f2424;
+    font-size: 16px;
+    -moz-osx-font-smoothing: grayscale;
+    -webkit-font-smoothing: antialiased;
+    min-width: 300px;
+    overflow-x: auto;
+    overflow-y: scroll;
+    text-rendering: optimizeLegibility;
+    text-size-adjust: 100%; }
+  html.theme--documenter-dark article,
+  html.theme--documenter-dark aside,
+  html.theme--documenter-dark figure,
+  html.theme--documenter-dark footer,
+  html.theme--documenter-dark header,
+  html.theme--documenter-dark hgroup,
+  html.theme--documenter-dark section {
+    display: block; }
+  html.theme--documenter-dark body,
+  html.theme--documenter-dark button,
+  html.theme--documenter-dark input,
+  html.theme--documenter-dark select,
+  html.theme--documenter-dark textarea {
+    font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif; }
+  html.theme--documenter-dark code,
+  html.theme--documenter-dark pre {
+    -moz-osx-font-smoothing: auto;
+    -webkit-font-smoothing: auto;
+    font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace; }
+  html.theme--documenter-dark body {
+    color: #fff;
+    font-size: 1em;
+    font-weight: 400;
+    line-height: 1.5; }
+  html.theme--documenter-dark a {
+    color: #1abc9c;
+    cursor: pointer;
+    text-decoration: none; }
+    html.theme--documenter-dark a strong {
+      color: currentColor; }
+    html.theme--documenter-dark a:hover {
+      color: #1dd2af; }
+  html.theme--documenter-dark code {
+    background-color: rgba(255, 255, 255, 0.05);
+    color: #e74c3c;
+    font-size: 0.875em;
+    font-weight: normal;
+    padding: 0.1em; }
+  html.theme--documenter-dark hr {
+    background-color: #282f2f;
+    border: none;
+    display: block;
+    height: 2px;
+    margin: 1.5rem 0; }
+  html.theme--documenter-dark img {
+    height: auto;
+    max-width: 100%; }
+  html.theme--documenter-dark input[type="checkbox"],
+  html.theme--documenter-dark input[type="radio"] {
+    vertical-align: baseline; }
+  html.theme--documenter-dark small {
+    font-size: 0.875em; }
+  html.theme--documenter-dark span {
+    font-style: inherit;
+    font-weight: inherit; }
+  html.theme--documenter-dark strong {
+    color: #f2f2f2;
+    font-weight: 700; }
+  html.theme--documenter-dark fieldset {
+    border: none; }
+  html.theme--documenter-dark pre {
+    -webkit-overflow-scrolling: touch;
+    background-color: #282f2f;
+    color: #fff;
+    font-size: 0.875em;
+    overflow-x: auto;
+    padding: 1.25rem 1.5rem;
+    white-space: pre;
+    word-wrap: normal; }
+    html.theme--documenter-dark pre code {
+      background-color: transparent;
+      color: currentColor;
+      font-size: 1em;
+      padding: 0; }
+  html.theme--documenter-dark table td,
+  html.theme--documenter-dark table th {
+    vertical-align: top; }
+    html.theme--documenter-dark table td:not([align]),
+    html.theme--documenter-dark table th:not([align]) {
+      text-align: left; }
+  html.theme--documenter-dark table th {
+    color: #f2f2f2; }
+  html.theme--documenter-dark .box {
+    background-color: #343c3d;
+    border-radius: 8px;
+    box-shadow: none;
+    color: #fff;
+    display: block;
+    padding: 1.25rem; }
+  html.theme--documenter-dark a.box:hover, html.theme--documenter-dark a.box:focus {
+    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #1abc9c; }
+  html.theme--documenter-dark a.box:active {
+    box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #1abc9c; }
+  html.theme--documenter-dark .button {
+    background-color: #282f2f;
+    border-color: #4c5759;
+    border-width: 1px;
+    color: #375a7f;
+    cursor: pointer;
+    justify-content: center;
+    padding-bottom: calc(0.375em - 1px);
+    padding-left: 0.75em;
+    padding-right: 0.75em;
+    padding-top: calc(0.375em - 1px);
+    text-align: center;
+    white-space: nowrap; }
+    html.theme--documenter-dark .button strong {
+      color: inherit; }
+    html.theme--documenter-dark .button .icon, html.theme--documenter-dark .button .icon.is-small, html.theme--documenter-dark .button #documenter .docs-sidebar form.docs-search > input.icon, html.theme--documenter-dark #documenter .docs-sidebar .button form.docs-search > input.icon, html.theme--documenter-dark .button .icon.is-medium, html.theme--documenter-dark .button .icon.is-large {
+      height: 1.5em;
+      width: 1.5em; }
+    html.theme--documenter-dark .button .icon:first-child:not(:last-child) {
+      margin-left: calc(-0.375em - 1px);
+      margin-right: 0.1875em; }
+    html.theme--documenter-dark .button .icon:last-child:not(:first-child) {
+      margin-left: 0.1875em;
+      margin-right: calc(-0.375em - 1px); }
+    html.theme--documenter-dark .button .icon:first-child:last-child {
+      margin-left: calc(-0.375em - 1px);
+      margin-right: calc(-0.375em - 1px); }
+    html.theme--documenter-dark .button:hover, html.theme--documenter-dark .button.is-hovered {
+      border-color: #8c9b9d;
+      color: #f2f2f2; }
+    html.theme--documenter-dark .button:focus, html.theme--documenter-dark .button.is-focused {
+      border-color: #8c9b9d;
+      color: #17a689; }
+      html.theme--documenter-dark .button:focus:not(:active), html.theme--documenter-dark .button.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); }
+    html.theme--documenter-dark .button:active, html.theme--documenter-dark .button.is-active {
+      border-color: #343c3d;
+      color: #f2f2f2; }
+    html.theme--documenter-dark .button.is-text {
+      background-color: transparent;
+      border-color: transparent;
+      color: #fff;
+      text-decoration: underline; }
+      html.theme--documenter-dark .button.is-text:hover, html.theme--documenter-dark .button.is-text.is-hovered, html.theme--documenter-dark .button.is-text:focus, html.theme--documenter-dark .button.is-text.is-focused {
+        background-color: #282f2f;
+        color: #f2f2f2; }
+      html.theme--documenter-dark .button.is-text:active, html.theme--documenter-dark .button.is-text.is-active {
+        background-color: #1d2122;
+        color: #f2f2f2; }
+      html.theme--documenter-dark .button.is-text[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-text {
+        background-color: transparent;
+        border-color: transparent;
+        box-shadow: none; }
+    html.theme--documenter-dark .button.is-white {
+      background-color: white;
+      border-color: transparent;
+      color: #0a0a0a; }
+      html.theme--documenter-dark .button.is-white:hover, html.theme--documenter-dark .button.is-white.is-hovered {
+        background-color: #f9f9f9;
+        border-color: transparent;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .button.is-white:focus, html.theme--documenter-dark .button.is-white.is-focused {
+        border-color: transparent;
+        color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-white:focus:not(:active), html.theme--documenter-dark .button.is-white.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+      html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white.is-active {
+        background-color: #f2f2f2;
+        border-color: transparent;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .button.is-white[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-white {
+        background-color: white;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-white.is-inverted {
+        background-color: #0a0a0a;
+        color: white; }
+        html.theme--documenter-dark .button.is-white.is-inverted:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-hovered {
+          background-color: black; }
+        html.theme--documenter-dark .button.is-white.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted {
+          background-color: #0a0a0a;
+          border-color: transparent;
+          box-shadow: none;
+          color: white; }
+      html.theme--documenter-dark .button.is-white.is-loading::after {
+        border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+      html.theme--documenter-dark .button.is-white.is-outlined {
+        background-color: transparent;
+        border-color: white;
+        color: white; }
+        html.theme--documenter-dark .button.is-white.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-outlined.is-focused {
+          background-color: white;
+          border-color: white;
+          color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-white.is-outlined.is-loading::after {
+          border-color: transparent transparent white white !important; }
+        html.theme--documenter-dark .button.is-white.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+        html.theme--documenter-dark .button.is-white.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-outlined {
+          background-color: transparent;
+          border-color: white;
+          box-shadow: none;
+          color: white; }
+      html.theme--documenter-dark .button.is-white.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #0a0a0a;
+        color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-focused {
+          background-color: #0a0a0a;
+          color: white; }
+        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent white white !important; }
+        html.theme--documenter-dark .button.is-white.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-white.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #0a0a0a;
+          box-shadow: none;
+          color: #0a0a0a; }
+    html.theme--documenter-dark .button.is-black {
+      background-color: #0a0a0a;
+      border-color: transparent;
+      color: white; }
+      html.theme--documenter-dark .button.is-black:hover, html.theme--documenter-dark .button.is-black.is-hovered {
+        background-color: #040404;
+        border-color: transparent;
+        color: white; }
+      html.theme--documenter-dark .button.is-black:focus, html.theme--documenter-dark .button.is-black.is-focused {
+        border-color: transparent;
+        color: white; }
+        html.theme--documenter-dark .button.is-black:focus:not(:active), html.theme--documenter-dark .button.is-black.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+      html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black.is-active {
+        background-color: black;
+        border-color: transparent;
+        color: white; }
+      html.theme--documenter-dark .button.is-black[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-black {
+        background-color: #0a0a0a;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-black.is-inverted {
+        background-color: white;
+        color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-black.is-inverted:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-black.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted {
+          background-color: white;
+          border-color: transparent;
+          box-shadow: none;
+          color: #0a0a0a; }
+      html.theme--documenter-dark .button.is-black.is-loading::after {
+        border-color: transparent transparent white white !important; }
+      html.theme--documenter-dark .button.is-black.is-outlined {
+        background-color: transparent;
+        border-color: #0a0a0a;
+        color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-black.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-outlined.is-focused {
+          background-color: #0a0a0a;
+          border-color: #0a0a0a;
+          color: white; }
+        html.theme--documenter-dark .button.is-black.is-outlined.is-loading::after {
+          border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+        html.theme--documenter-dark .button.is-black.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent white white !important; }
+        html.theme--documenter-dark .button.is-black.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-outlined {
+          background-color: transparent;
+          border-color: #0a0a0a;
+          box-shadow: none;
+          color: #0a0a0a; }
+      html.theme--documenter-dark .button.is-black.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: white;
+        color: white; }
+        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-focused {
+          background-color: white;
+          color: #0a0a0a; }
+        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+        html.theme--documenter-dark .button.is-black.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-black.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: white;
+          box-shadow: none;
+          color: white; }
+    html.theme--documenter-dark .button.is-light {
+      background-color: #ecf0f1;
+      border-color: transparent;
+      color: #282f2f; }
+      html.theme--documenter-dark .button.is-light:hover, html.theme--documenter-dark .button.is-light.is-hovered {
+        background-color: #e5eaec;
+        border-color: transparent;
+        color: #282f2f; }
+      html.theme--documenter-dark .button.is-light:focus, html.theme--documenter-dark .button.is-light.is-focused {
+        border-color: transparent;
+        color: #282f2f; }
+        html.theme--documenter-dark .button.is-light:focus:not(:active), html.theme--documenter-dark .button.is-light.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); }
+      html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light.is-active {
+        background-color: #dde4e6;
+        border-color: transparent;
+        color: #282f2f; }
+      html.theme--documenter-dark .button.is-light[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-light {
+        background-color: #ecf0f1;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-light.is-inverted {
+        background-color: #282f2f;
+        color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-light.is-inverted:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-hovered {
+          background-color: #1d2122; }
+        html.theme--documenter-dark .button.is-light.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted {
+          background-color: #282f2f;
+          border-color: transparent;
+          box-shadow: none;
+          color: #ecf0f1; }
+      html.theme--documenter-dark .button.is-light.is-loading::after {
+        border-color: transparent transparent #282f2f #282f2f !important; }
+      html.theme--documenter-dark .button.is-light.is-outlined {
+        background-color: transparent;
+        border-color: #ecf0f1;
+        color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-light.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-outlined.is-focused {
+          background-color: #ecf0f1;
+          border-color: #ecf0f1;
+          color: #282f2f; }
+        html.theme--documenter-dark .button.is-light.is-outlined.is-loading::after {
+          border-color: transparent transparent #ecf0f1 #ecf0f1 !important; }
+        html.theme--documenter-dark .button.is-light.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #282f2f #282f2f !important; }
+        html.theme--documenter-dark .button.is-light.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-outlined {
+          background-color: transparent;
+          border-color: #ecf0f1;
+          box-shadow: none;
+          color: #ecf0f1; }
+      html.theme--documenter-dark .button.is-light.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #282f2f;
+        color: #282f2f; }
+        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-focused {
+          background-color: #282f2f;
+          color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #ecf0f1 #ecf0f1 !important; }
+        html.theme--documenter-dark .button.is-light.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-light.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #282f2f;
+          box-shadow: none;
+          color: #282f2f; }
+    html.theme--documenter-dark .button.is-dark, html.theme--documenter-dark .content kbd.button {
+      background-color: #282f2f;
+      border-color: transparent;
+      color: #ecf0f1; }
+      html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover, html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered {
+        background-color: #232829;
+        border-color: transparent;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused {
+        border-color: transparent;
+        color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-dark:focus:not(:active), html.theme--documenter-dark .content kbd.button:focus:not(:active), html.theme--documenter-dark .button.is-dark.is-focused:not(:active), html.theme--documenter-dark .content kbd.button.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); }
+      html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active {
+        background-color: #1d2122;
+        border-color: transparent;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .button.is-dark[disabled], html.theme--documenter-dark .content kbd.button[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-dark,
+      fieldset[disabled] html.theme--documenter-dark .content kbd.button {
+        background-color: #282f2f;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-dark.is-inverted, html.theme--documenter-dark .content kbd.button.is-inverted {
+        background-color: #ecf0f1;
+        color: #282f2f; }
+        html.theme--documenter-dark .button.is-dark.is-inverted:hover, html.theme--documenter-dark .content kbd.button.is-inverted:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-hovered {
+          background-color: #dde4e6; }
+        html.theme--documenter-dark .button.is-dark.is-inverted[disabled], html.theme--documenter-dark .content kbd.button.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted,
+        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted {
+          background-color: #ecf0f1;
+          border-color: transparent;
+          box-shadow: none;
+          color: #282f2f; }
+      html.theme--documenter-dark .button.is-dark.is-loading::after, html.theme--documenter-dark .content kbd.button.is-loading::after {
+        border-color: transparent transparent #ecf0f1 #ecf0f1 !important; }
+      html.theme--documenter-dark .button.is-dark.is-outlined, html.theme--documenter-dark .content kbd.button.is-outlined {
+        background-color: transparent;
+        border-color: #282f2f;
+        color: #282f2f; }
+        html.theme--documenter-dark .button.is-dark.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-outlined.is-focused {
+          background-color: #282f2f;
+          border-color: #282f2f;
+          color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-dark.is-outlined.is-loading::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading::after {
+          border-color: transparent transparent #282f2f #282f2f !important; }
+        html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #ecf0f1 #ecf0f1 !important; }
+        html.theme--documenter-dark .button.is-dark.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-outlined,
+        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-outlined {
+          background-color: transparent;
+          border-color: #282f2f;
+          box-shadow: none;
+          color: #282f2f; }
+      html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #ecf0f1;
+        color: #ecf0f1; }
+        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:hover, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined:focus, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-focused {
+          background-color: #ecf0f1;
+          color: #282f2f; }
+        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #282f2f #282f2f !important; }
+        html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined[disabled], html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-dark.is-inverted.is-outlined,
+        fieldset[disabled] html.theme--documenter-dark .content kbd.button.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #ecf0f1;
+          box-shadow: none;
+          color: #ecf0f1; }
+    html.theme--documenter-dark .button.is-primary, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink {
+      background-color: #375a7f;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink {
+        background-color: #335476;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-primary:focus:not(:active), html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus:not(:active), html.theme--documenter-dark .button.is-primary.is-focused:not(:active), html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); }
+      html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink {
+        background-color: #2f4d6d;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-primary[disabled], html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-primary,
+      fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink {
+        background-color: #375a7f;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-primary.is-inverted, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink {
+        background-color: #fff;
+        color: #375a7f; }
+        html.theme--documenter-dark .button.is-primary.is-inverted:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-primary.is-inverted[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted,
+        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.docs-sourcelink {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #375a7f; }
+      html.theme--documenter-dark .button.is-primary.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-loading.docs-sourcelink::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-primary.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink {
+        background-color: transparent;
+        border-color: #375a7f;
+        color: #375a7f; }
+        html.theme--documenter-dark .button.is-primary.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink {
+          background-color: #375a7f;
+          border-color: #375a7f;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-primary.is-outlined.is-loading::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after {
+          border-color: transparent transparent #375a7f #375a7f !important; }
+        html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-primary.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-outlined,
+        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-outlined.docs-sourcelink {
+          background-color: transparent;
+          border-color: #375a7f;
+          box-shadow: none;
+          color: #375a7f; }
+      html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:hover, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined:focus, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink {
+          background-color: #fff;
+          color: #375a7f; }
+        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after {
+          border-color: transparent transparent #375a7f #375a7f !important; }
+        html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined[disabled], html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-primary.is-inverted.is-outlined,
+        fieldset[disabled] html.theme--documenter-dark .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-link {
+      background-color: #1abc9c;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-link:hover, html.theme--documenter-dark .button.is-link.is-hovered {
+        background-color: #18b193;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-link:focus, html.theme--documenter-dark .button.is-link.is-focused {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-link:focus:not(:active), html.theme--documenter-dark .button.is-link.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); }
+      html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link.is-active {
+        background-color: #17a689;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-link[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-link {
+        background-color: #1abc9c;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-link.is-inverted {
+        background-color: #fff;
+        color: #1abc9c; }
+        html.theme--documenter-dark .button.is-link.is-inverted:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-link.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #1abc9c; }
+      html.theme--documenter-dark .button.is-link.is-loading::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-link.is-outlined {
+        background-color: transparent;
+        border-color: #1abc9c;
+        color: #1abc9c; }
+        html.theme--documenter-dark .button.is-link.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-outlined.is-focused {
+          background-color: #1abc9c;
+          border-color: #1abc9c;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-link.is-outlined.is-loading::after {
+          border-color: transparent transparent #1abc9c #1abc9c !important; }
+        html.theme--documenter-dark .button.is-link.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-link.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-outlined {
+          background-color: transparent;
+          border-color: #1abc9c;
+          box-shadow: none;
+          color: #1abc9c; }
+      html.theme--documenter-dark .button.is-link.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-focused {
+          background-color: #fff;
+          color: #1abc9c; }
+        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #1abc9c #1abc9c !important; }
+        html.theme--documenter-dark .button.is-link.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-link.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-info {
+      background-color: #024c7d;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-info:hover, html.theme--documenter-dark .button.is-info.is-hovered {
+        background-color: #024470;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-info:focus, html.theme--documenter-dark .button.is-info.is-focused {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-info:focus:not(:active), html.theme--documenter-dark .button.is-info.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); }
+      html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info.is-active {
+        background-color: #023d64;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-info[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-info {
+        background-color: #024c7d;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-info.is-inverted {
+        background-color: #fff;
+        color: #024c7d; }
+        html.theme--documenter-dark .button.is-info.is-inverted:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-info.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #024c7d; }
+      html.theme--documenter-dark .button.is-info.is-loading::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-info.is-outlined {
+        background-color: transparent;
+        border-color: #024c7d;
+        color: #024c7d; }
+        html.theme--documenter-dark .button.is-info.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-outlined.is-focused {
+          background-color: #024c7d;
+          border-color: #024c7d;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-info.is-outlined.is-loading::after {
+          border-color: transparent transparent #024c7d #024c7d !important; }
+        html.theme--documenter-dark .button.is-info.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-info.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-outlined {
+          background-color: transparent;
+          border-color: #024c7d;
+          box-shadow: none;
+          color: #024c7d; }
+      html.theme--documenter-dark .button.is-info.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-focused {
+          background-color: #fff;
+          color: #024c7d; }
+        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #024c7d #024c7d !important; }
+        html.theme--documenter-dark .button.is-info.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-info.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-success {
+      background-color: #008438;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-success:hover, html.theme--documenter-dark .button.is-success.is-hovered {
+        background-color: #007733;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-success:focus, html.theme--documenter-dark .button.is-success.is-focused {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-success:focus:not(:active), html.theme--documenter-dark .button.is-success.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); }
+      html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success.is-active {
+        background-color: #006b2d;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-success[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-success {
+        background-color: #008438;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-success.is-inverted {
+        background-color: #fff;
+        color: #008438; }
+        html.theme--documenter-dark .button.is-success.is-inverted:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-success.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #008438; }
+      html.theme--documenter-dark .button.is-success.is-loading::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-success.is-outlined {
+        background-color: transparent;
+        border-color: #008438;
+        color: #008438; }
+        html.theme--documenter-dark .button.is-success.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-outlined.is-focused {
+          background-color: #008438;
+          border-color: #008438;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-success.is-outlined.is-loading::after {
+          border-color: transparent transparent #008438 #008438 !important; }
+        html.theme--documenter-dark .button.is-success.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-success.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-outlined {
+          background-color: transparent;
+          border-color: #008438;
+          box-shadow: none;
+          color: #008438; }
+      html.theme--documenter-dark .button.is-success.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-focused {
+          background-color: #fff;
+          color: #008438; }
+        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #008438 #008438 !important; }
+        html.theme--documenter-dark .button.is-success.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-success.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-warning {
+      background-color: #ad8100;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-warning:hover, html.theme--documenter-dark .button.is-warning.is-hovered {
+        background-color: #a07700;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-warning:focus, html.theme--documenter-dark .button.is-warning.is-focused {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-warning:focus:not(:active), html.theme--documenter-dark .button.is-warning.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); }
+      html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning.is-active {
+        background-color: #946e00;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-warning[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-warning {
+        background-color: #ad8100;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-warning.is-inverted {
+        background-color: #fff;
+        color: #ad8100; }
+        html.theme--documenter-dark .button.is-warning.is-inverted:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-warning.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #ad8100; }
+      html.theme--documenter-dark .button.is-warning.is-loading::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-warning.is-outlined {
+        background-color: transparent;
+        border-color: #ad8100;
+        color: #ad8100; }
+        html.theme--documenter-dark .button.is-warning.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-outlined.is-focused {
+          background-color: #ad8100;
+          border-color: #ad8100;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-warning.is-outlined.is-loading::after {
+          border-color: transparent transparent #ad8100 #ad8100 !important; }
+        html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-warning.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-outlined {
+          background-color: transparent;
+          border-color: #ad8100;
+          box-shadow: none;
+          color: #ad8100; }
+      html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-focused {
+          background-color: #fff;
+          color: #ad8100; }
+        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #ad8100 #ad8100 !important; }
+        html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-warning.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-danger {
+      background-color: #9e1b0d;
+      border-color: transparent;
+      color: #fff; }
+      html.theme--documenter-dark .button.is-danger:hover, html.theme--documenter-dark .button.is-danger.is-hovered {
+        background-color: #92190c;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-danger:focus, html.theme--documenter-dark .button.is-danger.is-focused {
+        border-color: transparent;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-danger:focus:not(:active), html.theme--documenter-dark .button.is-danger.is-focused:not(:active) {
+          box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); }
+      html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger.is-active {
+        background-color: #86170b;
+        border-color: transparent;
+        color: #fff; }
+      html.theme--documenter-dark .button.is-danger[disabled],
+      fieldset[disabled] html.theme--documenter-dark .button.is-danger {
+        background-color: #9e1b0d;
+        border-color: transparent;
+        box-shadow: none; }
+      html.theme--documenter-dark .button.is-danger.is-inverted {
+        background-color: #fff;
+        color: #9e1b0d; }
+        html.theme--documenter-dark .button.is-danger.is-inverted:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-hovered {
+          background-color: #f2f2f2; }
+        html.theme--documenter-dark .button.is-danger.is-inverted[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted {
+          background-color: #fff;
+          border-color: transparent;
+          box-shadow: none;
+          color: #9e1b0d; }
+      html.theme--documenter-dark .button.is-danger.is-loading::after {
+        border-color: transparent transparent #fff #fff !important; }
+      html.theme--documenter-dark .button.is-danger.is-outlined {
+        background-color: transparent;
+        border-color: #9e1b0d;
+        color: #9e1b0d; }
+        html.theme--documenter-dark .button.is-danger.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-outlined.is-focused {
+          background-color: #9e1b0d;
+          border-color: #9e1b0d;
+          color: #fff; }
+        html.theme--documenter-dark .button.is-danger.is-outlined.is-loading::after {
+          border-color: transparent transparent #9e1b0d #9e1b0d !important; }
+        html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #fff #fff !important; }
+        html.theme--documenter-dark .button.is-danger.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-outlined {
+          background-color: transparent;
+          border-color: #9e1b0d;
+          box-shadow: none;
+          color: #9e1b0d; }
+      html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        color: #fff; }
+        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:hover, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-hovered, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined:focus, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-focused {
+          background-color: #fff;
+          color: #9e1b0d; }
+        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after {
+          border-color: transparent transparent #9e1b0d #9e1b0d !important; }
+        html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined[disabled],
+        fieldset[disabled] html.theme--documenter-dark .button.is-danger.is-inverted.is-outlined {
+          background-color: transparent;
+          border-color: #fff;
+          box-shadow: none;
+          color: #fff; }
+    html.theme--documenter-dark .button.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button {
+      border-radius: 3px;
+      font-size: 0.85em; }
+    html.theme--documenter-dark .button.is-normal {
+      font-size: 15px; }
+    html.theme--documenter-dark .button.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .button.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .button[disabled],
+    fieldset[disabled] html.theme--documenter-dark .button {
+      background-color: #8c9b9d;
+      border-color: #dbdee0;
+      box-shadow: none;
+      opacity: 0.5; }
+    html.theme--documenter-dark .button.is-fullwidth {
+      display: flex;
+      width: 100%; }
+    html.theme--documenter-dark .button.is-loading {
+      color: transparent !important;
+      pointer-events: none; }
+      html.theme--documenter-dark .button.is-loading::after {
+        position: absolute;
+        left: calc(50% - (1em / 2));
+        top: calc(50% - (1em / 2));
+        position: absolute !important; }
+    html.theme--documenter-dark .button.is-static {
+      background-color: #282f2f;
+      border-color: #5e6d6f;
+      color: #dbdee0;
+      box-shadow: none;
+      pointer-events: none; }
+    html.theme--documenter-dark .button.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.button {
+      border-radius: 290486px;
+      padding-left: 1em;
+      padding-right: 1em; }
+  html.theme--documenter-dark .buttons {
+    align-items: center;
+    display: flex;
+    flex-wrap: wrap;
+    justify-content: flex-start; }
+    html.theme--documenter-dark .buttons .button {
+      margin-bottom: 0.5rem; }
+      html.theme--documenter-dark .buttons .button:not(:last-child):not(.is-fullwidth) {
+        margin-right: 0.5rem; }
+    html.theme--documenter-dark .buttons:last-child {
+      margin-bottom: -0.5rem; }
+    html.theme--documenter-dark .buttons:not(:last-child) {
+      margin-bottom: 1rem; }
+    html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) {
+      border-radius: 3px;
+      font-size: 0.85em; }
+    html.theme--documenter-dark .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .buttons.has-addons .button:not(:first-child) {
+      border-bottom-left-radius: 0;
+      border-top-left-radius: 0; }
+    html.theme--documenter-dark .buttons.has-addons .button:not(:last-child) {
+      border-bottom-right-radius: 0;
+      border-top-right-radius: 0;
+      margin-right: -1px; }
+    html.theme--documenter-dark .buttons.has-addons .button:last-child {
+      margin-right: 0; }
+    html.theme--documenter-dark .buttons.has-addons .button:hover, html.theme--documenter-dark .buttons.has-addons .button.is-hovered {
+      z-index: 2; }
+    html.theme--documenter-dark .buttons.has-addons .button:focus, html.theme--documenter-dark .buttons.has-addons .button.is-focused, html.theme--documenter-dark .buttons.has-addons .button:active, html.theme--documenter-dark .buttons.has-addons .button.is-active, html.theme--documenter-dark .buttons.has-addons .button.is-selected {
+      z-index: 3; }
+      html.theme--documenter-dark .buttons.has-addons .button:focus:hover, html.theme--documenter-dark .buttons.has-addons .button.is-focused:hover, html.theme--documenter-dark .buttons.has-addons .button:active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-active:hover, html.theme--documenter-dark .buttons.has-addons .button.is-selected:hover {
+        z-index: 4; }
+    html.theme--documenter-dark .buttons.has-addons .button.is-expanded {
+      flex-grow: 1;
+      flex-shrink: 1; }
+    html.theme--documenter-dark .buttons.is-centered {
+      justify-content: center; }
+      html.theme--documenter-dark .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) {
+        margin-left: 0.25rem;
+        margin-right: 0.25rem; }
+    html.theme--documenter-dark .buttons.is-right {
+      justify-content: flex-end; }
+      html.theme--documenter-dark .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) {
+        margin-left: 0.25rem;
+        margin-right: 0.25rem; }
+  html.theme--documenter-dark .container {
+    flex-grow: 1;
+    margin: 0 auto;
+    position: relative;
+    width: auto; }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .container {
+        max-width: 992px; }
+        html.theme--documenter-dark .container.is-fluid {
+          margin-left: 32px;
+          margin-right: 32px;
+          max-width: none; } }
+    @media screen and (max-width: 1215px) {
+      html.theme--documenter-dark .container.is-widescreen {
+        max-width: 1152px; } }
+    @media screen and (max-width: 1407px) {
+      html.theme--documenter-dark .container.is-fullhd {
+        max-width: 1344px; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .container {
+        max-width: 1152px; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .container {
+        max-width: 1344px; } }
+  html.theme--documenter-dark .content li + li {
+    margin-top: 0.25em; }
+  html.theme--documenter-dark .content p:not(:last-child),
+  html.theme--documenter-dark .content dl:not(:last-child),
+  html.theme--documenter-dark .content ol:not(:last-child),
+  html.theme--documenter-dark .content ul:not(:last-child),
+  html.theme--documenter-dark .content blockquote:not(:last-child),
+  html.theme--documenter-dark .content pre:not(:last-child),
+  html.theme--documenter-dark .content table:not(:last-child) {
+    margin-bottom: 1em; }
+  html.theme--documenter-dark .content h1,
+  html.theme--documenter-dark .content h2,
+  html.theme--documenter-dark .content h3,
+  html.theme--documenter-dark .content h4,
+  html.theme--documenter-dark .content h5,
+  html.theme--documenter-dark .content h6 {
+    color: #f2f2f2;
+    font-weight: 600;
+    line-height: 1.125; }
+  html.theme--documenter-dark .content h1 {
+    font-size: 2em;
+    margin-bottom: 0.5em; }
+    html.theme--documenter-dark .content h1:not(:first-child) {
+      margin-top: 1em; }
+  html.theme--documenter-dark .content h2 {
+    font-size: 1.75em;
+    margin-bottom: 0.5714em; }
+    html.theme--documenter-dark .content h2:not(:first-child) {
+      margin-top: 1.1428em; }
+  html.theme--documenter-dark .content h3 {
+    font-size: 1.5em;
+    margin-bottom: 0.6666em; }
+    html.theme--documenter-dark .content h3:not(:first-child) {
+      margin-top: 1.3333em; }
+  html.theme--documenter-dark .content h4 {
+    font-size: 1.25em;
+    margin-bottom: 0.8em; }
+  html.theme--documenter-dark .content h5 {
+    font-size: 1.125em;
+    margin-bottom: 0.8888em; }
+  html.theme--documenter-dark .content h6 {
+    font-size: 1em;
+    margin-bottom: 1em; }
+  html.theme--documenter-dark .content blockquote {
+    background-color: #282f2f;
+    border-left: 5px solid #5e6d6f;
+    padding: 1.25em 1.5em; }
+  html.theme--documenter-dark .content ol {
+    list-style-position: outside;
+    margin-left: 2em;
+    margin-top: 1em; }
+    html.theme--documenter-dark .content ol:not([type]) {
+      list-style-type: decimal; }
+      html.theme--documenter-dark .content ol:not([type]).is-lower-alpha {
+        list-style-type: lower-alpha; }
+      html.theme--documenter-dark .content ol:not([type]).is-lower-roman {
+        list-style-type: lower-roman; }
+      html.theme--documenter-dark .content ol:not([type]).is-upper-alpha {
+        list-style-type: upper-alpha; }
+      html.theme--documenter-dark .content ol:not([type]).is-upper-roman {
+        list-style-type: upper-roman; }
+  html.theme--documenter-dark .content ul {
+    list-style: disc outside;
+    margin-left: 2em;
+    margin-top: 1em; }
+    html.theme--documenter-dark .content ul ul {
+      list-style-type: circle;
+      margin-top: 0.5em; }
+      html.theme--documenter-dark .content ul ul ul {
+        list-style-type: square; }
+  html.theme--documenter-dark .content dd {
+    margin-left: 2em; }
+  html.theme--documenter-dark .content figure {
+    margin-left: 2em;
+    margin-right: 2em;
+    text-align: center; }
+    html.theme--documenter-dark .content figure:not(:first-child) {
+      margin-top: 2em; }
+    html.theme--documenter-dark .content figure:not(:last-child) {
+      margin-bottom: 2em; }
+    html.theme--documenter-dark .content figure img {
+      display: inline-block; }
+    html.theme--documenter-dark .content figure figcaption {
+      font-style: italic; }
+  html.theme--documenter-dark .content pre {
+    -webkit-overflow-scrolling: touch;
+    overflow-x: auto;
+    padding: 0.7rem 0.5rem;
+    white-space: pre;
+    word-wrap: normal; }
+  html.theme--documenter-dark .content sup,
+  html.theme--documenter-dark .content sub {
+    font-size: 75%; }
+  html.theme--documenter-dark .content table {
+    width: 100%; }
+    html.theme--documenter-dark .content table td,
+    html.theme--documenter-dark .content table th {
+      border: 1px solid #5e6d6f;
+      border-width: 0 0 1px;
+      padding: 0.5em 0.75em;
+      vertical-align: top; }
+    html.theme--documenter-dark .content table th {
+      color: #f2f2f2; }
+      html.theme--documenter-dark .content table th:not([align]) {
+        text-align: left; }
+    html.theme--documenter-dark .content table thead td,
+    html.theme--documenter-dark .content table thead th {
+      border-width: 0 0 2px;
+      color: #f2f2f2; }
+    html.theme--documenter-dark .content table tfoot td,
+    html.theme--documenter-dark .content table tfoot th {
+      border-width: 2px 0 0;
+      color: #f2f2f2; }
+    html.theme--documenter-dark .content table tbody tr:last-child td,
+    html.theme--documenter-dark .content table tbody tr:last-child th {
+      border-bottom-width: 0; }
+  html.theme--documenter-dark .content .tabs li + li {
+    margin-top: 0; }
+  html.theme--documenter-dark .content.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.content {
+    font-size: 0.85em; }
+  html.theme--documenter-dark .content.is-medium {
+    font-size: 1.25rem; }
+  html.theme--documenter-dark .content.is-large {
+    font-size: 1.5rem; }
+  html.theme--documenter-dark .icon {
+    align-items: center;
+    display: inline-flex;
+    justify-content: center;
+    height: 1.5rem;
+    width: 1.5rem; }
+    html.theme--documenter-dark .icon.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.icon {
+      height: 1rem;
+      width: 1rem; }
+    html.theme--documenter-dark .icon.is-medium {
+      height: 2rem;
+      width: 2rem; }
+    html.theme--documenter-dark .icon.is-large {
+      height: 3rem;
+      width: 3rem; }
+  html.theme--documenter-dark .image, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img {
+    display: block;
+    position: relative; }
+    html.theme--documenter-dark .image img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img {
+      display: block;
+      height: auto;
+      width: 100%; }
+      html.theme--documenter-dark .image img.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img img.is-rounded {
+        border-radius: 290486px; }
+    html.theme--documenter-dark .image.is-square img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square img,
+    html.theme--documenter-dark .image.is-square .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, html.theme--documenter-dark .image.is-1by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 img,
+    html.theme--documenter-dark .image.is-1by1 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, html.theme--documenter-dark .image.is-5by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 img,
+    html.theme--documenter-dark .image.is-5by4 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, html.theme--documenter-dark .image.is-4by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 img,
+    html.theme--documenter-dark .image.is-4by3 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, html.theme--documenter-dark .image.is-3by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 img,
+    html.theme--documenter-dark .image.is-3by2 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, html.theme--documenter-dark .image.is-5by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 img,
+    html.theme--documenter-dark .image.is-5by3 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, html.theme--documenter-dark .image.is-16by9 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 img,
+    html.theme--documenter-dark .image.is-16by9 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, html.theme--documenter-dark .image.is-2by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 img,
+    html.theme--documenter-dark .image.is-2by1 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, html.theme--documenter-dark .image.is-3by1 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 img,
+    html.theme--documenter-dark .image.is-3by1 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, html.theme--documenter-dark .image.is-4by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 img,
+    html.theme--documenter-dark .image.is-4by5 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, html.theme--documenter-dark .image.is-3by4 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 img,
+    html.theme--documenter-dark .image.is-3by4 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, html.theme--documenter-dark .image.is-2by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 img,
+    html.theme--documenter-dark .image.is-2by3 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, html.theme--documenter-dark .image.is-3by5 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 img,
+    html.theme--documenter-dark .image.is-3by5 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, html.theme--documenter-dark .image.is-9by16 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 img,
+    html.theme--documenter-dark .image.is-9by16 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, html.theme--documenter-dark .image.is-1by2 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 img,
+    html.theme--documenter-dark .image.is-1by2 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, html.theme--documenter-dark .image.is-1by3 img, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 img,
+    html.theme--documenter-dark .image.is-1by3 .has-ratio,
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio {
+      height: 100%;
+      width: 100%; }
+    html.theme--documenter-dark .image.is-square, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-square, html.theme--documenter-dark .image.is-1by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by1 {
+      padding-top: 100%; }
+    html.theme--documenter-dark .image.is-5by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by4 {
+      padding-top: 80%; }
+    html.theme--documenter-dark .image.is-4by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by3 {
+      padding-top: 75%; }
+    html.theme--documenter-dark .image.is-3by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by2 {
+      padding-top: 66.6666%; }
+    html.theme--documenter-dark .image.is-5by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-5by3 {
+      padding-top: 60%; }
+    html.theme--documenter-dark .image.is-16by9, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16by9 {
+      padding-top: 56.25%; }
+    html.theme--documenter-dark .image.is-2by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by1 {
+      padding-top: 50%; }
+    html.theme--documenter-dark .image.is-3by1, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by1 {
+      padding-top: 33.3333%; }
+    html.theme--documenter-dark .image.is-4by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-4by5 {
+      padding-top: 125%; }
+    html.theme--documenter-dark .image.is-3by4, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by4 {
+      padding-top: 133.3333%; }
+    html.theme--documenter-dark .image.is-2by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-2by3 {
+      padding-top: 150%; }
+    html.theme--documenter-dark .image.is-3by5, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-3by5 {
+      padding-top: 166.6666%; }
+    html.theme--documenter-dark .image.is-9by16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-9by16 {
+      padding-top: 177.7777%; }
+    html.theme--documenter-dark .image.is-1by2, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by2 {
+      padding-top: 200%; }
+    html.theme--documenter-dark .image.is-1by3, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-1by3 {
+      padding-top: 300%; }
+    html.theme--documenter-dark .image.is-16x16, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-16x16 {
+      height: 16px;
+      width: 16px; }
+    html.theme--documenter-dark .image.is-24x24, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-24x24 {
+      height: 24px;
+      width: 24px; }
+    html.theme--documenter-dark .image.is-32x32, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-32x32 {
+      height: 32px;
+      width: 32px; }
+    html.theme--documenter-dark .image.is-48x48, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-48x48 {
+      height: 48px;
+      width: 48px; }
+    html.theme--documenter-dark .image.is-64x64, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-64x64 {
+      height: 64px;
+      width: 64px; }
+    html.theme--documenter-dark .image.is-96x96, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-96x96 {
+      height: 96px;
+      width: 96px; }
+    html.theme--documenter-dark .image.is-128x128, html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img.is-128x128 {
+      height: 128px;
+      width: 128px; }
+  html.theme--documenter-dark .notification {
+    background-color: #282f2f;
+    border-radius: 0.4em;
+    padding: 1.25rem 2.5rem 1.25rem 1.5rem;
+    position: relative; }
+    html.theme--documenter-dark .notification a:not(.button):not(.dropdown-item) {
+      color: currentColor;
+      text-decoration: underline; }
+    html.theme--documenter-dark .notification strong {
+      color: currentColor; }
+    html.theme--documenter-dark .notification code,
+    html.theme--documenter-dark .notification pre {
+      background: white; }
+    html.theme--documenter-dark .notification pre code {
+      background: transparent; }
+    html.theme--documenter-dark .notification > .delete {
+      position: absolute;
+      right: 0.5rem;
+      top: 0.5rem; }
+    html.theme--documenter-dark .notification .title,
+    html.theme--documenter-dark .notification .subtitle,
+    html.theme--documenter-dark .notification .content {
+      color: currentColor; }
+    html.theme--documenter-dark .notification.is-white {
+      background-color: white;
+      color: #0a0a0a; }
+    html.theme--documenter-dark .notification.is-black {
+      background-color: #0a0a0a;
+      color: white; }
+    html.theme--documenter-dark .notification.is-light {
+      background-color: #ecf0f1;
+      color: #282f2f; }
+    html.theme--documenter-dark .notification.is-dark, html.theme--documenter-dark .content kbd.notification {
+      background-color: #282f2f;
+      color: #ecf0f1; }
+    html.theme--documenter-dark .notification.is-primary, html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink {
+      background-color: #375a7f;
+      color: #fff; }
+    html.theme--documenter-dark .notification.is-link {
+      background-color: #1abc9c;
+      color: #fff; }
+    html.theme--documenter-dark .notification.is-info {
+      background-color: #024c7d;
+      color: #fff; }
+    html.theme--documenter-dark .notification.is-success {
+      background-color: #008438;
+      color: #fff; }
+    html.theme--documenter-dark .notification.is-warning {
+      background-color: #ad8100;
+      color: #fff; }
+    html.theme--documenter-dark .notification.is-danger {
+      background-color: #9e1b0d;
+      color: #fff; }
+  html.theme--documenter-dark .progress {
+    -moz-appearance: none;
+    -webkit-appearance: none;
+    border: none;
+    border-radius: 290486px;
+    display: block;
+    height: 15px;
+    overflow: hidden;
+    padding: 0;
+    width: 100%; }
+    html.theme--documenter-dark .progress::-webkit-progress-bar {
+      background-color: #5e6d6f; }
+    html.theme--documenter-dark .progress::-webkit-progress-value {
+      background-color: #dbdee0; }
+    html.theme--documenter-dark .progress::-moz-progress-bar {
+      background-color: #dbdee0; }
+    html.theme--documenter-dark .progress::-ms-fill {
+      background-color: #dbdee0;
+      border: none; }
+    html.theme--documenter-dark .progress.is-white::-webkit-progress-value {
+      background-color: white; }
+    html.theme--documenter-dark .progress.is-white::-moz-progress-bar {
+      background-color: white; }
+    html.theme--documenter-dark .progress.is-white::-ms-fill {
+      background-color: white; }
+    html.theme--documenter-dark .progress.is-white:indeterminate {
+      background-image: linear-gradient(to right, white 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-black::-webkit-progress-value {
+      background-color: #0a0a0a; }
+    html.theme--documenter-dark .progress.is-black::-moz-progress-bar {
+      background-color: #0a0a0a; }
+    html.theme--documenter-dark .progress.is-black::-ms-fill {
+      background-color: #0a0a0a; }
+    html.theme--documenter-dark .progress.is-black:indeterminate {
+      background-image: linear-gradient(to right, #0a0a0a 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-light::-webkit-progress-value {
+      background-color: #ecf0f1; }
+    html.theme--documenter-dark .progress.is-light::-moz-progress-bar {
+      background-color: #ecf0f1; }
+    html.theme--documenter-dark .progress.is-light::-ms-fill {
+      background-color: #ecf0f1; }
+    html.theme--documenter-dark .progress.is-light:indeterminate {
+      background-image: linear-gradient(to right, #ecf0f1 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-dark::-webkit-progress-value, html.theme--documenter-dark .content kbd.progress::-webkit-progress-value {
+      background-color: #282f2f; }
+    html.theme--documenter-dark .progress.is-dark::-moz-progress-bar, html.theme--documenter-dark .content kbd.progress::-moz-progress-bar {
+      background-color: #282f2f; }
+    html.theme--documenter-dark .progress.is-dark::-ms-fill, html.theme--documenter-dark .content kbd.progress::-ms-fill {
+      background-color: #282f2f; }
+    html.theme--documenter-dark .progress.is-dark:indeterminate, html.theme--documenter-dark .content kbd.progress:indeterminate {
+      background-image: linear-gradient(to right, #282f2f 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-primary::-webkit-progress-value, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value {
+      background-color: #375a7f; }
+    html.theme--documenter-dark .progress.is-primary::-moz-progress-bar, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar {
+      background-color: #375a7f; }
+    html.theme--documenter-dark .progress.is-primary::-ms-fill, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink::-ms-fill {
+      background-color: #375a7f; }
+    html.theme--documenter-dark .progress.is-primary:indeterminate, html.theme--documenter-dark .docstring > section > a.progress.docs-sourcelink:indeterminate {
+      background-image: linear-gradient(to right, #375a7f 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-link::-webkit-progress-value {
+      background-color: #1abc9c; }
+    html.theme--documenter-dark .progress.is-link::-moz-progress-bar {
+      background-color: #1abc9c; }
+    html.theme--documenter-dark .progress.is-link::-ms-fill {
+      background-color: #1abc9c; }
+    html.theme--documenter-dark .progress.is-link:indeterminate {
+      background-image: linear-gradient(to right, #1abc9c 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-info::-webkit-progress-value {
+      background-color: #024c7d; }
+    html.theme--documenter-dark .progress.is-info::-moz-progress-bar {
+      background-color: #024c7d; }
+    html.theme--documenter-dark .progress.is-info::-ms-fill {
+      background-color: #024c7d; }
+    html.theme--documenter-dark .progress.is-info:indeterminate {
+      background-image: linear-gradient(to right, #024c7d 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-success::-webkit-progress-value {
+      background-color: #008438; }
+    html.theme--documenter-dark .progress.is-success::-moz-progress-bar {
+      background-color: #008438; }
+    html.theme--documenter-dark .progress.is-success::-ms-fill {
+      background-color: #008438; }
+    html.theme--documenter-dark .progress.is-success:indeterminate {
+      background-image: linear-gradient(to right, #008438 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-warning::-webkit-progress-value {
+      background-color: #ad8100; }
+    html.theme--documenter-dark .progress.is-warning::-moz-progress-bar {
+      background-color: #ad8100; }
+    html.theme--documenter-dark .progress.is-warning::-ms-fill {
+      background-color: #ad8100; }
+    html.theme--documenter-dark .progress.is-warning:indeterminate {
+      background-image: linear-gradient(to right, #ad8100 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress.is-danger::-webkit-progress-value {
+      background-color: #9e1b0d; }
+    html.theme--documenter-dark .progress.is-danger::-moz-progress-bar {
+      background-color: #9e1b0d; }
+    html.theme--documenter-dark .progress.is-danger::-ms-fill {
+      background-color: #9e1b0d; }
+    html.theme--documenter-dark .progress.is-danger:indeterminate {
+      background-image: linear-gradient(to right, #9e1b0d 30%, #5e6d6f 30%); }
+    html.theme--documenter-dark .progress:indeterminate {
+      animation-duration: 1.5s;
+      animation-iteration-count: infinite;
+      animation-name: moveIndeterminate;
+      animation-timing-function: linear;
+      background-color: #5e6d6f;
+      background-image: linear-gradient(to right, #fff 30%, #5e6d6f 30%);
+      background-position: top left;
+      background-repeat: no-repeat;
+      background-size: 150% 150%; }
+      html.theme--documenter-dark .progress:indeterminate::-webkit-progress-bar {
+        background-color: transparent; }
+      html.theme--documenter-dark .progress:indeterminate::-moz-progress-bar {
+        background-color: transparent; }
+    html.theme--documenter-dark .progress.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.progress {
+      height: 0.85em; }
+    html.theme--documenter-dark .progress.is-medium {
+      height: 1.25rem; }
+    html.theme--documenter-dark .progress.is-large {
+      height: 1.5rem; }
+
+@keyframes moveIndeterminate {
+  from {
+    background-position: 200% 0; }
+  to {
+    background-position: -200% 0; } }
+  html.theme--documenter-dark .table {
+    background-color: #343c3d;
+    color: #fff; }
+    html.theme--documenter-dark .table td,
+    html.theme--documenter-dark .table th {
+      border: 1px solid #5e6d6f;
+      border-width: 0 0 1px;
+      padding: 0.5em 0.75em;
+      vertical-align: top; }
+      html.theme--documenter-dark .table td.is-white,
+      html.theme--documenter-dark .table th.is-white {
+        background-color: white;
+        border-color: white;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .table td.is-black,
+      html.theme--documenter-dark .table th.is-black {
+        background-color: #0a0a0a;
+        border-color: #0a0a0a;
+        color: white; }
+      html.theme--documenter-dark .table td.is-light,
+      html.theme--documenter-dark .table th.is-light {
+        background-color: #ecf0f1;
+        border-color: #ecf0f1;
+        color: #282f2f; }
+      html.theme--documenter-dark .table td.is-dark,
+      html.theme--documenter-dark .table th.is-dark {
+        background-color: #282f2f;
+        border-color: #282f2f;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .table td.is-primary,
+      html.theme--documenter-dark .table th.is-primary {
+        background-color: #375a7f;
+        border-color: #375a7f;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-link,
+      html.theme--documenter-dark .table th.is-link {
+        background-color: #1abc9c;
+        border-color: #1abc9c;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-info,
+      html.theme--documenter-dark .table th.is-info {
+        background-color: #024c7d;
+        border-color: #024c7d;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-success,
+      html.theme--documenter-dark .table th.is-success {
+        background-color: #008438;
+        border-color: #008438;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-warning,
+      html.theme--documenter-dark .table th.is-warning {
+        background-color: #ad8100;
+        border-color: #ad8100;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-danger,
+      html.theme--documenter-dark .table th.is-danger {
+        background-color: #9e1b0d;
+        border-color: #9e1b0d;
+        color: #fff; }
+      html.theme--documenter-dark .table td.is-narrow,
+      html.theme--documenter-dark .table th.is-narrow {
+        white-space: nowrap;
+        width: 1%; }
+      html.theme--documenter-dark .table td.is-selected,
+      html.theme--documenter-dark .table th.is-selected {
+        background-color: #375a7f;
+        color: #fff; }
+        html.theme--documenter-dark .table td.is-selected a,
+        html.theme--documenter-dark .table td.is-selected strong,
+        html.theme--documenter-dark .table th.is-selected a,
+        html.theme--documenter-dark .table th.is-selected strong {
+          color: currentColor; }
+    html.theme--documenter-dark .table th {
+      color: #f2f2f2; }
+      html.theme--documenter-dark .table th:not([align]) {
+        text-align: left; }
+    html.theme--documenter-dark .table tr.is-selected {
+      background-color: #375a7f;
+      color: #fff; }
+      html.theme--documenter-dark .table tr.is-selected a,
+      html.theme--documenter-dark .table tr.is-selected strong {
+        color: currentColor; }
+      html.theme--documenter-dark .table tr.is-selected td,
+      html.theme--documenter-dark .table tr.is-selected th {
+        border-color: #fff;
+        color: currentColor; }
+    html.theme--documenter-dark .table thead {
+      background-color: transparent; }
+      html.theme--documenter-dark .table thead td,
+      html.theme--documenter-dark .table thead th {
+        border-width: 0 0 2px;
+        color: #f2f2f2; }
+    html.theme--documenter-dark .table tfoot {
+      background-color: transparent; }
+      html.theme--documenter-dark .table tfoot td,
+      html.theme--documenter-dark .table tfoot th {
+        border-width: 2px 0 0;
+        color: #f2f2f2; }
+    html.theme--documenter-dark .table tbody {
+      background-color: transparent; }
+      html.theme--documenter-dark .table tbody tr:last-child td,
+      html.theme--documenter-dark .table tbody tr:last-child th {
+        border-bottom-width: 0; }
+    html.theme--documenter-dark .table.is-bordered td,
+    html.theme--documenter-dark .table.is-bordered th {
+      border-width: 1px; }
+    html.theme--documenter-dark .table.is-bordered tr:last-child td,
+    html.theme--documenter-dark .table.is-bordered tr:last-child th {
+      border-bottom-width: 1px; }
+    html.theme--documenter-dark .table.is-fullwidth {
+      width: 100%; }
+    html.theme--documenter-dark .table.is-hoverable tbody tr:not(.is-selected):hover {
+      background-color: #282f2f; }
+    html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover {
+      background-color: #282f2f; }
+      html.theme--documenter-dark .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) {
+        background-color: #2d3435; }
+    html.theme--documenter-dark .table.is-narrow td,
+    html.theme--documenter-dark .table.is-narrow th {
+      padding: 0.25em 0.5em; }
+    html.theme--documenter-dark .table.is-striped tbody tr:not(.is-selected):nth-child(even) {
+      background-color: #282f2f; }
+  html.theme--documenter-dark .table-container {
+    -webkit-overflow-scrolling: touch;
+    overflow: auto;
+    overflow-y: hidden;
+    max-width: 100%; }
+  html.theme--documenter-dark .tags {
+    align-items: center;
+    display: flex;
+    flex-wrap: wrap;
+    justify-content: flex-start; }
+    html.theme--documenter-dark .tags .tag, html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags .content kbd, html.theme--documenter-dark .content .tags kbd {
+      margin-bottom: 0.5rem; }
+      html.theme--documenter-dark .tags .tag:not(:last-child), html.theme--documenter-dark .tags .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags .content kbd:not(:last-child), html.theme--documenter-dark .content .tags kbd:not(:last-child) {
+        margin-right: 0.5rem; }
+    html.theme--documenter-dark .tags:last-child {
+      margin-bottom: -0.5rem; }
+    html.theme--documenter-dark .tags:not(:last-child) {
+      margin-bottom: 1rem; }
+    html.theme--documenter-dark .tags.are-medium .tag:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large), html.theme--documenter-dark .tags.are-medium .content kbd:not(.is-normal):not(.is-large), html.theme--documenter-dark .content .tags.are-medium kbd:not(.is-normal):not(.is-large) {
+      font-size: 15px; }
+    html.theme--documenter-dark .tags.are-large .tag:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium), html.theme--documenter-dark .tags.are-large .content kbd:not(.is-normal):not(.is-medium), html.theme--documenter-dark .content .tags.are-large kbd:not(.is-normal):not(.is-medium) {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .tags.is-centered {
+      justify-content: center; }
+      html.theme--documenter-dark .tags.is-centered .tag, html.theme--documenter-dark .tags.is-centered .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags.is-centered .content kbd, html.theme--documenter-dark .content .tags.is-centered kbd {
+        margin-right: 0.25rem;
+        margin-left: 0.25rem; }
+    html.theme--documenter-dark .tags.is-right {
+      justify-content: flex-end; }
+      html.theme--documenter-dark .tags.is-right .tag:not(:first-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:first-child) {
+        margin-left: 0.5rem; }
+      html.theme--documenter-dark .tags.is-right .tag:not(:last-child), html.theme--documenter-dark .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags.is-right .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.is-right kbd:not(:last-child) {
+        margin-right: 0; }
+    html.theme--documenter-dark .tags.has-addons .tag, html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .tags.has-addons .content kbd, html.theme--documenter-dark .content .tags.has-addons kbd {
+      margin-right: 0; }
+      html.theme--documenter-dark .tags.has-addons .tag:not(:first-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:first-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:first-child) {
+        margin-left: 0;
+        border-bottom-left-radius: 0;
+        border-top-left-radius: 0; }
+      html.theme--documenter-dark .tags.has-addons .tag:not(:last-child), html.theme--documenter-dark .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child), html.theme--documenter-dark .tags.has-addons .content kbd:not(:last-child), html.theme--documenter-dark .content .tags.has-addons kbd:not(:last-child) {
+        border-bottom-right-radius: 0;
+        border-top-right-radius: 0; }
+  html.theme--documenter-dark .tag:not(body), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body), html.theme--documenter-dark .content kbd:not(body) {
+    align-items: center;
+    background-color: #282f2f;
+    border-radius: 0.4em;
+    color: #fff;
+    display: inline-flex;
+    font-size: 0.85em;
+    height: 2em;
+    justify-content: center;
+    line-height: 1.5;
+    padding-left: 0.75em;
+    padding-right: 0.75em;
+    white-space: nowrap; }
+    html.theme--documenter-dark .tag:not(body) .delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .delete, html.theme--documenter-dark .content kbd:not(body) .delete {
+      margin-left: 0.25rem;
+      margin-right: -0.375rem; }
+    html.theme--documenter-dark .tag:not(body).is-white, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-white, html.theme--documenter-dark .content kbd:not(body).is-white {
+      background-color: white;
+      color: #0a0a0a; }
+    html.theme--documenter-dark .tag:not(body).is-black, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-black, html.theme--documenter-dark .content kbd:not(body).is-black {
+      background-color: #0a0a0a;
+      color: white; }
+    html.theme--documenter-dark .tag:not(body).is-light, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-light, html.theme--documenter-dark .content kbd:not(body).is-light {
+      background-color: #ecf0f1;
+      color: #282f2f; }
+    html.theme--documenter-dark .tag:not(body).is-dark, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-dark, html.theme--documenter-dark .content kbd:not(body) {
+      background-color: #282f2f;
+      color: #ecf0f1; }
+    html.theme--documenter-dark .tag:not(body).is-primary, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body), html.theme--documenter-dark .content kbd:not(body).is-primary {
+      background-color: #375a7f;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-link, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-link, html.theme--documenter-dark .content kbd:not(body).is-link {
+      background-color: #1abc9c;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-info, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-info, html.theme--documenter-dark .content kbd:not(body).is-info {
+      background-color: #024c7d;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-success, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-success, html.theme--documenter-dark .content kbd:not(body).is-success {
+      background-color: #008438;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-warning, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-warning, html.theme--documenter-dark .content kbd:not(body).is-warning {
+      background-color: #ad8100;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-danger, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-danger, html.theme--documenter-dark .content kbd:not(body).is-danger {
+      background-color: #9e1b0d;
+      color: #fff; }
+    html.theme--documenter-dark .tag:not(body).is-normal, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-normal, html.theme--documenter-dark .content kbd:not(body).is-normal {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .tag:not(body).is-medium, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-medium, html.theme--documenter-dark .content kbd:not(body).is-medium {
+      font-size: 15px; }
+    html.theme--documenter-dark .tag:not(body).is-large, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-large, html.theme--documenter-dark .content kbd:not(body).is-large {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .tag:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child), html.theme--documenter-dark .content kbd:not(body) .icon:first-child:not(:last-child) {
+      margin-left: -0.375em;
+      margin-right: 0.1875em; }
+    html.theme--documenter-dark .tag:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child), html.theme--documenter-dark .content kbd:not(body) .icon:last-child:not(:first-child) {
+      margin-left: 0.1875em;
+      margin-right: -0.375em; }
+    html.theme--documenter-dark .tag:not(body) .icon:first-child:last-child, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child, html.theme--documenter-dark .content kbd:not(body) .icon:first-child:last-child {
+      margin-left: -0.375em;
+      margin-right: -0.375em; }
+    html.theme--documenter-dark .tag:not(body).is-delete, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete, html.theme--documenter-dark .content kbd:not(body).is-delete {
+      margin-left: 1px;
+      padding: 0;
+      position: relative;
+      width: 2em; }
+      html.theme--documenter-dark .tag:not(body).is-delete::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::before, html.theme--documenter-dark .content kbd:not(body).is-delete::before, html.theme--documenter-dark .tag:not(body).is-delete::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::after, html.theme--documenter-dark .content kbd:not(body).is-delete::after {
+        background-color: currentColor;
+        content: "";
+        display: block;
+        left: 50%;
+        position: absolute;
+        top: 50%;
+        transform: translateX(-50%) translateY(-50%) rotate(45deg);
+        transform-origin: center center; }
+      html.theme--documenter-dark .tag:not(body).is-delete::before, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::before, html.theme--documenter-dark .content kbd:not(body).is-delete::before {
+        height: 1px;
+        width: 50%; }
+      html.theme--documenter-dark .tag:not(body).is-delete::after, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete::after, html.theme--documenter-dark .content kbd:not(body).is-delete::after {
+        height: 50%;
+        width: 1px; }
+      html.theme--documenter-dark .tag:not(body).is-delete:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:hover, html.theme--documenter-dark .content kbd:not(body).is-delete:hover, html.theme--documenter-dark .tag:not(body).is-delete:focus, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:focus, html.theme--documenter-dark .content kbd:not(body).is-delete:focus {
+        background-color: #1d2122; }
+      html.theme--documenter-dark .tag:not(body).is-delete:active, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-delete:active, html.theme--documenter-dark .content kbd:not(body).is-delete:active {
+        background-color: #111414; }
+    html.theme--documenter-dark .tag:not(body).is-rounded, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:not(body).is-rounded, html.theme--documenter-dark .content kbd:not(body).is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tag:not(body) {
+      border-radius: 290486px; }
+  html.theme--documenter-dark a.tag:hover, html.theme--documenter-dark .docstring > section > a.docs-sourcelink:hover {
+    text-decoration: underline; }
+  html.theme--documenter-dark .title,
+  html.theme--documenter-dark .subtitle {
+    word-break: break-word; }
+    html.theme--documenter-dark .title em,
+    html.theme--documenter-dark .title span,
+    html.theme--documenter-dark .subtitle em,
+    html.theme--documenter-dark .subtitle span {
+      font-weight: inherit; }
+    html.theme--documenter-dark .title sub,
+    html.theme--documenter-dark .subtitle sub {
+      font-size: 0.75em; }
+    html.theme--documenter-dark .title sup,
+    html.theme--documenter-dark .subtitle sup {
+      font-size: 0.75em; }
+    html.theme--documenter-dark .title .tag, html.theme--documenter-dark .title .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .title .content kbd, html.theme--documenter-dark .content .title kbd,
+    html.theme--documenter-dark .subtitle .tag,
+    html.theme--documenter-dark .subtitle .docstring > section > a.docs-sourcelink,
+    html.theme--documenter-dark .subtitle .content kbd,
+    html.theme--documenter-dark .content .subtitle kbd {
+      vertical-align: middle; }
+  html.theme--documenter-dark .title {
+    color: #fff;
+    font-size: 2rem;
+    font-weight: 500;
+    line-height: 1.125; }
+    html.theme--documenter-dark .title strong {
+      color: inherit;
+      font-weight: inherit; }
+    html.theme--documenter-dark .title + .highlight {
+      margin-top: -0.75rem; }
+    html.theme--documenter-dark .title:not(.is-spaced) + .subtitle {
+      margin-top: -1.25rem; }
+    html.theme--documenter-dark .title.is-1 {
+      font-size: 3rem; }
+    html.theme--documenter-dark .title.is-2 {
+      font-size: 2.5rem; }
+    html.theme--documenter-dark .title.is-3 {
+      font-size: 2rem; }
+    html.theme--documenter-dark .title.is-4 {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .title.is-5 {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .title.is-6 {
+      font-size: 15px; }
+    html.theme--documenter-dark .title.is-7 {
+      font-size: 0.85em; }
+  html.theme--documenter-dark .subtitle {
+    color: #8c9b9d;
+    font-size: 1.25rem;
+    font-weight: 400;
+    line-height: 1.25; }
+    html.theme--documenter-dark .subtitle strong {
+      color: #8c9b9d;
+      font-weight: 600; }
+    html.theme--documenter-dark .subtitle:not(.is-spaced) + .title {
+      margin-top: -1.25rem; }
+    html.theme--documenter-dark .subtitle.is-1 {
+      font-size: 3rem; }
+    html.theme--documenter-dark .subtitle.is-2 {
+      font-size: 2.5rem; }
+    html.theme--documenter-dark .subtitle.is-3 {
+      font-size: 2rem; }
+    html.theme--documenter-dark .subtitle.is-4 {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .subtitle.is-5 {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .subtitle.is-6 {
+      font-size: 15px; }
+    html.theme--documenter-dark .subtitle.is-7 {
+      font-size: 0.85em; }
+  html.theme--documenter-dark .heading {
+    display: block;
+    font-size: 11px;
+    letter-spacing: 1px;
+    margin-bottom: 5px;
+    text-transform: uppercase; }
+  html.theme--documenter-dark .highlight {
+    font-weight: 400;
+    max-width: 100%;
+    overflow: hidden;
+    padding: 0; }
+    html.theme--documenter-dark .highlight pre {
+      overflow: auto;
+      max-width: 100%; }
+  html.theme--documenter-dark .number {
+    align-items: center;
+    background-color: #282f2f;
+    border-radius: 290486px;
+    display: inline-flex;
+    font-size: 1.25rem;
+    height: 2em;
+    justify-content: center;
+    margin-right: 1.5rem;
+    min-width: 2.5em;
+    padding: 0.25rem 0.5rem;
+    text-align: center;
+    vertical-align: top; }
+  html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea, html.theme--documenter-dark .select select {
+    background-color: #1f2424;
+    border-color: #5e6d6f;
+    border-radius: 0.4em;
+    color: #dbdee0; }
+    html.theme--documenter-dark .input::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, html.theme--documenter-dark .textarea::-moz-placeholder, html.theme--documenter-dark .select select::-moz-placeholder {
+      color: rgba(219, 222, 224, 0.3); }
+    html.theme--documenter-dark .input::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, html.theme--documenter-dark .textarea::-webkit-input-placeholder, html.theme--documenter-dark .select select::-webkit-input-placeholder {
+      color: rgba(219, 222, 224, 0.3); }
+    html.theme--documenter-dark .input:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, html.theme--documenter-dark .textarea:-moz-placeholder, html.theme--documenter-dark .select select:-moz-placeholder {
+      color: rgba(219, 222, 224, 0.3); }
+    html.theme--documenter-dark .input:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, html.theme--documenter-dark .textarea:-ms-input-placeholder, html.theme--documenter-dark .select select:-ms-input-placeholder {
+      color: rgba(219, 222, 224, 0.3); }
+    html.theme--documenter-dark .input:hover, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:hover, html.theme--documenter-dark .textarea:hover, html.theme--documenter-dark .select select:hover, html.theme--documenter-dark .is-hovered.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-hovered, html.theme--documenter-dark .is-hovered.textarea, html.theme--documenter-dark .select select.is-hovered {
+      border-color: #8c9b9d; }
+    html.theme--documenter-dark .input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:focus, html.theme--documenter-dark .textarea:focus, html.theme--documenter-dark .select select:focus, html.theme--documenter-dark .is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-focused, html.theme--documenter-dark .is-focused.textarea, html.theme--documenter-dark .select select.is-focused, html.theme--documenter-dark .input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:active, html.theme--documenter-dark .textarea:active, html.theme--documenter-dark .select select:active, html.theme--documenter-dark .is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-active, html.theme--documenter-dark .is-active.textarea, html.theme--documenter-dark .select select.is-active {
+      border-color: #1abc9c;
+      box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); }
+    html.theme--documenter-dark .input[disabled], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled], html.theme--documenter-dark .textarea[disabled], html.theme--documenter-dark .select select[disabled],
+    fieldset[disabled] html.theme--documenter-dark .input,
+    fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,
+    fieldset[disabled] html.theme--documenter-dark .textarea,
+    fieldset[disabled] html.theme--documenter-dark .select select {
+      background-color: #8c9b9d;
+      border-color: #282f2f;
+      box-shadow: none;
+      color: white; }
+      html.theme--documenter-dark .input[disabled]::-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, html.theme--documenter-dark .textarea[disabled]::-moz-placeholder, html.theme--documenter-dark .select select[disabled]::-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .input::-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .textarea::-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .select select::-moz-placeholder {
+        color: rgba(255, 255, 255, 0.3); }
+      html.theme--documenter-dark .input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .textarea[disabled]::-webkit-input-placeholder, html.theme--documenter-dark .select select[disabled]::-webkit-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .input::-webkit-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .textarea::-webkit-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .select select::-webkit-input-placeholder {
+        color: rgba(255, 255, 255, 0.3); }
+      html.theme--documenter-dark .input[disabled]:-moz-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, html.theme--documenter-dark .textarea[disabled]:-moz-placeholder, html.theme--documenter-dark .select select[disabled]:-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .input:-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .textarea:-moz-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .select select:-moz-placeholder {
+        color: rgba(255, 255, 255, 0.3); }
+      html.theme--documenter-dark .input[disabled]:-ms-input-placeholder, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, html.theme--documenter-dark .textarea[disabled]:-ms-input-placeholder, html.theme--documenter-dark .select select[disabled]:-ms-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .input:-ms-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .textarea:-ms-input-placeholder,
+      fieldset[disabled] html.theme--documenter-dark .select select:-ms-input-placeholder {
+        color: rgba(255, 255, 255, 0.3); }
+  html.theme--documenter-dark .input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .textarea {
+    box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1);
+    max-width: 100%;
+    width: 100%; }
+    html.theme--documenter-dark .input[readonly], html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input[readonly], html.theme--documenter-dark .textarea[readonly] {
+      box-shadow: none; }
+    html.theme--documenter-dark .is-white.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white, html.theme--documenter-dark .is-white.textarea {
+      border-color: white; }
+      html.theme--documenter-dark .is-white.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:focus, html.theme--documenter-dark .is-white.textarea:focus, html.theme--documenter-dark .is-white.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white.is-focused, html.theme--documenter-dark .is-white.is-focused.textarea, html.theme--documenter-dark .is-white.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white:active, html.theme--documenter-dark .is-white.textarea:active, html.theme--documenter-dark .is-white.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-white.is-active, html.theme--documenter-dark .is-white.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+    html.theme--documenter-dark .is-black.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black, html.theme--documenter-dark .is-black.textarea {
+      border-color: #0a0a0a; }
+      html.theme--documenter-dark .is-black.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:focus, html.theme--documenter-dark .is-black.textarea:focus, html.theme--documenter-dark .is-black.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black.is-focused, html.theme--documenter-dark .is-black.is-focused.textarea, html.theme--documenter-dark .is-black.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black:active, html.theme--documenter-dark .is-black.textarea:active, html.theme--documenter-dark .is-black.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-black.is-active, html.theme--documenter-dark .is-black.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+    html.theme--documenter-dark .is-light.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light, html.theme--documenter-dark .is-light.textarea {
+      border-color: #ecf0f1; }
+      html.theme--documenter-dark .is-light.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:focus, html.theme--documenter-dark .is-light.textarea:focus, html.theme--documenter-dark .is-light.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light.is-focused, html.theme--documenter-dark .is-light.is-focused.textarea, html.theme--documenter-dark .is-light.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light:active, html.theme--documenter-dark .is-light.textarea:active, html.theme--documenter-dark .is-light.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-light.is-active, html.theme--documenter-dark .is-light.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); }
+    html.theme--documenter-dark .is-dark.input, html.theme--documenter-dark .content kbd.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark, html.theme--documenter-dark .is-dark.textarea, html.theme--documenter-dark .content kbd.textarea {
+      border-color: #282f2f; }
+      html.theme--documenter-dark .is-dark.input:focus, html.theme--documenter-dark .content kbd.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:focus, html.theme--documenter-dark .is-dark.textarea:focus, html.theme--documenter-dark .content kbd.textarea:focus, html.theme--documenter-dark .is-dark.is-focused.input, html.theme--documenter-dark .content kbd.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark.is-focused, html.theme--documenter-dark .is-dark.is-focused.textarea, html.theme--documenter-dark .content kbd.is-focused.textarea, html.theme--documenter-dark .is-dark.input:active, html.theme--documenter-dark .content kbd.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark:active, html.theme--documenter-dark .is-dark.textarea:active, html.theme--documenter-dark .content kbd.textarea:active, html.theme--documenter-dark .is-dark.is-active.input, html.theme--documenter-dark .content kbd.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-dark.is-active, html.theme--documenter-dark .is-dark.is-active.textarea, html.theme--documenter-dark .content kbd.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); }
+    html.theme--documenter-dark .is-primary.input, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary, html.theme--documenter-dark .is-primary.textarea, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink {
+      border-color: #375a7f; }
+      html.theme--documenter-dark .is-primary.input:focus, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:focus, html.theme--documenter-dark .is-primary.textarea:focus, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:focus, html.theme--documenter-dark .is-primary.is-focused.input, html.theme--documenter-dark .docstring > section > a.is-focused.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary.is-focused, html.theme--documenter-dark .is-primary.is-focused.textarea, html.theme--documenter-dark .docstring > section > a.is-focused.textarea.docs-sourcelink, html.theme--documenter-dark .is-primary.input:active, html.theme--documenter-dark .docstring > section > a.input.docs-sourcelink:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary:active, html.theme--documenter-dark .is-primary.textarea:active, html.theme--documenter-dark .docstring > section > a.textarea.docs-sourcelink:active, html.theme--documenter-dark .is-primary.is-active.input, html.theme--documenter-dark .docstring > section > a.is-active.input.docs-sourcelink, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-primary.is-active, html.theme--documenter-dark .is-primary.is-active.textarea, html.theme--documenter-dark .docstring > section > a.is-active.textarea.docs-sourcelink {
+        box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); }
+    html.theme--documenter-dark .is-link.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link, html.theme--documenter-dark .is-link.textarea {
+      border-color: #1abc9c; }
+      html.theme--documenter-dark .is-link.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:focus, html.theme--documenter-dark .is-link.textarea:focus, html.theme--documenter-dark .is-link.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link.is-focused, html.theme--documenter-dark .is-link.is-focused.textarea, html.theme--documenter-dark .is-link.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link:active, html.theme--documenter-dark .is-link.textarea:active, html.theme--documenter-dark .is-link.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-link.is-active, html.theme--documenter-dark .is-link.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); }
+    html.theme--documenter-dark .is-info.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info, html.theme--documenter-dark .is-info.textarea {
+      border-color: #024c7d; }
+      html.theme--documenter-dark .is-info.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:focus, html.theme--documenter-dark .is-info.textarea:focus, html.theme--documenter-dark .is-info.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info.is-focused, html.theme--documenter-dark .is-info.is-focused.textarea, html.theme--documenter-dark .is-info.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info:active, html.theme--documenter-dark .is-info.textarea:active, html.theme--documenter-dark .is-info.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-info.is-active, html.theme--documenter-dark .is-info.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); }
+    html.theme--documenter-dark .is-success.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success, html.theme--documenter-dark .is-success.textarea {
+      border-color: #008438; }
+      html.theme--documenter-dark .is-success.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:focus, html.theme--documenter-dark .is-success.textarea:focus, html.theme--documenter-dark .is-success.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success.is-focused, html.theme--documenter-dark .is-success.is-focused.textarea, html.theme--documenter-dark .is-success.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success:active, html.theme--documenter-dark .is-success.textarea:active, html.theme--documenter-dark .is-success.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-success.is-active, html.theme--documenter-dark .is-success.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); }
+    html.theme--documenter-dark .is-warning.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning, html.theme--documenter-dark .is-warning.textarea {
+      border-color: #ad8100; }
+      html.theme--documenter-dark .is-warning.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:focus, html.theme--documenter-dark .is-warning.textarea:focus, html.theme--documenter-dark .is-warning.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning.is-focused, html.theme--documenter-dark .is-warning.is-focused.textarea, html.theme--documenter-dark .is-warning.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning:active, html.theme--documenter-dark .is-warning.textarea:active, html.theme--documenter-dark .is-warning.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-warning.is-active, html.theme--documenter-dark .is-warning.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); }
+    html.theme--documenter-dark .is-danger.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger, html.theme--documenter-dark .is-danger.textarea {
+      border-color: #9e1b0d; }
+      html.theme--documenter-dark .is-danger.input:focus, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:focus, html.theme--documenter-dark .is-danger.textarea:focus, html.theme--documenter-dark .is-danger.is-focused.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger.is-focused, html.theme--documenter-dark .is-danger.is-focused.textarea, html.theme--documenter-dark .is-danger.input:active, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger:active, html.theme--documenter-dark .is-danger.textarea:active, html.theme--documenter-dark .is-danger.is-active.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-danger.is-active, html.theme--documenter-dark .is-danger.is-active.textarea {
+        box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); }
+    html.theme--documenter-dark .is-small.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark .is-small.textarea {
+      border-radius: 3px;
+      font-size: 0.85em; }
+    html.theme--documenter-dark .is-medium.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-medium, html.theme--documenter-dark .is-medium.textarea {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .is-large.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-large, html.theme--documenter-dark .is-large.textarea {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .is-fullwidth.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-fullwidth, html.theme--documenter-dark .is-fullwidth.textarea {
+      display: block;
+      width: 100%; }
+    html.theme--documenter-dark .is-inline.input, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-inline, html.theme--documenter-dark .is-inline.textarea {
+      display: inline;
+      width: auto; }
+  html.theme--documenter-dark .input.is-rounded, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input {
+    border-radius: 290486px;
+    padding-left: 1em;
+    padding-right: 1em; }
+  html.theme--documenter-dark .input.is-static, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.is-static {
+    background-color: transparent;
+    border-color: transparent;
+    box-shadow: none;
+    padding-left: 0;
+    padding-right: 0; }
+  html.theme--documenter-dark .textarea {
+    display: block;
+    max-width: 100%;
+    min-width: 100%;
+    padding: 0.625em;
+    resize: vertical; }
+    html.theme--documenter-dark .textarea:not([rows]) {
+      max-height: 600px;
+      min-height: 120px; }
+    html.theme--documenter-dark .textarea[rows] {
+      height: initial; }
+    html.theme--documenter-dark .textarea.has-fixed-size {
+      resize: none; }
+  html.theme--documenter-dark .checkbox, html.theme--documenter-dark .radio {
+    cursor: pointer;
+    display: inline-block;
+    line-height: 1.25;
+    position: relative; }
+    html.theme--documenter-dark .checkbox input, html.theme--documenter-dark .radio input {
+      cursor: pointer; }
+    html.theme--documenter-dark .checkbox:hover, html.theme--documenter-dark .radio:hover {
+      color: #8c9b9d; }
+    html.theme--documenter-dark .checkbox[disabled], html.theme--documenter-dark .radio[disabled],
+    fieldset[disabled] html.theme--documenter-dark .checkbox,
+    fieldset[disabled] html.theme--documenter-dark .radio {
+      color: white;
+      cursor: not-allowed; }
+  html.theme--documenter-dark .radio + .radio {
+    margin-left: 0.5em; }
+  html.theme--documenter-dark .select {
+    display: inline-block;
+    max-width: 100%;
+    position: relative;
+    vertical-align: top; }
+    html.theme--documenter-dark .select:not(.is-multiple) {
+      height: 2.25em; }
+    html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after {
+      border-color: #1abc9c;
+      right: 1.125em;
+      z-index: 4; }
+    html.theme--documenter-dark .select.is-rounded select, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select select {
+      border-radius: 290486px;
+      padding-left: 1em; }
+    html.theme--documenter-dark .select select {
+      cursor: pointer;
+      display: block;
+      font-size: 1em;
+      max-width: 100%;
+      outline: none; }
+      html.theme--documenter-dark .select select::-ms-expand {
+        display: none; }
+      html.theme--documenter-dark .select select[disabled]:hover,
+      fieldset[disabled] html.theme--documenter-dark .select select:hover {
+        border-color: #282f2f; }
+      html.theme--documenter-dark .select select:not([multiple]) {
+        padding-right: 2.5em; }
+      html.theme--documenter-dark .select select[multiple] {
+        height: auto;
+        padding: 0; }
+        html.theme--documenter-dark .select select[multiple] option {
+          padding: 0.5em 1em; }
+    html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading):hover::after {
+      border-color: #8c9b9d; }
+    html.theme--documenter-dark .select.is-white:not(:hover)::after {
+      border-color: white; }
+    html.theme--documenter-dark .select.is-white select {
+      border-color: white; }
+      html.theme--documenter-dark .select.is-white select:hover, html.theme--documenter-dark .select.is-white select.is-hovered {
+        border-color: #f2f2f2; }
+      html.theme--documenter-dark .select.is-white select:focus, html.theme--documenter-dark .select.is-white select.is-focused, html.theme--documenter-dark .select.is-white select:active, html.theme--documenter-dark .select.is-white select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+    html.theme--documenter-dark .select.is-black:not(:hover)::after {
+      border-color: #0a0a0a; }
+    html.theme--documenter-dark .select.is-black select {
+      border-color: #0a0a0a; }
+      html.theme--documenter-dark .select.is-black select:hover, html.theme--documenter-dark .select.is-black select.is-hovered {
+        border-color: black; }
+      html.theme--documenter-dark .select.is-black select:focus, html.theme--documenter-dark .select.is-black select.is-focused, html.theme--documenter-dark .select.is-black select:active, html.theme--documenter-dark .select.is-black select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+    html.theme--documenter-dark .select.is-light:not(:hover)::after {
+      border-color: #ecf0f1; }
+    html.theme--documenter-dark .select.is-light select {
+      border-color: #ecf0f1; }
+      html.theme--documenter-dark .select.is-light select:hover, html.theme--documenter-dark .select.is-light select.is-hovered {
+        border-color: #dde4e6; }
+      html.theme--documenter-dark .select.is-light select:focus, html.theme--documenter-dark .select.is-light select.is-focused, html.theme--documenter-dark .select.is-light select:active, html.theme--documenter-dark .select.is-light select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(236, 240, 241, 0.25); }
+    html.theme--documenter-dark .select.is-dark:not(:hover)::after, html.theme--documenter-dark .content kbd.select:not(:hover)::after {
+      border-color: #282f2f; }
+    html.theme--documenter-dark .select.is-dark select, html.theme--documenter-dark .content kbd.select select {
+      border-color: #282f2f; }
+      html.theme--documenter-dark .select.is-dark select:hover, html.theme--documenter-dark .content kbd.select select:hover, html.theme--documenter-dark .select.is-dark select.is-hovered, html.theme--documenter-dark .content kbd.select select.is-hovered {
+        border-color: #1d2122; }
+      html.theme--documenter-dark .select.is-dark select:focus, html.theme--documenter-dark .content kbd.select select:focus, html.theme--documenter-dark .select.is-dark select.is-focused, html.theme--documenter-dark .content kbd.select select.is-focused, html.theme--documenter-dark .select.is-dark select:active, html.theme--documenter-dark .content kbd.select select:active, html.theme--documenter-dark .select.is-dark select.is-active, html.theme--documenter-dark .content kbd.select select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(40, 47, 47, 0.25); }
+    html.theme--documenter-dark .select.is-primary:not(:hover)::after, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink:not(:hover)::after {
+      border-color: #375a7f; }
+    html.theme--documenter-dark .select.is-primary select, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select {
+      border-color: #375a7f; }
+      html.theme--documenter-dark .select.is-primary select:hover, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:hover, html.theme--documenter-dark .select.is-primary select.is-hovered, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-hovered {
+        border-color: #2f4d6d; }
+      html.theme--documenter-dark .select.is-primary select:focus, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:focus, html.theme--documenter-dark .select.is-primary select.is-focused, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-focused, html.theme--documenter-dark .select.is-primary select:active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select:active, html.theme--documenter-dark .select.is-primary select.is-active, html.theme--documenter-dark .docstring > section > a.select.docs-sourcelink select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(55, 90, 127, 0.25); }
+    html.theme--documenter-dark .select.is-link:not(:hover)::after {
+      border-color: #1abc9c; }
+    html.theme--documenter-dark .select.is-link select {
+      border-color: #1abc9c; }
+      html.theme--documenter-dark .select.is-link select:hover, html.theme--documenter-dark .select.is-link select.is-hovered {
+        border-color: #17a689; }
+      html.theme--documenter-dark .select.is-link select:focus, html.theme--documenter-dark .select.is-link select.is-focused, html.theme--documenter-dark .select.is-link select:active, html.theme--documenter-dark .select.is-link select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(26, 188, 156, 0.25); }
+    html.theme--documenter-dark .select.is-info:not(:hover)::after {
+      border-color: #024c7d; }
+    html.theme--documenter-dark .select.is-info select {
+      border-color: #024c7d; }
+      html.theme--documenter-dark .select.is-info select:hover, html.theme--documenter-dark .select.is-info select.is-hovered {
+        border-color: #023d64; }
+      html.theme--documenter-dark .select.is-info select:focus, html.theme--documenter-dark .select.is-info select.is-focused, html.theme--documenter-dark .select.is-info select:active, html.theme--documenter-dark .select.is-info select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(2, 76, 125, 0.25); }
+    html.theme--documenter-dark .select.is-success:not(:hover)::after {
+      border-color: #008438; }
+    html.theme--documenter-dark .select.is-success select {
+      border-color: #008438; }
+      html.theme--documenter-dark .select.is-success select:hover, html.theme--documenter-dark .select.is-success select.is-hovered {
+        border-color: #006b2d; }
+      html.theme--documenter-dark .select.is-success select:focus, html.theme--documenter-dark .select.is-success select.is-focused, html.theme--documenter-dark .select.is-success select:active, html.theme--documenter-dark .select.is-success select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(0, 132, 56, 0.25); }
+    html.theme--documenter-dark .select.is-warning:not(:hover)::after {
+      border-color: #ad8100; }
+    html.theme--documenter-dark .select.is-warning select {
+      border-color: #ad8100; }
+      html.theme--documenter-dark .select.is-warning select:hover, html.theme--documenter-dark .select.is-warning select.is-hovered {
+        border-color: #946e00; }
+      html.theme--documenter-dark .select.is-warning select:focus, html.theme--documenter-dark .select.is-warning select.is-focused, html.theme--documenter-dark .select.is-warning select:active, html.theme--documenter-dark .select.is-warning select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(173, 129, 0, 0.25); }
+    html.theme--documenter-dark .select.is-danger:not(:hover)::after {
+      border-color: #9e1b0d; }
+    html.theme--documenter-dark .select.is-danger select {
+      border-color: #9e1b0d; }
+      html.theme--documenter-dark .select.is-danger select:hover, html.theme--documenter-dark .select.is-danger select.is-hovered {
+        border-color: #86170b; }
+      html.theme--documenter-dark .select.is-danger select:focus, html.theme--documenter-dark .select.is-danger select.is-focused, html.theme--documenter-dark .select.is-danger select:active, html.theme--documenter-dark .select.is-danger select.is-active {
+        box-shadow: 0 0 0 0.125em rgba(158, 27, 13, 0.25); }
+    html.theme--documenter-dark .select.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select {
+      border-radius: 3px;
+      font-size: 0.85em; }
+    html.theme--documenter-dark .select.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .select.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .select.is-disabled::after {
+      border-color: white; }
+    html.theme--documenter-dark .select.is-fullwidth {
+      width: 100%; }
+      html.theme--documenter-dark .select.is-fullwidth select {
+        width: 100%; }
+    html.theme--documenter-dark .select.is-loading::after {
+      margin-top: 0;
+      position: absolute;
+      right: 0.625em;
+      top: 0.625em;
+      transform: none; }
+    html.theme--documenter-dark .select.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.select.is-loading:after {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .select.is-loading.is-medium:after {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .select.is-loading.is-large:after {
+      font-size: 1.5rem; }
+  html.theme--documenter-dark .file {
+    align-items: stretch;
+    display: flex;
+    justify-content: flex-start;
+    position: relative; }
+    html.theme--documenter-dark .file.is-white .file-cta {
+      background-color: white;
+      border-color: transparent;
+      color: #0a0a0a; }
+    html.theme--documenter-dark .file.is-white:hover .file-cta, html.theme--documenter-dark .file.is-white.is-hovered .file-cta {
+      background-color: #f9f9f9;
+      border-color: transparent;
+      color: #0a0a0a; }
+    html.theme--documenter-dark .file.is-white:focus .file-cta, html.theme--documenter-dark .file.is-white.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25);
+      color: #0a0a0a; }
+    html.theme--documenter-dark .file.is-white:active .file-cta, html.theme--documenter-dark .file.is-white.is-active .file-cta {
+      background-color: #f2f2f2;
+      border-color: transparent;
+      color: #0a0a0a; }
+    html.theme--documenter-dark .file.is-black .file-cta {
+      background-color: #0a0a0a;
+      border-color: transparent;
+      color: white; }
+    html.theme--documenter-dark .file.is-black:hover .file-cta, html.theme--documenter-dark .file.is-black.is-hovered .file-cta {
+      background-color: #040404;
+      border-color: transparent;
+      color: white; }
+    html.theme--documenter-dark .file.is-black:focus .file-cta, html.theme--documenter-dark .file.is-black.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25);
+      color: white; }
+    html.theme--documenter-dark .file.is-black:active .file-cta, html.theme--documenter-dark .file.is-black.is-active .file-cta {
+      background-color: black;
+      border-color: transparent;
+      color: white; }
+    html.theme--documenter-dark .file.is-light .file-cta {
+      background-color: #ecf0f1;
+      border-color: transparent;
+      color: #282f2f; }
+    html.theme--documenter-dark .file.is-light:hover .file-cta, html.theme--documenter-dark .file.is-light.is-hovered .file-cta {
+      background-color: #e5eaec;
+      border-color: transparent;
+      color: #282f2f; }
+    html.theme--documenter-dark .file.is-light:focus .file-cta, html.theme--documenter-dark .file.is-light.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(236, 240, 241, 0.25);
+      color: #282f2f; }
+    html.theme--documenter-dark .file.is-light:active .file-cta, html.theme--documenter-dark .file.is-light.is-active .file-cta {
+      background-color: #dde4e6;
+      border-color: transparent;
+      color: #282f2f; }
+    html.theme--documenter-dark .file.is-dark .file-cta, html.theme--documenter-dark .content kbd.file .file-cta {
+      background-color: #282f2f;
+      border-color: transparent;
+      color: #ecf0f1; }
+    html.theme--documenter-dark .file.is-dark:hover .file-cta, html.theme--documenter-dark .content kbd.file:hover .file-cta, html.theme--documenter-dark .file.is-dark.is-hovered .file-cta, html.theme--documenter-dark .content kbd.file.is-hovered .file-cta {
+      background-color: #232829;
+      border-color: transparent;
+      color: #ecf0f1; }
+    html.theme--documenter-dark .file.is-dark:focus .file-cta, html.theme--documenter-dark .content kbd.file:focus .file-cta, html.theme--documenter-dark .file.is-dark.is-focused .file-cta, html.theme--documenter-dark .content kbd.file.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(40, 47, 47, 0.25);
+      color: #ecf0f1; }
+    html.theme--documenter-dark .file.is-dark:active .file-cta, html.theme--documenter-dark .content kbd.file:active .file-cta, html.theme--documenter-dark .file.is-dark.is-active .file-cta, html.theme--documenter-dark .content kbd.file.is-active .file-cta {
+      background-color: #1d2122;
+      border-color: transparent;
+      color: #ecf0f1; }
+    html.theme--documenter-dark .file.is-primary .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink .file-cta {
+      background-color: #375a7f;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-primary:hover .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:hover .file-cta, html.theme--documenter-dark .file.is-primary.is-hovered .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta {
+      background-color: #335476;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-primary:focus .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:focus .file-cta, html.theme--documenter-dark .file.is-primary.is-focused .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-focused.docs-sourcelink .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(55, 90, 127, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-primary:active .file-cta, html.theme--documenter-dark .docstring > section > a.file.docs-sourcelink:active .file-cta, html.theme--documenter-dark .file.is-primary.is-active .file-cta, html.theme--documenter-dark .docstring > section > a.file.is-active.docs-sourcelink .file-cta {
+      background-color: #2f4d6d;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-link .file-cta {
+      background-color: #1abc9c;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-link:hover .file-cta, html.theme--documenter-dark .file.is-link.is-hovered .file-cta {
+      background-color: #18b193;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-link:focus .file-cta, html.theme--documenter-dark .file.is-link.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(26, 188, 156, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-link:active .file-cta, html.theme--documenter-dark .file.is-link.is-active .file-cta {
+      background-color: #17a689;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-info .file-cta {
+      background-color: #024c7d;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-info:hover .file-cta, html.theme--documenter-dark .file.is-info.is-hovered .file-cta {
+      background-color: #024470;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-info:focus .file-cta, html.theme--documenter-dark .file.is-info.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(2, 76, 125, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-info:active .file-cta, html.theme--documenter-dark .file.is-info.is-active .file-cta {
+      background-color: #023d64;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-success .file-cta {
+      background-color: #008438;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-success:hover .file-cta, html.theme--documenter-dark .file.is-success.is-hovered .file-cta {
+      background-color: #007733;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-success:focus .file-cta, html.theme--documenter-dark .file.is-success.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(0, 132, 56, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-success:active .file-cta, html.theme--documenter-dark .file.is-success.is-active .file-cta {
+      background-color: #006b2d;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-warning .file-cta {
+      background-color: #ad8100;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-warning:hover .file-cta, html.theme--documenter-dark .file.is-warning.is-hovered .file-cta {
+      background-color: #a07700;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-warning:focus .file-cta, html.theme--documenter-dark .file.is-warning.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(173, 129, 0, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-warning:active .file-cta, html.theme--documenter-dark .file.is-warning.is-active .file-cta {
+      background-color: #946e00;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-danger .file-cta {
+      background-color: #9e1b0d;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-danger:hover .file-cta, html.theme--documenter-dark .file.is-danger.is-hovered .file-cta {
+      background-color: #92190c;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-danger:focus .file-cta, html.theme--documenter-dark .file.is-danger.is-focused .file-cta {
+      border-color: transparent;
+      box-shadow: 0 0 0.5em rgba(158, 27, 13, 0.25);
+      color: #fff; }
+    html.theme--documenter-dark .file.is-danger:active .file-cta, html.theme--documenter-dark .file.is-danger.is-active .file-cta {
+      background-color: #86170b;
+      border-color: transparent;
+      color: #fff; }
+    html.theme--documenter-dark .file.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .file.is-medium {
+      font-size: 1.25rem; }
+      html.theme--documenter-dark .file.is-medium .file-icon .fa {
+        font-size: 21px; }
+    html.theme--documenter-dark .file.is-large {
+      font-size: 1.5rem; }
+      html.theme--documenter-dark .file.is-large .file-icon .fa {
+        font-size: 28px; }
+    html.theme--documenter-dark .file.has-name .file-cta {
+      border-bottom-right-radius: 0;
+      border-top-right-radius: 0; }
+    html.theme--documenter-dark .file.has-name .file-name {
+      border-bottom-left-radius: 0;
+      border-top-left-radius: 0; }
+    html.theme--documenter-dark .file.has-name.is-empty .file-cta {
+      border-radius: 0.4em; }
+    html.theme--documenter-dark .file.has-name.is-empty .file-name {
+      display: none; }
+    html.theme--documenter-dark .file.is-boxed .file-label {
+      flex-direction: column; }
+    html.theme--documenter-dark .file.is-boxed .file-cta {
+      flex-direction: column;
+      height: auto;
+      padding: 1em 3em; }
+    html.theme--documenter-dark .file.is-boxed .file-name {
+      border-width: 0 1px 1px; }
+    html.theme--documenter-dark .file.is-boxed .file-icon {
+      height: 1.5em;
+      width: 1.5em; }
+      html.theme--documenter-dark .file.is-boxed .file-icon .fa {
+        font-size: 21px; }
+    html.theme--documenter-dark .file.is-boxed.is-small .file-icon .fa, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.file.is-boxed .file-icon .fa {
+      font-size: 14px; }
+    html.theme--documenter-dark .file.is-boxed.is-medium .file-icon .fa {
+      font-size: 28px; }
+    html.theme--documenter-dark .file.is-boxed.is-large .file-icon .fa {
+      font-size: 35px; }
+    html.theme--documenter-dark .file.is-boxed.has-name .file-cta {
+      border-radius: 0.4em 0.4em 0 0; }
+    html.theme--documenter-dark .file.is-boxed.has-name .file-name {
+      border-radius: 0 0 0.4em 0.4em;
+      border-width: 0 1px 1px; }
+    html.theme--documenter-dark .file.is-centered {
+      justify-content: center; }
+    html.theme--documenter-dark .file.is-fullwidth .file-label {
+      width: 100%; }
+    html.theme--documenter-dark .file.is-fullwidth .file-name {
+      flex-grow: 1;
+      max-width: none; }
+    html.theme--documenter-dark .file.is-right {
+      justify-content: flex-end; }
+      html.theme--documenter-dark .file.is-right .file-cta {
+        border-radius: 0 0.4em 0.4em 0; }
+      html.theme--documenter-dark .file.is-right .file-name {
+        border-radius: 0.4em 0 0 0.4em;
+        border-width: 1px 0 1px 1px;
+        order: -1; }
+  html.theme--documenter-dark .file-label {
+    align-items: stretch;
+    display: flex;
+    cursor: pointer;
+    justify-content: flex-start;
+    overflow: hidden;
+    position: relative; }
+    html.theme--documenter-dark .file-label:hover .file-cta {
+      background-color: #e5eaec;
+      color: #282f2f; }
+    html.theme--documenter-dark .file-label:hover .file-name {
+      border-color: #596668; }
+    html.theme--documenter-dark .file-label:active .file-cta {
+      background-color: #dde4e6;
+      color: #282f2f; }
+    html.theme--documenter-dark .file-label:active .file-name {
+      border-color: #535f61; }
+  html.theme--documenter-dark .file-input {
+    height: 100%;
+    left: 0;
+    opacity: 0;
+    outline: none;
+    position: absolute;
+    top: 0;
+    width: 100%; }
+  html.theme--documenter-dark .file-cta,
+  html.theme--documenter-dark .file-name {
+    border-color: #5e6d6f;
+    border-radius: 0.4em;
+    font-size: 1em;
+    padding-left: 1em;
+    padding-right: 1em;
+    white-space: nowrap; }
+  html.theme--documenter-dark .file-cta {
+    background-color: #ecf0f1;
+    color: #343c3d; }
+  html.theme--documenter-dark .file-name {
+    border-color: #5e6d6f;
+    border-style: solid;
+    border-width: 1px 1px 1px 0;
+    display: block;
+    max-width: 16em;
+    overflow: hidden;
+    text-align: left;
+    text-overflow: ellipsis; }
+  html.theme--documenter-dark .file-icon {
+    align-items: center;
+    display: flex;
+    height: 1em;
+    justify-content: center;
+    margin-right: 0.5em;
+    width: 1em; }
+    html.theme--documenter-dark .file-icon .fa {
+      font-size: 14px; }
+  html.theme--documenter-dark .label {
+    color: #282f2f;
+    display: block;
+    font-size: 15px;
+    font-weight: 700; }
+    html.theme--documenter-dark .label:not(:last-child) {
+      margin-bottom: 0.5em; }
+    html.theme--documenter-dark .label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.label {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .label.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .label.is-large {
+      font-size: 1.5rem; }
+  html.theme--documenter-dark .help {
+    display: block;
+    font-size: 0.85em;
+    margin-top: 0.25rem; }
+    html.theme--documenter-dark .help.is-white {
+      color: white; }
+    html.theme--documenter-dark .help.is-black {
+      color: #0a0a0a; }
+    html.theme--documenter-dark .help.is-light {
+      color: #ecf0f1; }
+    html.theme--documenter-dark .help.is-dark, html.theme--documenter-dark .content kbd.help {
+      color: #282f2f; }
+    html.theme--documenter-dark .help.is-primary, html.theme--documenter-dark .docstring > section > a.help.docs-sourcelink {
+      color: #375a7f; }
+    html.theme--documenter-dark .help.is-link {
+      color: #1abc9c; }
+    html.theme--documenter-dark .help.is-info {
+      color: #024c7d; }
+    html.theme--documenter-dark .help.is-success {
+      color: #008438; }
+    html.theme--documenter-dark .help.is-warning {
+      color: #ad8100; }
+    html.theme--documenter-dark .help.is-danger {
+      color: #9e1b0d; }
+  html.theme--documenter-dark .field:not(:last-child) {
+    margin-bottom: 0.75rem; }
+  html.theme--documenter-dark .field.has-addons {
+    display: flex;
+    justify-content: flex-start; }
+    html.theme--documenter-dark .field.has-addons .control:not(:last-child) {
+      margin-right: -1px; }
+    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .button,
+    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .input,
+    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input,
+    html.theme--documenter-dark .field.has-addons .control:not(:first-child):not(:last-child) .select select {
+      border-radius: 0; }
+    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .button,
+    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .input,
+    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input,
+    html.theme--documenter-dark .field.has-addons .control:first-child:not(:only-child) .select select {
+      border-bottom-right-radius: 0;
+      border-top-right-radius: 0; }
+    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .button,
+    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .input,
+    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input,
+    html.theme--documenter-dark .field.has-addons .control:last-child:not(:only-child) .select select {
+      border-bottom-left-radius: 0;
+      border-top-left-radius: 0; }
+    html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-hovered,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):hover,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-hovered,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-hovered,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-hovered,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):hover,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-hovered {
+      z-index: 2; }
+    html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-focused, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-active,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-focused,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active,
+    html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-active,
+    html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active,
+    html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-focused,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active,
+    html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-active {
+      z-index: 3; }
+      html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):focus:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-focused:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]):active:hover, html.theme--documenter-dark .field.has-addons .control .button:not([disabled]).is-active:hover,
+      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):focus:hover,
+      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover,
+      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover,
+      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-focused:hover,
+      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused:hover,
+      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused:hover,
+      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]):active:hover,
+      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover,
+      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover,
+      html.theme--documenter-dark .field.has-addons .control .input:not([disabled]).is-active:hover,
+      html.theme--documenter-dark .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active:hover,
+      html.theme--documenter-dark #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active:hover,
+      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):focus:hover,
+      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-focused:hover,
+      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]):active:hover,
+      html.theme--documenter-dark .field.has-addons .control .select select:not([disabled]).is-active:hover {
+        z-index: 4; }
+    html.theme--documenter-dark .field.has-addons .control.is-expanded {
+      flex-grow: 1;
+      flex-shrink: 1; }
+    html.theme--documenter-dark .field.has-addons.has-addons-centered {
+      justify-content: center; }
+    html.theme--documenter-dark .field.has-addons.has-addons-right {
+      justify-content: flex-end; }
+    html.theme--documenter-dark .field.has-addons.has-addons-fullwidth .control {
+      flex-grow: 1;
+      flex-shrink: 0; }
+  html.theme--documenter-dark .field.is-grouped {
+    display: flex;
+    justify-content: flex-start; }
+    html.theme--documenter-dark .field.is-grouped > .control {
+      flex-shrink: 0; }
+      html.theme--documenter-dark .field.is-grouped > .control:not(:last-child) {
+        margin-bottom: 0;
+        margin-right: 0.75rem; }
+      html.theme--documenter-dark .field.is-grouped > .control.is-expanded {
+        flex-grow: 1;
+        flex-shrink: 1; }
+    html.theme--documenter-dark .field.is-grouped.is-grouped-centered {
+      justify-content: center; }
+    html.theme--documenter-dark .field.is-grouped.is-grouped-right {
+      justify-content: flex-end; }
+    html.theme--documenter-dark .field.is-grouped.is-grouped-multiline {
+      flex-wrap: wrap; }
+      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:last-child, html.theme--documenter-dark .field.is-grouped.is-grouped-multiline > .control:not(:last-child) {
+        margin-bottom: 0.75rem; }
+      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:last-child {
+        margin-bottom: -0.75rem; }
+      html.theme--documenter-dark .field.is-grouped.is-grouped-multiline:not(:last-child) {
+        margin-bottom: 0; }
+  @media screen and (min-width: 769px), print {
+    html.theme--documenter-dark .field.is-horizontal {
+      display: flex; } }
+  html.theme--documenter-dark .field-label .label {
+    font-size: inherit; }
+  @media screen and (max-width: 768px) {
+    html.theme--documenter-dark .field-label {
+      margin-bottom: 0.5rem; } }
+  @media screen and (min-width: 769px), print {
+    html.theme--documenter-dark .field-label {
+      flex-basis: 0;
+      flex-grow: 1;
+      flex-shrink: 0;
+      margin-right: 1.5rem;
+      text-align: right; }
+      html.theme--documenter-dark .field-label.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.field-label {
+        font-size: 0.85em;
+        padding-top: 0.375em; }
+      html.theme--documenter-dark .field-label.is-normal {
+        padding-top: 0.375em; }
+      html.theme--documenter-dark .field-label.is-medium {
+        font-size: 1.25rem;
+        padding-top: 0.375em; }
+      html.theme--documenter-dark .field-label.is-large {
+        font-size: 1.5rem;
+        padding-top: 0.375em; } }
+  html.theme--documenter-dark .field-body .field .field {
+    margin-bottom: 0; }
+  @media screen and (min-width: 769px), print {
+    html.theme--documenter-dark .field-body {
+      display: flex;
+      flex-basis: 0;
+      flex-grow: 5;
+      flex-shrink: 1; }
+      html.theme--documenter-dark .field-body .field {
+        margin-bottom: 0; }
+      html.theme--documenter-dark .field-body > .field {
+        flex-shrink: 1; }
+        html.theme--documenter-dark .field-body > .field:not(.is-narrow) {
+          flex-grow: 1; }
+        html.theme--documenter-dark .field-body > .field:not(:last-child) {
+          margin-right: 0.75rem; } }
+  html.theme--documenter-dark .control {
+    box-sizing: border-box;
+    clear: both;
+    font-size: 15px;
+    position: relative;
+    text-align: left; }
+    html.theme--documenter-dark .control.has-icons-left .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon,
+    html.theme--documenter-dark .control.has-icons-left .select:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right .input:focus ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon,
+    html.theme--documenter-dark .control.has-icons-right .select:focus ~ .icon {
+      color: #5e6d6f; }
+    html.theme--documenter-dark .control.has-icons-left .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon,
+    html.theme--documenter-dark .control.has-icons-left .select.is-small ~ .icon,
+    html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.select ~ .icon,
+    html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.select ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-small ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon,
+    html.theme--documenter-dark .control.has-icons-right .select.is-small ~ .icon,
+    html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.select ~ .icon,
+    html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.select ~ .icon {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .control.has-icons-left .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon,
+    html.theme--documenter-dark .control.has-icons-left .select.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-medium ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon,
+    html.theme--documenter-dark .control.has-icons-right .select.is-medium ~ .icon {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .control.has-icons-left .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon,
+    html.theme--documenter-dark .control.has-icons-left .select.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right .input.is-large ~ .icon, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon,
+    html.theme--documenter-dark .control.has-icons-right .select.is-large ~ .icon {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .control.has-icons-left .icon, html.theme--documenter-dark .control.has-icons-right .icon {
+      color: #dbdee0;
+      height: 2.25em;
+      pointer-events: none;
+      position: absolute;
+      top: 0;
+      width: 2.25em;
+      z-index: 4; }
+    html.theme--documenter-dark .control.has-icons-left .input, html.theme--documenter-dark .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-left form.docs-search > input,
+    html.theme--documenter-dark .control.has-icons-left .select select {
+      padding-left: 2.25em; }
+    html.theme--documenter-dark .control.has-icons-left .icon.is-left {
+      left: 0; }
+    html.theme--documenter-dark .control.has-icons-right .input, html.theme--documenter-dark .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, html.theme--documenter-dark #documenter .docs-sidebar .control.has-icons-right form.docs-search > input,
+    html.theme--documenter-dark .control.has-icons-right .select select {
+      padding-right: 2.25em; }
+    html.theme--documenter-dark .control.has-icons-right .icon.is-right {
+      right: 0; }
+    html.theme--documenter-dark .control.is-loading::after {
+      position: absolute !important;
+      right: 0.625em;
+      top: 0.625em;
+      z-index: 4; }
+    html.theme--documenter-dark .control.is-loading.is-small:after, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.control.is-loading:after {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .control.is-loading.is-medium:after {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .control.is-loading.is-large:after {
+      font-size: 1.5rem; }
+  html.theme--documenter-dark .breadcrumb {
+    font-size: 15px;
+    white-space: nowrap; }
+    html.theme--documenter-dark .breadcrumb a {
+      align-items: center;
+      color: #1abc9c;
+      display: flex;
+      justify-content: center;
+      padding: 0 0.75em; }
+      html.theme--documenter-dark .breadcrumb a:hover {
+        color: #1dd2af; }
+    html.theme--documenter-dark .breadcrumb li {
+      align-items: center;
+      display: flex; }
+      html.theme--documenter-dark .breadcrumb li:first-child a {
+        padding-left: 0; }
+      html.theme--documenter-dark .breadcrumb li.is-active a {
+        color: #f2f2f2;
+        cursor: default;
+        pointer-events: none; }
+      html.theme--documenter-dark .breadcrumb li + li::before {
+        color: #8c9b9d;
+        content: "\0002f"; }
+    html.theme--documenter-dark .breadcrumb ul,
+    html.theme--documenter-dark .breadcrumb ol {
+      align-items: flex-start;
+      display: flex;
+      flex-wrap: wrap;
+      justify-content: flex-start; }
+    html.theme--documenter-dark .breadcrumb .icon:first-child {
+      margin-right: 0.5em; }
+    html.theme--documenter-dark .breadcrumb .icon:last-child {
+      margin-left: 0.5em; }
+    html.theme--documenter-dark .breadcrumb.is-centered ol,
+    html.theme--documenter-dark .breadcrumb.is-centered ul {
+      justify-content: center; }
+    html.theme--documenter-dark .breadcrumb.is-right ol,
+    html.theme--documenter-dark .breadcrumb.is-right ul {
+      justify-content: flex-end; }
+    html.theme--documenter-dark .breadcrumb.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.breadcrumb {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .breadcrumb.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .breadcrumb.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .breadcrumb.has-arrow-separator li + li::before {
+      content: "\02192"; }
+    html.theme--documenter-dark .breadcrumb.has-bullet-separator li + li::before {
+      content: "\02022"; }
+    html.theme--documenter-dark .breadcrumb.has-dot-separator li + li::before {
+      content: "\000b7"; }
+    html.theme--documenter-dark .breadcrumb.has-succeeds-separator li + li::before {
+      content: "\0227B"; }
+  html.theme--documenter-dark .card {
+    background-color: white;
+    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+    color: #fff;
+    max-width: 100%;
+    position: relative; }
+  html.theme--documenter-dark .card-header {
+    background-color: transparent;
+    align-items: stretch;
+    box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);
+    display: flex; }
+  html.theme--documenter-dark .card-header-title {
+    align-items: center;
+    color: #f2f2f2;
+    display: flex;
+    flex-grow: 1;
+    font-weight: 700;
+    padding: 0.75rem; }
+    html.theme--documenter-dark .card-header-title.is-centered {
+      justify-content: center; }
+  html.theme--documenter-dark .card-header-icon {
+    align-items: center;
+    cursor: pointer;
+    display: flex;
+    justify-content: center;
+    padding: 0.75rem; }
+  html.theme--documenter-dark .card-image {
+    display: block;
+    position: relative; }
+  html.theme--documenter-dark .card-content {
+    background-color: transparent;
+    padding: 1rem 1.25rem; }
+  html.theme--documenter-dark .card-footer {
+    background-color: transparent;
+    border-top: 1px solid #5e6d6f;
+    align-items: stretch;
+    display: flex; }
+  html.theme--documenter-dark .card-footer-item {
+    align-items: center;
+    display: flex;
+    flex-basis: 0;
+    flex-grow: 1;
+    flex-shrink: 0;
+    justify-content: center;
+    padding: 0.75rem; }
+    html.theme--documenter-dark .card-footer-item:not(:last-child) {
+      border-right: 1px solid #5e6d6f; }
+  html.theme--documenter-dark .card .media:not(:last-child) {
+    margin-bottom: 1.5rem; }
+  html.theme--documenter-dark .dropdown {
+    display: inline-flex;
+    position: relative;
+    vertical-align: top; }
+    html.theme--documenter-dark .dropdown.is-active .dropdown-menu, html.theme--documenter-dark .dropdown.is-hoverable:hover .dropdown-menu {
+      display: block; }
+    html.theme--documenter-dark .dropdown.is-right .dropdown-menu {
+      left: auto;
+      right: 0; }
+    html.theme--documenter-dark .dropdown.is-up .dropdown-menu {
+      bottom: 100%;
+      padding-bottom: 4px;
+      padding-top: initial;
+      top: auto; }
+  html.theme--documenter-dark .dropdown-menu {
+    display: none;
+    left: 0;
+    min-width: 12rem;
+    padding-top: 4px;
+    position: absolute;
+    top: 100%;
+    z-index: 20; }
+  html.theme--documenter-dark .dropdown-content {
+    background-color: #282f2f;
+    border-radius: 0.4em;
+    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+    padding-bottom: 0.5rem;
+    padding-top: 0.5rem; }
+  html.theme--documenter-dark .dropdown-item {
+    color: #fff;
+    display: block;
+    font-size: 0.875rem;
+    line-height: 1.5;
+    padding: 0.375rem 1rem;
+    position: relative; }
+  html.theme--documenter-dark a.dropdown-item,
+  html.theme--documenter-dark button.dropdown-item {
+    padding-right: 3rem;
+    text-align: left;
+    white-space: nowrap;
+    width: 100%; }
+    html.theme--documenter-dark a.dropdown-item:hover,
+    html.theme--documenter-dark button.dropdown-item:hover {
+      background-color: #282f2f;
+      color: #0a0a0a; }
+    html.theme--documenter-dark a.dropdown-item.is-active,
+    html.theme--documenter-dark button.dropdown-item.is-active {
+      background-color: #1abc9c;
+      color: #fff; }
+  html.theme--documenter-dark .dropdown-divider {
+    background-color: #5e6d6f;
+    border: none;
+    display: block;
+    height: 1px;
+    margin: 0.5rem 0; }
+  html.theme--documenter-dark .level {
+    align-items: center;
+    justify-content: space-between; }
+    html.theme--documenter-dark .level code {
+      border-radius: 0.4em; }
+    html.theme--documenter-dark .level img {
+      display: inline-block;
+      vertical-align: top; }
+    html.theme--documenter-dark .level.is-mobile {
+      display: flex; }
+      html.theme--documenter-dark .level.is-mobile .level-left,
+      html.theme--documenter-dark .level.is-mobile .level-right {
+        display: flex; }
+      html.theme--documenter-dark .level.is-mobile .level-left + .level-right {
+        margin-top: 0; }
+      html.theme--documenter-dark .level.is-mobile .level-item:not(:last-child) {
+        margin-bottom: 0;
+        margin-right: 0.75rem; }
+      html.theme--documenter-dark .level.is-mobile .level-item:not(.is-narrow) {
+        flex-grow: 1; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .level {
+        display: flex; }
+        html.theme--documenter-dark .level > .level-item:not(.is-narrow) {
+          flex-grow: 1; } }
+  html.theme--documenter-dark .level-item {
+    align-items: center;
+    display: flex;
+    flex-basis: auto;
+    flex-grow: 0;
+    flex-shrink: 0;
+    justify-content: center; }
+    html.theme--documenter-dark .level-item .title,
+    html.theme--documenter-dark .level-item .subtitle {
+      margin-bottom: 0; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .level-item:not(:last-child) {
+        margin-bottom: 0.75rem; } }
+  html.theme--documenter-dark .level-left,
+  html.theme--documenter-dark .level-right {
+    flex-basis: auto;
+    flex-grow: 0;
+    flex-shrink: 0; }
+    html.theme--documenter-dark .level-left .level-item.is-flexible,
+    html.theme--documenter-dark .level-right .level-item.is-flexible {
+      flex-grow: 1; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .level-left .level-item:not(:last-child),
+      html.theme--documenter-dark .level-right .level-item:not(:last-child) {
+        margin-right: 0.75rem; } }
+  html.theme--documenter-dark .level-left {
+    align-items: center;
+    justify-content: flex-start; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .level-left + .level-right {
+        margin-top: 1.5rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .level-left {
+        display: flex; } }
+  html.theme--documenter-dark .level-right {
+    align-items: center;
+    justify-content: flex-end; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .level-right {
+        display: flex; } }
+  html.theme--documenter-dark .list {
+    background-color: white;
+    border-radius: 0.4em;
+    box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); }
+  html.theme--documenter-dark .list-item {
+    display: block;
+    padding: 0.5em 1em; }
+    html.theme--documenter-dark .list-item:not(a) {
+      color: #fff; }
+    html.theme--documenter-dark .list-item:first-child {
+      border-top-left-radius: 0.4em;
+      border-top-right-radius: 0.4em; }
+    html.theme--documenter-dark .list-item:last-child {
+      border-bottom-left-radius: 0.4em;
+      border-bottom-right-radius: 0.4em; }
+    html.theme--documenter-dark .list-item:not(:last-child) {
+      border-bottom: 1px solid #5e6d6f; }
+    html.theme--documenter-dark .list-item.is-active {
+      background-color: #1abc9c;
+      color: #fff; }
+  html.theme--documenter-dark a.list-item {
+    background-color: #282f2f;
+    cursor: pointer; }
+  html.theme--documenter-dark .media {
+    align-items: flex-start;
+    display: flex;
+    text-align: left; }
+    html.theme--documenter-dark .media .content:not(:last-child) {
+      margin-bottom: 0.75rem; }
+    html.theme--documenter-dark .media .media {
+      border-top: 1px solid rgba(94, 109, 111, 0.5);
+      display: flex;
+      padding-top: 0.75rem; }
+      html.theme--documenter-dark .media .media .content:not(:last-child),
+      html.theme--documenter-dark .media .media .control:not(:last-child) {
+        margin-bottom: 0.5rem; }
+      html.theme--documenter-dark .media .media .media {
+        padding-top: 0.5rem; }
+        html.theme--documenter-dark .media .media .media + .media {
+          margin-top: 0.5rem; }
+    html.theme--documenter-dark .media + .media {
+      border-top: 1px solid rgba(94, 109, 111, 0.5);
+      margin-top: 1rem;
+      padding-top: 1rem; }
+    html.theme--documenter-dark .media.is-large + .media {
+      margin-top: 1.5rem;
+      padding-top: 1.5rem; }
+  html.theme--documenter-dark .media-left,
+  html.theme--documenter-dark .media-right {
+    flex-basis: auto;
+    flex-grow: 0;
+    flex-shrink: 0; }
+  html.theme--documenter-dark .media-left {
+    margin-right: 1rem; }
+  html.theme--documenter-dark .media-right {
+    margin-left: 1rem; }
+  html.theme--documenter-dark .media-content {
+    flex-basis: auto;
+    flex-grow: 1;
+    flex-shrink: 1;
+    text-align: left; }
+  @media screen and (max-width: 768px) {
+    html.theme--documenter-dark .media-content {
+      overflow-x: auto; } }
+  html.theme--documenter-dark .menu {
+    font-size: 15px; }
+    html.theme--documenter-dark .menu.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.menu {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .menu.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .menu.is-large {
+      font-size: 1.5rem; }
+  html.theme--documenter-dark .menu-list {
+    line-height: 1.25; }
+    html.theme--documenter-dark .menu-list a {
+      border-radius: 3px;
+      color: #fff;
+      display: block;
+      padding: 0.5em 0.75em; }
+      html.theme--documenter-dark .menu-list a:hover {
+        background-color: #282f2f;
+        color: #f2f2f2; }
+      html.theme--documenter-dark .menu-list a.is-active {
+        background-color: #1abc9c;
+        color: #fff; }
+    html.theme--documenter-dark .menu-list li ul {
+      border-left: 1px solid #5e6d6f;
+      margin: 0.75em;
+      padding-left: 0.75em; }
+  html.theme--documenter-dark .menu-label {
+    color: white;
+    font-size: 0.75em;
+    letter-spacing: 0.1em;
+    text-transform: uppercase; }
+    html.theme--documenter-dark .menu-label:not(:first-child) {
+      margin-top: 1em; }
+    html.theme--documenter-dark .menu-label:not(:last-child) {
+      margin-bottom: 1em; }
+  html.theme--documenter-dark .message {
+    background-color: #282f2f;
+    border-radius: 0.4em;
+    font-size: 15px; }
+    html.theme--documenter-dark .message strong {
+      color: currentColor; }
+    html.theme--documenter-dark .message a:not(.button):not(.tag):not(.dropdown-item) {
+      color: currentColor;
+      text-decoration: underline; }
+    html.theme--documenter-dark .message.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.message {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .message.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .message.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .message.is-white {
+      background-color: white; }
+      html.theme--documenter-dark .message.is-white .message-header {
+        background-color: white;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .message.is-white .message-body {
+        border-color: white;
+        color: #4d4d4d; }
+    html.theme--documenter-dark .message.is-black {
+      background-color: #fafafa; }
+      html.theme--documenter-dark .message.is-black .message-header {
+        background-color: #0a0a0a;
+        color: white; }
+      html.theme--documenter-dark .message.is-black .message-body {
+        border-color: #0a0a0a;
+        color: #090909; }
+    html.theme--documenter-dark .message.is-light {
+      background-color: #f9fafb; }
+      html.theme--documenter-dark .message.is-light .message-header {
+        background-color: #ecf0f1;
+        color: #282f2f; }
+      html.theme--documenter-dark .message.is-light .message-body {
+        border-color: #ecf0f1;
+        color: #505050; }
+    html.theme--documenter-dark .message.is-dark, html.theme--documenter-dark .content kbd.message {
+      background-color: #f9fafa; }
+      html.theme--documenter-dark .message.is-dark .message-header, html.theme--documenter-dark .content kbd.message .message-header {
+        background-color: #282f2f;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .message.is-dark .message-body, html.theme--documenter-dark .content kbd.message .message-body {
+        border-color: #282f2f;
+        color: #212526; }
+    html.theme--documenter-dark .message.is-primary, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink {
+      background-color: #f8fafc; }
+      html.theme--documenter-dark .message.is-primary .message-header, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-header {
+        background-color: #375a7f;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-primary .message-body, html.theme--documenter-dark .docstring > section > a.message.docs-sourcelink .message-body {
+        border-color: #375a7f;
+        color: #2b4159; }
+    html.theme--documenter-dark .message.is-link {
+      background-color: #f6fefc; }
+      html.theme--documenter-dark .message.is-link .message-header {
+        background-color: #1abc9c;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-link .message-body {
+        border-color: #1abc9c;
+        color: #0b2f28; }
+    html.theme--documenter-dark .message.is-info {
+      background-color: #f5fbff; }
+      html.theme--documenter-dark .message.is-info .message-header {
+        background-color: #024c7d;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-info .message-body {
+        border-color: #024c7d;
+        color: #033659; }
+    html.theme--documenter-dark .message.is-success {
+      background-color: #f5fff9; }
+      html.theme--documenter-dark .message.is-success .message-header {
+        background-color: #008438;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-success .message-body {
+        border-color: #008438;
+        color: #023518; }
+    html.theme--documenter-dark .message.is-warning {
+      background-color: #fffcf5; }
+      html.theme--documenter-dark .message.is-warning .message-header {
+        background-color: #ad8100;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-warning .message-body {
+        border-color: #ad8100;
+        color: #3d2e03; }
+    html.theme--documenter-dark .message.is-danger {
+      background-color: #fef6f6; }
+      html.theme--documenter-dark .message.is-danger .message-header {
+        background-color: #9e1b0d;
+        color: #fff; }
+      html.theme--documenter-dark .message.is-danger .message-body {
+        border-color: #9e1b0d;
+        color: #7a170c; }
+  html.theme--documenter-dark .message-header {
+    align-items: center;
+    background-color: #fff;
+    border-radius: 0.4em 0.4em 0 0;
+    color: rgba(0, 0, 0, 0.7);
+    display: flex;
+    font-weight: 700;
+    justify-content: space-between;
+    line-height: 1.25;
+    padding: 0.75em;
+    position: relative; }
+    html.theme--documenter-dark .message-header .delete {
+      flex-grow: 0;
+      flex-shrink: 0;
+      margin-left: 0.75em; }
+    html.theme--documenter-dark .message-header + .message-body {
+      border-width: 0;
+      border-top-left-radius: 0;
+      border-top-right-radius: 0; }
+  html.theme--documenter-dark .message-body {
+    border-color: #5e6d6f;
+    border-radius: 0.4em;
+    border-style: solid;
+    border-width: 0 0 0 4px;
+    color: #fff;
+    padding: 1em 1.25em; }
+    html.theme--documenter-dark .message-body code,
+    html.theme--documenter-dark .message-body pre {
+      background-color: white; }
+    html.theme--documenter-dark .message-body pre code {
+      background-color: transparent; }
+  html.theme--documenter-dark .modal {
+    align-items: center;
+    display: none;
+    flex-direction: column;
+    justify-content: center;
+    overflow: hidden;
+    position: fixed;
+    z-index: 40; }
+    html.theme--documenter-dark .modal.is-active {
+      display: flex; }
+  html.theme--documenter-dark .modal-background {
+    background-color: rgba(10, 10, 10, 0.86); }
+  html.theme--documenter-dark .modal-content,
+  html.theme--documenter-dark .modal-card {
+    margin: 0 20px;
+    max-height: calc(100vh - 160px);
+    overflow: auto;
+    position: relative;
+    width: 100%; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .modal-content,
+      html.theme--documenter-dark .modal-card {
+        margin: 0 auto;
+        max-height: calc(100vh - 40px);
+        width: 640px; } }
+  html.theme--documenter-dark .modal-close {
+    background: none;
+    height: 40px;
+    position: fixed;
+    right: 20px;
+    top: 20px;
+    width: 40px; }
+  html.theme--documenter-dark .modal-card {
+    display: flex;
+    flex-direction: column;
+    max-height: calc(100vh - 40px);
+    overflow: hidden;
+    -ms-overflow-y: visible; }
+  html.theme--documenter-dark .modal-card-head,
+  html.theme--documenter-dark .modal-card-foot {
+    align-items: center;
+    background-color: #282f2f;
+    display: flex;
+    flex-shrink: 0;
+    justify-content: flex-start;
+    padding: 20px;
+    position: relative; }
+  html.theme--documenter-dark .modal-card-head {
+    border-bottom: 1px solid #5e6d6f;
+    border-top-left-radius: 8px;
+    border-top-right-radius: 8px; }
+  html.theme--documenter-dark .modal-card-title {
+    color: #f2f2f2;
+    flex-grow: 1;
+    flex-shrink: 0;
+    font-size: 1.5rem;
+    line-height: 1; }
+  html.theme--documenter-dark .modal-card-foot {
+    border-bottom-left-radius: 8px;
+    border-bottom-right-radius: 8px;
+    border-top: 1px solid #5e6d6f; }
+    html.theme--documenter-dark .modal-card-foot .button:not(:last-child) {
+      margin-right: 0.5em; }
+  html.theme--documenter-dark .modal-card-body {
+    -webkit-overflow-scrolling: touch;
+    background-color: white;
+    flex-grow: 1;
+    flex-shrink: 1;
+    overflow: auto;
+    padding: 20px; }
+  html.theme--documenter-dark .navbar {
+    background-color: #375a7f;
+    min-height: 4rem;
+    position: relative;
+    z-index: 30; }
+    html.theme--documenter-dark .navbar.is-white {
+      background-color: white;
+      color: #0a0a0a; }
+      html.theme--documenter-dark .navbar.is-white .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link {
+        color: #0a0a0a; }
+      html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link.is-active {
+        background-color: #f2f2f2;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .navbar.is-white .navbar-brand .navbar-link::after {
+        border-color: #0a0a0a; }
+      html.theme--documenter-dark .navbar.is-white .navbar-burger {
+        color: #0a0a0a; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-white .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-white .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link {
+          color: #0a0a0a; }
+        html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-white .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-white .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link.is-active {
+          background-color: #f2f2f2;
+          color: #0a0a0a; }
+        html.theme--documenter-dark .navbar.is-white .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-white .navbar-end .navbar-link::after {
+          border-color: #0a0a0a; }
+        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #f2f2f2;
+          color: #0a0a0a; }
+        html.theme--documenter-dark .navbar.is-white .navbar-dropdown a.navbar-item.is-active {
+          background-color: white;
+          color: #0a0a0a; } }
+    html.theme--documenter-dark .navbar.is-black {
+      background-color: #0a0a0a;
+      color: white; }
+      html.theme--documenter-dark .navbar.is-black .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link {
+        color: white; }
+      html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link.is-active {
+        background-color: black;
+        color: white; }
+      html.theme--documenter-dark .navbar.is-black .navbar-brand .navbar-link::after {
+        border-color: white; }
+      html.theme--documenter-dark .navbar.is-black .navbar-burger {
+        color: white; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-black .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-black .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link {
+          color: white; }
+        html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-black .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-black .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link.is-active {
+          background-color: black;
+          color: white; }
+        html.theme--documenter-dark .navbar.is-black .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-black .navbar-end .navbar-link::after {
+          border-color: white; }
+        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: black;
+          color: white; }
+        html.theme--documenter-dark .navbar.is-black .navbar-dropdown a.navbar-item.is-active {
+          background-color: #0a0a0a;
+          color: white; } }
+    html.theme--documenter-dark .navbar.is-light {
+      background-color: #ecf0f1;
+      color: #282f2f; }
+      html.theme--documenter-dark .navbar.is-light .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link {
+        color: #282f2f; }
+      html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link.is-active {
+        background-color: #dde4e6;
+        color: #282f2f; }
+      html.theme--documenter-dark .navbar.is-light .navbar-brand .navbar-link::after {
+        border-color: #282f2f; }
+      html.theme--documenter-dark .navbar.is-light .navbar-burger {
+        color: #282f2f; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-light .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-light .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link {
+          color: #282f2f; }
+        html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-light .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-light .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link.is-active {
+          background-color: #dde4e6;
+          color: #282f2f; }
+        html.theme--documenter-dark .navbar.is-light .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-light .navbar-end .navbar-link::after {
+          border-color: #282f2f; }
+        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #dde4e6;
+          color: #282f2f; }
+        html.theme--documenter-dark .navbar.is-light .navbar-dropdown a.navbar-item.is-active {
+          background-color: #ecf0f1;
+          color: #282f2f; } }
+    html.theme--documenter-dark .navbar.is-dark, html.theme--documenter-dark .content kbd.navbar {
+      background-color: #282f2f;
+      color: #ecf0f1; }
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link,
+      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link {
+        color: #ecf0f1; }
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link.is-active,
+      html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link.is-active {
+        background-color: #1d2122;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .navbar.is-dark .navbar-brand .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-brand .navbar-link::after {
+        border-color: #ecf0f1; }
+      html.theme--documenter-dark .navbar.is-dark .navbar-burger, html.theme--documenter-dark .content kbd.navbar .navbar-burger {
+        color: #ecf0f1; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-dark .navbar-start > .navbar-item, html.theme--documenter-dark .content kbd.navbar .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link,
+        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end > .navbar-item,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link {
+          color: #ecf0f1; }
+        html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-dark .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link.is-active,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link.is-active {
+          background-color: #1d2122;
+          color: #ecf0f1; }
+        html.theme--documenter-dark .navbar.is-dark .navbar-start .navbar-link::after, html.theme--documenter-dark .content kbd.navbar .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-dark .navbar-end .navbar-link::after,
+        html.theme--documenter-dark .content kbd.navbar .navbar-end .navbar-link::after {
+          border-color: #ecf0f1; }
+        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link,
+        html.theme--documenter-dark .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #1d2122;
+          color: #ecf0f1; }
+        html.theme--documenter-dark .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .content kbd.navbar .navbar-dropdown a.navbar-item.is-active {
+          background-color: #282f2f;
+          color: #ecf0f1; } }
+    html.theme--documenter-dark .navbar.is-primary, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink {
+      background-color: #375a7f;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link,
+      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-brand > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link.is-active,
+      html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active {
+        background-color: #2f4d6d;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-primary .navbar-brand .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-primary .navbar-burger, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-primary .navbar-start > .navbar-item, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end > .navbar-item,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-primary .navbar-start > a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link.is-active,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active {
+          background-color: #2f4d6d;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-primary .navbar-start .navbar-link::after, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-primary .navbar-end .navbar-link::after,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link,
+        html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #2f4d6d;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active {
+          background-color: #375a7f;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar.is-link {
+      background-color: #1abc9c;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-link .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link.is-active {
+        background-color: #17a689;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-link .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-link .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-link .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-link .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-link .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-link .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link.is-active {
+          background-color: #17a689;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-link .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-link .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #17a689;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-link .navbar-dropdown a.navbar-item.is-active {
+          background-color: #1abc9c;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar.is-info {
+      background-color: #024c7d;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-info .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link.is-active {
+        background-color: #023d64;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-info .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-info .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-info .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-info .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-info .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-info .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link.is-active {
+          background-color: #023d64;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-info .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-info .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #023d64;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-info .navbar-dropdown a.navbar-item.is-active {
+          background-color: #024c7d;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar.is-success {
+      background-color: #008438;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-success .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link.is-active {
+        background-color: #006b2d;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-success .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-success .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-success .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-success .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-success .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-success .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link.is-active {
+          background-color: #006b2d;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-success .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-success .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #006b2d;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-success .navbar-dropdown a.navbar-item.is-active {
+          background-color: #008438;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar.is-warning {
+      background-color: #ad8100;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link.is-active {
+        background-color: #946e00;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-warning .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-warning .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-warning .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-warning .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link.is-active {
+          background-color: #946e00;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-warning .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-warning .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #946e00;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-warning .navbar-dropdown a.navbar-item.is-active {
+          background-color: #ad8100;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar.is-danger {
+      background-color: #9e1b0d;
+      color: #fff; }
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand > .navbar-item,
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link {
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-brand > a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link.is-active {
+        background-color: #86170b;
+        color: #fff; }
+      html.theme--documenter-dark .navbar.is-danger .navbar-brand .navbar-link::after {
+        border-color: #fff; }
+      html.theme--documenter-dark .navbar.is-danger .navbar-burger {
+        color: #fff; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark .navbar.is-danger .navbar-start > .navbar-item,
+        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end > .navbar-item,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link {
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:focus, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item:hover, html.theme--documenter-dark .navbar.is-danger .navbar-start > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link.is-active,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:focus,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item:hover,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end > a.navbar-item.is-active,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:focus,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link:hover,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link.is-active {
+          background-color: #86170b;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-danger .navbar-start .navbar-link::after,
+        html.theme--documenter-dark .navbar.is-danger .navbar-end .navbar-link::after {
+          border-color: #fff; }
+        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link,
+        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link,
+        html.theme--documenter-dark .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link {
+          background-color: #86170b;
+          color: #fff; }
+        html.theme--documenter-dark .navbar.is-danger .navbar-dropdown a.navbar-item.is-active {
+          background-color: #9e1b0d;
+          color: #fff; } }
+    html.theme--documenter-dark .navbar > .container {
+      align-items: stretch;
+      display: flex;
+      min-height: 4rem;
+      width: 100%; }
+    html.theme--documenter-dark .navbar.has-shadow {
+      box-shadow: 0 2px 0 0 #282f2f; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom, html.theme--documenter-dark .navbar.is-fixed-top {
+      left: 0;
+      position: fixed;
+      right: 0;
+      z-index: 30; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom {
+      bottom: 0; }
+      html.theme--documenter-dark .navbar.is-fixed-bottom.has-shadow {
+        box-shadow: 0 -2px 0 0 #282f2f; }
+    html.theme--documenter-dark .navbar.is-fixed-top {
+      top: 0; }
+  html.theme--documenter-dark html.has-navbar-fixed-top,
+  html.theme--documenter-dark body.has-navbar-fixed-top {
+    padding-top: 4rem; }
+  html.theme--documenter-dark html.has-navbar-fixed-bottom,
+  html.theme--documenter-dark body.has-navbar-fixed-bottom {
+    padding-bottom: 4rem; }
+  html.theme--documenter-dark .navbar-brand,
+  html.theme--documenter-dark .navbar-tabs {
+    align-items: stretch;
+    display: flex;
+    flex-shrink: 0;
+    min-height: 4rem; }
+  html.theme--documenter-dark .navbar-brand a.navbar-item:focus, html.theme--documenter-dark .navbar-brand a.navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .navbar-tabs {
+    -webkit-overflow-scrolling: touch;
+    max-width: 100vw;
+    overflow-x: auto;
+    overflow-y: hidden; }
+  html.theme--documenter-dark .navbar-burger {
+    color: #fff;
+    cursor: pointer;
+    display: block;
+    height: 4rem;
+    position: relative;
+    width: 4rem;
+    margin-left: auto; }
+    html.theme--documenter-dark .navbar-burger span {
+      background-color: currentColor;
+      display: block;
+      height: 1px;
+      left: calc(50% - 8px);
+      position: absolute;
+      transform-origin: center;
+      transition-duration: 86ms;
+      transition-property: background-color, opacity, transform;
+      transition-timing-function: ease-out;
+      width: 16px; }
+      html.theme--documenter-dark .navbar-burger span:nth-child(1) {
+        top: calc(50% - 6px); }
+      html.theme--documenter-dark .navbar-burger span:nth-child(2) {
+        top: calc(50% - 1px); }
+      html.theme--documenter-dark .navbar-burger span:nth-child(3) {
+        top: calc(50% + 4px); }
+    html.theme--documenter-dark .navbar-burger:hover {
+      background-color: rgba(0, 0, 0, 0.05); }
+    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(1) {
+      transform: translateY(5px) rotate(45deg); }
+    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(2) {
+      opacity: 0; }
+    html.theme--documenter-dark .navbar-burger.is-active span:nth-child(3) {
+      transform: translateY(-5px) rotate(-45deg); }
+  html.theme--documenter-dark .navbar-menu {
+    display: none; }
+  html.theme--documenter-dark .navbar-item,
+  html.theme--documenter-dark .navbar-link {
+    color: #fff;
+    display: block;
+    line-height: 1.5;
+    padding: 0.5rem 0.75rem;
+    position: relative; }
+    html.theme--documenter-dark .navbar-item .icon:only-child,
+    html.theme--documenter-dark .navbar-link .icon:only-child {
+      margin-left: -0.25rem;
+      margin-right: -0.25rem; }
+  html.theme--documenter-dark a.navbar-item,
+  html.theme--documenter-dark .navbar-link {
+    cursor: pointer; }
+    html.theme--documenter-dark a.navbar-item:focus, html.theme--documenter-dark a.navbar-item:focus-within, html.theme--documenter-dark a.navbar-item:hover, html.theme--documenter-dark a.navbar-item.is-active,
+    html.theme--documenter-dark .navbar-link:focus,
+    html.theme--documenter-dark .navbar-link:focus-within,
+    html.theme--documenter-dark .navbar-link:hover,
+    html.theme--documenter-dark .navbar-link.is-active {
+      background-color: transparent;
+      color: #1abc9c; }
+  html.theme--documenter-dark .navbar-item {
+    display: block;
+    flex-grow: 0;
+    flex-shrink: 0; }
+    html.theme--documenter-dark .navbar-item img {
+      max-height: 1.75rem; }
+    html.theme--documenter-dark .navbar-item.has-dropdown {
+      padding: 0; }
+    html.theme--documenter-dark .navbar-item.is-expanded {
+      flex-grow: 1;
+      flex-shrink: 1; }
+    html.theme--documenter-dark .navbar-item.is-tab {
+      border-bottom: 1px solid transparent;
+      min-height: 4rem;
+      padding-bottom: calc(0.5rem - 1px); }
+      html.theme--documenter-dark .navbar-item.is-tab:focus, html.theme--documenter-dark .navbar-item.is-tab:hover {
+        background-color: transparent;
+        border-bottom-color: #1abc9c; }
+      html.theme--documenter-dark .navbar-item.is-tab.is-active {
+        background-color: transparent;
+        border-bottom-color: #1abc9c;
+        border-bottom-style: solid;
+        border-bottom-width: 3px;
+        color: #1abc9c;
+        padding-bottom: calc(0.5rem - 3px); }
+  html.theme--documenter-dark .navbar-content {
+    flex-grow: 1;
+    flex-shrink: 1; }
+  html.theme--documenter-dark .navbar-link:not(.is-arrowless) {
+    padding-right: 2.5em; }
+    html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after {
+      border-color: #fff;
+      margin-top: -0.375em;
+      right: 1.125em; }
+  html.theme--documenter-dark .navbar-dropdown {
+    font-size: 0.875rem;
+    padding-bottom: 0.5rem;
+    padding-top: 0.5rem; }
+    html.theme--documenter-dark .navbar-dropdown .navbar-item {
+      padding-left: 1.5rem;
+      padding-right: 1.5rem; }
+  html.theme--documenter-dark .navbar-divider {
+    background-color: rgba(0, 0, 0, 0.2);
+    border: none;
+    display: none;
+    height: 2px;
+    margin: 0.5rem 0; }
+  @media screen and (max-width: 1055px) {
+    html.theme--documenter-dark .navbar > .container {
+      display: block; }
+    html.theme--documenter-dark .navbar-brand .navbar-item,
+    html.theme--documenter-dark .navbar-tabs .navbar-item {
+      align-items: center;
+      display: flex; }
+    html.theme--documenter-dark .navbar-link::after {
+      display: none; }
+    html.theme--documenter-dark .navbar-menu {
+      background-color: #375a7f;
+      box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1);
+      padding: 0.5rem 0; }
+      html.theme--documenter-dark .navbar-menu.is-active {
+        display: block; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom-touch, html.theme--documenter-dark .navbar.is-fixed-top-touch {
+      left: 0;
+      position: fixed;
+      right: 0;
+      z-index: 30; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom-touch {
+      bottom: 0; }
+      html.theme--documenter-dark .navbar.is-fixed-bottom-touch.has-shadow {
+        box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }
+    html.theme--documenter-dark .navbar.is-fixed-top-touch {
+      top: 0; }
+    html.theme--documenter-dark .navbar.is-fixed-top .navbar-menu, html.theme--documenter-dark .navbar.is-fixed-top-touch .navbar-menu {
+      -webkit-overflow-scrolling: touch;
+      max-height: calc(100vh - 4rem);
+      overflow: auto; }
+    html.theme--documenter-dark html.has-navbar-fixed-top-touch,
+    html.theme--documenter-dark body.has-navbar-fixed-top-touch {
+      padding-top: 4rem; }
+    html.theme--documenter-dark html.has-navbar-fixed-bottom-touch,
+    html.theme--documenter-dark body.has-navbar-fixed-bottom-touch {
+      padding-bottom: 4rem; } }
+  @media screen and (min-width: 1056px) {
+    html.theme--documenter-dark .navbar,
+    html.theme--documenter-dark .navbar-menu,
+    html.theme--documenter-dark .navbar-start,
+    html.theme--documenter-dark .navbar-end {
+      align-items: stretch;
+      display: flex; }
+    html.theme--documenter-dark .navbar {
+      min-height: 4rem; }
+      html.theme--documenter-dark .navbar.is-spaced {
+        padding: 1rem 2rem; }
+        html.theme--documenter-dark .navbar.is-spaced .navbar-start,
+        html.theme--documenter-dark .navbar.is-spaced .navbar-end {
+          align-items: center; }
+        html.theme--documenter-dark .navbar.is-spaced a.navbar-item,
+        html.theme--documenter-dark .navbar.is-spaced .navbar-link {
+          border-radius: 0.4em; }
+      html.theme--documenter-dark .navbar.is-transparent a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent a.navbar-item:hover, html.theme--documenter-dark .navbar.is-transparent a.navbar-item.is-active,
+      html.theme--documenter-dark .navbar.is-transparent .navbar-link:focus,
+      html.theme--documenter-dark .navbar.is-transparent .navbar-link:hover,
+      html.theme--documenter-dark .navbar.is-transparent .navbar-link.is-active {
+        background-color: transparent !important; }
+      html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, html.theme--documenter-dark .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link {
+        background-color: transparent !important; }
+      html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item:hover {
+        background-color: transparent;
+        color: #dbdee0; }
+      html.theme--documenter-dark .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active {
+        background-color: transparent;
+        color: #1abc9c; }
+    html.theme--documenter-dark .navbar-burger {
+      display: none; }
+    html.theme--documenter-dark .navbar-item,
+    html.theme--documenter-dark .navbar-link {
+      align-items: center;
+      display: flex; }
+    html.theme--documenter-dark .navbar-item {
+      display: flex; }
+      html.theme--documenter-dark .navbar-item.has-dropdown {
+        align-items: stretch; }
+      html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-link::after {
+        transform: rotate(135deg) translate(0.25em, -0.25em); }
+      html.theme--documenter-dark .navbar-item.has-dropdown-up .navbar-dropdown {
+        border-bottom: 1px solid rgba(0, 0, 0, 0.2);
+        border-radius: 8px 8px 0 0;
+        border-top: none;
+        bottom: 100%;
+        box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1);
+        top: auto; }
+      html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown {
+        display: block; }
+        .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown, html.theme--documenter-dark .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed {
+          opacity: 1;
+          pointer-events: auto;
+          transform: translateY(0); }
+    html.theme--documenter-dark .navbar-menu {
+      flex-grow: 1;
+      flex-shrink: 0; }
+    html.theme--documenter-dark .navbar-start {
+      justify-content: flex-start;
+      margin-right: auto; }
+    html.theme--documenter-dark .navbar-end {
+      justify-content: flex-end;
+      margin-left: auto; }
+    html.theme--documenter-dark .navbar-dropdown {
+      background-color: #375a7f;
+      border-bottom-left-radius: 8px;
+      border-bottom-right-radius: 8px;
+      border-top: 1px solid rgba(0, 0, 0, 0.2);
+      box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1);
+      display: none;
+      font-size: 0.875rem;
+      left: 0;
+      min-width: 100%;
+      position: absolute;
+      top: 100%;
+      z-index: 20; }
+      html.theme--documenter-dark .navbar-dropdown .navbar-item {
+        padding: 0.375rem 1rem;
+        white-space: nowrap; }
+      html.theme--documenter-dark .navbar-dropdown a.navbar-item {
+        padding-right: 3rem; }
+        html.theme--documenter-dark .navbar-dropdown a.navbar-item:focus, html.theme--documenter-dark .navbar-dropdown a.navbar-item:hover {
+          background-color: transparent;
+          color: #dbdee0; }
+        html.theme--documenter-dark .navbar-dropdown a.navbar-item.is-active {
+          background-color: transparent;
+          color: #1abc9c; }
+      .navbar.is-spaced html.theme--documenter-dark .navbar-dropdown, html.theme--documenter-dark .navbar-dropdown.is-boxed {
+        border-radius: 8px;
+        border-top: none;
+        box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+        display: block;
+        opacity: 0;
+        pointer-events: none;
+        top: calc(100% + (-4px));
+        transform: translateY(-5px);
+        transition-duration: 86ms;
+        transition-property: opacity, transform; }
+      html.theme--documenter-dark .navbar-dropdown.is-right {
+        left: auto;
+        right: 0; }
+    html.theme--documenter-dark .navbar-divider {
+      display: block; }
+    html.theme--documenter-dark .navbar > .container .navbar-brand,
+    html.theme--documenter-dark .container > .navbar .navbar-brand {
+      margin-left: -.75rem; }
+    html.theme--documenter-dark .navbar > .container .navbar-menu,
+    html.theme--documenter-dark .container > .navbar .navbar-menu {
+      margin-right: -.75rem; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom-desktop, html.theme--documenter-dark .navbar.is-fixed-top-desktop {
+      left: 0;
+      position: fixed;
+      right: 0;
+      z-index: 30; }
+    html.theme--documenter-dark .navbar.is-fixed-bottom-desktop {
+      bottom: 0; }
+      html.theme--documenter-dark .navbar.is-fixed-bottom-desktop.has-shadow {
+        box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }
+    html.theme--documenter-dark .navbar.is-fixed-top-desktop {
+      top: 0; }
+    html.theme--documenter-dark html.has-navbar-fixed-top-desktop,
+    html.theme--documenter-dark body.has-navbar-fixed-top-desktop {
+      padding-top: 4rem; }
+    html.theme--documenter-dark html.has-navbar-fixed-bottom-desktop,
+    html.theme--documenter-dark body.has-navbar-fixed-bottom-desktop {
+      padding-bottom: 4rem; }
+    html.theme--documenter-dark html.has-spaced-navbar-fixed-top,
+    html.theme--documenter-dark body.has-spaced-navbar-fixed-top {
+      padding-top: 6rem; }
+    html.theme--documenter-dark html.has-spaced-navbar-fixed-bottom,
+    html.theme--documenter-dark body.has-spaced-navbar-fixed-bottom {
+      padding-bottom: 6rem; }
+    html.theme--documenter-dark a.navbar-item.is-active,
+    html.theme--documenter-dark .navbar-link.is-active {
+      color: #1abc9c; }
+    html.theme--documenter-dark a.navbar-item.is-active:not(:focus):not(:hover),
+    html.theme--documenter-dark .navbar-link.is-active:not(:focus):not(:hover) {
+      background-color: transparent; }
+    html.theme--documenter-dark .navbar-item.has-dropdown:focus .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown:hover .navbar-link, html.theme--documenter-dark .navbar-item.has-dropdown.is-active .navbar-link {
+      background-color: transparent; } }
+  html.theme--documenter-dark .hero.is-fullheight-with-navbar {
+    min-height: calc(100vh - 4rem); }
+  html.theme--documenter-dark .pagination {
+    font-size: 15px;
+    margin: -0.25rem; }
+    html.theme--documenter-dark .pagination.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .pagination.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .pagination.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .pagination.is-rounded .pagination-previous, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous,
+    html.theme--documenter-dark .pagination.is-rounded .pagination-next,
+    html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next {
+      padding-left: 1em;
+      padding-right: 1em;
+      border-radius: 290486px; }
+    html.theme--documenter-dark .pagination.is-rounded .pagination-link, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link {
+      border-radius: 290486px; }
+  html.theme--documenter-dark .pagination,
+  html.theme--documenter-dark .pagination-list {
+    align-items: center;
+    display: flex;
+    justify-content: center;
+    text-align: center; }
+  html.theme--documenter-dark .pagination-previous,
+  html.theme--documenter-dark .pagination-next,
+  html.theme--documenter-dark .pagination-link,
+  html.theme--documenter-dark .pagination-ellipsis {
+    font-size: 1em;
+    justify-content: center;
+    margin: 0.25rem;
+    padding-left: 0.5em;
+    padding-right: 0.5em;
+    text-align: center; }
+  html.theme--documenter-dark .pagination-previous,
+  html.theme--documenter-dark .pagination-next,
+  html.theme--documenter-dark .pagination-link {
+    border-color: #5e6d6f;
+    color: #1abc9c;
+    min-width: 2.25em; }
+    html.theme--documenter-dark .pagination-previous:hover,
+    html.theme--documenter-dark .pagination-next:hover,
+    html.theme--documenter-dark .pagination-link:hover {
+      border-color: #8c9b9d;
+      color: #1dd2af; }
+    html.theme--documenter-dark .pagination-previous:focus,
+    html.theme--documenter-dark .pagination-next:focus,
+    html.theme--documenter-dark .pagination-link:focus {
+      border-color: #8c9b9d; }
+    html.theme--documenter-dark .pagination-previous:active,
+    html.theme--documenter-dark .pagination-next:active,
+    html.theme--documenter-dark .pagination-link:active {
+      box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); }
+    html.theme--documenter-dark .pagination-previous[disabled],
+    html.theme--documenter-dark .pagination-next[disabled],
+    html.theme--documenter-dark .pagination-link[disabled] {
+      background-color: #dbdee0;
+      border-color: #dbdee0;
+      box-shadow: none;
+      color: #5e6d6f;
+      opacity: 0.5; }
+  html.theme--documenter-dark .pagination-previous,
+  html.theme--documenter-dark .pagination-next {
+    padding-left: 0.75em;
+    padding-right: 0.75em;
+    white-space: nowrap; }
+  html.theme--documenter-dark .pagination-link.is-current {
+    background-color: #1abc9c;
+    border-color: #1abc9c;
+    color: #fff; }
+  html.theme--documenter-dark .pagination-ellipsis {
+    color: #8c9b9d;
+    pointer-events: none; }
+  html.theme--documenter-dark .pagination-list {
+    flex-wrap: wrap; }
+  @media screen and (max-width: 768px) {
+    html.theme--documenter-dark .pagination {
+      flex-wrap: wrap; }
+    html.theme--documenter-dark .pagination-previous,
+    html.theme--documenter-dark .pagination-next {
+      flex-grow: 1;
+      flex-shrink: 1; }
+    html.theme--documenter-dark .pagination-list li {
+      flex-grow: 1;
+      flex-shrink: 1; } }
+  @media screen and (min-width: 769px), print {
+    html.theme--documenter-dark .pagination-list {
+      flex-grow: 1;
+      flex-shrink: 1;
+      justify-content: flex-start;
+      order: 1; }
+    html.theme--documenter-dark .pagination-previous {
+      order: 2; }
+    html.theme--documenter-dark .pagination-next {
+      order: 3; }
+    html.theme--documenter-dark .pagination {
+      justify-content: space-between; }
+      html.theme--documenter-dark .pagination.is-centered .pagination-previous {
+        order: 1; }
+      html.theme--documenter-dark .pagination.is-centered .pagination-list {
+        justify-content: center;
+        order: 2; }
+      html.theme--documenter-dark .pagination.is-centered .pagination-next {
+        order: 3; }
+      html.theme--documenter-dark .pagination.is-right .pagination-previous {
+        order: 1; }
+      html.theme--documenter-dark .pagination.is-right .pagination-next {
+        order: 2; }
+      html.theme--documenter-dark .pagination.is-right .pagination-list {
+        justify-content: flex-end;
+        order: 3; } }
+  html.theme--documenter-dark .panel {
+    font-size: 15px; }
+    html.theme--documenter-dark .panel:not(:last-child) {
+      margin-bottom: 1.5rem; }
+  html.theme--documenter-dark .panel-heading,
+  html.theme--documenter-dark .panel-tabs,
+  html.theme--documenter-dark .panel-block {
+    border-bottom: 1px solid #5e6d6f;
+    border-left: 1px solid #5e6d6f;
+    border-right: 1px solid #5e6d6f; }
+    html.theme--documenter-dark .panel-heading:first-child,
+    html.theme--documenter-dark .panel-tabs:first-child,
+    html.theme--documenter-dark .panel-block:first-child {
+      border-top: 1px solid #5e6d6f; }
+  html.theme--documenter-dark .panel-heading {
+    background-color: #282f2f;
+    border-radius: 0.4em 0.4em 0 0;
+    color: #f2f2f2;
+    font-size: 1.25em;
+    font-weight: 300;
+    line-height: 1.25;
+    padding: 0.5em 0.75em; }
+  html.theme--documenter-dark .panel-tabs {
+    align-items: flex-end;
+    display: flex;
+    font-size: 0.875em;
+    justify-content: center; }
+    html.theme--documenter-dark .panel-tabs a {
+      border-bottom: 1px solid #5e6d6f;
+      margin-bottom: -1px;
+      padding: 0.5em; }
+      html.theme--documenter-dark .panel-tabs a.is-active {
+        border-bottom-color: #343c3d;
+        color: #17a689; }
+  html.theme--documenter-dark .panel-list a {
+    color: #fff; }
+    html.theme--documenter-dark .panel-list a:hover {
+      color: #1abc9c; }
+  html.theme--documenter-dark .panel-block {
+    align-items: center;
+    color: #f2f2f2;
+    display: flex;
+    justify-content: flex-start;
+    padding: 0.5em 0.75em; }
+    html.theme--documenter-dark .panel-block input[type="checkbox"] {
+      margin-right: 0.75em; }
+    html.theme--documenter-dark .panel-block > .control {
+      flex-grow: 1;
+      flex-shrink: 1;
+      width: 100%; }
+    html.theme--documenter-dark .panel-block.is-wrapped {
+      flex-wrap: wrap; }
+    html.theme--documenter-dark .panel-block.is-active {
+      border-left-color: #1abc9c;
+      color: #17a689; }
+      html.theme--documenter-dark .panel-block.is-active .panel-icon {
+        color: #1abc9c; }
+  html.theme--documenter-dark a.panel-block,
+  html.theme--documenter-dark label.panel-block {
+    cursor: pointer; }
+    html.theme--documenter-dark a.panel-block:hover,
+    html.theme--documenter-dark label.panel-block:hover {
+      background-color: #282f2f; }
+  html.theme--documenter-dark .panel-icon {
+    display: inline-block;
+    font-size: 14px;
+    height: 1em;
+    line-height: 1em;
+    text-align: center;
+    vertical-align: top;
+    width: 1em;
+    color: white;
+    margin-right: 0.75em; }
+    html.theme--documenter-dark .panel-icon .fa {
+      font-size: inherit;
+      line-height: inherit; }
+  html.theme--documenter-dark .tabs {
+    -webkit-overflow-scrolling: touch;
+    align-items: stretch;
+    display: flex;
+    font-size: 15px;
+    justify-content: space-between;
+    overflow: hidden;
+    overflow-x: auto;
+    white-space: nowrap; }
+    html.theme--documenter-dark .tabs a {
+      align-items: center;
+      border-bottom-color: #5e6d6f;
+      border-bottom-style: solid;
+      border-bottom-width: 1px;
+      color: #fff;
+      display: flex;
+      justify-content: center;
+      margin-bottom: -1px;
+      padding: 0.5em 1em;
+      vertical-align: top; }
+      html.theme--documenter-dark .tabs a:hover {
+        border-bottom-color: #f2f2f2;
+        color: #f2f2f2; }
+    html.theme--documenter-dark .tabs li {
+      display: block; }
+      html.theme--documenter-dark .tabs li.is-active a {
+        border-bottom-color: #1abc9c;
+        color: #1abc9c; }
+    html.theme--documenter-dark .tabs ul {
+      align-items: center;
+      border-bottom-color: #5e6d6f;
+      border-bottom-style: solid;
+      border-bottom-width: 1px;
+      display: flex;
+      flex-grow: 1;
+      flex-shrink: 0;
+      justify-content: flex-start; }
+      html.theme--documenter-dark .tabs ul.is-left {
+        padding-right: 0.75em; }
+      html.theme--documenter-dark .tabs ul.is-center {
+        flex: none;
+        justify-content: center;
+        padding-left: 0.75em;
+        padding-right: 0.75em; }
+      html.theme--documenter-dark .tabs ul.is-right {
+        justify-content: flex-end;
+        padding-left: 0.75em; }
+    html.theme--documenter-dark .tabs .icon:first-child {
+      margin-right: 0.5em; }
+    html.theme--documenter-dark .tabs .icon:last-child {
+      margin-left: 0.5em; }
+    html.theme--documenter-dark .tabs.is-centered ul {
+      justify-content: center; }
+    html.theme--documenter-dark .tabs.is-right ul {
+      justify-content: flex-end; }
+    html.theme--documenter-dark .tabs.is-boxed a {
+      border: 1px solid transparent;
+      border-radius: 0.4em 0.4em 0 0; }
+      html.theme--documenter-dark .tabs.is-boxed a:hover {
+        background-color: #282f2f;
+        border-bottom-color: #5e6d6f; }
+    html.theme--documenter-dark .tabs.is-boxed li.is-active a {
+      background-color: white;
+      border-color: #5e6d6f;
+      border-bottom-color: transparent !important; }
+    html.theme--documenter-dark .tabs.is-fullwidth li {
+      flex-grow: 1;
+      flex-shrink: 0; }
+    html.theme--documenter-dark .tabs.is-toggle a {
+      border-color: #5e6d6f;
+      border-style: solid;
+      border-width: 1px;
+      margin-bottom: 0;
+      position: relative; }
+      html.theme--documenter-dark .tabs.is-toggle a:hover {
+        background-color: #282f2f;
+        border-color: #8c9b9d;
+        z-index: 2; }
+    html.theme--documenter-dark .tabs.is-toggle li + li {
+      margin-left: -1px; }
+    html.theme--documenter-dark .tabs.is-toggle li:first-child a {
+      border-radius: 0.4em 0 0 0.4em; }
+    html.theme--documenter-dark .tabs.is-toggle li:last-child a {
+      border-radius: 0 0.4em 0.4em 0; }
+    html.theme--documenter-dark .tabs.is-toggle li.is-active a {
+      background-color: #1abc9c;
+      border-color: #1abc9c;
+      color: #fff;
+      z-index: 1; }
+    html.theme--documenter-dark .tabs.is-toggle ul {
+      border-bottom: none; }
+    html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:first-child a {
+      border-bottom-left-radius: 290486px;
+      border-top-left-radius: 290486px;
+      padding-left: 1.25em; }
+    html.theme--documenter-dark .tabs.is-toggle.is-toggle-rounded li:last-child a {
+      border-bottom-right-radius: 290486px;
+      border-top-right-radius: 290486px;
+      padding-right: 1.25em; }
+    html.theme--documenter-dark .tabs.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.tabs {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .tabs.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .tabs.is-large {
+      font-size: 1.5rem; }
+  html.theme--documenter-dark .column {
+    display: block;
+    flex-basis: 0;
+    flex-grow: 1;
+    flex-shrink: 1;
+    padding: 0.75rem; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-narrow {
+      flex: none; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-full {
+      flex: none;
+      width: 100%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-three-quarters {
+      flex: none;
+      width: 75%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-two-thirds {
+      flex: none;
+      width: 66.6666%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-half {
+      flex: none;
+      width: 50%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-one-third {
+      flex: none;
+      width: 33.3333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-one-quarter {
+      flex: none;
+      width: 25%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-one-fifth {
+      flex: none;
+      width: 20%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-two-fifths {
+      flex: none;
+      width: 40%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-three-fifths {
+      flex: none;
+      width: 60%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-four-fifths {
+      flex: none;
+      width: 80%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-quarters {
+      margin-left: 75%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-thirds {
+      margin-left: 66.6666%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-half {
+      margin-left: 50%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-third {
+      margin-left: 33.3333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-quarter {
+      margin-left: 25%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-one-fifth {
+      margin-left: 20%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-two-fifths {
+      margin-left: 40%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-three-fifths {
+      margin-left: 60%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-four-fifths {
+      margin-left: 80%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-0 {
+      flex: none;
+      width: 0%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-0 {
+      margin-left: 0%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-1 {
+      flex: none;
+      width: 8.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-1 {
+      margin-left: 8.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-2 {
+      flex: none;
+      width: 16.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-2 {
+      margin-left: 16.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-3 {
+      flex: none;
+      width: 25%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-3 {
+      margin-left: 25%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-4 {
+      flex: none;
+      width: 33.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-4 {
+      margin-left: 33.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-5 {
+      flex: none;
+      width: 41.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-5 {
+      margin-left: 41.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-6 {
+      flex: none;
+      width: 50%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-6 {
+      margin-left: 50%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-7 {
+      flex: none;
+      width: 58.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-7 {
+      margin-left: 58.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-8 {
+      flex: none;
+      width: 66.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-8 {
+      margin-left: 66.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-9 {
+      flex: none;
+      width: 75%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-9 {
+      margin-left: 75%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-10 {
+      flex: none;
+      width: 83.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-10 {
+      margin-left: 83.33333%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-11 {
+      flex: none;
+      width: 91.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-11 {
+      margin-left: 91.66667%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-12 {
+      flex: none;
+      width: 100%; }
+    .columns.is-mobile > html.theme--documenter-dark .column.is-offset-12 {
+      margin-left: 100%; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .column.is-narrow-mobile {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full-mobile {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters-mobile {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds-mobile {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half-mobile {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third-mobile {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter-mobile {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth-mobile {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths-mobile {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths-mobile {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths-mobile {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters-mobile {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds-mobile {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half-mobile {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third-mobile {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter-mobile {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth-mobile {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths-mobile {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths-mobile {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths-mobile {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0-mobile {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0-mobile {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1-mobile {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1-mobile {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2-mobile {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2-mobile {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3-mobile {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3-mobile {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4-mobile {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4-mobile {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5-mobile {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5-mobile {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6-mobile {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6-mobile {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7-mobile {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7-mobile {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8-mobile {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8-mobile {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9-mobile {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9-mobile {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10-mobile {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10-mobile {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11-mobile {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11-mobile {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12-mobile {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12-mobile {
+        margin-left: 100%; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .column.is-narrow, html.theme--documenter-dark .column.is-narrow-tablet {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full, html.theme--documenter-dark .column.is-full-tablet {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters, html.theme--documenter-dark .column.is-three-quarters-tablet {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds, html.theme--documenter-dark .column.is-two-thirds-tablet {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half, html.theme--documenter-dark .column.is-half-tablet {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third, html.theme--documenter-dark .column.is-one-third-tablet {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter, html.theme--documenter-dark .column.is-one-quarter-tablet {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth, html.theme--documenter-dark .column.is-one-fifth-tablet {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths, html.theme--documenter-dark .column.is-two-fifths-tablet {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths, html.theme--documenter-dark .column.is-three-fifths-tablet {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths, html.theme--documenter-dark .column.is-four-fifths-tablet {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters, html.theme--documenter-dark .column.is-offset-three-quarters-tablet {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds, html.theme--documenter-dark .column.is-offset-two-thirds-tablet {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half, html.theme--documenter-dark .column.is-offset-half-tablet {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third, html.theme--documenter-dark .column.is-offset-one-third-tablet {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter, html.theme--documenter-dark .column.is-offset-one-quarter-tablet {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth, html.theme--documenter-dark .column.is-offset-one-fifth-tablet {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths, html.theme--documenter-dark .column.is-offset-two-fifths-tablet {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths, html.theme--documenter-dark .column.is-offset-three-fifths-tablet {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths, html.theme--documenter-dark .column.is-offset-four-fifths-tablet {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0, html.theme--documenter-dark .column.is-0-tablet {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0, html.theme--documenter-dark .column.is-offset-0-tablet {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1, html.theme--documenter-dark .column.is-1-tablet {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1, html.theme--documenter-dark .column.is-offset-1-tablet {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2, html.theme--documenter-dark .column.is-2-tablet {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2, html.theme--documenter-dark .column.is-offset-2-tablet {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3, html.theme--documenter-dark .column.is-3-tablet {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3, html.theme--documenter-dark .column.is-offset-3-tablet {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4, html.theme--documenter-dark .column.is-4-tablet {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4, html.theme--documenter-dark .column.is-offset-4-tablet {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5, html.theme--documenter-dark .column.is-5-tablet {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5, html.theme--documenter-dark .column.is-offset-5-tablet {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6, html.theme--documenter-dark .column.is-6-tablet {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6, html.theme--documenter-dark .column.is-offset-6-tablet {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7, html.theme--documenter-dark .column.is-7-tablet {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7, html.theme--documenter-dark .column.is-offset-7-tablet {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8, html.theme--documenter-dark .column.is-8-tablet {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8, html.theme--documenter-dark .column.is-offset-8-tablet {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9, html.theme--documenter-dark .column.is-9-tablet {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9, html.theme--documenter-dark .column.is-offset-9-tablet {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10, html.theme--documenter-dark .column.is-10-tablet {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10, html.theme--documenter-dark .column.is-offset-10-tablet {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11, html.theme--documenter-dark .column.is-11-tablet {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11, html.theme--documenter-dark .column.is-offset-11-tablet {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12, html.theme--documenter-dark .column.is-12-tablet {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12, html.theme--documenter-dark .column.is-offset-12-tablet {
+        margin-left: 100%; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .column.is-narrow-touch {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full-touch {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters-touch {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds-touch {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half-touch {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third-touch {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter-touch {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth-touch {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths-touch {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths-touch {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths-touch {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters-touch {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds-touch {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half-touch {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third-touch {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter-touch {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth-touch {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths-touch {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths-touch {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths-touch {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0-touch {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0-touch {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1-touch {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1-touch {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2-touch {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2-touch {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3-touch {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3-touch {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4-touch {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4-touch {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5-touch {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5-touch {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6-touch {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6-touch {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7-touch {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7-touch {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8-touch {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8-touch {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9-touch {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9-touch {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10-touch {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10-touch {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11-touch {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11-touch {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12-touch {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12-touch {
+        margin-left: 100%; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .column.is-narrow-desktop {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full-desktop {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters-desktop {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds-desktop {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half-desktop {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third-desktop {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter-desktop {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth-desktop {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths-desktop {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths-desktop {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths-desktop {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters-desktop {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds-desktop {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half-desktop {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third-desktop {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter-desktop {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth-desktop {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths-desktop {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths-desktop {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths-desktop {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0-desktop {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0-desktop {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1-desktop {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1-desktop {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2-desktop {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2-desktop {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3-desktop {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3-desktop {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4-desktop {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4-desktop {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5-desktop {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5-desktop {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6-desktop {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6-desktop {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7-desktop {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7-desktop {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8-desktop {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8-desktop {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9-desktop {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9-desktop {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10-desktop {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10-desktop {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11-desktop {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11-desktop {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12-desktop {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12-desktop {
+        margin-left: 100%; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .column.is-narrow-widescreen {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full-widescreen {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters-widescreen {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds-widescreen {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half-widescreen {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third-widescreen {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter-widescreen {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth-widescreen {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths-widescreen {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths-widescreen {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths-widescreen {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters-widescreen {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds-widescreen {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half-widescreen {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third-widescreen {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter-widescreen {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth-widescreen {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths-widescreen {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths-widescreen {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths-widescreen {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0-widescreen {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0-widescreen {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1-widescreen {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1-widescreen {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2-widescreen {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2-widescreen {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3-widescreen {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3-widescreen {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4-widescreen {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4-widescreen {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5-widescreen {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5-widescreen {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6-widescreen {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6-widescreen {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7-widescreen {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7-widescreen {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8-widescreen {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8-widescreen {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9-widescreen {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9-widescreen {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10-widescreen {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10-widescreen {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11-widescreen {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11-widescreen {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12-widescreen {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12-widescreen {
+        margin-left: 100%; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .column.is-narrow-fullhd {
+        flex: none; }
+      html.theme--documenter-dark .column.is-full-fullhd {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-three-quarters-fullhd {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-two-thirds-fullhd {
+        flex: none;
+        width: 66.6666%; }
+      html.theme--documenter-dark .column.is-half-fullhd {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-one-third-fullhd {
+        flex: none;
+        width: 33.3333%; }
+      html.theme--documenter-dark .column.is-one-quarter-fullhd {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-one-fifth-fullhd {
+        flex: none;
+        width: 20%; }
+      html.theme--documenter-dark .column.is-two-fifths-fullhd {
+        flex: none;
+        width: 40%; }
+      html.theme--documenter-dark .column.is-three-fifths-fullhd {
+        flex: none;
+        width: 60%; }
+      html.theme--documenter-dark .column.is-four-fifths-fullhd {
+        flex: none;
+        width: 80%; }
+      html.theme--documenter-dark .column.is-offset-three-quarters-fullhd {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-offset-two-thirds-fullhd {
+        margin-left: 66.6666%; }
+      html.theme--documenter-dark .column.is-offset-half-fullhd {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-offset-one-third-fullhd {
+        margin-left: 33.3333%; }
+      html.theme--documenter-dark .column.is-offset-one-quarter-fullhd {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-offset-one-fifth-fullhd {
+        margin-left: 20%; }
+      html.theme--documenter-dark .column.is-offset-two-fifths-fullhd {
+        margin-left: 40%; }
+      html.theme--documenter-dark .column.is-offset-three-fifths-fullhd {
+        margin-left: 60%; }
+      html.theme--documenter-dark .column.is-offset-four-fifths-fullhd {
+        margin-left: 80%; }
+      html.theme--documenter-dark .column.is-0-fullhd {
+        flex: none;
+        width: 0%; }
+      html.theme--documenter-dark .column.is-offset-0-fullhd {
+        margin-left: 0%; }
+      html.theme--documenter-dark .column.is-1-fullhd {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .column.is-offset-1-fullhd {
+        margin-left: 8.33333%; }
+      html.theme--documenter-dark .column.is-2-fullhd {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .column.is-offset-2-fullhd {
+        margin-left: 16.66667%; }
+      html.theme--documenter-dark .column.is-3-fullhd {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .column.is-offset-3-fullhd {
+        margin-left: 25%; }
+      html.theme--documenter-dark .column.is-4-fullhd {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .column.is-offset-4-fullhd {
+        margin-left: 33.33333%; }
+      html.theme--documenter-dark .column.is-5-fullhd {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .column.is-offset-5-fullhd {
+        margin-left: 41.66667%; }
+      html.theme--documenter-dark .column.is-6-fullhd {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .column.is-offset-6-fullhd {
+        margin-left: 50%; }
+      html.theme--documenter-dark .column.is-7-fullhd {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .column.is-offset-7-fullhd {
+        margin-left: 58.33333%; }
+      html.theme--documenter-dark .column.is-8-fullhd {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .column.is-offset-8-fullhd {
+        margin-left: 66.66667%; }
+      html.theme--documenter-dark .column.is-9-fullhd {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .column.is-offset-9-fullhd {
+        margin-left: 75%; }
+      html.theme--documenter-dark .column.is-10-fullhd {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .column.is-offset-10-fullhd {
+        margin-left: 83.33333%; }
+      html.theme--documenter-dark .column.is-11-fullhd {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .column.is-offset-11-fullhd {
+        margin-left: 91.66667%; }
+      html.theme--documenter-dark .column.is-12-fullhd {
+        flex: none;
+        width: 100%; }
+      html.theme--documenter-dark .column.is-offset-12-fullhd {
+        margin-left: 100%; } }
+  html.theme--documenter-dark .columns {
+    margin-left: -0.75rem;
+    margin-right: -0.75rem;
+    margin-top: -0.75rem; }
+    html.theme--documenter-dark .columns:last-child {
+      margin-bottom: -0.75rem; }
+    html.theme--documenter-dark .columns:not(:last-child) {
+      margin-bottom: calc(1.5rem - 0.75rem); }
+    html.theme--documenter-dark .columns.is-centered {
+      justify-content: center; }
+    html.theme--documenter-dark .columns.is-gapless {
+      margin-left: 0;
+      margin-right: 0;
+      margin-top: 0; }
+      html.theme--documenter-dark .columns.is-gapless > .column {
+        margin: 0;
+        padding: 0 !important; }
+      html.theme--documenter-dark .columns.is-gapless:not(:last-child) {
+        margin-bottom: 1.5rem; }
+      html.theme--documenter-dark .columns.is-gapless:last-child {
+        margin-bottom: 0; }
+    html.theme--documenter-dark .columns.is-mobile {
+      display: flex; }
+    html.theme--documenter-dark .columns.is-multiline {
+      flex-wrap: wrap; }
+    html.theme--documenter-dark .columns.is-vcentered {
+      align-items: center; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns:not(.is-desktop) {
+        display: flex; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-desktop {
+        display: flex; } }
+  html.theme--documenter-dark .columns.is-variable {
+    --columnGap: 0.75rem;
+    margin-left: calc(-1 * var(--columnGap));
+    margin-right: calc(-1 * var(--columnGap)); }
+    html.theme--documenter-dark .columns.is-variable .column {
+      padding-left: var(--columnGap);
+      padding-right: var(--columnGap); }
+    html.theme--documenter-dark .columns.is-variable.is-0 {
+      --columnGap: 0rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-mobile {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-0-tablet {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-tablet-only {
+        --columnGap: 0rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-touch {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-desktop {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-desktop-only {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-widescreen {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-widescreen-only {
+        --columnGap: 0rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-0-fullhd {
+        --columnGap: 0rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-1 {
+      --columnGap: 0.25rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-mobile {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-1-tablet {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-tablet-only {
+        --columnGap: 0.25rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-touch {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-desktop {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-desktop-only {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-widescreen {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-widescreen-only {
+        --columnGap: 0.25rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-1-fullhd {
+        --columnGap: 0.25rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-2 {
+      --columnGap: 0.5rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-mobile {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-2-tablet {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-tablet-only {
+        --columnGap: 0.5rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-touch {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-desktop {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-desktop-only {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-widescreen {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-widescreen-only {
+        --columnGap: 0.5rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-2-fullhd {
+        --columnGap: 0.5rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-3 {
+      --columnGap: 0.75rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-mobile {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-3-tablet {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-tablet-only {
+        --columnGap: 0.75rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-touch {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-desktop {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-desktop-only {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-widescreen {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-widescreen-only {
+        --columnGap: 0.75rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-3-fullhd {
+        --columnGap: 0.75rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-4 {
+      --columnGap: 1rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-mobile {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-4-tablet {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-tablet-only {
+        --columnGap: 1rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-touch {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-desktop {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-desktop-only {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-widescreen {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-widescreen-only {
+        --columnGap: 1rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-4-fullhd {
+        --columnGap: 1rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-5 {
+      --columnGap: 1.25rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-mobile {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-5-tablet {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-tablet-only {
+        --columnGap: 1.25rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-touch {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-desktop {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-desktop-only {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-widescreen {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-widescreen-only {
+        --columnGap: 1.25rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-5-fullhd {
+        --columnGap: 1.25rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-6 {
+      --columnGap: 1.5rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-mobile {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-6-tablet {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-tablet-only {
+        --columnGap: 1.5rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-touch {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-desktop {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-desktop-only {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-widescreen {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-widescreen-only {
+        --columnGap: 1.5rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-6-fullhd {
+        --columnGap: 1.5rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-7 {
+      --columnGap: 1.75rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-mobile {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-7-tablet {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-tablet-only {
+        --columnGap: 1.75rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-touch {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-desktop {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-desktop-only {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-widescreen {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-widescreen-only {
+        --columnGap: 1.75rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-7-fullhd {
+        --columnGap: 1.75rem; } }
+    html.theme--documenter-dark .columns.is-variable.is-8 {
+      --columnGap: 2rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-mobile {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .columns.is-variable.is-8-tablet {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 769px) and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-tablet-only {
+        --columnGap: 2rem; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-touch {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-desktop {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 1056px) and (max-width: 1215px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-desktop-only {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 1216px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-widescreen {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 1216px) and (max-width: 1407px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-widescreen-only {
+        --columnGap: 2rem; } }
+    @media screen and (min-width: 1408px) {
+      html.theme--documenter-dark .columns.is-variable.is-8-fullhd {
+        --columnGap: 2rem; } }
+  html.theme--documenter-dark .tile {
+    align-items: stretch;
+    display: block;
+    flex-basis: 0;
+    flex-grow: 1;
+    flex-shrink: 1;
+    min-height: min-content; }
+    html.theme--documenter-dark .tile.is-ancestor {
+      margin-left: -0.75rem;
+      margin-right: -0.75rem;
+      margin-top: -0.75rem; }
+      html.theme--documenter-dark .tile.is-ancestor:last-child {
+        margin-bottom: -0.75rem; }
+      html.theme--documenter-dark .tile.is-ancestor:not(:last-child) {
+        margin-bottom: 0.75rem; }
+    html.theme--documenter-dark .tile.is-child {
+      margin: 0 !important; }
+    html.theme--documenter-dark .tile.is-parent {
+      padding: 0.75rem; }
+    html.theme--documenter-dark .tile.is-vertical {
+      flex-direction: column; }
+      html.theme--documenter-dark .tile.is-vertical > .tile.is-child:not(:last-child) {
+        margin-bottom: 1.5rem !important; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .tile:not(.is-child) {
+        display: flex; }
+      html.theme--documenter-dark .tile.is-1 {
+        flex: none;
+        width: 8.33333%; }
+      html.theme--documenter-dark .tile.is-2 {
+        flex: none;
+        width: 16.66667%; }
+      html.theme--documenter-dark .tile.is-3 {
+        flex: none;
+        width: 25%; }
+      html.theme--documenter-dark .tile.is-4 {
+        flex: none;
+        width: 33.33333%; }
+      html.theme--documenter-dark .tile.is-5 {
+        flex: none;
+        width: 41.66667%; }
+      html.theme--documenter-dark .tile.is-6 {
+        flex: none;
+        width: 50%; }
+      html.theme--documenter-dark .tile.is-7 {
+        flex: none;
+        width: 58.33333%; }
+      html.theme--documenter-dark .tile.is-8 {
+        flex: none;
+        width: 66.66667%; }
+      html.theme--documenter-dark .tile.is-9 {
+        flex: none;
+        width: 75%; }
+      html.theme--documenter-dark .tile.is-10 {
+        flex: none;
+        width: 83.33333%; }
+      html.theme--documenter-dark .tile.is-11 {
+        flex: none;
+        width: 91.66667%; }
+      html.theme--documenter-dark .tile.is-12 {
+        flex: none;
+        width: 100%; } }
+  html.theme--documenter-dark .hero {
+    align-items: stretch;
+    display: flex;
+    flex-direction: column;
+    justify-content: space-between; }
+    html.theme--documenter-dark .hero .navbar {
+      background: none; }
+    html.theme--documenter-dark .hero .tabs ul {
+      border-bottom: none; }
+    html.theme--documenter-dark .hero.is-white {
+      background-color: white;
+      color: #0a0a0a; }
+      html.theme--documenter-dark .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-white strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-white .title {
+        color: #0a0a0a; }
+      html.theme--documenter-dark .hero.is-white .subtitle {
+        color: rgba(10, 10, 10, 0.9); }
+        html.theme--documenter-dark .hero.is-white .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-white .subtitle strong {
+          color: #0a0a0a; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-white .navbar-menu {
+          background-color: white; } }
+      html.theme--documenter-dark .hero.is-white .navbar-item,
+      html.theme--documenter-dark .hero.is-white .navbar-link {
+        color: rgba(10, 10, 10, 0.7); }
+      html.theme--documenter-dark .hero.is-white a.navbar-item:hover, html.theme--documenter-dark .hero.is-white a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-white .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-white .navbar-link.is-active {
+        background-color: #f2f2f2;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .hero.is-white .tabs a {
+        color: #0a0a0a;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-white .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-white .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-white .tabs.is-boxed a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a {
+        color: #0a0a0a; }
+        html.theme--documenter-dark .hero.is-white .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-white .tabs.is-toggle li.is-active a:hover {
+        background-color: #0a0a0a;
+        border-color: #0a0a0a;
+        color: white; }
+      html.theme--documenter-dark .hero.is-white.is-bold {
+        background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-white.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); } }
+    html.theme--documenter-dark .hero.is-black {
+      background-color: #0a0a0a;
+      color: white; }
+      html.theme--documenter-dark .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-black strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-black .title {
+        color: white; }
+      html.theme--documenter-dark .hero.is-black .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-black .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-black .subtitle strong {
+          color: white; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-black .navbar-menu {
+          background-color: #0a0a0a; } }
+      html.theme--documenter-dark .hero.is-black .navbar-item,
+      html.theme--documenter-dark .hero.is-black .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-black a.navbar-item:hover, html.theme--documenter-dark .hero.is-black a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-black .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-black .navbar-link.is-active {
+        background-color: black;
+        color: white; }
+      html.theme--documenter-dark .hero.is-black .tabs a {
+        color: white;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-black .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-black .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-black .tabs.is-boxed a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a {
+        color: white; }
+        html.theme--documenter-dark .hero.is-black .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-black .tabs.is-toggle li.is-active a:hover {
+        background-color: white;
+        border-color: white;
+        color: #0a0a0a; }
+      html.theme--documenter-dark .hero.is-black.is-bold {
+        background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-black.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } }
+    html.theme--documenter-dark .hero.is-light {
+      background-color: #ecf0f1;
+      color: #282f2f; }
+      html.theme--documenter-dark .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-light strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-light .title {
+        color: #282f2f; }
+      html.theme--documenter-dark .hero.is-light .subtitle {
+        color: rgba(40, 47, 47, 0.9); }
+        html.theme--documenter-dark .hero.is-light .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-light .subtitle strong {
+          color: #282f2f; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-light .navbar-menu {
+          background-color: #ecf0f1; } }
+      html.theme--documenter-dark .hero.is-light .navbar-item,
+      html.theme--documenter-dark .hero.is-light .navbar-link {
+        color: rgba(40, 47, 47, 0.7); }
+      html.theme--documenter-dark .hero.is-light a.navbar-item:hover, html.theme--documenter-dark .hero.is-light a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-light .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-light .navbar-link.is-active {
+        background-color: #dde4e6;
+        color: #282f2f; }
+      html.theme--documenter-dark .hero.is-light .tabs a {
+        color: #282f2f;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-light .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-light .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-light .tabs.is-boxed a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a {
+        color: #282f2f; }
+        html.theme--documenter-dark .hero.is-light .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-light .tabs.is-toggle li.is-active a:hover {
+        background-color: #282f2f;
+        border-color: #282f2f;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .hero.is-light.is-bold {
+        background-image: linear-gradient(141deg, #cadfe0 0%, #ecf0f1 71%, #fafbfc 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-light.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #cadfe0 0%, #ecf0f1 71%, #fafbfc 100%); } }
+    html.theme--documenter-dark .hero.is-dark, html.theme--documenter-dark .content kbd.hero {
+      background-color: #282f2f;
+      color: #ecf0f1; }
+      html.theme--documenter-dark .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-dark strong,
+      html.theme--documenter-dark .content kbd.hero strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-dark .title, html.theme--documenter-dark .content kbd.hero .title {
+        color: #ecf0f1; }
+      html.theme--documenter-dark .hero.is-dark .subtitle, html.theme--documenter-dark .content kbd.hero .subtitle {
+        color: rgba(236, 240, 241, 0.9); }
+        html.theme--documenter-dark .hero.is-dark .subtitle a:not(.button), html.theme--documenter-dark .content kbd.hero .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-dark .subtitle strong,
+        html.theme--documenter-dark .content kbd.hero .subtitle strong {
+          color: #ecf0f1; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-dark .navbar-menu, html.theme--documenter-dark .content kbd.hero .navbar-menu {
+          background-color: #282f2f; } }
+      html.theme--documenter-dark .hero.is-dark .navbar-item, html.theme--documenter-dark .content kbd.hero .navbar-item,
+      html.theme--documenter-dark .hero.is-dark .navbar-link,
+      html.theme--documenter-dark .content kbd.hero .navbar-link {
+        color: rgba(236, 240, 241, 0.7); }
+      html.theme--documenter-dark .hero.is-dark a.navbar-item:hover, html.theme--documenter-dark .content kbd.hero a.navbar-item:hover, html.theme--documenter-dark .hero.is-dark a.navbar-item.is-active, html.theme--documenter-dark .content kbd.hero a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-dark .navbar-link:hover,
+      html.theme--documenter-dark .content kbd.hero .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-dark .navbar-link.is-active,
+      html.theme--documenter-dark .content kbd.hero .navbar-link.is-active {
+        background-color: #1d2122;
+        color: #ecf0f1; }
+      html.theme--documenter-dark .hero.is-dark .tabs a, html.theme--documenter-dark .content kbd.hero .tabs a {
+        color: #ecf0f1;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-dark .tabs a:hover, html.theme--documenter-dark .content kbd.hero .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-dark .tabs li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a {
+        color: #ecf0f1; }
+        html.theme--documenter-dark .hero.is-dark .tabs.is-boxed a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-dark .tabs.is-toggle li.is-active a:hover, html.theme--documenter-dark .content kbd.hero .tabs.is-toggle li.is-active a:hover {
+        background-color: #ecf0f1;
+        border-color: #ecf0f1;
+        color: #282f2f; }
+      html.theme--documenter-dark .hero.is-dark.is-bold, html.theme--documenter-dark .content kbd.hero.is-bold {
+        background-image: linear-gradient(141deg, #0f1615 0%, #282f2f 71%, #313c40 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-dark.is-bold .navbar-menu, html.theme--documenter-dark .content kbd.hero.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #0f1615 0%, #282f2f 71%, #313c40 100%); } }
+    html.theme--documenter-dark .hero.is-primary, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink {
+      background-color: #375a7f;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-primary strong,
+      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-primary .title, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-primary .subtitle, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-primary .subtitle a:not(.button), html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-primary .subtitle strong,
+        html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-primary .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-menu {
+          background-color: #375a7f; } }
+      html.theme--documenter-dark .hero.is-primary .navbar-item, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-item,
+      html.theme--documenter-dark .hero.is-primary .navbar-link,
+      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-primary a.navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, html.theme--documenter-dark .hero.is-primary a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-primary .navbar-link:hover,
+      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-primary .navbar-link.is-active,
+      html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active {
+        background-color: #2f4d6d;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-primary .tabs a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-primary .tabs a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-primary .tabs li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-primary .tabs.is-boxed a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-primary .tabs.is-toggle li.is-active a:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #375a7f; }
+      html.theme--documenter-dark .hero.is-primary.is-bold, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink {
+        background-image: linear-gradient(141deg, #214b62 0%, #375a7f 71%, #3a5796 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-primary.is-bold .navbar-menu, html.theme--documenter-dark .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu {
+            background-image: linear-gradient(141deg, #214b62 0%, #375a7f 71%, #3a5796 100%); } }
+    html.theme--documenter-dark .hero.is-link {
+      background-color: #1abc9c;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-link strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-link .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-link .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-link .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-link .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-link .navbar-menu {
+          background-color: #1abc9c; } }
+      html.theme--documenter-dark .hero.is-link .navbar-item,
+      html.theme--documenter-dark .hero.is-link .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-link a.navbar-item:hover, html.theme--documenter-dark .hero.is-link a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-link .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-link .navbar-link.is-active {
+        background-color: #17a689;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-link .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-link .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-link .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-link .tabs.is-boxed a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-link .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-link .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #1abc9c; }
+      html.theme--documenter-dark .hero.is-link.is-bold {
+        background-image: linear-gradient(141deg, #0c9764 0%, #1abc9c 71%, #17d8d2 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-link.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #0c9764 0%, #1abc9c 71%, #17d8d2 100%); } }
+    html.theme--documenter-dark .hero.is-info {
+      background-color: #024c7d;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-info strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-info .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-info .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-info .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-info .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-info .navbar-menu {
+          background-color: #024c7d; } }
+      html.theme--documenter-dark .hero.is-info .navbar-item,
+      html.theme--documenter-dark .hero.is-info .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-info a.navbar-item:hover, html.theme--documenter-dark .hero.is-info a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-info .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-info .navbar-link.is-active {
+        background-color: #023d64;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-info .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-info .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-info .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-info .tabs.is-boxed a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-info .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-info .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #024c7d; }
+      html.theme--documenter-dark .hero.is-info.is-bold {
+        background-image: linear-gradient(141deg, #003a4c 0%, #024c7d 71%, #004299 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-info.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #003a4c 0%, #024c7d 71%, #004299 100%); } }
+    html.theme--documenter-dark .hero.is-success {
+      background-color: #008438;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-success strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-success .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-success .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-success .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-success .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-success .navbar-menu {
+          background-color: #008438; } }
+      html.theme--documenter-dark .hero.is-success .navbar-item,
+      html.theme--documenter-dark .hero.is-success .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-success a.navbar-item:hover, html.theme--documenter-dark .hero.is-success a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-success .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-success .navbar-link.is-active {
+        background-color: #006b2d;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-success .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-success .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-success .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-success .tabs.is-boxed a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-success .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-success .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #008438; }
+      html.theme--documenter-dark .hero.is-success.is-bold {
+        background-image: linear-gradient(141deg, #005115 0%, #008438 71%, #009e5d 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-success.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #005115 0%, #008438 71%, #009e5d 100%); } }
+    html.theme--documenter-dark .hero.is-warning {
+      background-color: #ad8100;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-warning strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-warning .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-warning .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-warning .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-warning .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-warning .navbar-menu {
+          background-color: #ad8100; } }
+      html.theme--documenter-dark .hero.is-warning .navbar-item,
+      html.theme--documenter-dark .hero.is-warning .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-warning a.navbar-item:hover, html.theme--documenter-dark .hero.is-warning a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-warning .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-warning .navbar-link.is-active {
+        background-color: #946e00;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-warning .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-warning .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-warning .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-warning .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-warning .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #ad8100; }
+      html.theme--documenter-dark .hero.is-warning.is-bold {
+        background-image: linear-gradient(141deg, #7a4700 0%, #ad8100 71%, #c7b500 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-warning.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #7a4700 0%, #ad8100 71%, #c7b500 100%); } }
+    html.theme--documenter-dark .hero.is-danger {
+      background-color: #9e1b0d;
+      color: #fff; }
+      html.theme--documenter-dark .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+      html.theme--documenter-dark .hero.is-danger strong {
+        color: inherit; }
+      html.theme--documenter-dark .hero.is-danger .title {
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-danger .subtitle {
+        color: rgba(255, 255, 255, 0.9); }
+        html.theme--documenter-dark .hero.is-danger .subtitle a:not(.button),
+        html.theme--documenter-dark .hero.is-danger .subtitle strong {
+          color: #fff; }
+      @media screen and (max-width: 1055px) {
+        html.theme--documenter-dark .hero.is-danger .navbar-menu {
+          background-color: #9e1b0d; } }
+      html.theme--documenter-dark .hero.is-danger .navbar-item,
+      html.theme--documenter-dark .hero.is-danger .navbar-link {
+        color: rgba(255, 255, 255, 0.7); }
+      html.theme--documenter-dark .hero.is-danger a.navbar-item:hover, html.theme--documenter-dark .hero.is-danger a.navbar-item.is-active,
+      html.theme--documenter-dark .hero.is-danger .navbar-link:hover,
+      html.theme--documenter-dark .hero.is-danger .navbar-link.is-active {
+        background-color: #86170b;
+        color: #fff; }
+      html.theme--documenter-dark .hero.is-danger .tabs a {
+        color: #fff;
+        opacity: 0.9; }
+        html.theme--documenter-dark .hero.is-danger .tabs a:hover {
+          opacity: 1; }
+      html.theme--documenter-dark .hero.is-danger .tabs li.is-active a {
+        opacity: 1; }
+      html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a {
+        color: #fff; }
+        html.theme--documenter-dark .hero.is-danger .tabs.is-boxed a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle a:hover {
+          background-color: rgba(10, 10, 10, 0.1); }
+      html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-boxed li.is-active a:hover, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a, html.theme--documenter-dark .hero.is-danger .tabs.is-toggle li.is-active a:hover {
+        background-color: #fff;
+        border-color: #fff;
+        color: #9e1b0d; }
+      html.theme--documenter-dark .hero.is-danger.is-bold {
+        background-image: linear-gradient(141deg, #75030b 0%, #9e1b0d 71%, #ba380a 100%); }
+        @media screen and (max-width: 768px) {
+          html.theme--documenter-dark .hero.is-danger.is-bold .navbar-menu {
+            background-image: linear-gradient(141deg, #75030b 0%, #9e1b0d 71%, #ba380a 100%); } }
+    html.theme--documenter-dark .hero.is-small .hero-body, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.hero .hero-body {
+      padding-bottom: 1.5rem;
+      padding-top: 1.5rem; }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .hero.is-medium .hero-body {
+        padding-bottom: 9rem;
+        padding-top: 9rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .hero.is-large .hero-body {
+        padding-bottom: 18rem;
+        padding-top: 18rem; } }
+    html.theme--documenter-dark .hero.is-halfheight .hero-body, html.theme--documenter-dark .hero.is-fullheight .hero-body, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body {
+      align-items: center;
+      display: flex; }
+      html.theme--documenter-dark .hero.is-halfheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight .hero-body > .container, html.theme--documenter-dark .hero.is-fullheight-with-navbar .hero-body > .container {
+        flex-grow: 1;
+        flex-shrink: 1; }
+    html.theme--documenter-dark .hero.is-halfheight {
+      min-height: 50vh; }
+    html.theme--documenter-dark .hero.is-fullheight {
+      min-height: 100vh; }
+  html.theme--documenter-dark .hero-video {
+    overflow: hidden; }
+    html.theme--documenter-dark .hero-video video {
+      left: 50%;
+      min-height: 100%;
+      min-width: 100%;
+      position: absolute;
+      top: 50%;
+      transform: translate3d(-50%, -50%, 0); }
+    html.theme--documenter-dark .hero-video.is-transparent {
+      opacity: 0.3; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .hero-video {
+        display: none; } }
+  html.theme--documenter-dark .hero-buttons {
+    margin-top: 1.5rem; }
+    @media screen and (max-width: 768px) {
+      html.theme--documenter-dark .hero-buttons .button {
+        display: flex; }
+        html.theme--documenter-dark .hero-buttons .button:not(:last-child) {
+          margin-bottom: 0.75rem; } }
+    @media screen and (min-width: 769px), print {
+      html.theme--documenter-dark .hero-buttons {
+        display: flex;
+        justify-content: center; }
+        html.theme--documenter-dark .hero-buttons .button:not(:last-child) {
+          margin-right: 1.5rem; } }
+  html.theme--documenter-dark .hero-head,
+  html.theme--documenter-dark .hero-foot {
+    flex-grow: 0;
+    flex-shrink: 0; }
+  html.theme--documenter-dark .hero-body {
+    flex-grow: 1;
+    flex-shrink: 0;
+    padding: 3rem 1.5rem; }
+  html.theme--documenter-dark .section {
+    padding: 3rem 1.5rem; }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark .section.is-medium {
+        padding: 9rem 1.5rem; }
+      html.theme--documenter-dark .section.is-large {
+        padding: 18rem 1.5rem; } }
+  html.theme--documenter-dark .footer {
+    background-color: #282f2f;
+    padding: 3rem 1.5rem 6rem; }
+  html.theme--documenter-dark hr {
+    height: 1px; }
+  html.theme--documenter-dark h6 {
+    text-transform: uppercase;
+    letter-spacing: 0.5px; }
+  html.theme--documenter-dark .hero {
+    background-color: #343c3d; }
+  html.theme--documenter-dark a {
+    transition: all 200ms ease; }
+  html.theme--documenter-dark .button {
+    transition: all 200ms ease;
+    border-width: 1px;
+    color: white; }
+    html.theme--documenter-dark .button.is-active, html.theme--documenter-dark .button.is-focused, html.theme--documenter-dark .button:active, html.theme--documenter-dark .button:focus {
+      box-shadow: 0 0 0 2px rgba(140, 155, 157, 0.5); }
+    html.theme--documenter-dark .button.is-white.is-hovered, html.theme--documenter-dark .button.is-white:hover {
+      background-color: white; }
+    html.theme--documenter-dark .button.is-white.is-active, html.theme--documenter-dark .button.is-white.is-focused, html.theme--documenter-dark .button.is-white:active, html.theme--documenter-dark .button.is-white:focus {
+      border-color: white;
+      box-shadow: 0 0 0 2px rgba(255, 255, 255, 0.5); }
+    html.theme--documenter-dark .button.is-black.is-hovered, html.theme--documenter-dark .button.is-black:hover {
+      background-color: #1d1d1d; }
+    html.theme--documenter-dark .button.is-black.is-active, html.theme--documenter-dark .button.is-black.is-focused, html.theme--documenter-dark .button.is-black:active, html.theme--documenter-dark .button.is-black:focus {
+      border-color: #0a0a0a;
+      box-shadow: 0 0 0 2px rgba(10, 10, 10, 0.5); }
+    html.theme--documenter-dark .button.is-light.is-hovered, html.theme--documenter-dark .button.is-light:hover {
+      background-color: white; }
+    html.theme--documenter-dark .button.is-light.is-active, html.theme--documenter-dark .button.is-light.is-focused, html.theme--documenter-dark .button.is-light:active, html.theme--documenter-dark .button.is-light:focus {
+      border-color: #ecf0f1;
+      box-shadow: 0 0 0 2px rgba(236, 240, 241, 0.5); }
+    html.theme--documenter-dark .button.is-dark.is-hovered, html.theme--documenter-dark .content kbd.button.is-hovered, html.theme--documenter-dark .button.is-dark:hover, html.theme--documenter-dark .content kbd.button:hover {
+      background-color: #3a4344; }
+    html.theme--documenter-dark .button.is-dark.is-active, html.theme--documenter-dark .content kbd.button.is-active, html.theme--documenter-dark .button.is-dark.is-focused, html.theme--documenter-dark .content kbd.button.is-focused, html.theme--documenter-dark .button.is-dark:active, html.theme--documenter-dark .content kbd.button:active, html.theme--documenter-dark .button.is-dark:focus, html.theme--documenter-dark .content kbd.button:focus {
+      border-color: #282f2f;
+      box-shadow: 0 0 0 2px rgba(40, 47, 47, 0.5); }
+    html.theme--documenter-dark .button.is-primary.is-hovered, html.theme--documenter-dark .docstring > section > a.button.is-hovered.docs-sourcelink, html.theme--documenter-dark .button.is-primary:hover, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:hover {
+      background-color: #436d9a; }
+    html.theme--documenter-dark .button.is-primary.is-active, html.theme--documenter-dark .docstring > section > a.button.is-active.docs-sourcelink, html.theme--documenter-dark .button.is-primary.is-focused, html.theme--documenter-dark .docstring > section > a.button.is-focused.docs-sourcelink, html.theme--documenter-dark .button.is-primary:active, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:active, html.theme--documenter-dark .button.is-primary:focus, html.theme--documenter-dark .docstring > section > a.button.docs-sourcelink:focus {
+      border-color: #375a7f;
+      box-shadow: 0 0 0 2px rgba(55, 90, 127, 0.5); }
+    html.theme--documenter-dark .button.is-link.is-hovered, html.theme--documenter-dark .button.is-link:hover {
+      background-color: #1fdeb8; }
+    html.theme--documenter-dark .button.is-link.is-active, html.theme--documenter-dark .button.is-link.is-focused, html.theme--documenter-dark .button.is-link:active, html.theme--documenter-dark .button.is-link:focus {
+      border-color: #1abc9c;
+      box-shadow: 0 0 0 2px rgba(26, 188, 156, 0.5); }
+    html.theme--documenter-dark .button.is-info.is-hovered, html.theme--documenter-dark .button.is-info:hover {
+      background-color: #0363a3; }
+    html.theme--documenter-dark .button.is-info.is-active, html.theme--documenter-dark .button.is-info.is-focused, html.theme--documenter-dark .button.is-info:active, html.theme--documenter-dark .button.is-info:focus {
+      border-color: #024c7d;
+      box-shadow: 0 0 0 2px rgba(2, 76, 125, 0.5); }
+    html.theme--documenter-dark .button.is-success.is-hovered, html.theme--documenter-dark .button.is-success:hover {
+      background-color: #00aa48; }
+    html.theme--documenter-dark .button.is-success.is-active, html.theme--documenter-dark .button.is-success.is-focused, html.theme--documenter-dark .button.is-success:active, html.theme--documenter-dark .button.is-success:focus {
+      border-color: #008438;
+      box-shadow: 0 0 0 2px rgba(0, 132, 56, 0.5); }
+    html.theme--documenter-dark .button.is-warning.is-hovered, html.theme--documenter-dark .button.is-warning:hover {
+      background-color: #d39e00; }
+    html.theme--documenter-dark .button.is-warning.is-active, html.theme--documenter-dark .button.is-warning.is-focused, html.theme--documenter-dark .button.is-warning:active, html.theme--documenter-dark .button.is-warning:focus {
+      border-color: #ad8100;
+      box-shadow: 0 0 0 2px rgba(173, 129, 0, 0.5); }
+    html.theme--documenter-dark .button.is-danger.is-hovered, html.theme--documenter-dark .button.is-danger:hover {
+      background-color: #c12110; }
+    html.theme--documenter-dark .button.is-danger.is-active, html.theme--documenter-dark .button.is-danger.is-focused, html.theme--documenter-dark .button.is-danger:active, html.theme--documenter-dark .button.is-danger:focus {
+      border-color: #9e1b0d;
+      box-shadow: 0 0 0 2px rgba(158, 27, 13, 0.5); }
+  html.theme--documenter-dark .label {
+    color: #dbdee0; }
+  html.theme--documenter-dark .button,
+  html.theme--documenter-dark .control.has-icons-left .icon,
+  html.theme--documenter-dark .control.has-icons-right .icon,
+  html.theme--documenter-dark .input,
+  html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,
+  html.theme--documenter-dark .pagination-ellipsis,
+  html.theme--documenter-dark .pagination-link,
+  html.theme--documenter-dark .pagination-next,
+  html.theme--documenter-dark .pagination-previous,
+  html.theme--documenter-dark .select,
+  html.theme--documenter-dark .select select,
+  html.theme--documenter-dark .textarea {
+    height: 2.5em; }
+  
+  html.theme--documenter-dark .input,
+  html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input,
+  html.theme--documenter-dark .textarea {
+    transition: all 200ms ease;
+    box-shadow: none;
+    border-width: 1px;
+    padding-left: 1em;
+    padding-right: 1em; }
+  html.theme--documenter-dark .select:after,
+  html.theme--documenter-dark .select select {
+    border-width: 1px; }
+  html.theme--documenter-dark .control.has-addons .button,
+  html.theme--documenter-dark .control.has-addons .input,
+  html.theme--documenter-dark .control.has-addons #documenter .docs-sidebar form.docs-search > input,
+  html.theme--documenter-dark #documenter .docs-sidebar .control.has-addons form.docs-search > input,
+  html.theme--documenter-dark .control.has-addons .select {
+    margin-right: -1px; }
+  html.theme--documenter-dark .notification {
+    background-color: #343c3d; }
+  html.theme--documenter-dark .card {
+    box-shadow: none;
+    border: 1px solid #343c3d;
+    background-color: #282f2f;
+    border-radius: 0.4em; }
+    html.theme--documenter-dark .card .card-image img {
+      border-radius: 0.4em 0.4em 0 0; }
+    html.theme--documenter-dark .card .card-header {
+      box-shadow: none;
+      background-color: rgba(18, 18, 18, 0.2);
+      border-radius: 0.4em 0.4em 0 0; }
+    html.theme--documenter-dark .card .card-footer {
+      background-color: rgba(18, 18, 18, 0.2); }
+    html.theme--documenter-dark .card .card-footer,
+    html.theme--documenter-dark .card .card-footer-item {
+      border-width: 1px;
+      border-color: #343c3d; }
+  html.theme--documenter-dark .notification.is-white a:not(.button) {
+    color: #0a0a0a;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-black a:not(.button) {
+    color: white;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-light a:not(.button) {
+    color: #282f2f;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-dark a:not(.button), html.theme--documenter-dark .content kbd.notification a:not(.button) {
+    color: #ecf0f1;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-primary a:not(.button), html.theme--documenter-dark .docstring > section > a.notification.docs-sourcelink a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-link a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-info a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-success a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-warning a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .notification.is-danger a:not(.button) {
+    color: #fff;
+    text-decoration: underline; }
+  html.theme--documenter-dark .tag, html.theme--documenter-dark .docstring > section > a.docs-sourcelink, html.theme--documenter-dark .content kbd {
+    border-radius: 0.4em; }
+  html.theme--documenter-dark .menu-list a {
+    transition: all 300ms ease; }
+  html.theme--documenter-dark .modal-card-body {
+    background-color: #282f2f; }
+  html.theme--documenter-dark .modal-card-foot,
+  html.theme--documenter-dark .modal-card-head {
+    border-color: #343c3d; }
+  html.theme--documenter-dark .message-header {
+    font-weight: 700;
+    background-color: #343c3d;
+    color: white; }
+  html.theme--documenter-dark .message-body {
+    border-width: 1px;
+    border-color: #343c3d; }
+  html.theme--documenter-dark .navbar {
+    border-radius: 0.4em; }
+    html.theme--documenter-dark .navbar.is-transparent {
+      background: none; }
+    html.theme--documenter-dark .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, html.theme--documenter-dark .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active {
+      background-color: #1abc9c; }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark .navbar .navbar-menu {
+        background-color: #375a7f;
+        border-radius: 0 0 0.4em 0.4em; } }
+  html.theme--documenter-dark .hero .navbar,
+  html.theme--documenter-dark body > .navbar {
+    border-radius: 0; }
+  html.theme--documenter-dark .pagination-link,
+  html.theme--documenter-dark .pagination-next,
+  html.theme--documenter-dark .pagination-previous {
+    border-width: 1px; }
+  html.theme--documenter-dark .panel-block,
+  html.theme--documenter-dark .panel-heading,
+  html.theme--documenter-dark .panel-tabs {
+    border-width: 1px; }
+    html.theme--documenter-dark .panel-block:first-child,
+    html.theme--documenter-dark .panel-heading:first-child,
+    html.theme--documenter-dark .panel-tabs:first-child {
+      border-top-width: 1px; }
+  html.theme--documenter-dark .panel-heading {
+    font-weight: 700; }
+  html.theme--documenter-dark .panel-tabs a {
+    border-width: 1px;
+    margin-bottom: -1px; }
+    html.theme--documenter-dark .panel-tabs a.is-active {
+      border-bottom-color: #17a689; }
+  html.theme--documenter-dark .panel-block:hover {
+    color: #1dd2af; }
+    html.theme--documenter-dark .panel-block:hover .panel-icon {
+      color: #1dd2af; }
+  html.theme--documenter-dark .panel-block.is-active .panel-icon {
+    color: #17a689; }
+  html.theme--documenter-dark .tabs a {
+    border-bottom-width: 1px;
+    margin-bottom: -1px; }
+  html.theme--documenter-dark .tabs ul {
+    border-bottom-width: 1px; }
+  html.theme--documenter-dark .tabs.is-boxed a {
+    border-width: 1px; }
+  html.theme--documenter-dark .tabs.is-boxed li.is-active a {
+    background-color: #1f2424; }
+  html.theme--documenter-dark .tabs.is-toggle li a {
+    border-width: 1px;
+    margin-bottom: 0; }
+  html.theme--documenter-dark .tabs.is-toggle li + li {
+    margin-left: -1px; }
+  html.theme--documenter-dark .hero.is-white .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-black .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-light .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-dark .navbar .navbar-dropdown .navbar-item:hover, html.theme--documenter-dark .content kbd.hero .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-primary .navbar .navbar-dropdown .navbar-item:hover, html.theme--documenter-dark .docstring > section > a.hero.docs-sourcelink .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-link .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-info .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-success .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-warning .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark .hero.is-danger .navbar .navbar-dropdown .navbar-item:hover {
+    background-color: transparent; }
+  html.theme--documenter-dark h1 .docs-heading-anchor, html.theme--documenter-dark h1 .docs-heading-anchor:hover, html.theme--documenter-dark h1 .docs-heading-anchor:visited, html.theme--documenter-dark h2 .docs-heading-anchor, html.theme--documenter-dark h2 .docs-heading-anchor:hover, html.theme--documenter-dark h2 .docs-heading-anchor:visited, html.theme--documenter-dark h3 .docs-heading-anchor, html.theme--documenter-dark h3 .docs-heading-anchor:hover, html.theme--documenter-dark h3 .docs-heading-anchor:visited, html.theme--documenter-dark h4 .docs-heading-anchor, html.theme--documenter-dark h4 .docs-heading-anchor:hover, html.theme--documenter-dark h4 .docs-heading-anchor:visited, html.theme--documenter-dark h5 .docs-heading-anchor, html.theme--documenter-dark h5 .docs-heading-anchor:hover, html.theme--documenter-dark h5 .docs-heading-anchor:visited, html.theme--documenter-dark h6 .docs-heading-anchor, html.theme--documenter-dark h6 .docs-heading-anchor:hover, html.theme--documenter-dark h6 .docs-heading-anchor:visited {
+    color: #f2f2f2; }
+  html.theme--documenter-dark h1 .docs-heading-anchor-permalink, html.theme--documenter-dark h2 .docs-heading-anchor-permalink, html.theme--documenter-dark h3 .docs-heading-anchor-permalink, html.theme--documenter-dark h4 .docs-heading-anchor-permalink, html.theme--documenter-dark h5 .docs-heading-anchor-permalink, html.theme--documenter-dark h6 .docs-heading-anchor-permalink {
+    visibility: hidden;
+    vertical-align: middle;
+    margin-left: 0.5em;
+    font-size: 0.7rem; }
+    html.theme--documenter-dark h1 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h2 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h3 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h4 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h5 .docs-heading-anchor-permalink::before, html.theme--documenter-dark h6 .docs-heading-anchor-permalink::before {
+      font-family: "Font Awesome 5 Free";
+      font-weight: 900;
+      content: "\f0c1"; }
+  html.theme--documenter-dark h1:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h2:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h3:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h4:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h5:hover .docs-heading-anchor-permalink, html.theme--documenter-dark h6:hover .docs-heading-anchor-permalink {
+    visibility: visible; }
+  html.theme--documenter-dark .docs-light-only {
+    display: none !important; }
+  html.theme--documenter-dark .admonition {
+    background-color: #282f2f;
+    border-style: solid;
+    border-width: 1px;
+    border-color: #5e6d6f;
+    border-radius: 0.4em;
+    font-size: 15px; }
+    html.theme--documenter-dark .admonition strong {
+      color: currentColor; }
+    html.theme--documenter-dark .admonition.is-small, html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input.admonition {
+      font-size: 0.85em; }
+    html.theme--documenter-dark .admonition.is-medium {
+      font-size: 1.25rem; }
+    html.theme--documenter-dark .admonition.is-large {
+      font-size: 1.5rem; }
+    html.theme--documenter-dark .admonition.is-default {
+      background-color: #282f2f;
+      border-color: #5e6d6f; }
+      html.theme--documenter-dark .admonition.is-default > .admonition-header {
+        background-color: #5e6d6f; }
+    html.theme--documenter-dark .admonition.is-info {
+      background-color: #282f2f;
+      border-color: #024c7d; }
+      html.theme--documenter-dark .admonition.is-info > .admonition-header {
+        background-color: #024c7d; }
+    html.theme--documenter-dark .admonition.is-success {
+      background-color: #282f2f;
+      border-color: #008438; }
+      html.theme--documenter-dark .admonition.is-success > .admonition-header {
+        background-color: #008438; }
+    html.theme--documenter-dark .admonition.is-warning {
+      background-color: #282f2f;
+      border-color: #ad8100; }
+      html.theme--documenter-dark .admonition.is-warning > .admonition-header {
+        background-color: #ad8100; }
+    html.theme--documenter-dark .admonition.is-danger {
+      background-color: #282f2f;
+      border-color: #9e1b0d; }
+      html.theme--documenter-dark .admonition.is-danger > .admonition-header {
+        background-color: #9e1b0d; }
+    html.theme--documenter-dark .admonition.is-compat {
+      background-color: #282f2f;
+      border-color: #137886; }
+      html.theme--documenter-dark .admonition.is-compat > .admonition-header {
+        background-color: #137886; }
+  html.theme--documenter-dark .admonition-header {
+    background-color: #5e6d6f;
+    align-items: center;
+    font-weight: 700;
+    justify-content: space-between;
+    line-height: 1.25;
+    padding: 0.75em;
+    position: relative; }
+    html.theme--documenter-dark .admonition-header:before {
+      font-family: "Font Awesome 5 Free";
+      font-weight: 900;
+      margin-right: 0.75em;
+      content: "\f06a"; }
+  html.theme--documenter-dark .admonition-body {
+    color: #fff;
+    padding: 1em 1.25em; }
+    html.theme--documenter-dark .admonition-body pre {
+      background-color: #282f2f; }
+    html.theme--documenter-dark .admonition-body code {
+      background-color: rgba(255, 255, 255, 0.05); }
+  html.theme--documenter-dark .docstring {
+    margin-bottom: 1em;
+    background-color: transparent;
+    border: 1px solid #5e6d6f;
+    box-shadow: none;
+    max-width: 100%; }
+    html.theme--documenter-dark .docstring > header {
+      display: flex;
+      flex-grow: 1;
+      align-items: stretch;
+      padding: 0.75rem;
+      background-color: #282f2f;
+      box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);
+      box-shadow: none;
+      border-bottom: 1px solid #5e6d6f; }
+      html.theme--documenter-dark .docstring > header code {
+        background-color: transparent; }
+      html.theme--documenter-dark .docstring > header .docstring-binding {
+        margin-right: 0.3em; }
+      html.theme--documenter-dark .docstring > header .docstring-category {
+        margin-left: 0.3em; }
+    html.theme--documenter-dark .docstring > section {
+      position: relative;
+      padding: 1rem 1.25rem;
+      border-bottom: 1px solid #5e6d6f; }
+      html.theme--documenter-dark .docstring > section:last-child {
+        border-bottom: none; }
+      html.theme--documenter-dark .docstring > section > a.docs-sourcelink {
+        transition: opacity 0.3s;
+        opacity: 0;
+        position: absolute;
+        right: 0.625rem;
+        bottom: 0.5rem; }
+    html.theme--documenter-dark .docstring:hover > section > a.docs-sourcelink {
+      opacity: 0.2; }
+    html.theme--documenter-dark .docstring > section:hover a.docs-sourcelink {
+      opacity: 1; }
+  html.theme--documenter-dark .content pre {
+    border: 1px solid #5e6d6f; }
+  html.theme--documenter-dark .content code {
+    font-weight: inherit; }
+  html.theme--documenter-dark .content a code {
+    color: #1abc9c; }
+  html.theme--documenter-dark .content h1 code, html.theme--documenter-dark .content h2 code, html.theme--documenter-dark .content h3 code, html.theme--documenter-dark .content h4 code, html.theme--documenter-dark .content h5 code, html.theme--documenter-dark .content h6 code {
+    color: #f2f2f2; }
+  html.theme--documenter-dark .content table {
+    display: block;
+    width: initial;
+    max-width: 100%;
+    overflow-x: auto; }
+  html.theme--documenter-dark .content blockquote > ul:first-child, html.theme--documenter-dark .content blockquote > ol:first-child, html.theme--documenter-dark .content .admonition-body > ul:first-child, html.theme--documenter-dark .content .admonition-body > ol:first-child {
+    margin-top: 0; }
+  html.theme--documenter-dark .breadcrumb a.is-disabled {
+    cursor: default;
+    pointer-events: none; }
+    html.theme--documenter-dark .breadcrumb a.is-disabled, html.theme--documenter-dark .breadcrumb a.is-disabled:hover {
+      color: #f2f2f2; }
+  html.theme--documenter-dark .hljs {
+    background: initial !important;
+    padding: initial !important; }
+  html.theme--documenter-dark .katex .katex-mathml {
+    top: 0;
+    right: 0; }
+  html.theme--documenter-dark html {
+    -moz-osx-font-smoothing: auto;
+    -webkit-font-smoothing: auto; }
+  html.theme--documenter-dark #documenter .docs-main > article {
+    overflow-wrap: break-word; }
+  @media screen and (min-width: 1056px) {
+    html.theme--documenter-dark #documenter .docs-main {
+      max-width: 52rem;
+      margin-left: 20rem;
+      padding-right: 1rem; } }
+  @media screen and (max-width: 1055px) {
+    html.theme--documenter-dark #documenter .docs-main {
+      width: 100%; }
+      html.theme--documenter-dark #documenter .docs-main > article {
+        max-width: 52rem;
+        margin-left: auto;
+        margin-right: auto;
+        margin-bottom: 1rem;
+        padding: 0 1rem; }
+      html.theme--documenter-dark #documenter .docs-main > header, html.theme--documenter-dark #documenter .docs-main > nav {
+        max-width: 100%;
+        width: 100%;
+        margin: 0; } }
+  html.theme--documenter-dark #documenter .docs-main header.docs-navbar {
+    background-color: #1f2424;
+    border-bottom: 1px solid #5e6d6f;
+    z-index: 2;
+    min-height: 4rem;
+    margin-bottom: 1rem;
+    display: flex; }
+    html.theme--documenter-dark #documenter .docs-main header.docs-navbar .breadcrumb {
+      flex-grow: 1; }
+    html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right {
+      display: flex;
+      white-space: nowrap; }
+      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-icon, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label, html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button {
+        display: inline-block; }
+      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-label {
+        padding: 0;
+        margin-left: 0.3em; }
+      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-settings-button {
+        margin: auto 0 auto 1rem; }
+      html.theme--documenter-dark #documenter .docs-main header.docs-navbar .docs-right .docs-sidebar-button {
+        font-size: 1.5rem;
+        margin: auto 0 auto 1rem; }
+    html.theme--documenter-dark #documenter .docs-main header.docs-navbar > * {
+      margin: auto 0; }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark #documenter .docs-main header.docs-navbar {
+        position: sticky;
+        top: 0;
+        padding: 0 1rem;
+        /* For Headroom.js */
+        transition-property: top, box-shadow;
+        -webkit-transition-property: top, box-shadow;
+        /* Safari */
+        transition-duration: 0.3s;
+        -webkit-transition-duration: 0.3s;
+        /* Safari */ }
+        html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--not-top {
+          box-shadow: 0.2rem 0rem 0.4rem #171717;
+          transition-duration: 0.7s;
+          -webkit-transition-duration: 0.7s;
+          /* Safari */ }
+        html.theme--documenter-dark #documenter .docs-main header.docs-navbar.headroom--unpinned.headroom--not-top.headroom--not-bottom {
+          top: -4.5rem;
+          transition-duration: 0.7s;
+          -webkit-transition-duration: 0.7s;
+          /* Safari */ } }
+  html.theme--documenter-dark #documenter .docs-main section.footnotes {
+    border-top: 1px solid #5e6d6f; }
+    html.theme--documenter-dark #documenter .docs-main section.footnotes li .tag:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .docstring > section > a.docs-sourcelink:first-child, html.theme--documenter-dark #documenter .docs-main section.footnotes li .content kbd:first-child, html.theme--documenter-dark .content #documenter .docs-main section.footnotes li kbd:first-child {
+      margin-right: 1em;
+      margin-bottom: 0.4em; }
+  html.theme--documenter-dark #documenter .docs-main .docs-footer {
+    display: flex;
+    margin-left: 0;
+    margin-right: 0;
+    border-top: 1px solid #5e6d6f;
+    padding-top: 1rem;
+    padding-bottom: 1rem; }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark #documenter .docs-main .docs-footer {
+        padding-left: 1rem;
+        padding-right: 1rem; } }
+    html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage, html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-prevpage {
+      flex-grow: 1; }
+    html.theme--documenter-dark #documenter .docs-main .docs-footer .docs-footer-nextpage {
+      text-align: right; }
+  html.theme--documenter-dark #documenter .docs-sidebar {
+    display: flex;
+    flex-direction: column;
+    color: #fff;
+    background-color: #282f2f;
+    border-right: 1px solid #5e6d6f;
+    padding: 0;
+    flex: 0 0 18rem;
+    z-index: 5;
+    font-size: 15px;
+    position: fixed;
+    left: -18rem;
+    width: 18rem;
+    height: 100%;
+    transition: left 0.3s;
+    /* Setting up a nicer theme style for the scrollbar */ }
+    html.theme--documenter-dark #documenter .docs-sidebar.visible {
+      left: 0;
+      box-shadow: 0.4rem 0rem 0.8rem #171717; }
+      @media screen and (min-width: 1056px) {
+        html.theme--documenter-dark #documenter .docs-sidebar.visible {
+          box-shadow: none; } }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark #documenter .docs-sidebar {
+        left: 0;
+        top: 0; } }
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-logo {
+      margin-top: 1rem;
+      padding: 0 1rem; }
+      html.theme--documenter-dark #documenter .docs-sidebar .docs-logo > img {
+        max-height: 6rem;
+        margin: auto; }
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name {
+      flex-shrink: 0;
+      font-size: 1.5rem;
+      font-weight: 700;
+      text-align: center;
+      white-space: nowrap;
+      overflow: hidden;
+      padding: 0.5rem 0; }
+      html.theme--documenter-dark #documenter .docs-sidebar .docs-package-name .docs-autofit {
+        max-width: 16.2rem; }
+    html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector {
+      border-top: 1px solid #5e6d6f;
+      display: none;
+      padding: 0.5rem; }
+      html.theme--documenter-dark #documenter .docs-sidebar .docs-version-selector.visible {
+        display: flex; }
+    html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu {
+      flex-grow: 1;
+      user-select: none;
+      border-top: 1px solid #5e6d6f;
+      padding-bottom: 1.5rem;
+      /* Managing collapsible submenus */ }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li > .tocitem {
+        font-weight: bold; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li li {
+        font-size: 14.25px;
+        margin-left: 1em;
+        border-left: 1px solid #5e6d6f; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input.collapse-toggle {
+        display: none; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.collapsed {
+        display: none; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ ul.collapsed {
+        display: block; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem {
+        display: flex; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-label {
+          flex-grow: 2; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron {
+          display: inline-block;
+          font-style: normal;
+          font-variant: normal;
+          text-rendering: auto;
+          line-height: 1;
+          font-size: 11.25px;
+          margin-left: 1rem;
+          margin-top: auto;
+          margin-bottom: auto; }
+          html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem .docs-chevron::before {
+            font-family: "Font Awesome 5 Free";
+            font-weight: 900;
+            content: "\f054"; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu input:checked ~ label.tocitem .docs-chevron::before {
+        content: "\f078"; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem {
+        display: block;
+        padding: 0.5rem 0.5rem; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu .tocitem:hover {
+          color: #fff;
+          background: #282f2f; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu a.tocitem:hover, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu label.tocitem:hover {
+        color: #fff;
+        background-color: #32393a; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active {
+        border-top: 1px solid #5e6d6f;
+        border-bottom: 1px solid #5e6d6f;
+        background-color: #1f2424; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem, html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active .tocitem:hover {
+          background-color: #1f2424;
+          color: #fff; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu li.is-active ul.internal .tocitem:hover {
+          background-color: #32393a;
+          color: #fff; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu > li.is-active:first-child {
+        border-top: none; }
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal {
+        margin: 0 0.5rem 0.5rem;
+        border-top: 1px solid #5e6d6f; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal li {
+          font-size: 12.75px;
+          border-left: none;
+          margin-left: 0;
+          margin-top: 0.5rem; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem {
+          width: 100%;
+          padding: 0; }
+          html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu ul.internal .tocitem::before {
+            content: "⚬";
+            margin-right: 0.4em; }
+    html.theme--documenter-dark #documenter .docs-sidebar form.docs-search {
+      margin: auto;
+      margin-top: 0.5rem;
+      margin-bottom: 0.5rem; }
+      html.theme--documenter-dark #documenter .docs-sidebar form.docs-search > input {
+        width: 14.4rem; }
+    @media screen and (min-width: 1056px) {
+      html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu {
+        overflow-y: auto;
+        -webkit-overflow-scroll: touch; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar {
+          width: .3rem;
+          background: none; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb {
+          border-radius: 5px 0px 0px 5px;
+          background: #3b4445; }
+        html.theme--documenter-dark #documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover {
+          background: #4e5a5c; } }
+    @media screen and (max-width: 1055px) {
+      html.theme--documenter-dark #documenter .docs-sidebar {
+        overflow-y: auto;
+        -webkit-overflow-scroll: touch; }
+        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar {
+          width: .3rem;
+          background: none; }
+        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb {
+          border-radius: 5px 0px 0px 5px;
+          background: #3b4445; }
+        html.theme--documenter-dark #documenter .docs-sidebar::-webkit-scrollbar-thumb:hover {
+          background: #4e5a5c; } }
+  html.theme--documenter-dark #documenter .docs-main #documenter-search-info {
+    margin-bottom: 1rem; }
+  html.theme--documenter-dark #documenter .docs-main #documenter-search-results {
+    list-style-type: circle;
+    list-style-position: outside; }
+    html.theme--documenter-dark #documenter .docs-main #documenter-search-results li {
+      margin-left: 2rem; }
+    html.theme--documenter-dark #documenter .docs-main #documenter-search-results .docs-highlight {
+      background-color: yellow; }
+  html.theme--documenter-dark {
+    background-color: #1f2424;
+    font-size: 16px;
+    min-width: 300px;
+    overflow-x: auto;
+    overflow-y: scroll;
+    text-rendering: optimizeLegibility;
+    text-size-adjust: 100%; }
+  html.theme--documenter-dark .hljs-comment,
+  html.theme--documenter-dark .hljs-quote {
+    color: #d4d0ab; }
+  html.theme--documenter-dark .hljs-variable,
+  html.theme--documenter-dark .hljs-template-variable,
+  html.theme--documenter-dark .hljs-tag,
+  html.theme--documenter-dark .hljs-name,
+  html.theme--documenter-dark .hljs-selector-id,
+  html.theme--documenter-dark .hljs-selector-class,
+  html.theme--documenter-dark .hljs-regexp,
+  html.theme--documenter-dark .hljs-deletion {
+    color: #ffa07a; }
+  html.theme--documenter-dark .hljs-number,
+  html.theme--documenter-dark .hljs-built_in,
+  html.theme--documenter-dark .hljs-builtin-name,
+  html.theme--documenter-dark .hljs-literal,
+  html.theme--documenter-dark .hljs-type,
+  html.theme--documenter-dark .hljs-params,
+  html.theme--documenter-dark .hljs-meta,
+  html.theme--documenter-dark .hljs-link {
+    color: #f5ab35; }
+  html.theme--documenter-dark .hljs-attribute {
+    color: #ffd700; }
+  html.theme--documenter-dark .hljs-string,
+  html.theme--documenter-dark .hljs-symbol,
+  html.theme--documenter-dark .hljs-bullet,
+  html.theme--documenter-dark .hljs-addition {
+    color: #abe338; }
+  html.theme--documenter-dark .hljs-title,
+  html.theme--documenter-dark .hljs-section {
+    color: #00e0e0; }
+  html.theme--documenter-dark .hljs-keyword,
+  html.theme--documenter-dark .hljs-selector-tag {
+    color: #dcc6e0; }
+  html.theme--documenter-dark .hljs {
+    display: block;
+    overflow-x: auto;
+    background: #2b2b2b;
+    color: #f8f8f2;
+    padding: 0.5em; }
+  html.theme--documenter-dark .hljs-emphasis {
+    font-style: italic; }
+  html.theme--documenter-dark .hljs-strong {
+    font-weight: bold; }
+  @media screen and (-ms-high-contrast: active) {
+    html.theme--documenter-dark .hljs-addition,
+    html.theme--documenter-dark .hljs-attribute,
+    html.theme--documenter-dark .hljs-built_in,
+    html.theme--documenter-dark .hljs-builtin-name,
+    html.theme--documenter-dark .hljs-bullet,
+    html.theme--documenter-dark .hljs-comment,
+    html.theme--documenter-dark .hljs-link,
+    html.theme--documenter-dark .hljs-literal,
+    html.theme--documenter-dark .hljs-meta,
+    html.theme--documenter-dark .hljs-number,
+    html.theme--documenter-dark .hljs-params,
+    html.theme--documenter-dark .hljs-string,
+    html.theme--documenter-dark .hljs-symbol,
+    html.theme--documenter-dark .hljs-type,
+    html.theme--documenter-dark .hljs-quote {
+      color: highlight; }
+    html.theme--documenter-dark .hljs-keyword,
+    html.theme--documenter-dark .hljs-selector-tag {
+      font-weight: bold; } }
+  html.theme--documenter-dark .hljs-subst {
+    color: #f8f8f2; }
diff --git a/v0.15.15/assets/themes/documenter-light.css b/v0.15.15/assets/themes/documenter-light.css
new file mode 100644
index 00000000..bfb4e9db
--- /dev/null
+++ b/v0.15.15/assets/themes/documenter-light.css
@@ -0,0 +1,7614 @@
+@charset "UTF-8";
+/* Font Awesome 5 mixin. Can be included in any rule that should render Font Awesome icons. */
+@keyframes spinAround {
+  from {
+    transform: rotate(0deg); }
+  to {
+    transform: rotate(359deg); } }
+
+.delete, .modal-close, .is-unselectable, .button, .file, .breadcrumb, .pagination-previous,
+.pagination-next,
+.pagination-link,
+.pagination-ellipsis, .tabs {
+  -webkit-touch-callout: none;
+  -webkit-user-select: none;
+  -moz-user-select: none;
+  -ms-user-select: none;
+  user-select: none; }
+
+.select:not(.is-multiple):not(.is-loading)::after, .navbar-link:not(.is-arrowless)::after {
+  border: 3px solid transparent;
+  border-radius: 2px;
+  border-right: 0;
+  border-top: 0;
+  content: " ";
+  display: block;
+  height: 0.625em;
+  margin-top: -0.4375em;
+  pointer-events: none;
+  position: absolute;
+  top: 50%;
+  transform: rotate(-45deg);
+  transform-origin: center;
+  width: 0.625em; }
+
+.box:not(:last-child), .content:not(:last-child), .notification:not(:last-child), .progress:not(:last-child), .table:not(:last-child), .table-container:not(:last-child), .title:not(:last-child),
+.subtitle:not(:last-child), .block:not(:last-child), .highlight:not(:last-child), .breadcrumb:not(:last-child), .level:not(:last-child), .list:not(:last-child), .message:not(:last-child), .tabs:not(:last-child), .admonition:not(:last-child) {
+  margin-bottom: 1.5rem; }
+
+.delete, .modal-close {
+  -moz-appearance: none;
+  -webkit-appearance: none;
+  background-color: rgba(10, 10, 10, 0.2);
+  border: none;
+  border-radius: 290486px;
+  cursor: pointer;
+  pointer-events: auto;
+  display: inline-block;
+  flex-grow: 0;
+  flex-shrink: 0;
+  font-size: 0;
+  height: 20px;
+  max-height: 20px;
+  max-width: 20px;
+  min-height: 20px;
+  min-width: 20px;
+  outline: none;
+  position: relative;
+  vertical-align: top;
+  width: 20px; }
+  .delete::before, .modal-close::before, .delete::after, .modal-close::after {
+    background-color: white;
+    content: "";
+    display: block;
+    left: 50%;
+    position: absolute;
+    top: 50%;
+    transform: translateX(-50%) translateY(-50%) rotate(45deg);
+    transform-origin: center center; }
+  .delete::before, .modal-close::before {
+    height: 2px;
+    width: 50%; }
+  .delete::after, .modal-close::after {
+    height: 50%;
+    width: 2px; }
+  .delete:hover, .modal-close:hover, .delete:focus, .modal-close:focus {
+    background-color: rgba(10, 10, 10, 0.3); }
+  .delete:active, .modal-close:active {
+    background-color: rgba(10, 10, 10, 0.4); }
+  .is-small.delete, #documenter .docs-sidebar form.docs-search > input.delete, .is-small.modal-close, #documenter .docs-sidebar form.docs-search > input.modal-close {
+    height: 16px;
+    max-height: 16px;
+    max-width: 16px;
+    min-height: 16px;
+    min-width: 16px;
+    width: 16px; }
+  .is-medium.delete, .is-medium.modal-close {
+    height: 24px;
+    max-height: 24px;
+    max-width: 24px;
+    min-height: 24px;
+    min-width: 24px;
+    width: 24px; }
+  .is-large.delete, .is-large.modal-close {
+    height: 32px;
+    max-height: 32px;
+    max-width: 32px;
+    min-height: 32px;
+    min-width: 32px;
+    width: 32px; }
+
+.button.is-loading::after, .loader, .select.is-loading::after, .control.is-loading::after {
+  animation: spinAround 500ms infinite linear;
+  border: 2px solid #dbdbdb;
+  border-radius: 290486px;
+  border-right-color: transparent;
+  border-top-color: transparent;
+  content: "";
+  display: block;
+  height: 1em;
+  position: relative;
+  width: 1em; }
+
+.is-overlay, .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img,
+.image.is-square .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img,
+.image.is-1by1 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img,
+.image.is-5by4 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img,
+.image.is-4by3 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img,
+.image.is-3by2 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img,
+.image.is-5by3 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img,
+.image.is-16by9 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img,
+.image.is-2by1 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img,
+.image.is-3by1 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img,
+.image.is-4by5 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img,
+.image.is-3by4 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img,
+.image.is-2by3 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img,
+.image.is-3by5 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img,
+.image.is-9by16 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img,
+.image.is-1by2 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img,
+.image.is-1by3 .has-ratio,
+#documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio, .modal, .modal-background, .hero-video {
+  bottom: 0;
+  left: 0;
+  position: absolute;
+  right: 0;
+  top: 0; }
+
+.button, .input, #documenter .docs-sidebar form.docs-search > input, .textarea, .select select, .file-cta,
+.file-name, .pagination-previous,
+.pagination-next,
+.pagination-link,
+.pagination-ellipsis {
+  -moz-appearance: none;
+  -webkit-appearance: none;
+  align-items: center;
+  border: 1px solid transparent;
+  border-radius: 4px;
+  box-shadow: none;
+  display: inline-flex;
+  font-size: 1rem;
+  height: 2.25em;
+  justify-content: flex-start;
+  line-height: 1.5;
+  padding-bottom: calc(0.375em - 1px);
+  padding-left: calc(0.625em - 1px);
+  padding-right: calc(0.625em - 1px);
+  padding-top: calc(0.375em - 1px);
+  position: relative;
+  vertical-align: top; }
+  .button:focus, .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .textarea:focus, .select select:focus, .file-cta:focus,
+  .file-name:focus, .pagination-previous:focus,
+  .pagination-next:focus,
+  .pagination-link:focus,
+  .pagination-ellipsis:focus, .is-focused.button, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.textarea, .select select.is-focused, .is-focused.file-cta,
+  .is-focused.file-name, .is-focused.pagination-previous,
+  .is-focused.pagination-next,
+  .is-focused.pagination-link,
+  .is-focused.pagination-ellipsis, .button:active, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .textarea:active, .select select:active, .file-cta:active,
+  .file-name:active, .pagination-previous:active,
+  .pagination-next:active,
+  .pagination-link:active,
+  .pagination-ellipsis:active, .is-active.button, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.textarea, .select select.is-active, .is-active.file-cta,
+  .is-active.file-name, .is-active.pagination-previous,
+  .is-active.pagination-next,
+  .is-active.pagination-link,
+  .is-active.pagination-ellipsis {
+    outline: none; }
+  .button[disabled], .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .textarea[disabled], .select select[disabled], .file-cta[disabled],
+  .file-name[disabled], .pagination-previous[disabled],
+  .pagination-next[disabled],
+  .pagination-link[disabled],
+  .pagination-ellipsis[disabled],
+  fieldset[disabled] .button,
+  fieldset[disabled] .input,
+  fieldset[disabled] #documenter .docs-sidebar form.docs-search > input,
+  #documenter .docs-sidebar fieldset[disabled] form.docs-search > input,
+  fieldset[disabled] .textarea,
+  fieldset[disabled] .select select,
+  .select fieldset[disabled] select,
+  fieldset[disabled] .file-cta,
+  fieldset[disabled] .file-name,
+  fieldset[disabled] .pagination-previous,
+  fieldset[disabled] .pagination-next,
+  fieldset[disabled] .pagination-link,
+  fieldset[disabled] .pagination-ellipsis {
+    cursor: not-allowed; }
+
+/*! minireset.css v0.0.4 | MIT License | github.com/jgthms/minireset.css */
+html,
+body,
+p,
+ol,
+ul,
+li,
+dl,
+dt,
+dd,
+blockquote,
+figure,
+fieldset,
+legend,
+textarea,
+pre,
+iframe,
+hr,
+h1,
+h2,
+h3,
+h4,
+h5,
+h6 {
+  margin: 0;
+  padding: 0; }
+
+h1,
+h2,
+h3,
+h4,
+h5,
+h6 {
+  font-size: 100%;
+  font-weight: normal; }
+
+ul {
+  list-style: none; }
+
+button,
+input,
+select,
+textarea {
+  margin: 0; }
+
+html {
+  box-sizing: border-box; }
+
+*, *::before, *::after {
+  box-sizing: inherit; }
+
+img,
+embed,
+iframe,
+object,
+video {
+  height: auto;
+  max-width: 100%; }
+
+audio {
+  max-width: 100%; }
+
+iframe {
+  border: 0; }
+
+table {
+  border-collapse: collapse;
+  border-spacing: 0; }
+
+td,
+th {
+  padding: 0; }
+  td:not([align]),
+  th:not([align]) {
+    text-align: left; }
+
+html {
+  background-color: white;
+  font-size: 16px;
+  -moz-osx-font-smoothing: grayscale;
+  -webkit-font-smoothing: antialiased;
+  min-width: 300px;
+  overflow-x: auto;
+  overflow-y: scroll;
+  text-rendering: optimizeLegibility;
+  text-size-adjust: 100%; }
+
+article,
+aside,
+figure,
+footer,
+header,
+hgroup,
+section {
+  display: block; }
+
+body,
+button,
+input,
+select,
+textarea {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif; }
+
+code,
+pre {
+  -moz-osx-font-smoothing: auto;
+  -webkit-font-smoothing: auto;
+  font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace; }
+
+body {
+  color: #222222;
+  font-size: 1em;
+  font-weight: 400;
+  line-height: 1.5; }
+
+a {
+  color: #2e63b8;
+  cursor: pointer;
+  text-decoration: none; }
+  a strong {
+    color: currentColor; }
+  a:hover {
+    color: #363636; }
+
+code {
+  background-color: rgba(0, 0, 0, 0.05);
+  color: #000000;
+  font-size: 0.875em;
+  font-weight: normal;
+  padding: 0.1em; }
+
+hr {
+  background-color: whitesmoke;
+  border: none;
+  display: block;
+  height: 2px;
+  margin: 1.5rem 0; }
+
+img {
+  height: auto;
+  max-width: 100%; }
+
+input[type="checkbox"],
+input[type="radio"] {
+  vertical-align: baseline; }
+
+small {
+  font-size: 0.875em; }
+
+span {
+  font-style: inherit;
+  font-weight: inherit; }
+
+strong {
+  color: #222222;
+  font-weight: 700; }
+
+fieldset {
+  border: none; }
+
+pre {
+  -webkit-overflow-scrolling: touch;
+  background-color: whitesmoke;
+  color: #222222;
+  font-size: 0.875em;
+  overflow-x: auto;
+  padding: 1.25rem 1.5rem;
+  white-space: pre;
+  word-wrap: normal; }
+  pre code {
+    background-color: transparent;
+    color: currentColor;
+    font-size: 1em;
+    padding: 0; }
+
+table td,
+table th {
+  vertical-align: top; }
+  table td:not([align]),
+  table th:not([align]) {
+    text-align: left; }
+
+table th {
+  color: #222222; }
+
+.is-clearfix::after {
+  clear: both;
+  content: " ";
+  display: table; }
+
+.is-pulled-left {
+  float: left !important; }
+
+.is-pulled-right {
+  float: right !important; }
+
+.is-clipped {
+  overflow: hidden !important; }
+
+.is-size-1 {
+  font-size: 3rem !important; }
+
+.is-size-2 {
+  font-size: 2.5rem !important; }
+
+.is-size-3 {
+  font-size: 2rem !important; }
+
+.is-size-4 {
+  font-size: 1.5rem !important; }
+
+.is-size-5 {
+  font-size: 1.25rem !important; }
+
+.is-size-6 {
+  font-size: 1rem !important; }
+
+.is-size-7, .docstring > section > a.docs-sourcelink {
+  font-size: 0.75rem !important; }
+
+@media screen and (max-width: 768px) {
+  .is-size-1-mobile {
+    font-size: 3rem !important; }
+  .is-size-2-mobile {
+    font-size: 2.5rem !important; }
+  .is-size-3-mobile {
+    font-size: 2rem !important; }
+  .is-size-4-mobile {
+    font-size: 1.5rem !important; }
+  .is-size-5-mobile {
+    font-size: 1.25rem !important; }
+  .is-size-6-mobile {
+    font-size: 1rem !important; }
+  .is-size-7-mobile {
+    font-size: 0.75rem !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-size-1-tablet {
+    font-size: 3rem !important; }
+  .is-size-2-tablet {
+    font-size: 2.5rem !important; }
+  .is-size-3-tablet {
+    font-size: 2rem !important; }
+  .is-size-4-tablet {
+    font-size: 1.5rem !important; }
+  .is-size-5-tablet {
+    font-size: 1.25rem !important; }
+  .is-size-6-tablet {
+    font-size: 1rem !important; }
+  .is-size-7-tablet {
+    font-size: 0.75rem !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-size-1-touch {
+    font-size: 3rem !important; }
+  .is-size-2-touch {
+    font-size: 2.5rem !important; }
+  .is-size-3-touch {
+    font-size: 2rem !important; }
+  .is-size-4-touch {
+    font-size: 1.5rem !important; }
+  .is-size-5-touch {
+    font-size: 1.25rem !important; }
+  .is-size-6-touch {
+    font-size: 1rem !important; }
+  .is-size-7-touch {
+    font-size: 0.75rem !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-size-1-desktop {
+    font-size: 3rem !important; }
+  .is-size-2-desktop {
+    font-size: 2.5rem !important; }
+  .is-size-3-desktop {
+    font-size: 2rem !important; }
+  .is-size-4-desktop {
+    font-size: 1.5rem !important; }
+  .is-size-5-desktop {
+    font-size: 1.25rem !important; }
+  .is-size-6-desktop {
+    font-size: 1rem !important; }
+  .is-size-7-desktop {
+    font-size: 0.75rem !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-size-1-widescreen {
+    font-size: 3rem !important; }
+  .is-size-2-widescreen {
+    font-size: 2.5rem !important; }
+  .is-size-3-widescreen {
+    font-size: 2rem !important; }
+  .is-size-4-widescreen {
+    font-size: 1.5rem !important; }
+  .is-size-5-widescreen {
+    font-size: 1.25rem !important; }
+  .is-size-6-widescreen {
+    font-size: 1rem !important; }
+  .is-size-7-widescreen {
+    font-size: 0.75rem !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-size-1-fullhd {
+    font-size: 3rem !important; }
+  .is-size-2-fullhd {
+    font-size: 2.5rem !important; }
+  .is-size-3-fullhd {
+    font-size: 2rem !important; }
+  .is-size-4-fullhd {
+    font-size: 1.5rem !important; }
+  .is-size-5-fullhd {
+    font-size: 1.25rem !important; }
+  .is-size-6-fullhd {
+    font-size: 1rem !important; }
+  .is-size-7-fullhd {
+    font-size: 0.75rem !important; } }
+
+.has-text-centered {
+  text-align: center !important; }
+
+.has-text-justified {
+  text-align: justify !important; }
+
+.has-text-left {
+  text-align: left !important; }
+
+.has-text-right {
+  text-align: right !important; }
+
+@media screen and (max-width: 768px) {
+  .has-text-centered-mobile {
+    text-align: center !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-centered-tablet {
+    text-align: center !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-centered-tablet-only {
+    text-align: center !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-centered-touch {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-centered-desktop {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-centered-desktop-only {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-centered-widescreen {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-centered-widescreen-only {
+    text-align: center !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-centered-fullhd {
+    text-align: center !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-justified-mobile {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-justified-tablet {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-justified-tablet-only {
+    text-align: justify !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-justified-touch {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-justified-desktop {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-justified-desktop-only {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-justified-widescreen {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-justified-widescreen-only {
+    text-align: justify !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-justified-fullhd {
+    text-align: justify !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-left-mobile {
+    text-align: left !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-left-tablet {
+    text-align: left !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-left-tablet-only {
+    text-align: left !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-left-touch {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-left-desktop {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-left-desktop-only {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-left-widescreen {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-left-widescreen-only {
+    text-align: left !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-left-fullhd {
+    text-align: left !important; } }
+
+@media screen and (max-width: 768px) {
+  .has-text-right-mobile {
+    text-align: right !important; } }
+
+@media screen and (min-width: 769px), print {
+  .has-text-right-tablet {
+    text-align: right !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .has-text-right-tablet-only {
+    text-align: right !important; } }
+
+@media screen and (max-width: 1055px) {
+  .has-text-right-touch {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1056px) {
+  .has-text-right-desktop {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .has-text-right-desktop-only {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1216px) {
+  .has-text-right-widescreen {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .has-text-right-widescreen-only {
+    text-align: right !important; } }
+
+@media screen and (min-width: 1408px) {
+  .has-text-right-fullhd {
+    text-align: right !important; } }
+
+.is-capitalized {
+  text-transform: capitalize !important; }
+
+.is-lowercase {
+  text-transform: lowercase !important; }
+
+.is-uppercase {
+  text-transform: uppercase !important; }
+
+.is-italic {
+  font-style: italic !important; }
+
+.has-text-white {
+  color: white !important; }
+
+a.has-text-white:hover, a.has-text-white:focus {
+  color: #e6e6e6 !important; }
+
+.has-background-white {
+  background-color: white !important; }
+
+.has-text-black {
+  color: #0a0a0a !important; }
+
+a.has-text-black:hover, a.has-text-black:focus {
+  color: black !important; }
+
+.has-background-black {
+  background-color: #0a0a0a !important; }
+
+.has-text-light {
+  color: whitesmoke !important; }
+
+a.has-text-light:hover, a.has-text-light:focus {
+  color: #dbdbdb !important; }
+
+.has-background-light {
+  background-color: whitesmoke !important; }
+
+.has-text-dark {
+  color: #363636 !important; }
+
+a.has-text-dark:hover, a.has-text-dark:focus {
+  color: #1c1c1c !important; }
+
+.has-background-dark {
+  background-color: #363636 !important; }
+
+.has-text-primary {
+  color: #4eb5de !important; }
+
+a.has-text-primary:hover, a.has-text-primary:focus {
+  color: #27a1d2 !important; }
+
+.has-background-primary {
+  background-color: #4eb5de !important; }
+
+.has-text-link {
+  color: #2e63b8 !important; }
+
+a.has-text-link:hover, a.has-text-link:focus {
+  color: #244d8f !important; }
+
+.has-background-link {
+  background-color: #2e63b8 !important; }
+
+.has-text-info {
+  color: #209cee !important; }
+
+a.has-text-info:hover, a.has-text-info:focus {
+  color: #0f81cc !important; }
+
+.has-background-info {
+  background-color: #209cee !important; }
+
+.has-text-success {
+  color: #22c35b !important; }
+
+a.has-text-success:hover, a.has-text-success:focus {
+  color: #1a9847 !important; }
+
+.has-background-success {
+  background-color: #22c35b !important; }
+
+.has-text-warning {
+  color: #ffdd57 !important; }
+
+a.has-text-warning:hover, a.has-text-warning:focus {
+  color: #ffd324 !important; }
+
+.has-background-warning {
+  background-color: #ffdd57 !important; }
+
+.has-text-danger {
+  color: #da0b00 !important; }
+
+a.has-text-danger:hover, a.has-text-danger:focus {
+  color: #a70800 !important; }
+
+.has-background-danger {
+  background-color: #da0b00 !important; }
+
+.has-text-black-bis {
+  color: #121212 !important; }
+
+.has-background-black-bis {
+  background-color: #121212 !important; }
+
+.has-text-black-ter {
+  color: #242424 !important; }
+
+.has-background-black-ter {
+  background-color: #242424 !important; }
+
+.has-text-grey-darker {
+  color: #363636 !important; }
+
+.has-background-grey-darker {
+  background-color: #363636 !important; }
+
+.has-text-grey-dark {
+  color: #4a4a4a !important; }
+
+.has-background-grey-dark {
+  background-color: #4a4a4a !important; }
+
+.has-text-grey {
+  color: #7a7a7a !important; }
+
+.has-background-grey {
+  background-color: #7a7a7a !important; }
+
+.has-text-grey-light {
+  color: #b5b5b5 !important; }
+
+.has-background-grey-light {
+  background-color: #b5b5b5 !important; }
+
+.has-text-grey-lighter {
+  color: #dbdbdb !important; }
+
+.has-background-grey-lighter {
+  background-color: #dbdbdb !important; }
+
+.has-text-white-ter {
+  color: whitesmoke !important; }
+
+.has-background-white-ter {
+  background-color: whitesmoke !important; }
+
+.has-text-white-bis {
+  color: #fafafa !important; }
+
+.has-background-white-bis {
+  background-color: #fafafa !important; }
+
+.has-text-weight-light {
+  font-weight: 300 !important; }
+
+.has-text-weight-normal {
+  font-weight: 400 !important; }
+
+.has-text-weight-medium {
+  font-weight: 500 !important; }
+
+.has-text-weight-semibold {
+  font-weight: 600 !important; }
+
+.has-text-weight-bold {
+  font-weight: 700 !important; }
+
+.is-family-primary {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-secondary {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-sans-serif {
+  font-family: "Lato", -apple-system, BlinkMacSystemFont, "Segoe UI", "Helvetica Neue", "Helvetica", "Arial", sans-serif !important; }
+
+.is-family-monospace {
+  font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; }
+
+.is-family-code {
+  font-family: "Roboto Mono", "SFMono-Regular", "Menlo", "Consolas", "Liberation Mono", "DejaVu Sans Mono", monospace !important; }
+
+.is-block {
+  display: block !important; }
+
+@media screen and (max-width: 768px) {
+  .is-block-mobile {
+    display: block !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-block-tablet {
+    display: block !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-block-tablet-only {
+    display: block !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-block-touch {
+    display: block !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-block-desktop {
+    display: block !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-block-desktop-only {
+    display: block !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-block-widescreen {
+    display: block !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-block-widescreen-only {
+    display: block !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-block-fullhd {
+    display: block !important; } }
+
+.is-flex {
+  display: flex !important; }
+
+@media screen and (max-width: 768px) {
+  .is-flex-mobile {
+    display: flex !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-flex-tablet {
+    display: flex !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-flex-tablet-only {
+    display: flex !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-flex-touch {
+    display: flex !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-flex-desktop {
+    display: flex !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-flex-desktop-only {
+    display: flex !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-flex-widescreen {
+    display: flex !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-flex-widescreen-only {
+    display: flex !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-flex-fullhd {
+    display: flex !important; } }
+
+.is-inline {
+  display: inline !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-mobile {
+    display: inline !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-tablet {
+    display: inline !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-tablet-only {
+    display: inline !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-touch {
+    display: inline !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-desktop {
+    display: inline !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-desktop-only {
+    display: inline !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-widescreen {
+    display: inline !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-widescreen-only {
+    display: inline !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-fullhd {
+    display: inline !important; } }
+
+.is-inline-block {
+  display: inline-block !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-block-mobile {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-block-tablet {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-block-tablet-only {
+    display: inline-block !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-block-touch {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-block-desktop {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-block-desktop-only {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-block-widescreen {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-block-widescreen-only {
+    display: inline-block !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-block-fullhd {
+    display: inline-block !important; } }
+
+.is-inline-flex {
+  display: inline-flex !important; }
+
+@media screen and (max-width: 768px) {
+  .is-inline-flex-mobile {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-inline-flex-tablet {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-inline-flex-tablet-only {
+    display: inline-flex !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-inline-flex-touch {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-inline-flex-desktop {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-inline-flex-desktop-only {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-inline-flex-widescreen {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-inline-flex-widescreen-only {
+    display: inline-flex !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-inline-flex-fullhd {
+    display: inline-flex !important; } }
+
+.is-hidden {
+  display: none !important; }
+
+.is-sr-only {
+  border: none !important;
+  clip: rect(0, 0, 0, 0) !important;
+  height: 0.01em !important;
+  overflow: hidden !important;
+  padding: 0 !important;
+  position: absolute !important;
+  white-space: nowrap !important;
+  width: 0.01em !important; }
+
+@media screen and (max-width: 768px) {
+  .is-hidden-mobile {
+    display: none !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-hidden-tablet {
+    display: none !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-hidden-tablet-only {
+    display: none !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-hidden-touch {
+    display: none !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-hidden-desktop {
+    display: none !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-hidden-desktop-only {
+    display: none !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-hidden-widescreen {
+    display: none !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-hidden-widescreen-only {
+    display: none !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-hidden-fullhd {
+    display: none !important; } }
+
+.is-invisible {
+  visibility: hidden !important; }
+
+@media screen and (max-width: 768px) {
+  .is-invisible-mobile {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 769px), print {
+  .is-invisible-tablet {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 769px) and (max-width: 1055px) {
+  .is-invisible-tablet-only {
+    visibility: hidden !important; } }
+
+@media screen and (max-width: 1055px) {
+  .is-invisible-touch {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1056px) {
+  .is-invisible-desktop {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1056px) and (max-width: 1215px) {
+  .is-invisible-desktop-only {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1216px) {
+  .is-invisible-widescreen {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1216px) and (max-width: 1407px) {
+  .is-invisible-widescreen-only {
+    visibility: hidden !important; } }
+
+@media screen and (min-width: 1408px) {
+  .is-invisible-fullhd {
+    visibility: hidden !important; } }
+
+.is-marginless {
+  margin: 0 !important; }
+
+.is-paddingless {
+  padding: 0 !important; }
+
+.is-radiusless {
+  border-radius: 0 !important; }
+
+.is-shadowless {
+  box-shadow: none !important; }
+
+.is-relative {
+  position: relative !important; }
+
+.box {
+  background-color: white;
+  border-radius: 6px;
+  box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+  color: #222222;
+  display: block;
+  padding: 1.25rem; }
+
+a.box:hover, a.box:focus {
+  box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px #2e63b8; }
+
+a.box:active {
+  box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2), 0 0 0 1px #2e63b8; }
+
+.button {
+  background-color: white;
+  border-color: #dbdbdb;
+  border-width: 1px;
+  color: #363636;
+  cursor: pointer;
+  justify-content: center;
+  padding-bottom: calc(0.375em - 1px);
+  padding-left: 0.75em;
+  padding-right: 0.75em;
+  padding-top: calc(0.375em - 1px);
+  text-align: center;
+  white-space: nowrap; }
+  .button strong {
+    color: inherit; }
+  .button .icon, .button .icon.is-small, .button #documenter .docs-sidebar form.docs-search > input.icon, #documenter .docs-sidebar .button form.docs-search > input.icon, .button .icon.is-medium, .button .icon.is-large {
+    height: 1.5em;
+    width: 1.5em; }
+  .button .icon:first-child:not(:last-child) {
+    margin-left: calc(-0.375em - 1px);
+    margin-right: 0.1875em; }
+  .button .icon:last-child:not(:first-child) {
+    margin-left: 0.1875em;
+    margin-right: calc(-0.375em - 1px); }
+  .button .icon:first-child:last-child {
+    margin-left: calc(-0.375em - 1px);
+    margin-right: calc(-0.375em - 1px); }
+  .button:hover, .button.is-hovered {
+    border-color: #b5b5b5;
+    color: #363636; }
+  .button:focus, .button.is-focused {
+    border-color: #2e63b8;
+    color: #363636; }
+    .button:focus:not(:active), .button.is-focused:not(:active) {
+      box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); }
+  .button:active, .button.is-active {
+    border-color: #4a4a4a;
+    color: #363636; }
+  .button.is-text {
+    background-color: transparent;
+    border-color: transparent;
+    color: #222222;
+    text-decoration: underline; }
+    .button.is-text:hover, .button.is-text.is-hovered, .button.is-text:focus, .button.is-text.is-focused {
+      background-color: whitesmoke;
+      color: #222222; }
+    .button.is-text:active, .button.is-text.is-active {
+      background-color: #e8e8e8;
+      color: #222222; }
+    .button.is-text[disabled],
+    fieldset[disabled] .button.is-text {
+      background-color: transparent;
+      border-color: transparent;
+      box-shadow: none; }
+  .button.is-white {
+    background-color: white;
+    border-color: transparent;
+    color: #0a0a0a; }
+    .button.is-white:hover, .button.is-white.is-hovered {
+      background-color: #f9f9f9;
+      border-color: transparent;
+      color: #0a0a0a; }
+    .button.is-white:focus, .button.is-white.is-focused {
+      border-color: transparent;
+      color: #0a0a0a; }
+      .button.is-white:focus:not(:active), .button.is-white.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+    .button.is-white:active, .button.is-white.is-active {
+      background-color: #f2f2f2;
+      border-color: transparent;
+      color: #0a0a0a; }
+    .button.is-white[disabled],
+    fieldset[disabled] .button.is-white {
+      background-color: white;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-white.is-inverted {
+      background-color: #0a0a0a;
+      color: white; }
+      .button.is-white.is-inverted:hover, .button.is-white.is-inverted.is-hovered {
+        background-color: black; }
+      .button.is-white.is-inverted[disabled],
+      fieldset[disabled] .button.is-white.is-inverted {
+        background-color: #0a0a0a;
+        border-color: transparent;
+        box-shadow: none;
+        color: white; }
+    .button.is-white.is-loading::after {
+      border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+    .button.is-white.is-outlined {
+      background-color: transparent;
+      border-color: white;
+      color: white; }
+      .button.is-white.is-outlined:hover, .button.is-white.is-outlined.is-hovered, .button.is-white.is-outlined:focus, .button.is-white.is-outlined.is-focused {
+        background-color: white;
+        border-color: white;
+        color: #0a0a0a; }
+      .button.is-white.is-outlined.is-loading::after {
+        border-color: transparent transparent white white !important; }
+      .button.is-white.is-outlined.is-loading:hover::after, .button.is-white.is-outlined.is-loading.is-hovered::after, .button.is-white.is-outlined.is-loading:focus::after, .button.is-white.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+      .button.is-white.is-outlined[disabled],
+      fieldset[disabled] .button.is-white.is-outlined {
+        background-color: transparent;
+        border-color: white;
+        box-shadow: none;
+        color: white; }
+    .button.is-white.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #0a0a0a;
+      color: #0a0a0a; }
+      .button.is-white.is-inverted.is-outlined:hover, .button.is-white.is-inverted.is-outlined.is-hovered, .button.is-white.is-inverted.is-outlined:focus, .button.is-white.is-inverted.is-outlined.is-focused {
+        background-color: #0a0a0a;
+        color: white; }
+      .button.is-white.is-inverted.is-outlined.is-loading:hover::after, .button.is-white.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-white.is-inverted.is-outlined.is-loading:focus::after, .button.is-white.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent white white !important; }
+      .button.is-white.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-white.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #0a0a0a;
+        box-shadow: none;
+        color: #0a0a0a; }
+  .button.is-black {
+    background-color: #0a0a0a;
+    border-color: transparent;
+    color: white; }
+    .button.is-black:hover, .button.is-black.is-hovered {
+      background-color: #040404;
+      border-color: transparent;
+      color: white; }
+    .button.is-black:focus, .button.is-black.is-focused {
+      border-color: transparent;
+      color: white; }
+      .button.is-black:focus:not(:active), .button.is-black.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+    .button.is-black:active, .button.is-black.is-active {
+      background-color: black;
+      border-color: transparent;
+      color: white; }
+    .button.is-black[disabled],
+    fieldset[disabled] .button.is-black {
+      background-color: #0a0a0a;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-black.is-inverted {
+      background-color: white;
+      color: #0a0a0a; }
+      .button.is-black.is-inverted:hover, .button.is-black.is-inverted.is-hovered {
+        background-color: #f2f2f2; }
+      .button.is-black.is-inverted[disabled],
+      fieldset[disabled] .button.is-black.is-inverted {
+        background-color: white;
+        border-color: transparent;
+        box-shadow: none;
+        color: #0a0a0a; }
+    .button.is-black.is-loading::after {
+      border-color: transparent transparent white white !important; }
+    .button.is-black.is-outlined {
+      background-color: transparent;
+      border-color: #0a0a0a;
+      color: #0a0a0a; }
+      .button.is-black.is-outlined:hover, .button.is-black.is-outlined.is-hovered, .button.is-black.is-outlined:focus, .button.is-black.is-outlined.is-focused {
+        background-color: #0a0a0a;
+        border-color: #0a0a0a;
+        color: white; }
+      .button.is-black.is-outlined.is-loading::after {
+        border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+      .button.is-black.is-outlined.is-loading:hover::after, .button.is-black.is-outlined.is-loading.is-hovered::after, .button.is-black.is-outlined.is-loading:focus::after, .button.is-black.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent white white !important; }
+      .button.is-black.is-outlined[disabled],
+      fieldset[disabled] .button.is-black.is-outlined {
+        background-color: transparent;
+        border-color: #0a0a0a;
+        box-shadow: none;
+        color: #0a0a0a; }
+    .button.is-black.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: white;
+      color: white; }
+      .button.is-black.is-inverted.is-outlined:hover, .button.is-black.is-inverted.is-outlined.is-hovered, .button.is-black.is-inverted.is-outlined:focus, .button.is-black.is-inverted.is-outlined.is-focused {
+        background-color: white;
+        color: #0a0a0a; }
+      .button.is-black.is-inverted.is-outlined.is-loading:hover::after, .button.is-black.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-black.is-inverted.is-outlined.is-loading:focus::after, .button.is-black.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #0a0a0a #0a0a0a !important; }
+      .button.is-black.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-black.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: white;
+        box-shadow: none;
+        color: white; }
+  .button.is-light {
+    background-color: whitesmoke;
+    border-color: transparent;
+    color: #363636; }
+    .button.is-light:hover, .button.is-light.is-hovered {
+      background-color: #eeeeee;
+      border-color: transparent;
+      color: #363636; }
+    .button.is-light:focus, .button.is-light.is-focused {
+      border-color: transparent;
+      color: #363636; }
+      .button.is-light:focus:not(:active), .button.is-light.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }
+    .button.is-light:active, .button.is-light.is-active {
+      background-color: #e8e8e8;
+      border-color: transparent;
+      color: #363636; }
+    .button.is-light[disabled],
+    fieldset[disabled] .button.is-light {
+      background-color: whitesmoke;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-light.is-inverted {
+      background-color: #363636;
+      color: whitesmoke; }
+      .button.is-light.is-inverted:hover, .button.is-light.is-inverted.is-hovered {
+        background-color: #292929; }
+      .button.is-light.is-inverted[disabled],
+      fieldset[disabled] .button.is-light.is-inverted {
+        background-color: #363636;
+        border-color: transparent;
+        box-shadow: none;
+        color: whitesmoke; }
+    .button.is-light.is-loading::after {
+      border-color: transparent transparent #363636 #363636 !important; }
+    .button.is-light.is-outlined {
+      background-color: transparent;
+      border-color: whitesmoke;
+      color: whitesmoke; }
+      .button.is-light.is-outlined:hover, .button.is-light.is-outlined.is-hovered, .button.is-light.is-outlined:focus, .button.is-light.is-outlined.is-focused {
+        background-color: whitesmoke;
+        border-color: whitesmoke;
+        color: #363636; }
+      .button.is-light.is-outlined.is-loading::after {
+        border-color: transparent transparent whitesmoke whitesmoke !important; }
+      .button.is-light.is-outlined.is-loading:hover::after, .button.is-light.is-outlined.is-loading.is-hovered::after, .button.is-light.is-outlined.is-loading:focus::after, .button.is-light.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #363636 #363636 !important; }
+      .button.is-light.is-outlined[disabled],
+      fieldset[disabled] .button.is-light.is-outlined {
+        background-color: transparent;
+        border-color: whitesmoke;
+        box-shadow: none;
+        color: whitesmoke; }
+    .button.is-light.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #363636;
+      color: #363636; }
+      .button.is-light.is-inverted.is-outlined:hover, .button.is-light.is-inverted.is-outlined.is-hovered, .button.is-light.is-inverted.is-outlined:focus, .button.is-light.is-inverted.is-outlined.is-focused {
+        background-color: #363636;
+        color: whitesmoke; }
+      .button.is-light.is-inverted.is-outlined.is-loading:hover::after, .button.is-light.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-light.is-inverted.is-outlined.is-loading:focus::after, .button.is-light.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent whitesmoke whitesmoke !important; }
+      .button.is-light.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-light.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #363636;
+        box-shadow: none;
+        color: #363636; }
+  .button.is-dark, .content kbd.button {
+    background-color: #363636;
+    border-color: transparent;
+    color: whitesmoke; }
+    .button.is-dark:hover, .content kbd.button:hover, .button.is-dark.is-hovered, .content kbd.button.is-hovered {
+      background-color: #2f2f2f;
+      border-color: transparent;
+      color: whitesmoke; }
+    .button.is-dark:focus, .content kbd.button:focus, .button.is-dark.is-focused, .content kbd.button.is-focused {
+      border-color: transparent;
+      color: whitesmoke; }
+      .button.is-dark:focus:not(:active), .content kbd.button:focus:not(:active), .button.is-dark.is-focused:not(:active), .content kbd.button.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }
+    .button.is-dark:active, .content kbd.button:active, .button.is-dark.is-active, .content kbd.button.is-active {
+      background-color: #292929;
+      border-color: transparent;
+      color: whitesmoke; }
+    .button.is-dark[disabled], .content kbd.button[disabled],
+    fieldset[disabled] .button.is-dark,
+    fieldset[disabled] .content kbd.button,
+    .content fieldset[disabled] kbd.button {
+      background-color: #363636;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-dark.is-inverted, .content kbd.button.is-inverted {
+      background-color: whitesmoke;
+      color: #363636; }
+      .button.is-dark.is-inverted:hover, .content kbd.button.is-inverted:hover, .button.is-dark.is-inverted.is-hovered, .content kbd.button.is-inverted.is-hovered {
+        background-color: #e8e8e8; }
+      .button.is-dark.is-inverted[disabled], .content kbd.button.is-inverted[disabled],
+      fieldset[disabled] .button.is-dark.is-inverted,
+      fieldset[disabled] .content kbd.button.is-inverted,
+      .content fieldset[disabled] kbd.button.is-inverted {
+        background-color: whitesmoke;
+        border-color: transparent;
+        box-shadow: none;
+        color: #363636; }
+    .button.is-dark.is-loading::after, .content kbd.button.is-loading::after {
+      border-color: transparent transparent whitesmoke whitesmoke !important; }
+    .button.is-dark.is-outlined, .content kbd.button.is-outlined {
+      background-color: transparent;
+      border-color: #363636;
+      color: #363636; }
+      .button.is-dark.is-outlined:hover, .content kbd.button.is-outlined:hover, .button.is-dark.is-outlined.is-hovered, .content kbd.button.is-outlined.is-hovered, .button.is-dark.is-outlined:focus, .content kbd.button.is-outlined:focus, .button.is-dark.is-outlined.is-focused, .content kbd.button.is-outlined.is-focused {
+        background-color: #363636;
+        border-color: #363636;
+        color: whitesmoke; }
+      .button.is-dark.is-outlined.is-loading::after, .content kbd.button.is-outlined.is-loading::after {
+        border-color: transparent transparent #363636 #363636 !important; }
+      .button.is-dark.is-outlined.is-loading:hover::after, .content kbd.button.is-outlined.is-loading:hover::after, .button.is-dark.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-outlined.is-loading:focus::after, .content kbd.button.is-outlined.is-loading:focus::after, .button.is-dark.is-outlined.is-loading.is-focused::after, .content kbd.button.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent whitesmoke whitesmoke !important; }
+      .button.is-dark.is-outlined[disabled], .content kbd.button.is-outlined[disabled],
+      fieldset[disabled] .button.is-dark.is-outlined,
+      fieldset[disabled] .content kbd.button.is-outlined,
+      .content fieldset[disabled] kbd.button.is-outlined {
+        background-color: transparent;
+        border-color: #363636;
+        box-shadow: none;
+        color: #363636; }
+    .button.is-dark.is-inverted.is-outlined, .content kbd.button.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: whitesmoke;
+      color: whitesmoke; }
+      .button.is-dark.is-inverted.is-outlined:hover, .content kbd.button.is-inverted.is-outlined:hover, .button.is-dark.is-inverted.is-outlined.is-hovered, .content kbd.button.is-inverted.is-outlined.is-hovered, .button.is-dark.is-inverted.is-outlined:focus, .content kbd.button.is-inverted.is-outlined:focus, .button.is-dark.is-inverted.is-outlined.is-focused, .content kbd.button.is-inverted.is-outlined.is-focused {
+        background-color: whitesmoke;
+        color: #363636; }
+      .button.is-dark.is-inverted.is-outlined.is-loading:hover::after, .content kbd.button.is-inverted.is-outlined.is-loading:hover::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-hovered::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-dark.is-inverted.is-outlined.is-loading:focus::after, .content kbd.button.is-inverted.is-outlined.is-loading:focus::after, .button.is-dark.is-inverted.is-outlined.is-loading.is-focused::after, .content kbd.button.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #363636 #363636 !important; }
+      .button.is-dark.is-inverted.is-outlined[disabled], .content kbd.button.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-dark.is-inverted.is-outlined,
+      fieldset[disabled] .content kbd.button.is-inverted.is-outlined,
+      .content fieldset[disabled] kbd.button.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: whitesmoke;
+        box-shadow: none;
+        color: whitesmoke; }
+  .button.is-primary, .docstring > section > a.button.docs-sourcelink {
+    background-color: #4eb5de;
+    border-color: transparent;
+    color: #fff; }
+    .button.is-primary:hover, .docstring > section > a.button.docs-sourcelink:hover, .button.is-primary.is-hovered, .docstring > section > a.button.is-hovered.docs-sourcelink {
+      background-color: #43b1dc;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-primary:focus, .docstring > section > a.button.docs-sourcelink:focus, .button.is-primary.is-focused, .docstring > section > a.button.is-focused.docs-sourcelink {
+      border-color: transparent;
+      color: #fff; }
+      .button.is-primary:focus:not(:active), .docstring > section > a.button.docs-sourcelink:focus:not(:active), .button.is-primary.is-focused:not(:active), .docstring > section > a.button.is-focused.docs-sourcelink:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }
+    .button.is-primary:active, .docstring > section > a.button.docs-sourcelink:active, .button.is-primary.is-active, .docstring > section > a.button.is-active.docs-sourcelink {
+      background-color: #39acda;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-primary[disabled], .docstring > section > a.button.docs-sourcelink[disabled],
+    fieldset[disabled] .button.is-primary,
+    fieldset[disabled] .docstring > section > a.button.docs-sourcelink {
+      background-color: #4eb5de;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-primary.is-inverted, .docstring > section > a.button.is-inverted.docs-sourcelink {
+      background-color: #fff;
+      color: #4eb5de; }
+      .button.is-primary.is-inverted:hover, .docstring > section > a.button.is-inverted.docs-sourcelink:hover, .button.is-primary.is-inverted.is-hovered, .docstring > section > a.button.is-inverted.is-hovered.docs-sourcelink {
+        background-color: #f2f2f2; }
+      .button.is-primary.is-inverted[disabled], .docstring > section > a.button.is-inverted.docs-sourcelink[disabled],
+      fieldset[disabled] .button.is-primary.is-inverted,
+      fieldset[disabled] .docstring > section > a.button.is-inverted.docs-sourcelink {
+        background-color: #fff;
+        border-color: transparent;
+        box-shadow: none;
+        color: #4eb5de; }
+    .button.is-primary.is-loading::after, .docstring > section > a.button.is-loading.docs-sourcelink::after {
+      border-color: transparent transparent #fff #fff !important; }
+    .button.is-primary.is-outlined, .docstring > section > a.button.is-outlined.docs-sourcelink {
+      background-color: transparent;
+      border-color: #4eb5de;
+      color: #4eb5de; }
+      .button.is-primary.is-outlined:hover, .docstring > section > a.button.is-outlined.docs-sourcelink:hover, .button.is-primary.is-outlined.is-hovered, .docstring > section > a.button.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-outlined:focus, .docstring > section > a.button.is-outlined.docs-sourcelink:focus, .button.is-primary.is-outlined.is-focused, .docstring > section > a.button.is-outlined.is-focused.docs-sourcelink {
+        background-color: #4eb5de;
+        border-color: #4eb5de;
+        color: #fff; }
+      .button.is-primary.is-outlined.is-loading::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink::after {
+        border-color: transparent transparent #4eb5de #4eb5de !important; }
+      .button.is-primary.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-outlined.is-loading.is-focused.docs-sourcelink::after {
+        border-color: transparent transparent #fff #fff !important; }
+      .button.is-primary.is-outlined[disabled], .docstring > section > a.button.is-outlined.docs-sourcelink[disabled],
+      fieldset[disabled] .button.is-primary.is-outlined,
+      fieldset[disabled] .docstring > section > a.button.is-outlined.docs-sourcelink {
+        background-color: transparent;
+        border-color: #4eb5de;
+        box-shadow: none;
+        color: #4eb5de; }
+    .button.is-primary.is-inverted.is-outlined, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {
+      background-color: transparent;
+      border-color: #fff;
+      color: #fff; }
+      .button.is-primary.is-inverted.is-outlined:hover, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:hover, .button.is-primary.is-inverted.is-outlined.is-hovered, .docstring > section > a.button.is-inverted.is-outlined.is-hovered.docs-sourcelink, .button.is-primary.is-inverted.is-outlined:focus, .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink:focus, .button.is-primary.is-inverted.is-outlined.is-focused, .docstring > section > a.button.is-inverted.is-outlined.is-focused.docs-sourcelink {
+        background-color: #fff;
+        color: #4eb5de; }
+      .button.is-primary.is-inverted.is-outlined.is-loading:hover::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:hover::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-hovered::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-hovered.docs-sourcelink::after, .button.is-primary.is-inverted.is-outlined.is-loading:focus::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.docs-sourcelink:focus::after, .button.is-primary.is-inverted.is-outlined.is-loading.is-focused::after, .docstring > section > a.button.is-inverted.is-outlined.is-loading.is-focused.docs-sourcelink::after {
+        border-color: transparent transparent #4eb5de #4eb5de !important; }
+      .button.is-primary.is-inverted.is-outlined[disabled], .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink[disabled],
+      fieldset[disabled] .button.is-primary.is-inverted.is-outlined,
+      fieldset[disabled] .docstring > section > a.button.is-inverted.is-outlined.docs-sourcelink {
+        background-color: transparent;
+        border-color: #fff;
+        box-shadow: none;
+        color: #fff; }
+  .button.is-link {
+    background-color: #2e63b8;
+    border-color: transparent;
+    color: #fff; }
+    .button.is-link:hover, .button.is-link.is-hovered {
+      background-color: #2b5eae;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-link:focus, .button.is-link.is-focused {
+      border-color: transparent;
+      color: #fff; }
+      .button.is-link:focus:not(:active), .button.is-link.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); }
+    .button.is-link:active, .button.is-link.is-active {
+      background-color: #2958a4;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-link[disabled],
+    fieldset[disabled] .button.is-link {
+      background-color: #2e63b8;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-link.is-inverted {
+      background-color: #fff;
+      color: #2e63b8; }
+      .button.is-link.is-inverted:hover, .button.is-link.is-inverted.is-hovered {
+        background-color: #f2f2f2; }
+      .button.is-link.is-inverted[disabled],
+      fieldset[disabled] .button.is-link.is-inverted {
+        background-color: #fff;
+        border-color: transparent;
+        box-shadow: none;
+        color: #2e63b8; }
+    .button.is-link.is-loading::after {
+      border-color: transparent transparent #fff #fff !important; }
+    .button.is-link.is-outlined {
+      background-color: transparent;
+      border-color: #2e63b8;
+      color: #2e63b8; }
+      .button.is-link.is-outlined:hover, .button.is-link.is-outlined.is-hovered, .button.is-link.is-outlined:focus, .button.is-link.is-outlined.is-focused {
+        background-color: #2e63b8;
+        border-color: #2e63b8;
+        color: #fff; }
+      .button.is-link.is-outlined.is-loading::after {
+        border-color: transparent transparent #2e63b8 #2e63b8 !important; }
+      .button.is-link.is-outlined.is-loading:hover::after, .button.is-link.is-outlined.is-loading.is-hovered::after, .button.is-link.is-outlined.is-loading:focus::after, .button.is-link.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #fff #fff !important; }
+      .button.is-link.is-outlined[disabled],
+      fieldset[disabled] .button.is-link.is-outlined {
+        background-color: transparent;
+        border-color: #2e63b8;
+        box-shadow: none;
+        color: #2e63b8; }
+    .button.is-link.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #fff;
+      color: #fff; }
+      .button.is-link.is-inverted.is-outlined:hover, .button.is-link.is-inverted.is-outlined.is-hovered, .button.is-link.is-inverted.is-outlined:focus, .button.is-link.is-inverted.is-outlined.is-focused {
+        background-color: #fff;
+        color: #2e63b8; }
+      .button.is-link.is-inverted.is-outlined.is-loading:hover::after, .button.is-link.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-link.is-inverted.is-outlined.is-loading:focus::after, .button.is-link.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #2e63b8 #2e63b8 !important; }
+      .button.is-link.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-link.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        box-shadow: none;
+        color: #fff; }
+  .button.is-info {
+    background-color: #209cee;
+    border-color: transparent;
+    color: #fff; }
+    .button.is-info:hover, .button.is-info.is-hovered {
+      background-color: #1496ed;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-info:focus, .button.is-info.is-focused {
+      border-color: transparent;
+      color: #fff; }
+      .button.is-info:focus:not(:active), .button.is-info.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }
+    .button.is-info:active, .button.is-info.is-active {
+      background-color: #118fe4;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-info[disabled],
+    fieldset[disabled] .button.is-info {
+      background-color: #209cee;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-info.is-inverted {
+      background-color: #fff;
+      color: #209cee; }
+      .button.is-info.is-inverted:hover, .button.is-info.is-inverted.is-hovered {
+        background-color: #f2f2f2; }
+      .button.is-info.is-inverted[disabled],
+      fieldset[disabled] .button.is-info.is-inverted {
+        background-color: #fff;
+        border-color: transparent;
+        box-shadow: none;
+        color: #209cee; }
+    .button.is-info.is-loading::after {
+      border-color: transparent transparent #fff #fff !important; }
+    .button.is-info.is-outlined {
+      background-color: transparent;
+      border-color: #209cee;
+      color: #209cee; }
+      .button.is-info.is-outlined:hover, .button.is-info.is-outlined.is-hovered, .button.is-info.is-outlined:focus, .button.is-info.is-outlined.is-focused {
+        background-color: #209cee;
+        border-color: #209cee;
+        color: #fff; }
+      .button.is-info.is-outlined.is-loading::after {
+        border-color: transparent transparent #209cee #209cee !important; }
+      .button.is-info.is-outlined.is-loading:hover::after, .button.is-info.is-outlined.is-loading.is-hovered::after, .button.is-info.is-outlined.is-loading:focus::after, .button.is-info.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #fff #fff !important; }
+      .button.is-info.is-outlined[disabled],
+      fieldset[disabled] .button.is-info.is-outlined {
+        background-color: transparent;
+        border-color: #209cee;
+        box-shadow: none;
+        color: #209cee; }
+    .button.is-info.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #fff;
+      color: #fff; }
+      .button.is-info.is-inverted.is-outlined:hover, .button.is-info.is-inverted.is-outlined.is-hovered, .button.is-info.is-inverted.is-outlined:focus, .button.is-info.is-inverted.is-outlined.is-focused {
+        background-color: #fff;
+        color: #209cee; }
+      .button.is-info.is-inverted.is-outlined.is-loading:hover::after, .button.is-info.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-info.is-inverted.is-outlined.is-loading:focus::after, .button.is-info.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #209cee #209cee !important; }
+      .button.is-info.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-info.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        box-shadow: none;
+        color: #fff; }
+  .button.is-success {
+    background-color: #22c35b;
+    border-color: transparent;
+    color: #fff; }
+    .button.is-success:hover, .button.is-success.is-hovered {
+      background-color: #20b856;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-success:focus, .button.is-success.is-focused {
+      border-color: transparent;
+      color: #fff; }
+      .button.is-success:focus:not(:active), .button.is-success.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }
+    .button.is-success:active, .button.is-success.is-active {
+      background-color: #1ead51;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-success[disabled],
+    fieldset[disabled] .button.is-success {
+      background-color: #22c35b;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-success.is-inverted {
+      background-color: #fff;
+      color: #22c35b; }
+      .button.is-success.is-inverted:hover, .button.is-success.is-inverted.is-hovered {
+        background-color: #f2f2f2; }
+      .button.is-success.is-inverted[disabled],
+      fieldset[disabled] .button.is-success.is-inverted {
+        background-color: #fff;
+        border-color: transparent;
+        box-shadow: none;
+        color: #22c35b; }
+    .button.is-success.is-loading::after {
+      border-color: transparent transparent #fff #fff !important; }
+    .button.is-success.is-outlined {
+      background-color: transparent;
+      border-color: #22c35b;
+      color: #22c35b; }
+      .button.is-success.is-outlined:hover, .button.is-success.is-outlined.is-hovered, .button.is-success.is-outlined:focus, .button.is-success.is-outlined.is-focused {
+        background-color: #22c35b;
+        border-color: #22c35b;
+        color: #fff; }
+      .button.is-success.is-outlined.is-loading::after {
+        border-color: transparent transparent #22c35b #22c35b !important; }
+      .button.is-success.is-outlined.is-loading:hover::after, .button.is-success.is-outlined.is-loading.is-hovered::after, .button.is-success.is-outlined.is-loading:focus::after, .button.is-success.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #fff #fff !important; }
+      .button.is-success.is-outlined[disabled],
+      fieldset[disabled] .button.is-success.is-outlined {
+        background-color: transparent;
+        border-color: #22c35b;
+        box-shadow: none;
+        color: #22c35b; }
+    .button.is-success.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #fff;
+      color: #fff; }
+      .button.is-success.is-inverted.is-outlined:hover, .button.is-success.is-inverted.is-outlined.is-hovered, .button.is-success.is-inverted.is-outlined:focus, .button.is-success.is-inverted.is-outlined.is-focused {
+        background-color: #fff;
+        color: #22c35b; }
+      .button.is-success.is-inverted.is-outlined.is-loading:hover::after, .button.is-success.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-success.is-inverted.is-outlined.is-loading:focus::after, .button.is-success.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #22c35b #22c35b !important; }
+      .button.is-success.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-success.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        box-shadow: none;
+        color: #fff; }
+  .button.is-warning {
+    background-color: #ffdd57;
+    border-color: transparent;
+    color: rgba(0, 0, 0, 0.7); }
+    .button.is-warning:hover, .button.is-warning.is-hovered {
+      background-color: #ffdb4a;
+      border-color: transparent;
+      color: rgba(0, 0, 0, 0.7); }
+    .button.is-warning:focus, .button.is-warning.is-focused {
+      border-color: transparent;
+      color: rgba(0, 0, 0, 0.7); }
+      .button.is-warning:focus:not(:active), .button.is-warning.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }
+    .button.is-warning:active, .button.is-warning.is-active {
+      background-color: #ffd83d;
+      border-color: transparent;
+      color: rgba(0, 0, 0, 0.7); }
+    .button.is-warning[disabled],
+    fieldset[disabled] .button.is-warning {
+      background-color: #ffdd57;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-warning.is-inverted {
+      background-color: rgba(0, 0, 0, 0.7);
+      color: #ffdd57; }
+      .button.is-warning.is-inverted:hover, .button.is-warning.is-inverted.is-hovered {
+        background-color: rgba(0, 0, 0, 0.7); }
+      .button.is-warning.is-inverted[disabled],
+      fieldset[disabled] .button.is-warning.is-inverted {
+        background-color: rgba(0, 0, 0, 0.7);
+        border-color: transparent;
+        box-shadow: none;
+        color: #ffdd57; }
+    .button.is-warning.is-loading::after {
+      border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; }
+    .button.is-warning.is-outlined {
+      background-color: transparent;
+      border-color: #ffdd57;
+      color: #ffdd57; }
+      .button.is-warning.is-outlined:hover, .button.is-warning.is-outlined.is-hovered, .button.is-warning.is-outlined:focus, .button.is-warning.is-outlined.is-focused {
+        background-color: #ffdd57;
+        border-color: #ffdd57;
+        color: rgba(0, 0, 0, 0.7); }
+      .button.is-warning.is-outlined.is-loading::after {
+        border-color: transparent transparent #ffdd57 #ffdd57 !important; }
+      .button.is-warning.is-outlined.is-loading:hover::after, .button.is-warning.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-outlined.is-loading:focus::after, .button.is-warning.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent rgba(0, 0, 0, 0.7) rgba(0, 0, 0, 0.7) !important; }
+      .button.is-warning.is-outlined[disabled],
+      fieldset[disabled] .button.is-warning.is-outlined {
+        background-color: transparent;
+        border-color: #ffdd57;
+        box-shadow: none;
+        color: #ffdd57; }
+    .button.is-warning.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: rgba(0, 0, 0, 0.7);
+      color: rgba(0, 0, 0, 0.7); }
+      .button.is-warning.is-inverted.is-outlined:hover, .button.is-warning.is-inverted.is-outlined.is-hovered, .button.is-warning.is-inverted.is-outlined:focus, .button.is-warning.is-inverted.is-outlined.is-focused {
+        background-color: rgba(0, 0, 0, 0.7);
+        color: #ffdd57; }
+      .button.is-warning.is-inverted.is-outlined.is-loading:hover::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-warning.is-inverted.is-outlined.is-loading:focus::after, .button.is-warning.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #ffdd57 #ffdd57 !important; }
+      .button.is-warning.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-warning.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: rgba(0, 0, 0, 0.7);
+        box-shadow: none;
+        color: rgba(0, 0, 0, 0.7); }
+  .button.is-danger {
+    background-color: #da0b00;
+    border-color: transparent;
+    color: #fff; }
+    .button.is-danger:hover, .button.is-danger.is-hovered {
+      background-color: #cd0a00;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-danger:focus, .button.is-danger.is-focused {
+      border-color: transparent;
+      color: #fff; }
+      .button.is-danger:focus:not(:active), .button.is-danger.is-focused:not(:active) {
+        box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }
+    .button.is-danger:active, .button.is-danger.is-active {
+      background-color: #c10a00;
+      border-color: transparent;
+      color: #fff; }
+    .button.is-danger[disabled],
+    fieldset[disabled] .button.is-danger {
+      background-color: #da0b00;
+      border-color: transparent;
+      box-shadow: none; }
+    .button.is-danger.is-inverted {
+      background-color: #fff;
+      color: #da0b00; }
+      .button.is-danger.is-inverted:hover, .button.is-danger.is-inverted.is-hovered {
+        background-color: #f2f2f2; }
+      .button.is-danger.is-inverted[disabled],
+      fieldset[disabled] .button.is-danger.is-inverted {
+        background-color: #fff;
+        border-color: transparent;
+        box-shadow: none;
+        color: #da0b00; }
+    .button.is-danger.is-loading::after {
+      border-color: transparent transparent #fff #fff !important; }
+    .button.is-danger.is-outlined {
+      background-color: transparent;
+      border-color: #da0b00;
+      color: #da0b00; }
+      .button.is-danger.is-outlined:hover, .button.is-danger.is-outlined.is-hovered, .button.is-danger.is-outlined:focus, .button.is-danger.is-outlined.is-focused {
+        background-color: #da0b00;
+        border-color: #da0b00;
+        color: #fff; }
+      .button.is-danger.is-outlined.is-loading::after {
+        border-color: transparent transparent #da0b00 #da0b00 !important; }
+      .button.is-danger.is-outlined.is-loading:hover::after, .button.is-danger.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-outlined.is-loading:focus::after, .button.is-danger.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #fff #fff !important; }
+      .button.is-danger.is-outlined[disabled],
+      fieldset[disabled] .button.is-danger.is-outlined {
+        background-color: transparent;
+        border-color: #da0b00;
+        box-shadow: none;
+        color: #da0b00; }
+    .button.is-danger.is-inverted.is-outlined {
+      background-color: transparent;
+      border-color: #fff;
+      color: #fff; }
+      .button.is-danger.is-inverted.is-outlined:hover, .button.is-danger.is-inverted.is-outlined.is-hovered, .button.is-danger.is-inverted.is-outlined:focus, .button.is-danger.is-inverted.is-outlined.is-focused {
+        background-color: #fff;
+        color: #da0b00; }
+      .button.is-danger.is-inverted.is-outlined.is-loading:hover::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-hovered::after, .button.is-danger.is-inverted.is-outlined.is-loading:focus::after, .button.is-danger.is-inverted.is-outlined.is-loading.is-focused::after {
+        border-color: transparent transparent #da0b00 #da0b00 !important; }
+      .button.is-danger.is-inverted.is-outlined[disabled],
+      fieldset[disabled] .button.is-danger.is-inverted.is-outlined {
+        background-color: transparent;
+        border-color: #fff;
+        box-shadow: none;
+        color: #fff; }
+  .button.is-small, #documenter .docs-sidebar form.docs-search > input.button {
+    border-radius: 2px;
+    font-size: 0.75rem; }
+  .button.is-normal {
+    font-size: 1rem; }
+  .button.is-medium {
+    font-size: 1.25rem; }
+  .button.is-large {
+    font-size: 1.5rem; }
+  .button[disabled],
+  fieldset[disabled] .button {
+    background-color: white;
+    border-color: #dbdbdb;
+    box-shadow: none;
+    opacity: 0.5; }
+  .button.is-fullwidth {
+    display: flex;
+    width: 100%; }
+  .button.is-loading {
+    color: transparent !important;
+    pointer-events: none; }
+    .button.is-loading::after {
+      position: absolute;
+      left: calc(50% - (1em / 2));
+      top: calc(50% - (1em / 2));
+      position: absolute !important; }
+  .button.is-static {
+    background-color: whitesmoke;
+    border-color: #dbdbdb;
+    color: #7a7a7a;
+    box-shadow: none;
+    pointer-events: none; }
+  .button.is-rounded, #documenter .docs-sidebar form.docs-search > input.button {
+    border-radius: 290486px;
+    padding-left: 1em;
+    padding-right: 1em; }
+
+.buttons {
+  align-items: center;
+  display: flex;
+  flex-wrap: wrap;
+  justify-content: flex-start; }
+  .buttons .button {
+    margin-bottom: 0.5rem; }
+    .buttons .button:not(:last-child):not(.is-fullwidth) {
+      margin-right: 0.5rem; }
+  .buttons:last-child {
+    margin-bottom: -0.5rem; }
+  .buttons:not(:last-child) {
+    margin-bottom: 1rem; }
+  .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large) {
+    border-radius: 2px;
+    font-size: 0.75rem; }
+  .buttons.are-medium .button:not(.is-small):not(.is-normal):not(.is-large) {
+    font-size: 1.25rem; }
+  .buttons.are-large .button:not(.is-small):not(.is-normal):not(.is-medium) {
+    font-size: 1.5rem; }
+  .buttons.has-addons .button:not(:first-child) {
+    border-bottom-left-radius: 0;
+    border-top-left-radius: 0; }
+  .buttons.has-addons .button:not(:last-child) {
+    border-bottom-right-radius: 0;
+    border-top-right-radius: 0;
+    margin-right: -1px; }
+  .buttons.has-addons .button:last-child {
+    margin-right: 0; }
+  .buttons.has-addons .button:hover, .buttons.has-addons .button.is-hovered {
+    z-index: 2; }
+  .buttons.has-addons .button:focus, .buttons.has-addons .button.is-focused, .buttons.has-addons .button:active, .buttons.has-addons .button.is-active, .buttons.has-addons .button.is-selected {
+    z-index: 3; }
+    .buttons.has-addons .button:focus:hover, .buttons.has-addons .button.is-focused:hover, .buttons.has-addons .button:active:hover, .buttons.has-addons .button.is-active:hover, .buttons.has-addons .button.is-selected:hover {
+      z-index: 4; }
+  .buttons.has-addons .button.is-expanded {
+    flex-grow: 1;
+    flex-shrink: 1; }
+  .buttons.is-centered {
+    justify-content: center; }
+    .buttons.is-centered:not(.has-addons) .button:not(.is-fullwidth) {
+      margin-left: 0.25rem;
+      margin-right: 0.25rem; }
+  .buttons.is-right {
+    justify-content: flex-end; }
+    .buttons.is-right:not(.has-addons) .button:not(.is-fullwidth) {
+      margin-left: 0.25rem;
+      margin-right: 0.25rem; }
+
+.container {
+  flex-grow: 1;
+  margin: 0 auto;
+  position: relative;
+  width: auto; }
+  @media screen and (min-width: 1056px) {
+    .container {
+      max-width: 992px; }
+      .container.is-fluid {
+        margin-left: 32px;
+        margin-right: 32px;
+        max-width: none; } }
+  @media screen and (max-width: 1215px) {
+    .container.is-widescreen {
+      max-width: 1152px; } }
+  @media screen and (max-width: 1407px) {
+    .container.is-fullhd {
+      max-width: 1344px; } }
+  @media screen and (min-width: 1216px) {
+    .container {
+      max-width: 1152px; } }
+  @media screen and (min-width: 1408px) {
+    .container {
+      max-width: 1344px; } }
+
+.content li + li {
+  margin-top: 0.25em; }
+
+.content p:not(:last-child),
+.content dl:not(:last-child),
+.content ol:not(:last-child),
+.content ul:not(:last-child),
+.content blockquote:not(:last-child),
+.content pre:not(:last-child),
+.content table:not(:last-child) {
+  margin-bottom: 1em; }
+
+.content h1,
+.content h2,
+.content h3,
+.content h4,
+.content h5,
+.content h6 {
+  color: #222222;
+  font-weight: 600;
+  line-height: 1.125; }
+
+.content h1 {
+  font-size: 2em;
+  margin-bottom: 0.5em; }
+  .content h1:not(:first-child) {
+    margin-top: 1em; }
+
+.content h2 {
+  font-size: 1.75em;
+  margin-bottom: 0.5714em; }
+  .content h2:not(:first-child) {
+    margin-top: 1.1428em; }
+
+.content h3 {
+  font-size: 1.5em;
+  margin-bottom: 0.6666em; }
+  .content h3:not(:first-child) {
+    margin-top: 1.3333em; }
+
+.content h4 {
+  font-size: 1.25em;
+  margin-bottom: 0.8em; }
+
+.content h5 {
+  font-size: 1.125em;
+  margin-bottom: 0.8888em; }
+
+.content h6 {
+  font-size: 1em;
+  margin-bottom: 1em; }
+
+.content blockquote {
+  background-color: whitesmoke;
+  border-left: 5px solid #dbdbdb;
+  padding: 1.25em 1.5em; }
+
+.content ol {
+  list-style-position: outside;
+  margin-left: 2em;
+  margin-top: 1em; }
+  .content ol:not([type]) {
+    list-style-type: decimal; }
+    .content ol:not([type]).is-lower-alpha {
+      list-style-type: lower-alpha; }
+    .content ol:not([type]).is-lower-roman {
+      list-style-type: lower-roman; }
+    .content ol:not([type]).is-upper-alpha {
+      list-style-type: upper-alpha; }
+    .content ol:not([type]).is-upper-roman {
+      list-style-type: upper-roman; }
+
+.content ul {
+  list-style: disc outside;
+  margin-left: 2em;
+  margin-top: 1em; }
+  .content ul ul {
+    list-style-type: circle;
+    margin-top: 0.5em; }
+    .content ul ul ul {
+      list-style-type: square; }
+
+.content dd {
+  margin-left: 2em; }
+
+.content figure {
+  margin-left: 2em;
+  margin-right: 2em;
+  text-align: center; }
+  .content figure:not(:first-child) {
+    margin-top: 2em; }
+  .content figure:not(:last-child) {
+    margin-bottom: 2em; }
+  .content figure img {
+    display: inline-block; }
+  .content figure figcaption {
+    font-style: italic; }
+
+.content pre {
+  -webkit-overflow-scrolling: touch;
+  overflow-x: auto;
+  padding: 0.7rem 0.5rem;
+  white-space: pre;
+  word-wrap: normal; }
+
+.content sup,
+.content sub {
+  font-size: 75%; }
+
+.content table {
+  width: 100%; }
+  .content table td,
+  .content table th {
+    border: 1px solid #dbdbdb;
+    border-width: 0 0 1px;
+    padding: 0.5em 0.75em;
+    vertical-align: top; }
+  .content table th {
+    color: #222222; }
+    .content table th:not([align]) {
+      text-align: left; }
+  .content table thead td,
+  .content table thead th {
+    border-width: 0 0 2px;
+    color: #222222; }
+  .content table tfoot td,
+  .content table tfoot th {
+    border-width: 2px 0 0;
+    color: #222222; }
+  .content table tbody tr:last-child td,
+  .content table tbody tr:last-child th {
+    border-bottom-width: 0; }
+
+.content .tabs li + li {
+  margin-top: 0; }
+
+.content.is-small, #documenter .docs-sidebar form.docs-search > input.content {
+  font-size: 0.75rem; }
+
+.content.is-medium {
+  font-size: 1.25rem; }
+
+.content.is-large {
+  font-size: 1.5rem; }
+
+.icon {
+  align-items: center;
+  display: inline-flex;
+  justify-content: center;
+  height: 1.5rem;
+  width: 1.5rem; }
+  .icon.is-small, #documenter .docs-sidebar form.docs-search > input.icon {
+    height: 1rem;
+    width: 1rem; }
+  .icon.is-medium {
+    height: 2rem;
+    width: 2rem; }
+  .icon.is-large {
+    height: 3rem;
+    width: 3rem; }
+
+.image, #documenter .docs-sidebar .docs-logo > img {
+  display: block;
+  position: relative; }
+  .image img, #documenter .docs-sidebar .docs-logo > img img {
+    display: block;
+    height: auto;
+    width: 100%; }
+    .image img.is-rounded, #documenter .docs-sidebar .docs-logo > img img.is-rounded {
+      border-radius: 290486px; }
+  .image.is-square img, #documenter .docs-sidebar .docs-logo > img.is-square img,
+  .image.is-square .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-square .has-ratio, .image.is-1by1 img, #documenter .docs-sidebar .docs-logo > img.is-1by1 img,
+  .image.is-1by1 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-1by1 .has-ratio, .image.is-5by4 img, #documenter .docs-sidebar .docs-logo > img.is-5by4 img,
+  .image.is-5by4 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-5by4 .has-ratio, .image.is-4by3 img, #documenter .docs-sidebar .docs-logo > img.is-4by3 img,
+  .image.is-4by3 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-4by3 .has-ratio, .image.is-3by2 img, #documenter .docs-sidebar .docs-logo > img.is-3by2 img,
+  .image.is-3by2 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-3by2 .has-ratio, .image.is-5by3 img, #documenter .docs-sidebar .docs-logo > img.is-5by3 img,
+  .image.is-5by3 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-5by3 .has-ratio, .image.is-16by9 img, #documenter .docs-sidebar .docs-logo > img.is-16by9 img,
+  .image.is-16by9 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-16by9 .has-ratio, .image.is-2by1 img, #documenter .docs-sidebar .docs-logo > img.is-2by1 img,
+  .image.is-2by1 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-2by1 .has-ratio, .image.is-3by1 img, #documenter .docs-sidebar .docs-logo > img.is-3by1 img,
+  .image.is-3by1 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-3by1 .has-ratio, .image.is-4by5 img, #documenter .docs-sidebar .docs-logo > img.is-4by5 img,
+  .image.is-4by5 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-4by5 .has-ratio, .image.is-3by4 img, #documenter .docs-sidebar .docs-logo > img.is-3by4 img,
+  .image.is-3by4 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-3by4 .has-ratio, .image.is-2by3 img, #documenter .docs-sidebar .docs-logo > img.is-2by3 img,
+  .image.is-2by3 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-2by3 .has-ratio, .image.is-3by5 img, #documenter .docs-sidebar .docs-logo > img.is-3by5 img,
+  .image.is-3by5 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-3by5 .has-ratio, .image.is-9by16 img, #documenter .docs-sidebar .docs-logo > img.is-9by16 img,
+  .image.is-9by16 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-9by16 .has-ratio, .image.is-1by2 img, #documenter .docs-sidebar .docs-logo > img.is-1by2 img,
+  .image.is-1by2 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-1by2 .has-ratio, .image.is-1by3 img, #documenter .docs-sidebar .docs-logo > img.is-1by3 img,
+  .image.is-1by3 .has-ratio,
+  #documenter .docs-sidebar .docs-logo > img.is-1by3 .has-ratio {
+    height: 100%;
+    width: 100%; }
+  .image.is-square, #documenter .docs-sidebar .docs-logo > img.is-square, .image.is-1by1, #documenter .docs-sidebar .docs-logo > img.is-1by1 {
+    padding-top: 100%; }
+  .image.is-5by4, #documenter .docs-sidebar .docs-logo > img.is-5by4 {
+    padding-top: 80%; }
+  .image.is-4by3, #documenter .docs-sidebar .docs-logo > img.is-4by3 {
+    padding-top: 75%; }
+  .image.is-3by2, #documenter .docs-sidebar .docs-logo > img.is-3by2 {
+    padding-top: 66.6666%; }
+  .image.is-5by3, #documenter .docs-sidebar .docs-logo > img.is-5by3 {
+    padding-top: 60%; }
+  .image.is-16by9, #documenter .docs-sidebar .docs-logo > img.is-16by9 {
+    padding-top: 56.25%; }
+  .image.is-2by1, #documenter .docs-sidebar .docs-logo > img.is-2by1 {
+    padding-top: 50%; }
+  .image.is-3by1, #documenter .docs-sidebar .docs-logo > img.is-3by1 {
+    padding-top: 33.3333%; }
+  .image.is-4by5, #documenter .docs-sidebar .docs-logo > img.is-4by5 {
+    padding-top: 125%; }
+  .image.is-3by4, #documenter .docs-sidebar .docs-logo > img.is-3by4 {
+    padding-top: 133.3333%; }
+  .image.is-2by3, #documenter .docs-sidebar .docs-logo > img.is-2by3 {
+    padding-top: 150%; }
+  .image.is-3by5, #documenter .docs-sidebar .docs-logo > img.is-3by5 {
+    padding-top: 166.6666%; }
+  .image.is-9by16, #documenter .docs-sidebar .docs-logo > img.is-9by16 {
+    padding-top: 177.7777%; }
+  .image.is-1by2, #documenter .docs-sidebar .docs-logo > img.is-1by2 {
+    padding-top: 200%; }
+  .image.is-1by3, #documenter .docs-sidebar .docs-logo > img.is-1by3 {
+    padding-top: 300%; }
+  .image.is-16x16, #documenter .docs-sidebar .docs-logo > img.is-16x16 {
+    height: 16px;
+    width: 16px; }
+  .image.is-24x24, #documenter .docs-sidebar .docs-logo > img.is-24x24 {
+    height: 24px;
+    width: 24px; }
+  .image.is-32x32, #documenter .docs-sidebar .docs-logo > img.is-32x32 {
+    height: 32px;
+    width: 32px; }
+  .image.is-48x48, #documenter .docs-sidebar .docs-logo > img.is-48x48 {
+    height: 48px;
+    width: 48px; }
+  .image.is-64x64, #documenter .docs-sidebar .docs-logo > img.is-64x64 {
+    height: 64px;
+    width: 64px; }
+  .image.is-96x96, #documenter .docs-sidebar .docs-logo > img.is-96x96 {
+    height: 96px;
+    width: 96px; }
+  .image.is-128x128, #documenter .docs-sidebar .docs-logo > img.is-128x128 {
+    height: 128px;
+    width: 128px; }
+
+.notification {
+  background-color: whitesmoke;
+  border-radius: 4px;
+  padding: 1.25rem 2.5rem 1.25rem 1.5rem;
+  position: relative; }
+  .notification a:not(.button):not(.dropdown-item) {
+    color: currentColor;
+    text-decoration: underline; }
+  .notification strong {
+    color: currentColor; }
+  .notification code,
+  .notification pre {
+    background: white; }
+  .notification pre code {
+    background: transparent; }
+  .notification > .delete {
+    position: absolute;
+    right: 0.5rem;
+    top: 0.5rem; }
+  .notification .title,
+  .notification .subtitle,
+  .notification .content {
+    color: currentColor; }
+  .notification.is-white {
+    background-color: white;
+    color: #0a0a0a; }
+  .notification.is-black {
+    background-color: #0a0a0a;
+    color: white; }
+  .notification.is-light {
+    background-color: whitesmoke;
+    color: #363636; }
+  .notification.is-dark, .content kbd.notification {
+    background-color: #363636;
+    color: whitesmoke; }
+  .notification.is-primary, .docstring > section > a.notification.docs-sourcelink {
+    background-color: #4eb5de;
+    color: #fff; }
+  .notification.is-link {
+    background-color: #2e63b8;
+    color: #fff; }
+  .notification.is-info {
+    background-color: #209cee;
+    color: #fff; }
+  .notification.is-success {
+    background-color: #22c35b;
+    color: #fff; }
+  .notification.is-warning {
+    background-color: #ffdd57;
+    color: rgba(0, 0, 0, 0.7); }
+  .notification.is-danger {
+    background-color: #da0b00;
+    color: #fff; }
+
+.progress {
+  -moz-appearance: none;
+  -webkit-appearance: none;
+  border: none;
+  border-radius: 290486px;
+  display: block;
+  height: 1rem;
+  overflow: hidden;
+  padding: 0;
+  width: 100%; }
+  .progress::-webkit-progress-bar {
+    background-color: #dbdbdb; }
+  .progress::-webkit-progress-value {
+    background-color: #222222; }
+  .progress::-moz-progress-bar {
+    background-color: #222222; }
+  .progress::-ms-fill {
+    background-color: #222222;
+    border: none; }
+  .progress.is-white::-webkit-progress-value {
+    background-color: white; }
+  .progress.is-white::-moz-progress-bar {
+    background-color: white; }
+  .progress.is-white::-ms-fill {
+    background-color: white; }
+  .progress.is-white:indeterminate {
+    background-image: linear-gradient(to right, white 30%, #dbdbdb 30%); }
+  .progress.is-black::-webkit-progress-value {
+    background-color: #0a0a0a; }
+  .progress.is-black::-moz-progress-bar {
+    background-color: #0a0a0a; }
+  .progress.is-black::-ms-fill {
+    background-color: #0a0a0a; }
+  .progress.is-black:indeterminate {
+    background-image: linear-gradient(to right, #0a0a0a 30%, #dbdbdb 30%); }
+  .progress.is-light::-webkit-progress-value {
+    background-color: whitesmoke; }
+  .progress.is-light::-moz-progress-bar {
+    background-color: whitesmoke; }
+  .progress.is-light::-ms-fill {
+    background-color: whitesmoke; }
+  .progress.is-light:indeterminate {
+    background-image: linear-gradient(to right, whitesmoke 30%, #dbdbdb 30%); }
+  .progress.is-dark::-webkit-progress-value, .content kbd.progress::-webkit-progress-value {
+    background-color: #363636; }
+  .progress.is-dark::-moz-progress-bar, .content kbd.progress::-moz-progress-bar {
+    background-color: #363636; }
+  .progress.is-dark::-ms-fill, .content kbd.progress::-ms-fill {
+    background-color: #363636; }
+  .progress.is-dark:indeterminate, .content kbd.progress:indeterminate {
+    background-image: linear-gradient(to right, #363636 30%, #dbdbdb 30%); }
+  .progress.is-primary::-webkit-progress-value, .docstring > section > a.progress.docs-sourcelink::-webkit-progress-value {
+    background-color: #4eb5de; }
+  .progress.is-primary::-moz-progress-bar, .docstring > section > a.progress.docs-sourcelink::-moz-progress-bar {
+    background-color: #4eb5de; }
+  .progress.is-primary::-ms-fill, .docstring > section > a.progress.docs-sourcelink::-ms-fill {
+    background-color: #4eb5de; }
+  .progress.is-primary:indeterminate, .docstring > section > a.progress.docs-sourcelink:indeterminate {
+    background-image: linear-gradient(to right, #4eb5de 30%, #dbdbdb 30%); }
+  .progress.is-link::-webkit-progress-value {
+    background-color: #2e63b8; }
+  .progress.is-link::-moz-progress-bar {
+    background-color: #2e63b8; }
+  .progress.is-link::-ms-fill {
+    background-color: #2e63b8; }
+  .progress.is-link:indeterminate {
+    background-image: linear-gradient(to right, #2e63b8 30%, #dbdbdb 30%); }
+  .progress.is-info::-webkit-progress-value {
+    background-color: #209cee; }
+  .progress.is-info::-moz-progress-bar {
+    background-color: #209cee; }
+  .progress.is-info::-ms-fill {
+    background-color: #209cee; }
+  .progress.is-info:indeterminate {
+    background-image: linear-gradient(to right, #209cee 30%, #dbdbdb 30%); }
+  .progress.is-success::-webkit-progress-value {
+    background-color: #22c35b; }
+  .progress.is-success::-moz-progress-bar {
+    background-color: #22c35b; }
+  .progress.is-success::-ms-fill {
+    background-color: #22c35b; }
+  .progress.is-success:indeterminate {
+    background-image: linear-gradient(to right, #22c35b 30%, #dbdbdb 30%); }
+  .progress.is-warning::-webkit-progress-value {
+    background-color: #ffdd57; }
+  .progress.is-warning::-moz-progress-bar {
+    background-color: #ffdd57; }
+  .progress.is-warning::-ms-fill {
+    background-color: #ffdd57; }
+  .progress.is-warning:indeterminate {
+    background-image: linear-gradient(to right, #ffdd57 30%, #dbdbdb 30%); }
+  .progress.is-danger::-webkit-progress-value {
+    background-color: #da0b00; }
+  .progress.is-danger::-moz-progress-bar {
+    background-color: #da0b00; }
+  .progress.is-danger::-ms-fill {
+    background-color: #da0b00; }
+  .progress.is-danger:indeterminate {
+    background-image: linear-gradient(to right, #da0b00 30%, #dbdbdb 30%); }
+  .progress:indeterminate {
+    animation-duration: 1.5s;
+    animation-iteration-count: infinite;
+    animation-name: moveIndeterminate;
+    animation-timing-function: linear;
+    background-color: #dbdbdb;
+    background-image: linear-gradient(to right, #222222 30%, #dbdbdb 30%);
+    background-position: top left;
+    background-repeat: no-repeat;
+    background-size: 150% 150%; }
+    .progress:indeterminate::-webkit-progress-bar {
+      background-color: transparent; }
+    .progress:indeterminate::-moz-progress-bar {
+      background-color: transparent; }
+  .progress.is-small, #documenter .docs-sidebar form.docs-search > input.progress {
+    height: 0.75rem; }
+  .progress.is-medium {
+    height: 1.25rem; }
+  .progress.is-large {
+    height: 1.5rem; }
+
+@keyframes moveIndeterminate {
+  from {
+    background-position: 200% 0; }
+  to {
+    background-position: -200% 0; } }
+
+.table {
+  background-color: white;
+  color: #363636; }
+  .table td,
+  .table th {
+    border: 1px solid #dbdbdb;
+    border-width: 0 0 1px;
+    padding: 0.5em 0.75em;
+    vertical-align: top; }
+    .table td.is-white,
+    .table th.is-white {
+      background-color: white;
+      border-color: white;
+      color: #0a0a0a; }
+    .table td.is-black,
+    .table th.is-black {
+      background-color: #0a0a0a;
+      border-color: #0a0a0a;
+      color: white; }
+    .table td.is-light,
+    .table th.is-light {
+      background-color: whitesmoke;
+      border-color: whitesmoke;
+      color: #363636; }
+    .table td.is-dark,
+    .table th.is-dark {
+      background-color: #363636;
+      border-color: #363636;
+      color: whitesmoke; }
+    .table td.is-primary,
+    .table th.is-primary {
+      background-color: #4eb5de;
+      border-color: #4eb5de;
+      color: #fff; }
+    .table td.is-link,
+    .table th.is-link {
+      background-color: #2e63b8;
+      border-color: #2e63b8;
+      color: #fff; }
+    .table td.is-info,
+    .table th.is-info {
+      background-color: #209cee;
+      border-color: #209cee;
+      color: #fff; }
+    .table td.is-success,
+    .table th.is-success {
+      background-color: #22c35b;
+      border-color: #22c35b;
+      color: #fff; }
+    .table td.is-warning,
+    .table th.is-warning {
+      background-color: #ffdd57;
+      border-color: #ffdd57;
+      color: rgba(0, 0, 0, 0.7); }
+    .table td.is-danger,
+    .table th.is-danger {
+      background-color: #da0b00;
+      border-color: #da0b00;
+      color: #fff; }
+    .table td.is-narrow,
+    .table th.is-narrow {
+      white-space: nowrap;
+      width: 1%; }
+    .table td.is-selected,
+    .table th.is-selected {
+      background-color: #4eb5de;
+      color: #fff; }
+      .table td.is-selected a,
+      .table td.is-selected strong,
+      .table th.is-selected a,
+      .table th.is-selected strong {
+        color: currentColor; }
+  .table th {
+    color: #222222; }
+    .table th:not([align]) {
+      text-align: left; }
+  .table tr.is-selected {
+    background-color: #4eb5de;
+    color: #fff; }
+    .table tr.is-selected a,
+    .table tr.is-selected strong {
+      color: currentColor; }
+    .table tr.is-selected td,
+    .table tr.is-selected th {
+      border-color: #fff;
+      color: currentColor; }
+  .table thead {
+    background-color: transparent; }
+    .table thead td,
+    .table thead th {
+      border-width: 0 0 2px;
+      color: #222222; }
+  .table tfoot {
+    background-color: transparent; }
+    .table tfoot td,
+    .table tfoot th {
+      border-width: 2px 0 0;
+      color: #222222; }
+  .table tbody {
+    background-color: transparent; }
+    .table tbody tr:last-child td,
+    .table tbody tr:last-child th {
+      border-bottom-width: 0; }
+  .table.is-bordered td,
+  .table.is-bordered th {
+    border-width: 1px; }
+  .table.is-bordered tr:last-child td,
+  .table.is-bordered tr:last-child th {
+    border-bottom-width: 1px; }
+  .table.is-fullwidth {
+    width: 100%; }
+  .table.is-hoverable tbody tr:not(.is-selected):hover {
+    background-color: #fafafa; }
+  .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover {
+    background-color: #fafafa; }
+    .table.is-hoverable.is-striped tbody tr:not(.is-selected):hover:nth-child(even) {
+      background-color: whitesmoke; }
+  .table.is-narrow td,
+  .table.is-narrow th {
+    padding: 0.25em 0.5em; }
+  .table.is-striped tbody tr:not(.is-selected):nth-child(even) {
+    background-color: #fafafa; }
+
+.table-container {
+  -webkit-overflow-scrolling: touch;
+  overflow: auto;
+  overflow-y: hidden;
+  max-width: 100%; }
+
+.tags {
+  align-items: center;
+  display: flex;
+  flex-wrap: wrap;
+  justify-content: flex-start; }
+  .tags .tag, .tags .docstring > section > a.docs-sourcelink, .tags .content kbd, .content .tags kbd {
+    margin-bottom: 0.5rem; }
+    .tags .tag:not(:last-child), .tags .docstring > section > a.docs-sourcelink:not(:last-child), .tags .content kbd:not(:last-child), .content .tags kbd:not(:last-child) {
+      margin-right: 0.5rem; }
+  .tags:last-child {
+    margin-bottom: -0.5rem; }
+  .tags:not(:last-child) {
+    margin-bottom: 1rem; }
+  .tags.are-medium .tag:not(.is-normal):not(.is-large), .tags.are-medium .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-large), .tags.are-medium .content kbd:not(.is-normal):not(.is-large), .content .tags.are-medium kbd:not(.is-normal):not(.is-large) {
+    font-size: 1rem; }
+  .tags.are-large .tag:not(.is-normal):not(.is-medium), .tags.are-large .docstring > section > a.docs-sourcelink:not(.is-normal):not(.is-medium), .tags.are-large .content kbd:not(.is-normal):not(.is-medium), .content .tags.are-large kbd:not(.is-normal):not(.is-medium) {
+    font-size: 1.25rem; }
+  .tags.is-centered {
+    justify-content: center; }
+    .tags.is-centered .tag, .tags.is-centered .docstring > section > a.docs-sourcelink, .tags.is-centered .content kbd, .content .tags.is-centered kbd {
+      margin-right: 0.25rem;
+      margin-left: 0.25rem; }
+  .tags.is-right {
+    justify-content: flex-end; }
+    .tags.is-right .tag:not(:first-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:first-child), .tags.is-right .content kbd:not(:first-child), .content .tags.is-right kbd:not(:first-child) {
+      margin-left: 0.5rem; }
+    .tags.is-right .tag:not(:last-child), .tags.is-right .docstring > section > a.docs-sourcelink:not(:last-child), .tags.is-right .content kbd:not(:last-child), .content .tags.is-right kbd:not(:last-child) {
+      margin-right: 0; }
+  .tags.has-addons .tag, .tags.has-addons .docstring > section > a.docs-sourcelink, .tags.has-addons .content kbd, .content .tags.has-addons kbd {
+    margin-right: 0; }
+    .tags.has-addons .tag:not(:first-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:first-child), .tags.has-addons .content kbd:not(:first-child), .content .tags.has-addons kbd:not(:first-child) {
+      margin-left: 0;
+      border-bottom-left-radius: 0;
+      border-top-left-radius: 0; }
+    .tags.has-addons .tag:not(:last-child), .tags.has-addons .docstring > section > a.docs-sourcelink:not(:last-child), .tags.has-addons .content kbd:not(:last-child), .content .tags.has-addons kbd:not(:last-child) {
+      border-bottom-right-radius: 0;
+      border-top-right-radius: 0; }
+
+.tag:not(body), .docstring > section > a.docs-sourcelink:not(body), .content kbd:not(body) {
+  align-items: center;
+  background-color: whitesmoke;
+  border-radius: 4px;
+  color: #222222;
+  display: inline-flex;
+  font-size: 0.75rem;
+  height: 2em;
+  justify-content: center;
+  line-height: 1.5;
+  padding-left: 0.75em;
+  padding-right: 0.75em;
+  white-space: nowrap; }
+  .tag:not(body) .delete, .docstring > section > a.docs-sourcelink:not(body) .delete, .content kbd:not(body) .delete {
+    margin-left: 0.25rem;
+    margin-right: -0.375rem; }
+  .tag:not(body).is-white, .docstring > section > a.docs-sourcelink:not(body).is-white, .content kbd:not(body).is-white {
+    background-color: white;
+    color: #0a0a0a; }
+  .tag:not(body).is-black, .docstring > section > a.docs-sourcelink:not(body).is-black, .content kbd:not(body).is-black {
+    background-color: #0a0a0a;
+    color: white; }
+  .tag:not(body).is-light, .docstring > section > a.docs-sourcelink:not(body).is-light, .content kbd:not(body).is-light {
+    background-color: whitesmoke;
+    color: #363636; }
+  .tag:not(body).is-dark, .docstring > section > a.docs-sourcelink:not(body).is-dark, .content kbd:not(body) {
+    background-color: #363636;
+    color: whitesmoke; }
+  .tag:not(body).is-primary, .docstring > section > a.docs-sourcelink:not(body), .content kbd:not(body).is-primary {
+    background-color: #4eb5de;
+    color: #fff; }
+  .tag:not(body).is-link, .docstring > section > a.docs-sourcelink:not(body).is-link, .content kbd:not(body).is-link {
+    background-color: #2e63b8;
+    color: #fff; }
+  .tag:not(body).is-info, .docstring > section > a.docs-sourcelink:not(body).is-info, .content kbd:not(body).is-info {
+    background-color: #209cee;
+    color: #fff; }
+  .tag:not(body).is-success, .docstring > section > a.docs-sourcelink:not(body).is-success, .content kbd:not(body).is-success {
+    background-color: #22c35b;
+    color: #fff; }
+  .tag:not(body).is-warning, .docstring > section > a.docs-sourcelink:not(body).is-warning, .content kbd:not(body).is-warning {
+    background-color: #ffdd57;
+    color: rgba(0, 0, 0, 0.7); }
+  .tag:not(body).is-danger, .docstring > section > a.docs-sourcelink:not(body).is-danger, .content kbd:not(body).is-danger {
+    background-color: #da0b00;
+    color: #fff; }
+  .tag:not(body).is-normal, .docstring > section > a.docs-sourcelink:not(body).is-normal, .content kbd:not(body).is-normal {
+    font-size: 0.75rem; }
+  .tag:not(body).is-medium, .docstring > section > a.docs-sourcelink:not(body).is-medium, .content kbd:not(body).is-medium {
+    font-size: 1rem; }
+  .tag:not(body).is-large, .docstring > section > a.docs-sourcelink:not(body).is-large, .content kbd:not(body).is-large {
+    font-size: 1.25rem; }
+  .tag:not(body) .icon:first-child:not(:last-child), .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:not(:last-child), .content kbd:not(body) .icon:first-child:not(:last-child) {
+    margin-left: -0.375em;
+    margin-right: 0.1875em; }
+  .tag:not(body) .icon:last-child:not(:first-child), .docstring > section > a.docs-sourcelink:not(body) .icon:last-child:not(:first-child), .content kbd:not(body) .icon:last-child:not(:first-child) {
+    margin-left: 0.1875em;
+    margin-right: -0.375em; }
+  .tag:not(body) .icon:first-child:last-child, .docstring > section > a.docs-sourcelink:not(body) .icon:first-child:last-child, .content kbd:not(body) .icon:first-child:last-child {
+    margin-left: -0.375em;
+    margin-right: -0.375em; }
+  .tag:not(body).is-delete, .docstring > section > a.docs-sourcelink:not(body).is-delete, .content kbd:not(body).is-delete {
+    margin-left: 1px;
+    padding: 0;
+    position: relative;
+    width: 2em; }
+    .tag:not(body).is-delete::before, .docstring > section > a.docs-sourcelink:not(body).is-delete::before, .content kbd:not(body).is-delete::before, .tag:not(body).is-delete::after, .docstring > section > a.docs-sourcelink:not(body).is-delete::after, .content kbd:not(body).is-delete::after {
+      background-color: currentColor;
+      content: "";
+      display: block;
+      left: 50%;
+      position: absolute;
+      top: 50%;
+      transform: translateX(-50%) translateY(-50%) rotate(45deg);
+      transform-origin: center center; }
+    .tag:not(body).is-delete::before, .docstring > section > a.docs-sourcelink:not(body).is-delete::before, .content kbd:not(body).is-delete::before {
+      height: 1px;
+      width: 50%; }
+    .tag:not(body).is-delete::after, .docstring > section > a.docs-sourcelink:not(body).is-delete::after, .content kbd:not(body).is-delete::after {
+      height: 50%;
+      width: 1px; }
+    .tag:not(body).is-delete:hover, .docstring > section > a.docs-sourcelink:not(body).is-delete:hover, .content kbd:not(body).is-delete:hover, .tag:not(body).is-delete:focus, .docstring > section > a.docs-sourcelink:not(body).is-delete:focus, .content kbd:not(body).is-delete:focus {
+      background-color: #e8e8e8; }
+    .tag:not(body).is-delete:active, .docstring > section > a.docs-sourcelink:not(body).is-delete:active, .content kbd:not(body).is-delete:active {
+      background-color: #dbdbdb; }
+  .tag:not(body).is-rounded, .docstring > section > a.docs-sourcelink:not(body).is-rounded, .content kbd:not(body).is-rounded, #documenter .docs-sidebar form.docs-search > input.tag:not(body) {
+    border-radius: 290486px; }
+
+a.tag:hover, .docstring > section > a.docs-sourcelink:hover {
+  text-decoration: underline; }
+
+.title,
+.subtitle {
+  word-break: break-word; }
+  .title em,
+  .title span,
+  .subtitle em,
+  .subtitle span {
+    font-weight: inherit; }
+  .title sub,
+  .subtitle sub {
+    font-size: 0.75em; }
+  .title sup,
+  .subtitle sup {
+    font-size: 0.75em; }
+  .title .tag, .title .docstring > section > a.docs-sourcelink, .title .content kbd, .content .title kbd,
+  .subtitle .tag,
+  .subtitle .docstring > section > a.docs-sourcelink,
+  .subtitle .content kbd,
+  .content .subtitle kbd {
+    vertical-align: middle; }
+
+.title {
+  color: #363636;
+  font-size: 2rem;
+  font-weight: 600;
+  line-height: 1.125; }
+  .title strong {
+    color: inherit;
+    font-weight: inherit; }
+  .title + .highlight {
+    margin-top: -0.75rem; }
+  .title:not(.is-spaced) + .subtitle {
+    margin-top: -1.25rem; }
+  .title.is-1 {
+    font-size: 3rem; }
+  .title.is-2 {
+    font-size: 2.5rem; }
+  .title.is-3 {
+    font-size: 2rem; }
+  .title.is-4 {
+    font-size: 1.5rem; }
+  .title.is-5 {
+    font-size: 1.25rem; }
+  .title.is-6 {
+    font-size: 1rem; }
+  .title.is-7 {
+    font-size: 0.75rem; }
+
+.subtitle {
+  color: #4a4a4a;
+  font-size: 1.25rem;
+  font-weight: 400;
+  line-height: 1.25; }
+  .subtitle strong {
+    color: #363636;
+    font-weight: 600; }
+  .subtitle:not(.is-spaced) + .title {
+    margin-top: -1.25rem; }
+  .subtitle.is-1 {
+    font-size: 3rem; }
+  .subtitle.is-2 {
+    font-size: 2.5rem; }
+  .subtitle.is-3 {
+    font-size: 2rem; }
+  .subtitle.is-4 {
+    font-size: 1.5rem; }
+  .subtitle.is-5 {
+    font-size: 1.25rem; }
+  .subtitle.is-6 {
+    font-size: 1rem; }
+  .subtitle.is-7 {
+    font-size: 0.75rem; }
+
+.heading {
+  display: block;
+  font-size: 11px;
+  letter-spacing: 1px;
+  margin-bottom: 5px;
+  text-transform: uppercase; }
+
+.highlight {
+  font-weight: 400;
+  max-width: 100%;
+  overflow: hidden;
+  padding: 0; }
+  .highlight pre {
+    overflow: auto;
+    max-width: 100%; }
+
+.number {
+  align-items: center;
+  background-color: whitesmoke;
+  border-radius: 290486px;
+  display: inline-flex;
+  font-size: 1.25rem;
+  height: 2em;
+  justify-content: center;
+  margin-right: 1.5rem;
+  min-width: 2.5em;
+  padding: 0.25rem 0.5rem;
+  text-align: center;
+  vertical-align: top; }
+
+.input, #documenter .docs-sidebar form.docs-search > input, .textarea, .select select {
+  background-color: white;
+  border-color: #dbdbdb;
+  border-radius: 4px;
+  color: #363636; }
+  .input::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input::-moz-placeholder, .textarea::-moz-placeholder, .select select::-moz-placeholder {
+    color: rgba(54, 54, 54, 0.3); }
+  .input::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder, .textarea::-webkit-input-placeholder, .select select::-webkit-input-placeholder {
+    color: rgba(54, 54, 54, 0.3); }
+  .input:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input:-moz-placeholder, .textarea:-moz-placeholder, .select select:-moz-placeholder {
+    color: rgba(54, 54, 54, 0.3); }
+  .input:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder, .textarea:-ms-input-placeholder, .select select:-ms-input-placeholder {
+    color: rgba(54, 54, 54, 0.3); }
+  .input:hover, #documenter .docs-sidebar form.docs-search > input:hover, .textarea:hover, .select select:hover, .is-hovered.input, #documenter .docs-sidebar form.docs-search > input.is-hovered, .is-hovered.textarea, .select select.is-hovered {
+    border-color: #b5b5b5; }
+  .input:focus, #documenter .docs-sidebar form.docs-search > input:focus, .textarea:focus, .select select:focus, .is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-focused, .is-focused.textarea, .select select.is-focused, .input:active, #documenter .docs-sidebar form.docs-search > input:active, .textarea:active, .select select:active, .is-active.input, #documenter .docs-sidebar form.docs-search > input.is-active, .is-active.textarea, .select select.is-active {
+    border-color: #2e63b8;
+    box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); }
+  .input[disabled], #documenter .docs-sidebar form.docs-search > input[disabled], .textarea[disabled], .select select[disabled],
+  fieldset[disabled] .input,
+  fieldset[disabled] #documenter .docs-sidebar form.docs-search > input,
+  #documenter .docs-sidebar fieldset[disabled] form.docs-search > input,
+  fieldset[disabled] .textarea,
+  fieldset[disabled] .select select,
+  .select fieldset[disabled] select {
+    background-color: whitesmoke;
+    border-color: whitesmoke;
+    box-shadow: none;
+    color: #7a7a7a; }
+    .input[disabled]::-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-moz-placeholder, .textarea[disabled]::-moz-placeholder, .select select[disabled]::-moz-placeholder,
+    fieldset[disabled] .input::-moz-placeholder,
+    fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-moz-placeholder,
+    #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-moz-placeholder,
+    fieldset[disabled] .textarea::-moz-placeholder,
+    fieldset[disabled] .select select::-moz-placeholder,
+    .select fieldset[disabled] select::-moz-placeholder {
+      color: rgba(122, 122, 122, 0.3); }
+    .input[disabled]::-webkit-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]::-webkit-input-placeholder, .textarea[disabled]::-webkit-input-placeholder, .select select[disabled]::-webkit-input-placeholder,
+    fieldset[disabled] .input::-webkit-input-placeholder,
+    fieldset[disabled] #documenter .docs-sidebar form.docs-search > input::-webkit-input-placeholder,
+    #documenter .docs-sidebar fieldset[disabled] form.docs-search > input::-webkit-input-placeholder,
+    fieldset[disabled] .textarea::-webkit-input-placeholder,
+    fieldset[disabled] .select select::-webkit-input-placeholder,
+    .select fieldset[disabled] select::-webkit-input-placeholder {
+      color: rgba(122, 122, 122, 0.3); }
+    .input[disabled]:-moz-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-moz-placeholder, .textarea[disabled]:-moz-placeholder, .select select[disabled]:-moz-placeholder,
+    fieldset[disabled] .input:-moz-placeholder,
+    fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-moz-placeholder,
+    #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-moz-placeholder,
+    fieldset[disabled] .textarea:-moz-placeholder,
+    fieldset[disabled] .select select:-moz-placeholder,
+    .select fieldset[disabled] select:-moz-placeholder {
+      color: rgba(122, 122, 122, 0.3); }
+    .input[disabled]:-ms-input-placeholder, #documenter .docs-sidebar form.docs-search > input[disabled]:-ms-input-placeholder, .textarea[disabled]:-ms-input-placeholder, .select select[disabled]:-ms-input-placeholder,
+    fieldset[disabled] .input:-ms-input-placeholder,
+    fieldset[disabled] #documenter .docs-sidebar form.docs-search > input:-ms-input-placeholder,
+    #documenter .docs-sidebar fieldset[disabled] form.docs-search > input:-ms-input-placeholder,
+    fieldset[disabled] .textarea:-ms-input-placeholder,
+    fieldset[disabled] .select select:-ms-input-placeholder,
+    .select fieldset[disabled] select:-ms-input-placeholder {
+      color: rgba(122, 122, 122, 0.3); }
+
+.input, #documenter .docs-sidebar form.docs-search > input, .textarea {
+  box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.1);
+  max-width: 100%;
+  width: 100%; }
+  .input[readonly], #documenter .docs-sidebar form.docs-search > input[readonly], .textarea[readonly] {
+    box-shadow: none; }
+  .is-white.input, #documenter .docs-sidebar form.docs-search > input.is-white, .is-white.textarea {
+    border-color: white; }
+    .is-white.input:focus, #documenter .docs-sidebar form.docs-search > input.is-white:focus, .is-white.textarea:focus, .is-white.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-white.is-focused, .is-white.is-focused.textarea, .is-white.input:active, #documenter .docs-sidebar form.docs-search > input.is-white:active, .is-white.textarea:active, .is-white.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-white.is-active, .is-white.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+  .is-black.input, #documenter .docs-sidebar form.docs-search > input.is-black, .is-black.textarea {
+    border-color: #0a0a0a; }
+    .is-black.input:focus, #documenter .docs-sidebar form.docs-search > input.is-black:focus, .is-black.textarea:focus, .is-black.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-black.is-focused, .is-black.is-focused.textarea, .is-black.input:active, #documenter .docs-sidebar form.docs-search > input.is-black:active, .is-black.textarea:active, .is-black.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-black.is-active, .is-black.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+  .is-light.input, #documenter .docs-sidebar form.docs-search > input.is-light, .is-light.textarea {
+    border-color: whitesmoke; }
+    .is-light.input:focus, #documenter .docs-sidebar form.docs-search > input.is-light:focus, .is-light.textarea:focus, .is-light.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-light.is-focused, .is-light.is-focused.textarea, .is-light.input:active, #documenter .docs-sidebar form.docs-search > input.is-light:active, .is-light.textarea:active, .is-light.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-light.is-active, .is-light.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }
+  .is-dark.input, .content kbd.input, #documenter .docs-sidebar form.docs-search > input.is-dark, .is-dark.textarea, .content kbd.textarea {
+    border-color: #363636; }
+    .is-dark.input:focus, .content kbd.input:focus, #documenter .docs-sidebar form.docs-search > input.is-dark:focus, .is-dark.textarea:focus, .content kbd.textarea:focus, .is-dark.is-focused.input, .content kbd.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-dark.is-focused, .is-dark.is-focused.textarea, .content kbd.is-focused.textarea, .is-dark.input:active, .content kbd.input:active, #documenter .docs-sidebar form.docs-search > input.is-dark:active, .is-dark.textarea:active, .content kbd.textarea:active, .is-dark.is-active.input, .content kbd.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-dark.is-active, .is-dark.is-active.textarea, .content kbd.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }
+  .is-primary.input, .docstring > section > a.input.docs-sourcelink, #documenter .docs-sidebar form.docs-search > input.is-primary, .is-primary.textarea, .docstring > section > a.textarea.docs-sourcelink {
+    border-color: #4eb5de; }
+    .is-primary.input:focus, .docstring > section > a.input.docs-sourcelink:focus, #documenter .docs-sidebar form.docs-search > input.is-primary:focus, .is-primary.textarea:focus, .docstring > section > a.textarea.docs-sourcelink:focus, .is-primary.is-focused.input, .docstring > section > a.is-focused.input.docs-sourcelink, #documenter .docs-sidebar form.docs-search > input.is-primary.is-focused, .is-primary.is-focused.textarea, .docstring > section > a.is-focused.textarea.docs-sourcelink, .is-primary.input:active, .docstring > section > a.input.docs-sourcelink:active, #documenter .docs-sidebar form.docs-search > input.is-primary:active, .is-primary.textarea:active, .docstring > section > a.textarea.docs-sourcelink:active, .is-primary.is-active.input, .docstring > section > a.is-active.input.docs-sourcelink, #documenter .docs-sidebar form.docs-search > input.is-primary.is-active, .is-primary.is-active.textarea, .docstring > section > a.is-active.textarea.docs-sourcelink {
+      box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }
+  .is-link.input, #documenter .docs-sidebar form.docs-search > input.is-link, .is-link.textarea {
+    border-color: #2e63b8; }
+    .is-link.input:focus, #documenter .docs-sidebar form.docs-search > input.is-link:focus, .is-link.textarea:focus, .is-link.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-link.is-focused, .is-link.is-focused.textarea, .is-link.input:active, #documenter .docs-sidebar form.docs-search > input.is-link:active, .is-link.textarea:active, .is-link.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-link.is-active, .is-link.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); }
+  .is-info.input, #documenter .docs-sidebar form.docs-search > input.is-info, .is-info.textarea {
+    border-color: #209cee; }
+    .is-info.input:focus, #documenter .docs-sidebar form.docs-search > input.is-info:focus, .is-info.textarea:focus, .is-info.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-info.is-focused, .is-info.is-focused.textarea, .is-info.input:active, #documenter .docs-sidebar form.docs-search > input.is-info:active, .is-info.textarea:active, .is-info.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-info.is-active, .is-info.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }
+  .is-success.input, #documenter .docs-sidebar form.docs-search > input.is-success, .is-success.textarea {
+    border-color: #22c35b; }
+    .is-success.input:focus, #documenter .docs-sidebar form.docs-search > input.is-success:focus, .is-success.textarea:focus, .is-success.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-success.is-focused, .is-success.is-focused.textarea, .is-success.input:active, #documenter .docs-sidebar form.docs-search > input.is-success:active, .is-success.textarea:active, .is-success.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-success.is-active, .is-success.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }
+  .is-warning.input, #documenter .docs-sidebar form.docs-search > input.is-warning, .is-warning.textarea {
+    border-color: #ffdd57; }
+    .is-warning.input:focus, #documenter .docs-sidebar form.docs-search > input.is-warning:focus, .is-warning.textarea:focus, .is-warning.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-warning.is-focused, .is-warning.is-focused.textarea, .is-warning.input:active, #documenter .docs-sidebar form.docs-search > input.is-warning:active, .is-warning.textarea:active, .is-warning.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-warning.is-active, .is-warning.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }
+  .is-danger.input, #documenter .docs-sidebar form.docs-search > input.is-danger, .is-danger.textarea {
+    border-color: #da0b00; }
+    .is-danger.input:focus, #documenter .docs-sidebar form.docs-search > input.is-danger:focus, .is-danger.textarea:focus, .is-danger.is-focused.input, #documenter .docs-sidebar form.docs-search > input.is-danger.is-focused, .is-danger.is-focused.textarea, .is-danger.input:active, #documenter .docs-sidebar form.docs-search > input.is-danger:active, .is-danger.textarea:active, .is-danger.is-active.input, #documenter .docs-sidebar form.docs-search > input.is-danger.is-active, .is-danger.is-active.textarea {
+      box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }
+  .is-small.input, #documenter .docs-sidebar form.docs-search > input, .is-small.textarea {
+    border-radius: 2px;
+    font-size: 0.75rem; }
+  .is-medium.input, #documenter .docs-sidebar form.docs-search > input.is-medium, .is-medium.textarea {
+    font-size: 1.25rem; }
+  .is-large.input, #documenter .docs-sidebar form.docs-search > input.is-large, .is-large.textarea {
+    font-size: 1.5rem; }
+  .is-fullwidth.input, #documenter .docs-sidebar form.docs-search > input.is-fullwidth, .is-fullwidth.textarea {
+    display: block;
+    width: 100%; }
+  .is-inline.input, #documenter .docs-sidebar form.docs-search > input.is-inline, .is-inline.textarea {
+    display: inline;
+    width: auto; }
+
+.input.is-rounded, #documenter .docs-sidebar form.docs-search > input {
+  border-radius: 290486px;
+  padding-left: 1em;
+  padding-right: 1em; }
+
+.input.is-static, #documenter .docs-sidebar form.docs-search > input.is-static {
+  background-color: transparent;
+  border-color: transparent;
+  box-shadow: none;
+  padding-left: 0;
+  padding-right: 0; }
+
+.textarea {
+  display: block;
+  max-width: 100%;
+  min-width: 100%;
+  padding: 0.625em;
+  resize: vertical; }
+  .textarea:not([rows]) {
+    max-height: 600px;
+    min-height: 120px; }
+  .textarea[rows] {
+    height: initial; }
+  .textarea.has-fixed-size {
+    resize: none; }
+
+.checkbox, .radio {
+  cursor: pointer;
+  display: inline-block;
+  line-height: 1.25;
+  position: relative; }
+  .checkbox input, .radio input {
+    cursor: pointer; }
+  .checkbox:hover, .radio:hover {
+    color: #363636; }
+  .checkbox[disabled], .radio[disabled],
+  fieldset[disabled] .checkbox,
+  fieldset[disabled] .radio {
+    color: #7a7a7a;
+    cursor: not-allowed; }
+
+.radio + .radio {
+  margin-left: 0.5em; }
+
+.select {
+  display: inline-block;
+  max-width: 100%;
+  position: relative;
+  vertical-align: top; }
+  .select:not(.is-multiple) {
+    height: 2.25em; }
+  .select:not(.is-multiple):not(.is-loading)::after {
+    border-color: #2e63b8;
+    right: 1.125em;
+    z-index: 4; }
+  .select.is-rounded select, #documenter .docs-sidebar form.docs-search > input.select select {
+    border-radius: 290486px;
+    padding-left: 1em; }
+  .select select {
+    cursor: pointer;
+    display: block;
+    font-size: 1em;
+    max-width: 100%;
+    outline: none; }
+    .select select::-ms-expand {
+      display: none; }
+    .select select[disabled]:hover,
+    fieldset[disabled] .select select:hover {
+      border-color: whitesmoke; }
+    .select select:not([multiple]) {
+      padding-right: 2.5em; }
+    .select select[multiple] {
+      height: auto;
+      padding: 0; }
+      .select select[multiple] option {
+        padding: 0.5em 1em; }
+  .select:not(.is-multiple):not(.is-loading):hover::after {
+    border-color: #363636; }
+  .select.is-white:not(:hover)::after {
+    border-color: white; }
+  .select.is-white select {
+    border-color: white; }
+    .select.is-white select:hover, .select.is-white select.is-hovered {
+      border-color: #f2f2f2; }
+    .select.is-white select:focus, .select.is-white select.is-focused, .select.is-white select:active, .select.is-white select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(255, 255, 255, 0.25); }
+  .select.is-black:not(:hover)::after {
+    border-color: #0a0a0a; }
+  .select.is-black select {
+    border-color: #0a0a0a; }
+    .select.is-black select:hover, .select.is-black select.is-hovered {
+      border-color: black; }
+    .select.is-black select:focus, .select.is-black select.is-focused, .select.is-black select:active, .select.is-black select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(10, 10, 10, 0.25); }
+  .select.is-light:not(:hover)::after {
+    border-color: whitesmoke; }
+  .select.is-light select {
+    border-color: whitesmoke; }
+    .select.is-light select:hover, .select.is-light select.is-hovered {
+      border-color: #e8e8e8; }
+    .select.is-light select:focus, .select.is-light select.is-focused, .select.is-light select:active, .select.is-light select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(245, 245, 245, 0.25); }
+  .select.is-dark:not(:hover)::after, .content kbd.select:not(:hover)::after {
+    border-color: #363636; }
+  .select.is-dark select, .content kbd.select select {
+    border-color: #363636; }
+    .select.is-dark select:hover, .content kbd.select select:hover, .select.is-dark select.is-hovered, .content kbd.select select.is-hovered {
+      border-color: #292929; }
+    .select.is-dark select:focus, .content kbd.select select:focus, .select.is-dark select.is-focused, .content kbd.select select.is-focused, .select.is-dark select:active, .content kbd.select select:active, .select.is-dark select.is-active, .content kbd.select select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(54, 54, 54, 0.25); }
+  .select.is-primary:not(:hover)::after, .docstring > section > a.select.docs-sourcelink:not(:hover)::after {
+    border-color: #4eb5de; }
+  .select.is-primary select, .docstring > section > a.select.docs-sourcelink select {
+    border-color: #4eb5de; }
+    .select.is-primary select:hover, .docstring > section > a.select.docs-sourcelink select:hover, .select.is-primary select.is-hovered, .docstring > section > a.select.docs-sourcelink select.is-hovered {
+      border-color: #39acda; }
+    .select.is-primary select:focus, .docstring > section > a.select.docs-sourcelink select:focus, .select.is-primary select.is-focused, .docstring > section > a.select.docs-sourcelink select.is-focused, .select.is-primary select:active, .docstring > section > a.select.docs-sourcelink select:active, .select.is-primary select.is-active, .docstring > section > a.select.docs-sourcelink select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(78, 181, 222, 0.25); }
+  .select.is-link:not(:hover)::after {
+    border-color: #2e63b8; }
+  .select.is-link select {
+    border-color: #2e63b8; }
+    .select.is-link select:hover, .select.is-link select.is-hovered {
+      border-color: #2958a4; }
+    .select.is-link select:focus, .select.is-link select.is-focused, .select.is-link select:active, .select.is-link select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(46, 99, 184, 0.25); }
+  .select.is-info:not(:hover)::after {
+    border-color: #209cee; }
+  .select.is-info select {
+    border-color: #209cee; }
+    .select.is-info select:hover, .select.is-info select.is-hovered {
+      border-color: #118fe4; }
+    .select.is-info select:focus, .select.is-info select.is-focused, .select.is-info select:active, .select.is-info select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(32, 156, 238, 0.25); }
+  .select.is-success:not(:hover)::after {
+    border-color: #22c35b; }
+  .select.is-success select {
+    border-color: #22c35b; }
+    .select.is-success select:hover, .select.is-success select.is-hovered {
+      border-color: #1ead51; }
+    .select.is-success select:focus, .select.is-success select.is-focused, .select.is-success select:active, .select.is-success select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(34, 195, 91, 0.25); }
+  .select.is-warning:not(:hover)::after {
+    border-color: #ffdd57; }
+  .select.is-warning select {
+    border-color: #ffdd57; }
+    .select.is-warning select:hover, .select.is-warning select.is-hovered {
+      border-color: #ffd83d; }
+    .select.is-warning select:focus, .select.is-warning select.is-focused, .select.is-warning select:active, .select.is-warning select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(255, 221, 87, 0.25); }
+  .select.is-danger:not(:hover)::after {
+    border-color: #da0b00; }
+  .select.is-danger select {
+    border-color: #da0b00; }
+    .select.is-danger select:hover, .select.is-danger select.is-hovered {
+      border-color: #c10a00; }
+    .select.is-danger select:focus, .select.is-danger select.is-focused, .select.is-danger select:active, .select.is-danger select.is-active {
+      box-shadow: 0 0 0 0.125em rgba(218, 11, 0, 0.25); }
+  .select.is-small, #documenter .docs-sidebar form.docs-search > input.select {
+    border-radius: 2px;
+    font-size: 0.75rem; }
+  .select.is-medium {
+    font-size: 1.25rem; }
+  .select.is-large {
+    font-size: 1.5rem; }
+  .select.is-disabled::after {
+    border-color: #7a7a7a; }
+  .select.is-fullwidth {
+    width: 100%; }
+    .select.is-fullwidth select {
+      width: 100%; }
+  .select.is-loading::after {
+    margin-top: 0;
+    position: absolute;
+    right: 0.625em;
+    top: 0.625em;
+    transform: none; }
+  .select.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.select.is-loading:after {
+    font-size: 0.75rem; }
+  .select.is-loading.is-medium:after {
+    font-size: 1.25rem; }
+  .select.is-loading.is-large:after {
+    font-size: 1.5rem; }
+
+.file {
+  align-items: stretch;
+  display: flex;
+  justify-content: flex-start;
+  position: relative; }
+  .file.is-white .file-cta {
+    background-color: white;
+    border-color: transparent;
+    color: #0a0a0a; }
+  .file.is-white:hover .file-cta, .file.is-white.is-hovered .file-cta {
+    background-color: #f9f9f9;
+    border-color: transparent;
+    color: #0a0a0a; }
+  .file.is-white:focus .file-cta, .file.is-white.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(255, 255, 255, 0.25);
+    color: #0a0a0a; }
+  .file.is-white:active .file-cta, .file.is-white.is-active .file-cta {
+    background-color: #f2f2f2;
+    border-color: transparent;
+    color: #0a0a0a; }
+  .file.is-black .file-cta {
+    background-color: #0a0a0a;
+    border-color: transparent;
+    color: white; }
+  .file.is-black:hover .file-cta, .file.is-black.is-hovered .file-cta {
+    background-color: #040404;
+    border-color: transparent;
+    color: white; }
+  .file.is-black:focus .file-cta, .file.is-black.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(10, 10, 10, 0.25);
+    color: white; }
+  .file.is-black:active .file-cta, .file.is-black.is-active .file-cta {
+    background-color: black;
+    border-color: transparent;
+    color: white; }
+  .file.is-light .file-cta {
+    background-color: whitesmoke;
+    border-color: transparent;
+    color: #363636; }
+  .file.is-light:hover .file-cta, .file.is-light.is-hovered .file-cta {
+    background-color: #eeeeee;
+    border-color: transparent;
+    color: #363636; }
+  .file.is-light:focus .file-cta, .file.is-light.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(245, 245, 245, 0.25);
+    color: #363636; }
+  .file.is-light:active .file-cta, .file.is-light.is-active .file-cta {
+    background-color: #e8e8e8;
+    border-color: transparent;
+    color: #363636; }
+  .file.is-dark .file-cta, .content kbd.file .file-cta {
+    background-color: #363636;
+    border-color: transparent;
+    color: whitesmoke; }
+  .file.is-dark:hover .file-cta, .content kbd.file:hover .file-cta, .file.is-dark.is-hovered .file-cta, .content kbd.file.is-hovered .file-cta {
+    background-color: #2f2f2f;
+    border-color: transparent;
+    color: whitesmoke; }
+  .file.is-dark:focus .file-cta, .content kbd.file:focus .file-cta, .file.is-dark.is-focused .file-cta, .content kbd.file.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(54, 54, 54, 0.25);
+    color: whitesmoke; }
+  .file.is-dark:active .file-cta, .content kbd.file:active .file-cta, .file.is-dark.is-active .file-cta, .content kbd.file.is-active .file-cta {
+    background-color: #292929;
+    border-color: transparent;
+    color: whitesmoke; }
+  .file.is-primary .file-cta, .docstring > section > a.file.docs-sourcelink .file-cta {
+    background-color: #4eb5de;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-primary:hover .file-cta, .docstring > section > a.file.docs-sourcelink:hover .file-cta, .file.is-primary.is-hovered .file-cta, .docstring > section > a.file.is-hovered.docs-sourcelink .file-cta {
+    background-color: #43b1dc;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-primary:focus .file-cta, .docstring > section > a.file.docs-sourcelink:focus .file-cta, .file.is-primary.is-focused .file-cta, .docstring > section > a.file.is-focused.docs-sourcelink .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(78, 181, 222, 0.25);
+    color: #fff; }
+  .file.is-primary:active .file-cta, .docstring > section > a.file.docs-sourcelink:active .file-cta, .file.is-primary.is-active .file-cta, .docstring > section > a.file.is-active.docs-sourcelink .file-cta {
+    background-color: #39acda;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-link .file-cta {
+    background-color: #2e63b8;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-link:hover .file-cta, .file.is-link.is-hovered .file-cta {
+    background-color: #2b5eae;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-link:focus .file-cta, .file.is-link.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(46, 99, 184, 0.25);
+    color: #fff; }
+  .file.is-link:active .file-cta, .file.is-link.is-active .file-cta {
+    background-color: #2958a4;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-info .file-cta {
+    background-color: #209cee;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-info:hover .file-cta, .file.is-info.is-hovered .file-cta {
+    background-color: #1496ed;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-info:focus .file-cta, .file.is-info.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(32, 156, 238, 0.25);
+    color: #fff; }
+  .file.is-info:active .file-cta, .file.is-info.is-active .file-cta {
+    background-color: #118fe4;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-success .file-cta {
+    background-color: #22c35b;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-success:hover .file-cta, .file.is-success.is-hovered .file-cta {
+    background-color: #20b856;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-success:focus .file-cta, .file.is-success.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(34, 195, 91, 0.25);
+    color: #fff; }
+  .file.is-success:active .file-cta, .file.is-success.is-active .file-cta {
+    background-color: #1ead51;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-warning .file-cta {
+    background-color: #ffdd57;
+    border-color: transparent;
+    color: rgba(0, 0, 0, 0.7); }
+  .file.is-warning:hover .file-cta, .file.is-warning.is-hovered .file-cta {
+    background-color: #ffdb4a;
+    border-color: transparent;
+    color: rgba(0, 0, 0, 0.7); }
+  .file.is-warning:focus .file-cta, .file.is-warning.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(255, 221, 87, 0.25);
+    color: rgba(0, 0, 0, 0.7); }
+  .file.is-warning:active .file-cta, .file.is-warning.is-active .file-cta {
+    background-color: #ffd83d;
+    border-color: transparent;
+    color: rgba(0, 0, 0, 0.7); }
+  .file.is-danger .file-cta {
+    background-color: #da0b00;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-danger:hover .file-cta, .file.is-danger.is-hovered .file-cta {
+    background-color: #cd0a00;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-danger:focus .file-cta, .file.is-danger.is-focused .file-cta {
+    border-color: transparent;
+    box-shadow: 0 0 0.5em rgba(218, 11, 0, 0.25);
+    color: #fff; }
+  .file.is-danger:active .file-cta, .file.is-danger.is-active .file-cta {
+    background-color: #c10a00;
+    border-color: transparent;
+    color: #fff; }
+  .file.is-small, #documenter .docs-sidebar form.docs-search > input.file {
+    font-size: 0.75rem; }
+  .file.is-medium {
+    font-size: 1.25rem; }
+    .file.is-medium .file-icon .fa {
+      font-size: 21px; }
+  .file.is-large {
+    font-size: 1.5rem; }
+    .file.is-large .file-icon .fa {
+      font-size: 28px; }
+  .file.has-name .file-cta {
+    border-bottom-right-radius: 0;
+    border-top-right-radius: 0; }
+  .file.has-name .file-name {
+    border-bottom-left-radius: 0;
+    border-top-left-radius: 0; }
+  .file.has-name.is-empty .file-cta {
+    border-radius: 4px; }
+  .file.has-name.is-empty .file-name {
+    display: none; }
+  .file.is-boxed .file-label {
+    flex-direction: column; }
+  .file.is-boxed .file-cta {
+    flex-direction: column;
+    height: auto;
+    padding: 1em 3em; }
+  .file.is-boxed .file-name {
+    border-width: 0 1px 1px; }
+  .file.is-boxed .file-icon {
+    height: 1.5em;
+    width: 1.5em; }
+    .file.is-boxed .file-icon .fa {
+      font-size: 21px; }
+  .file.is-boxed.is-small .file-icon .fa, #documenter .docs-sidebar form.docs-search > input.file.is-boxed .file-icon .fa {
+    font-size: 14px; }
+  .file.is-boxed.is-medium .file-icon .fa {
+    font-size: 28px; }
+  .file.is-boxed.is-large .file-icon .fa {
+    font-size: 35px; }
+  .file.is-boxed.has-name .file-cta {
+    border-radius: 4px 4px 0 0; }
+  .file.is-boxed.has-name .file-name {
+    border-radius: 0 0 4px 4px;
+    border-width: 0 1px 1px; }
+  .file.is-centered {
+    justify-content: center; }
+  .file.is-fullwidth .file-label {
+    width: 100%; }
+  .file.is-fullwidth .file-name {
+    flex-grow: 1;
+    max-width: none; }
+  .file.is-right {
+    justify-content: flex-end; }
+    .file.is-right .file-cta {
+      border-radius: 0 4px 4px 0; }
+    .file.is-right .file-name {
+      border-radius: 4px 0 0 4px;
+      border-width: 1px 0 1px 1px;
+      order: -1; }
+
+.file-label {
+  align-items: stretch;
+  display: flex;
+  cursor: pointer;
+  justify-content: flex-start;
+  overflow: hidden;
+  position: relative; }
+  .file-label:hover .file-cta {
+    background-color: #eeeeee;
+    color: #363636; }
+  .file-label:hover .file-name {
+    border-color: #d5d5d5; }
+  .file-label:active .file-cta {
+    background-color: #e8e8e8;
+    color: #363636; }
+  .file-label:active .file-name {
+    border-color: #cfcfcf; }
+
+.file-input {
+  height: 100%;
+  left: 0;
+  opacity: 0;
+  outline: none;
+  position: absolute;
+  top: 0;
+  width: 100%; }
+
+.file-cta,
+.file-name {
+  border-color: #dbdbdb;
+  border-radius: 4px;
+  font-size: 1em;
+  padding-left: 1em;
+  padding-right: 1em;
+  white-space: nowrap; }
+
+.file-cta {
+  background-color: whitesmoke;
+  color: #4a4a4a; }
+
+.file-name {
+  border-color: #dbdbdb;
+  border-style: solid;
+  border-width: 1px 1px 1px 0;
+  display: block;
+  max-width: 16em;
+  overflow: hidden;
+  text-align: left;
+  text-overflow: ellipsis; }
+
+.file-icon {
+  align-items: center;
+  display: flex;
+  height: 1em;
+  justify-content: center;
+  margin-right: 0.5em;
+  width: 1em; }
+  .file-icon .fa {
+    font-size: 14px; }
+
+.label {
+  color: #363636;
+  display: block;
+  font-size: 1rem;
+  font-weight: 700; }
+  .label:not(:last-child) {
+    margin-bottom: 0.5em; }
+  .label.is-small, #documenter .docs-sidebar form.docs-search > input.label {
+    font-size: 0.75rem; }
+  .label.is-medium {
+    font-size: 1.25rem; }
+  .label.is-large {
+    font-size: 1.5rem; }
+
+.help {
+  display: block;
+  font-size: 0.75rem;
+  margin-top: 0.25rem; }
+  .help.is-white {
+    color: white; }
+  .help.is-black {
+    color: #0a0a0a; }
+  .help.is-light {
+    color: whitesmoke; }
+  .help.is-dark, .content kbd.help {
+    color: #363636; }
+  .help.is-primary, .docstring > section > a.help.docs-sourcelink {
+    color: #4eb5de; }
+  .help.is-link {
+    color: #2e63b8; }
+  .help.is-info {
+    color: #209cee; }
+  .help.is-success {
+    color: #22c35b; }
+  .help.is-warning {
+    color: #ffdd57; }
+  .help.is-danger {
+    color: #da0b00; }
+
+.field:not(:last-child) {
+  margin-bottom: 0.75rem; }
+
+.field.has-addons {
+  display: flex;
+  justify-content: flex-start; }
+  .field.has-addons .control:not(:last-child) {
+    margin-right: -1px; }
+  .field.has-addons .control:not(:first-child):not(:last-child) .button,
+  .field.has-addons .control:not(:first-child):not(:last-child) .input,
+  .field.has-addons .control:not(:first-child):not(:last-child) #documenter .docs-sidebar form.docs-search > input,
+  #documenter .docs-sidebar .field.has-addons .control:not(:first-child):not(:last-child) form.docs-search > input,
+  .field.has-addons .control:not(:first-child):not(:last-child) .select select {
+    border-radius: 0; }
+  .field.has-addons .control:first-child:not(:only-child) .button,
+  .field.has-addons .control:first-child:not(:only-child) .input,
+  .field.has-addons .control:first-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,
+  #documenter .docs-sidebar .field.has-addons .control:first-child:not(:only-child) form.docs-search > input,
+  .field.has-addons .control:first-child:not(:only-child) .select select {
+    border-bottom-right-radius: 0;
+    border-top-right-radius: 0; }
+  .field.has-addons .control:last-child:not(:only-child) .button,
+  .field.has-addons .control:last-child:not(:only-child) .input,
+  .field.has-addons .control:last-child:not(:only-child) #documenter .docs-sidebar form.docs-search > input,
+  #documenter .docs-sidebar .field.has-addons .control:last-child:not(:only-child) form.docs-search > input,
+  .field.has-addons .control:last-child:not(:only-child) .select select {
+    border-bottom-left-radius: 0;
+    border-top-left-radius: 0; }
+  .field.has-addons .control .button:not([disabled]):hover, .field.has-addons .control .button:not([disabled]).is-hovered,
+  .field.has-addons .control .input:not([disabled]):hover,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):hover,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):hover,
+  .field.has-addons .control .input:not([disabled]).is-hovered,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-hovered,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-hovered,
+  .field.has-addons .control .select select:not([disabled]):hover,
+  .field.has-addons .control .select select:not([disabled]).is-hovered {
+    z-index: 2; }
+  .field.has-addons .control .button:not([disabled]):focus, .field.has-addons .control .button:not([disabled]).is-focused, .field.has-addons .control .button:not([disabled]):active, .field.has-addons .control .button:not([disabled]).is-active,
+  .field.has-addons .control .input:not([disabled]):focus,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus,
+  .field.has-addons .control .input:not([disabled]).is-focused,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused,
+  .field.has-addons .control .input:not([disabled]):active,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active,
+  .field.has-addons .control .input:not([disabled]).is-active,
+  .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active,
+  #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active,
+  .field.has-addons .control .select select:not([disabled]):focus,
+  .field.has-addons .control .select select:not([disabled]).is-focused,
+  .field.has-addons .control .select select:not([disabled]):active,
+  .field.has-addons .control .select select:not([disabled]).is-active {
+    z-index: 3; }
+    .field.has-addons .control .button:not([disabled]):focus:hover, .field.has-addons .control .button:not([disabled]).is-focused:hover, .field.has-addons .control .button:not([disabled]):active:hover, .field.has-addons .control .button:not([disabled]).is-active:hover,
+    .field.has-addons .control .input:not([disabled]):focus:hover,
+    .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):focus:hover,
+    #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):focus:hover,
+    .field.has-addons .control .input:not([disabled]).is-focused:hover,
+    .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-focused:hover,
+    #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-focused:hover,
+    .field.has-addons .control .input:not([disabled]):active:hover,
+    .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]):active:hover,
+    #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]):active:hover,
+    .field.has-addons .control .input:not([disabled]).is-active:hover,
+    .field.has-addons .control #documenter .docs-sidebar form.docs-search > input:not([disabled]).is-active:hover,
+    #documenter .docs-sidebar .field.has-addons .control form.docs-search > input:not([disabled]).is-active:hover,
+    .field.has-addons .control .select select:not([disabled]):focus:hover,
+    .field.has-addons .control .select select:not([disabled]).is-focused:hover,
+    .field.has-addons .control .select select:not([disabled]):active:hover,
+    .field.has-addons .control .select select:not([disabled]).is-active:hover {
+      z-index: 4; }
+  .field.has-addons .control.is-expanded {
+    flex-grow: 1;
+    flex-shrink: 1; }
+  .field.has-addons.has-addons-centered {
+    justify-content: center; }
+  .field.has-addons.has-addons-right {
+    justify-content: flex-end; }
+  .field.has-addons.has-addons-fullwidth .control {
+    flex-grow: 1;
+    flex-shrink: 0; }
+
+.field.is-grouped {
+  display: flex;
+  justify-content: flex-start; }
+  .field.is-grouped > .control {
+    flex-shrink: 0; }
+    .field.is-grouped > .control:not(:last-child) {
+      margin-bottom: 0;
+      margin-right: 0.75rem; }
+    .field.is-grouped > .control.is-expanded {
+      flex-grow: 1;
+      flex-shrink: 1; }
+  .field.is-grouped.is-grouped-centered {
+    justify-content: center; }
+  .field.is-grouped.is-grouped-right {
+    justify-content: flex-end; }
+  .field.is-grouped.is-grouped-multiline {
+    flex-wrap: wrap; }
+    .field.is-grouped.is-grouped-multiline > .control:last-child, .field.is-grouped.is-grouped-multiline > .control:not(:last-child) {
+      margin-bottom: 0.75rem; }
+    .field.is-grouped.is-grouped-multiline:last-child {
+      margin-bottom: -0.75rem; }
+    .field.is-grouped.is-grouped-multiline:not(:last-child) {
+      margin-bottom: 0; }
+
+@media screen and (min-width: 769px), print {
+  .field.is-horizontal {
+    display: flex; } }
+
+.field-label .label {
+  font-size: inherit; }
+
+@media screen and (max-width: 768px) {
+  .field-label {
+    margin-bottom: 0.5rem; } }
+
+@media screen and (min-width: 769px), print {
+  .field-label {
+    flex-basis: 0;
+    flex-grow: 1;
+    flex-shrink: 0;
+    margin-right: 1.5rem;
+    text-align: right; }
+    .field-label.is-small, #documenter .docs-sidebar form.docs-search > input.field-label {
+      font-size: 0.75rem;
+      padding-top: 0.375em; }
+    .field-label.is-normal {
+      padding-top: 0.375em; }
+    .field-label.is-medium {
+      font-size: 1.25rem;
+      padding-top: 0.375em; }
+    .field-label.is-large {
+      font-size: 1.5rem;
+      padding-top: 0.375em; } }
+
+.field-body .field .field {
+  margin-bottom: 0; }
+
+@media screen and (min-width: 769px), print {
+  .field-body {
+    display: flex;
+    flex-basis: 0;
+    flex-grow: 5;
+    flex-shrink: 1; }
+    .field-body .field {
+      margin-bottom: 0; }
+    .field-body > .field {
+      flex-shrink: 1; }
+      .field-body > .field:not(.is-narrow) {
+        flex-grow: 1; }
+      .field-body > .field:not(:last-child) {
+        margin-right: 0.75rem; } }
+
+.control {
+  box-sizing: border-box;
+  clear: both;
+  font-size: 1rem;
+  position: relative;
+  text-align: left; }
+  .control.has-icons-left .input:focus ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input:focus ~ .icon,
+  .control.has-icons-left .select:focus ~ .icon, .control.has-icons-right .input:focus ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input:focus ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input:focus ~ .icon,
+  .control.has-icons-right .select:focus ~ .icon {
+    color: #7a7a7a; }
+  .control.has-icons-left .input.is-small ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input ~ .icon,
+  .control.has-icons-left .select.is-small ~ .icon,
+  .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.select ~ .icon,
+  #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.select ~ .icon, .control.has-icons-right .input.is-small ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input ~ .icon,
+  .control.has-icons-right .select.is-small ~ .icon,
+  .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.select ~ .icon,
+  #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.select ~ .icon {
+    font-size: 0.75rem; }
+  .control.has-icons-left .input.is-medium ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-medium ~ .icon,
+  .control.has-icons-left .select.is-medium ~ .icon, .control.has-icons-right .input.is-medium ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-medium ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-medium ~ .icon,
+  .control.has-icons-right .select.is-medium ~ .icon {
+    font-size: 1.25rem; }
+  .control.has-icons-left .input.is-large ~ .icon, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input.is-large ~ .icon,
+  .control.has-icons-left .select.is-large ~ .icon, .control.has-icons-right .input.is-large ~ .icon, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input.is-large ~ .icon, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input.is-large ~ .icon,
+  .control.has-icons-right .select.is-large ~ .icon {
+    font-size: 1.5rem; }
+  .control.has-icons-left .icon, .control.has-icons-right .icon {
+    color: #dbdbdb;
+    height: 2.25em;
+    pointer-events: none;
+    position: absolute;
+    top: 0;
+    width: 2.25em;
+    z-index: 4; }
+  .control.has-icons-left .input, .control.has-icons-left #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-left form.docs-search > input,
+  .control.has-icons-left .select select {
+    padding-left: 2.25em; }
+  .control.has-icons-left .icon.is-left {
+    left: 0; }
+  .control.has-icons-right .input, .control.has-icons-right #documenter .docs-sidebar form.docs-search > input, #documenter .docs-sidebar .control.has-icons-right form.docs-search > input,
+  .control.has-icons-right .select select {
+    padding-right: 2.25em; }
+  .control.has-icons-right .icon.is-right {
+    right: 0; }
+  .control.is-loading::after {
+    position: absolute !important;
+    right: 0.625em;
+    top: 0.625em;
+    z-index: 4; }
+  .control.is-loading.is-small:after, #documenter .docs-sidebar form.docs-search > input.control.is-loading:after {
+    font-size: 0.75rem; }
+  .control.is-loading.is-medium:after {
+    font-size: 1.25rem; }
+  .control.is-loading.is-large:after {
+    font-size: 1.5rem; }
+
+.breadcrumb {
+  font-size: 1rem;
+  white-space: nowrap; }
+  .breadcrumb a {
+    align-items: center;
+    color: #2e63b8;
+    display: flex;
+    justify-content: center;
+    padding: 0 0.75em; }
+    .breadcrumb a:hover {
+      color: #363636; }
+  .breadcrumb li {
+    align-items: center;
+    display: flex; }
+    .breadcrumb li:first-child a {
+      padding-left: 0; }
+    .breadcrumb li.is-active a {
+      color: #222222;
+      cursor: default;
+      pointer-events: none; }
+    .breadcrumb li + li::before {
+      color: #b5b5b5;
+      content: "\0002f"; }
+  .breadcrumb ul,
+  .breadcrumb ol {
+    align-items: flex-start;
+    display: flex;
+    flex-wrap: wrap;
+    justify-content: flex-start; }
+  .breadcrumb .icon:first-child {
+    margin-right: 0.5em; }
+  .breadcrumb .icon:last-child {
+    margin-left: 0.5em; }
+  .breadcrumb.is-centered ol,
+  .breadcrumb.is-centered ul {
+    justify-content: center; }
+  .breadcrumb.is-right ol,
+  .breadcrumb.is-right ul {
+    justify-content: flex-end; }
+  .breadcrumb.is-small, #documenter .docs-sidebar form.docs-search > input.breadcrumb {
+    font-size: 0.75rem; }
+  .breadcrumb.is-medium {
+    font-size: 1.25rem; }
+  .breadcrumb.is-large {
+    font-size: 1.5rem; }
+  .breadcrumb.has-arrow-separator li + li::before {
+    content: "\02192"; }
+  .breadcrumb.has-bullet-separator li + li::before {
+    content: "\02022"; }
+  .breadcrumb.has-dot-separator li + li::before {
+    content: "\000b7"; }
+  .breadcrumb.has-succeeds-separator li + li::before {
+    content: "\0227B"; }
+
+.card {
+  background-color: white;
+  box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+  color: #222222;
+  max-width: 100%;
+  position: relative; }
+
+.card-header {
+  background-color: transparent;
+  align-items: stretch;
+  box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);
+  display: flex; }
+
+.card-header-title {
+  align-items: center;
+  color: #222222;
+  display: flex;
+  flex-grow: 1;
+  font-weight: 700;
+  padding: 0.75rem; }
+  .card-header-title.is-centered {
+    justify-content: center; }
+
+.card-header-icon {
+  align-items: center;
+  cursor: pointer;
+  display: flex;
+  justify-content: center;
+  padding: 0.75rem; }
+
+.card-image {
+  display: block;
+  position: relative; }
+
+.card-content {
+  background-color: transparent;
+  padding: 1rem 1.25rem; }
+
+.card-footer {
+  background-color: transparent;
+  border-top: 1px solid #dbdbdb;
+  align-items: stretch;
+  display: flex; }
+
+.card-footer-item {
+  align-items: center;
+  display: flex;
+  flex-basis: 0;
+  flex-grow: 1;
+  flex-shrink: 0;
+  justify-content: center;
+  padding: 0.75rem; }
+  .card-footer-item:not(:last-child) {
+    border-right: 1px solid #dbdbdb; }
+
+.card .media:not(:last-child) {
+  margin-bottom: 1.5rem; }
+
+.dropdown {
+  display: inline-flex;
+  position: relative;
+  vertical-align: top; }
+  .dropdown.is-active .dropdown-menu, .dropdown.is-hoverable:hover .dropdown-menu {
+    display: block; }
+  .dropdown.is-right .dropdown-menu {
+    left: auto;
+    right: 0; }
+  .dropdown.is-up .dropdown-menu {
+    bottom: 100%;
+    padding-bottom: 4px;
+    padding-top: initial;
+    top: auto; }
+
+.dropdown-menu {
+  display: none;
+  left: 0;
+  min-width: 12rem;
+  padding-top: 4px;
+  position: absolute;
+  top: 100%;
+  z-index: 20; }
+
+.dropdown-content {
+  background-color: white;
+  border-radius: 4px;
+  box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+  padding-bottom: 0.5rem;
+  padding-top: 0.5rem; }
+
+.dropdown-item {
+  color: #4a4a4a;
+  display: block;
+  font-size: 0.875rem;
+  line-height: 1.5;
+  padding: 0.375rem 1rem;
+  position: relative; }
+
+a.dropdown-item,
+button.dropdown-item {
+  padding-right: 3rem;
+  text-align: left;
+  white-space: nowrap;
+  width: 100%; }
+  a.dropdown-item:hover,
+  button.dropdown-item:hover {
+    background-color: whitesmoke;
+    color: #0a0a0a; }
+  a.dropdown-item.is-active,
+  button.dropdown-item.is-active {
+    background-color: #2e63b8;
+    color: #fff; }
+
+.dropdown-divider {
+  background-color: #dbdbdb;
+  border: none;
+  display: block;
+  height: 1px;
+  margin: 0.5rem 0; }
+
+.level {
+  align-items: center;
+  justify-content: space-between; }
+  .level code {
+    border-radius: 4px; }
+  .level img {
+    display: inline-block;
+    vertical-align: top; }
+  .level.is-mobile {
+    display: flex; }
+    .level.is-mobile .level-left,
+    .level.is-mobile .level-right {
+      display: flex; }
+    .level.is-mobile .level-left + .level-right {
+      margin-top: 0; }
+    .level.is-mobile .level-item:not(:last-child) {
+      margin-bottom: 0;
+      margin-right: 0.75rem; }
+    .level.is-mobile .level-item:not(.is-narrow) {
+      flex-grow: 1; }
+  @media screen and (min-width: 769px), print {
+    .level {
+      display: flex; }
+      .level > .level-item:not(.is-narrow) {
+        flex-grow: 1; } }
+
+.level-item {
+  align-items: center;
+  display: flex;
+  flex-basis: auto;
+  flex-grow: 0;
+  flex-shrink: 0;
+  justify-content: center; }
+  .level-item .title,
+  .level-item .subtitle {
+    margin-bottom: 0; }
+  @media screen and (max-width: 768px) {
+    .level-item:not(:last-child) {
+      margin-bottom: 0.75rem; } }
+
+.level-left,
+.level-right {
+  flex-basis: auto;
+  flex-grow: 0;
+  flex-shrink: 0; }
+  .level-left .level-item.is-flexible,
+  .level-right .level-item.is-flexible {
+    flex-grow: 1; }
+  @media screen and (min-width: 769px), print {
+    .level-left .level-item:not(:last-child),
+    .level-right .level-item:not(:last-child) {
+      margin-right: 0.75rem; } }
+
+.level-left {
+  align-items: center;
+  justify-content: flex-start; }
+  @media screen and (max-width: 768px) {
+    .level-left + .level-right {
+      margin-top: 1.5rem; } }
+  @media screen and (min-width: 769px), print {
+    .level-left {
+      display: flex; } }
+
+.level-right {
+  align-items: center;
+  justify-content: flex-end; }
+  @media screen and (min-width: 769px), print {
+    .level-right {
+      display: flex; } }
+
+.list {
+  background-color: white;
+  border-radius: 4px;
+  box-shadow: 0 2px 3px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1); }
+
+.list-item {
+  display: block;
+  padding: 0.5em 1em; }
+  .list-item:not(a) {
+    color: #222222; }
+  .list-item:first-child {
+    border-top-left-radius: 4px;
+    border-top-right-radius: 4px; }
+  .list-item:last-child {
+    border-bottom-left-radius: 4px;
+    border-bottom-right-radius: 4px; }
+  .list-item:not(:last-child) {
+    border-bottom: 1px solid #dbdbdb; }
+  .list-item.is-active {
+    background-color: #2e63b8;
+    color: #fff; }
+
+a.list-item {
+  background-color: whitesmoke;
+  cursor: pointer; }
+
+.media {
+  align-items: flex-start;
+  display: flex;
+  text-align: left; }
+  .media .content:not(:last-child) {
+    margin-bottom: 0.75rem; }
+  .media .media {
+    border-top: 1px solid rgba(219, 219, 219, 0.5);
+    display: flex;
+    padding-top: 0.75rem; }
+    .media .media .content:not(:last-child),
+    .media .media .control:not(:last-child) {
+      margin-bottom: 0.5rem; }
+    .media .media .media {
+      padding-top: 0.5rem; }
+      .media .media .media + .media {
+        margin-top: 0.5rem; }
+  .media + .media {
+    border-top: 1px solid rgba(219, 219, 219, 0.5);
+    margin-top: 1rem;
+    padding-top: 1rem; }
+  .media.is-large + .media {
+    margin-top: 1.5rem;
+    padding-top: 1.5rem; }
+
+.media-left,
+.media-right {
+  flex-basis: auto;
+  flex-grow: 0;
+  flex-shrink: 0; }
+
+.media-left {
+  margin-right: 1rem; }
+
+.media-right {
+  margin-left: 1rem; }
+
+.media-content {
+  flex-basis: auto;
+  flex-grow: 1;
+  flex-shrink: 1;
+  text-align: left; }
+
+@media screen and (max-width: 768px) {
+  .media-content {
+    overflow-x: auto; } }
+
+.menu {
+  font-size: 1rem; }
+  .menu.is-small, #documenter .docs-sidebar form.docs-search > input.menu {
+    font-size: 0.75rem; }
+  .menu.is-medium {
+    font-size: 1.25rem; }
+  .menu.is-large {
+    font-size: 1.5rem; }
+
+.menu-list {
+  line-height: 1.25; }
+  .menu-list a {
+    border-radius: 2px;
+    color: #222222;
+    display: block;
+    padding: 0.5em 0.75em; }
+    .menu-list a:hover {
+      background-color: whitesmoke;
+      color: #222222; }
+    .menu-list a.is-active {
+      background-color: #2e63b8;
+      color: #fff; }
+  .menu-list li ul {
+    border-left: 1px solid #dbdbdb;
+    margin: 0.75em;
+    padding-left: 0.75em; }
+
+.menu-label {
+  color: #7a7a7a;
+  font-size: 0.75em;
+  letter-spacing: 0.1em;
+  text-transform: uppercase; }
+  .menu-label:not(:first-child) {
+    margin-top: 1em; }
+  .menu-label:not(:last-child) {
+    margin-bottom: 1em; }
+
+.message {
+  background-color: whitesmoke;
+  border-radius: 4px;
+  font-size: 1rem; }
+  .message strong {
+    color: currentColor; }
+  .message a:not(.button):not(.tag):not(.dropdown-item) {
+    color: currentColor;
+    text-decoration: underline; }
+  .message.is-small, #documenter .docs-sidebar form.docs-search > input.message {
+    font-size: 0.75rem; }
+  .message.is-medium {
+    font-size: 1.25rem; }
+  .message.is-large {
+    font-size: 1.5rem; }
+  .message.is-white {
+    background-color: white; }
+    .message.is-white .message-header {
+      background-color: white;
+      color: #0a0a0a; }
+    .message.is-white .message-body {
+      border-color: white;
+      color: #4d4d4d; }
+  .message.is-black {
+    background-color: #fafafa; }
+    .message.is-black .message-header {
+      background-color: #0a0a0a;
+      color: white; }
+    .message.is-black .message-body {
+      border-color: #0a0a0a;
+      color: #090909; }
+  .message.is-light {
+    background-color: #fafafa; }
+    .message.is-light .message-header {
+      background-color: whitesmoke;
+      color: #363636; }
+    .message.is-light .message-body {
+      border-color: whitesmoke;
+      color: #505050; }
+  .message.is-dark, .content kbd.message {
+    background-color: #fafafa; }
+    .message.is-dark .message-header, .content kbd.message .message-header {
+      background-color: #363636;
+      color: whitesmoke; }
+    .message.is-dark .message-body, .content kbd.message .message-body {
+      border-color: #363636;
+      color: #2a2a2a; }
+  .message.is-primary, .docstring > section > a.message.docs-sourcelink {
+    background-color: #f6fbfd; }
+    .message.is-primary .message-header, .docstring > section > a.message.docs-sourcelink .message-header {
+      background-color: #4eb5de;
+      color: #fff; }
+    .message.is-primary .message-body, .docstring > section > a.message.docs-sourcelink .message-body {
+      border-color: #4eb5de;
+      color: #1f556a; }
+  .message.is-link {
+    background-color: #f7f9fd; }
+    .message.is-link .message-header {
+      background-color: #2e63b8;
+      color: #fff; }
+    .message.is-link .message-body {
+      border-color: #2e63b8;
+      color: #264981; }
+  .message.is-info {
+    background-color: #f6fbfe; }
+    .message.is-info .message-header {
+      background-color: #209cee;
+      color: #fff; }
+    .message.is-info .message-body {
+      border-color: #209cee;
+      color: #12537e; }
+  .message.is-success {
+    background-color: #f6fdf9; }
+    .message.is-success .message-header {
+      background-color: #22c35b;
+      color: #fff; }
+    .message.is-success .message-body {
+      border-color: #22c35b;
+      color: #0f361d; }
+  .message.is-warning {
+    background-color: #fffdf5; }
+    .message.is-warning .message-header {
+      background-color: #ffdd57;
+      color: rgba(0, 0, 0, 0.7); }
+    .message.is-warning .message-body {
+      border-color: #ffdd57;
+      color: #3b3108; }
+  .message.is-danger {
+    background-color: #fff5f5; }
+    .message.is-danger .message-header {
+      background-color: #da0b00;
+      color: #fff; }
+    .message.is-danger .message-body {
+      border-color: #da0b00;
+      color: #9b0c04; }
+
+.message-header {
+  align-items: center;
+  background-color: #222222;
+  border-radius: 4px 4px 0 0;
+  color: #fff;
+  display: flex;
+  font-weight: 700;
+  justify-content: space-between;
+  line-height: 1.25;
+  padding: 0.75em;
+  position: relative; }
+  .message-header .delete {
+    flex-grow: 0;
+    flex-shrink: 0;
+    margin-left: 0.75em; }
+  .message-header + .message-body {
+    border-width: 0;
+    border-top-left-radius: 0;
+    border-top-right-radius: 0; }
+
+.message-body {
+  border-color: #dbdbdb;
+  border-radius: 4px;
+  border-style: solid;
+  border-width: 0 0 0 4px;
+  color: #222222;
+  padding: 1em 1.25em; }
+  .message-body code,
+  .message-body pre {
+    background-color: white; }
+  .message-body pre code {
+    background-color: transparent; }
+
+.modal {
+  align-items: center;
+  display: none;
+  flex-direction: column;
+  justify-content: center;
+  overflow: hidden;
+  position: fixed;
+  z-index: 40; }
+  .modal.is-active {
+    display: flex; }
+
+.modal-background {
+  background-color: rgba(10, 10, 10, 0.86); }
+
+.modal-content,
+.modal-card {
+  margin: 0 20px;
+  max-height: calc(100vh - 160px);
+  overflow: auto;
+  position: relative;
+  width: 100%; }
+  @media screen and (min-width: 769px), print {
+    .modal-content,
+    .modal-card {
+      margin: 0 auto;
+      max-height: calc(100vh - 40px);
+      width: 640px; } }
+
+.modal-close {
+  background: none;
+  height: 40px;
+  position: fixed;
+  right: 20px;
+  top: 20px;
+  width: 40px; }
+
+.modal-card {
+  display: flex;
+  flex-direction: column;
+  max-height: calc(100vh - 40px);
+  overflow: hidden;
+  -ms-overflow-y: visible; }
+
+.modal-card-head,
+.modal-card-foot {
+  align-items: center;
+  background-color: whitesmoke;
+  display: flex;
+  flex-shrink: 0;
+  justify-content: flex-start;
+  padding: 20px;
+  position: relative; }
+
+.modal-card-head {
+  border-bottom: 1px solid #dbdbdb;
+  border-top-left-radius: 6px;
+  border-top-right-radius: 6px; }
+
+.modal-card-title {
+  color: #222222;
+  flex-grow: 1;
+  flex-shrink: 0;
+  font-size: 1.5rem;
+  line-height: 1; }
+
+.modal-card-foot {
+  border-bottom-left-radius: 6px;
+  border-bottom-right-radius: 6px;
+  border-top: 1px solid #dbdbdb; }
+  .modal-card-foot .button:not(:last-child) {
+    margin-right: 0.5em; }
+
+.modal-card-body {
+  -webkit-overflow-scrolling: touch;
+  background-color: white;
+  flex-grow: 1;
+  flex-shrink: 1;
+  overflow: auto;
+  padding: 20px; }
+
+.navbar {
+  background-color: white;
+  min-height: 3.25rem;
+  position: relative;
+  z-index: 30; }
+  .navbar.is-white {
+    background-color: white;
+    color: #0a0a0a; }
+    .navbar.is-white .navbar-brand > .navbar-item,
+    .navbar.is-white .navbar-brand .navbar-link {
+      color: #0a0a0a; }
+    .navbar.is-white .navbar-brand > a.navbar-item:focus, .navbar.is-white .navbar-brand > a.navbar-item:hover, .navbar.is-white .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-white .navbar-brand .navbar-link:focus,
+    .navbar.is-white .navbar-brand .navbar-link:hover,
+    .navbar.is-white .navbar-brand .navbar-link.is-active {
+      background-color: #f2f2f2;
+      color: #0a0a0a; }
+    .navbar.is-white .navbar-brand .navbar-link::after {
+      border-color: #0a0a0a; }
+    .navbar.is-white .navbar-burger {
+      color: #0a0a0a; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-white .navbar-start > .navbar-item,
+      .navbar.is-white .navbar-start .navbar-link,
+      .navbar.is-white .navbar-end > .navbar-item,
+      .navbar.is-white .navbar-end .navbar-link {
+        color: #0a0a0a; }
+      .navbar.is-white .navbar-start > a.navbar-item:focus, .navbar.is-white .navbar-start > a.navbar-item:hover, .navbar.is-white .navbar-start > a.navbar-item.is-active,
+      .navbar.is-white .navbar-start .navbar-link:focus,
+      .navbar.is-white .navbar-start .navbar-link:hover,
+      .navbar.is-white .navbar-start .navbar-link.is-active,
+      .navbar.is-white .navbar-end > a.navbar-item:focus,
+      .navbar.is-white .navbar-end > a.navbar-item:hover,
+      .navbar.is-white .navbar-end > a.navbar-item.is-active,
+      .navbar.is-white .navbar-end .navbar-link:focus,
+      .navbar.is-white .navbar-end .navbar-link:hover,
+      .navbar.is-white .navbar-end .navbar-link.is-active {
+        background-color: #f2f2f2;
+        color: #0a0a0a; }
+      .navbar.is-white .navbar-start .navbar-link::after,
+      .navbar.is-white .navbar-end .navbar-link::after {
+        border-color: #0a0a0a; }
+      .navbar.is-white .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-white .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-white .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #f2f2f2;
+        color: #0a0a0a; }
+      .navbar.is-white .navbar-dropdown a.navbar-item.is-active {
+        background-color: white;
+        color: #0a0a0a; } }
+  .navbar.is-black {
+    background-color: #0a0a0a;
+    color: white; }
+    .navbar.is-black .navbar-brand > .navbar-item,
+    .navbar.is-black .navbar-brand .navbar-link {
+      color: white; }
+    .navbar.is-black .navbar-brand > a.navbar-item:focus, .navbar.is-black .navbar-brand > a.navbar-item:hover, .navbar.is-black .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-black .navbar-brand .navbar-link:focus,
+    .navbar.is-black .navbar-brand .navbar-link:hover,
+    .navbar.is-black .navbar-brand .navbar-link.is-active {
+      background-color: black;
+      color: white; }
+    .navbar.is-black .navbar-brand .navbar-link::after {
+      border-color: white; }
+    .navbar.is-black .navbar-burger {
+      color: white; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-black .navbar-start > .navbar-item,
+      .navbar.is-black .navbar-start .navbar-link,
+      .navbar.is-black .navbar-end > .navbar-item,
+      .navbar.is-black .navbar-end .navbar-link {
+        color: white; }
+      .navbar.is-black .navbar-start > a.navbar-item:focus, .navbar.is-black .navbar-start > a.navbar-item:hover, .navbar.is-black .navbar-start > a.navbar-item.is-active,
+      .navbar.is-black .navbar-start .navbar-link:focus,
+      .navbar.is-black .navbar-start .navbar-link:hover,
+      .navbar.is-black .navbar-start .navbar-link.is-active,
+      .navbar.is-black .navbar-end > a.navbar-item:focus,
+      .navbar.is-black .navbar-end > a.navbar-item:hover,
+      .navbar.is-black .navbar-end > a.navbar-item.is-active,
+      .navbar.is-black .navbar-end .navbar-link:focus,
+      .navbar.is-black .navbar-end .navbar-link:hover,
+      .navbar.is-black .navbar-end .navbar-link.is-active {
+        background-color: black;
+        color: white; }
+      .navbar.is-black .navbar-start .navbar-link::after,
+      .navbar.is-black .navbar-end .navbar-link::after {
+        border-color: white; }
+      .navbar.is-black .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-black .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-black .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: black;
+        color: white; }
+      .navbar.is-black .navbar-dropdown a.navbar-item.is-active {
+        background-color: #0a0a0a;
+        color: white; } }
+  .navbar.is-light {
+    background-color: whitesmoke;
+    color: #363636; }
+    .navbar.is-light .navbar-brand > .navbar-item,
+    .navbar.is-light .navbar-brand .navbar-link {
+      color: #363636; }
+    .navbar.is-light .navbar-brand > a.navbar-item:focus, .navbar.is-light .navbar-brand > a.navbar-item:hover, .navbar.is-light .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-light .navbar-brand .navbar-link:focus,
+    .navbar.is-light .navbar-brand .navbar-link:hover,
+    .navbar.is-light .navbar-brand .navbar-link.is-active {
+      background-color: #e8e8e8;
+      color: #363636; }
+    .navbar.is-light .navbar-brand .navbar-link::after {
+      border-color: #363636; }
+    .navbar.is-light .navbar-burger {
+      color: #363636; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-light .navbar-start > .navbar-item,
+      .navbar.is-light .navbar-start .navbar-link,
+      .navbar.is-light .navbar-end > .navbar-item,
+      .navbar.is-light .navbar-end .navbar-link {
+        color: #363636; }
+      .navbar.is-light .navbar-start > a.navbar-item:focus, .navbar.is-light .navbar-start > a.navbar-item:hover, .navbar.is-light .navbar-start > a.navbar-item.is-active,
+      .navbar.is-light .navbar-start .navbar-link:focus,
+      .navbar.is-light .navbar-start .navbar-link:hover,
+      .navbar.is-light .navbar-start .navbar-link.is-active,
+      .navbar.is-light .navbar-end > a.navbar-item:focus,
+      .navbar.is-light .navbar-end > a.navbar-item:hover,
+      .navbar.is-light .navbar-end > a.navbar-item.is-active,
+      .navbar.is-light .navbar-end .navbar-link:focus,
+      .navbar.is-light .navbar-end .navbar-link:hover,
+      .navbar.is-light .navbar-end .navbar-link.is-active {
+        background-color: #e8e8e8;
+        color: #363636; }
+      .navbar.is-light .navbar-start .navbar-link::after,
+      .navbar.is-light .navbar-end .navbar-link::after {
+        border-color: #363636; }
+      .navbar.is-light .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-light .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-light .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #e8e8e8;
+        color: #363636; }
+      .navbar.is-light .navbar-dropdown a.navbar-item.is-active {
+        background-color: whitesmoke;
+        color: #363636; } }
+  .navbar.is-dark, .content kbd.navbar {
+    background-color: #363636;
+    color: whitesmoke; }
+    .navbar.is-dark .navbar-brand > .navbar-item, .content kbd.navbar .navbar-brand > .navbar-item,
+    .navbar.is-dark .navbar-brand .navbar-link,
+    .content kbd.navbar .navbar-brand .navbar-link {
+      color: whitesmoke; }
+    .navbar.is-dark .navbar-brand > a.navbar-item:focus, .content kbd.navbar .navbar-brand > a.navbar-item:focus, .navbar.is-dark .navbar-brand > a.navbar-item:hover, .content kbd.navbar .navbar-brand > a.navbar-item:hover, .navbar.is-dark .navbar-brand > a.navbar-item.is-active, .content kbd.navbar .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-dark .navbar-brand .navbar-link:focus,
+    .content kbd.navbar .navbar-brand .navbar-link:focus,
+    .navbar.is-dark .navbar-brand .navbar-link:hover,
+    .content kbd.navbar .navbar-brand .navbar-link:hover,
+    .navbar.is-dark .navbar-brand .navbar-link.is-active,
+    .content kbd.navbar .navbar-brand .navbar-link.is-active {
+      background-color: #292929;
+      color: whitesmoke; }
+    .navbar.is-dark .navbar-brand .navbar-link::after, .content kbd.navbar .navbar-brand .navbar-link::after {
+      border-color: whitesmoke; }
+    .navbar.is-dark .navbar-burger, .content kbd.navbar .navbar-burger {
+      color: whitesmoke; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-dark .navbar-start > .navbar-item, .content kbd.navbar .navbar-start > .navbar-item,
+      .navbar.is-dark .navbar-start .navbar-link,
+      .content kbd.navbar .navbar-start .navbar-link,
+      .navbar.is-dark .navbar-end > .navbar-item,
+      .content kbd.navbar .navbar-end > .navbar-item,
+      .navbar.is-dark .navbar-end .navbar-link,
+      .content kbd.navbar .navbar-end .navbar-link {
+        color: whitesmoke; }
+      .navbar.is-dark .navbar-start > a.navbar-item:focus, .content kbd.navbar .navbar-start > a.navbar-item:focus, .navbar.is-dark .navbar-start > a.navbar-item:hover, .content kbd.navbar .navbar-start > a.navbar-item:hover, .navbar.is-dark .navbar-start > a.navbar-item.is-active, .content kbd.navbar .navbar-start > a.navbar-item.is-active,
+      .navbar.is-dark .navbar-start .navbar-link:focus,
+      .content kbd.navbar .navbar-start .navbar-link:focus,
+      .navbar.is-dark .navbar-start .navbar-link:hover,
+      .content kbd.navbar .navbar-start .navbar-link:hover,
+      .navbar.is-dark .navbar-start .navbar-link.is-active,
+      .content kbd.navbar .navbar-start .navbar-link.is-active,
+      .navbar.is-dark .navbar-end > a.navbar-item:focus,
+      .content kbd.navbar .navbar-end > a.navbar-item:focus,
+      .navbar.is-dark .navbar-end > a.navbar-item:hover,
+      .content kbd.navbar .navbar-end > a.navbar-item:hover,
+      .navbar.is-dark .navbar-end > a.navbar-item.is-active,
+      .content kbd.navbar .navbar-end > a.navbar-item.is-active,
+      .navbar.is-dark .navbar-end .navbar-link:focus,
+      .content kbd.navbar .navbar-end .navbar-link:focus,
+      .navbar.is-dark .navbar-end .navbar-link:hover,
+      .content kbd.navbar .navbar-end .navbar-link:hover,
+      .navbar.is-dark .navbar-end .navbar-link.is-active,
+      .content kbd.navbar .navbar-end .navbar-link.is-active {
+        background-color: #292929;
+        color: whitesmoke; }
+      .navbar.is-dark .navbar-start .navbar-link::after, .content kbd.navbar .navbar-start .navbar-link::after,
+      .navbar.is-dark .navbar-end .navbar-link::after,
+      .content kbd.navbar .navbar-end .navbar-link::after {
+        border-color: whitesmoke; }
+      .navbar.is-dark .navbar-item.has-dropdown:focus .navbar-link, .content kbd.navbar .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-dark .navbar-item.has-dropdown:hover .navbar-link,
+      .content kbd.navbar .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-dark .navbar-item.has-dropdown.is-active .navbar-link,
+      .content kbd.navbar .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #292929;
+        color: whitesmoke; }
+      .navbar.is-dark .navbar-dropdown a.navbar-item.is-active, .content kbd.navbar .navbar-dropdown a.navbar-item.is-active {
+        background-color: #363636;
+        color: whitesmoke; } }
+  .navbar.is-primary, .docstring > section > a.navbar.docs-sourcelink {
+    background-color: #4eb5de;
+    color: #fff; }
+    .navbar.is-primary .navbar-brand > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > .navbar-item,
+    .navbar.is-primary .navbar-brand .navbar-link,
+    .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link {
+      color: #fff; }
+    .navbar.is-primary .navbar-brand > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:focus, .navbar.is-primary .navbar-brand > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item:hover, .navbar.is-primary .navbar-brand > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-primary .navbar-brand .navbar-link:focus,
+    .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:focus,
+    .navbar.is-primary .navbar-brand .navbar-link:hover,
+    .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link:hover,
+    .navbar.is-primary .navbar-brand .navbar-link.is-active,
+    .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link.is-active {
+      background-color: #39acda;
+      color: #fff; }
+    .navbar.is-primary .navbar-brand .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-brand .navbar-link::after {
+      border-color: #fff; }
+    .navbar.is-primary .navbar-burger, .docstring > section > a.navbar.docs-sourcelink .navbar-burger {
+      color: #fff; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-primary .navbar-start > .navbar-item, .docstring > section > a.navbar.docs-sourcelink .navbar-start > .navbar-item,
+      .navbar.is-primary .navbar-start .navbar-link,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link,
+      .navbar.is-primary .navbar-end > .navbar-item,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end > .navbar-item,
+      .navbar.is-primary .navbar-end .navbar-link,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link {
+        color: #fff; }
+      .navbar.is-primary .navbar-start > a.navbar-item:focus, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:focus, .navbar.is-primary .navbar-start > a.navbar-item:hover, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item:hover, .navbar.is-primary .navbar-start > a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-start > a.navbar-item.is-active,
+      .navbar.is-primary .navbar-start .navbar-link:focus,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:focus,
+      .navbar.is-primary .navbar-start .navbar-link:hover,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link:hover,
+      .navbar.is-primary .navbar-start .navbar-link.is-active,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link.is-active,
+      .navbar.is-primary .navbar-end > a.navbar-item:focus,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:focus,
+      .navbar.is-primary .navbar-end > a.navbar-item:hover,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item:hover,
+      .navbar.is-primary .navbar-end > a.navbar-item.is-active,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end > a.navbar-item.is-active,
+      .navbar.is-primary .navbar-end .navbar-link:focus,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:focus,
+      .navbar.is-primary .navbar-end .navbar-link:hover,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link:hover,
+      .navbar.is-primary .navbar-end .navbar-link.is-active,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link.is-active {
+        background-color: #39acda;
+        color: #fff; }
+      .navbar.is-primary .navbar-start .navbar-link::after, .docstring > section > a.navbar.docs-sourcelink .navbar-start .navbar-link::after,
+      .navbar.is-primary .navbar-end .navbar-link::after,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-end .navbar-link::after {
+        border-color: #fff; }
+      .navbar.is-primary .navbar-item.has-dropdown:focus .navbar-link, .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-primary .navbar-item.has-dropdown:hover .navbar-link,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-primary .navbar-item.has-dropdown.is-active .navbar-link,
+      .docstring > section > a.navbar.docs-sourcelink .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #39acda;
+        color: #fff; }
+      .navbar.is-primary .navbar-dropdown a.navbar-item.is-active, .docstring > section > a.navbar.docs-sourcelink .navbar-dropdown a.navbar-item.is-active {
+        background-color: #4eb5de;
+        color: #fff; } }
+  .navbar.is-link {
+    background-color: #2e63b8;
+    color: #fff; }
+    .navbar.is-link .navbar-brand > .navbar-item,
+    .navbar.is-link .navbar-brand .navbar-link {
+      color: #fff; }
+    .navbar.is-link .navbar-brand > a.navbar-item:focus, .navbar.is-link .navbar-brand > a.navbar-item:hover, .navbar.is-link .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-link .navbar-brand .navbar-link:focus,
+    .navbar.is-link .navbar-brand .navbar-link:hover,
+    .navbar.is-link .navbar-brand .navbar-link.is-active {
+      background-color: #2958a4;
+      color: #fff; }
+    .navbar.is-link .navbar-brand .navbar-link::after {
+      border-color: #fff; }
+    .navbar.is-link .navbar-burger {
+      color: #fff; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-link .navbar-start > .navbar-item,
+      .navbar.is-link .navbar-start .navbar-link,
+      .navbar.is-link .navbar-end > .navbar-item,
+      .navbar.is-link .navbar-end .navbar-link {
+        color: #fff; }
+      .navbar.is-link .navbar-start > a.navbar-item:focus, .navbar.is-link .navbar-start > a.navbar-item:hover, .navbar.is-link .navbar-start > a.navbar-item.is-active,
+      .navbar.is-link .navbar-start .navbar-link:focus,
+      .navbar.is-link .navbar-start .navbar-link:hover,
+      .navbar.is-link .navbar-start .navbar-link.is-active,
+      .navbar.is-link .navbar-end > a.navbar-item:focus,
+      .navbar.is-link .navbar-end > a.navbar-item:hover,
+      .navbar.is-link .navbar-end > a.navbar-item.is-active,
+      .navbar.is-link .navbar-end .navbar-link:focus,
+      .navbar.is-link .navbar-end .navbar-link:hover,
+      .navbar.is-link .navbar-end .navbar-link.is-active {
+        background-color: #2958a4;
+        color: #fff; }
+      .navbar.is-link .navbar-start .navbar-link::after,
+      .navbar.is-link .navbar-end .navbar-link::after {
+        border-color: #fff; }
+      .navbar.is-link .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-link .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-link .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #2958a4;
+        color: #fff; }
+      .navbar.is-link .navbar-dropdown a.navbar-item.is-active {
+        background-color: #2e63b8;
+        color: #fff; } }
+  .navbar.is-info {
+    background-color: #209cee;
+    color: #fff; }
+    .navbar.is-info .navbar-brand > .navbar-item,
+    .navbar.is-info .navbar-brand .navbar-link {
+      color: #fff; }
+    .navbar.is-info .navbar-brand > a.navbar-item:focus, .navbar.is-info .navbar-brand > a.navbar-item:hover, .navbar.is-info .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-info .navbar-brand .navbar-link:focus,
+    .navbar.is-info .navbar-brand .navbar-link:hover,
+    .navbar.is-info .navbar-brand .navbar-link.is-active {
+      background-color: #118fe4;
+      color: #fff; }
+    .navbar.is-info .navbar-brand .navbar-link::after {
+      border-color: #fff; }
+    .navbar.is-info .navbar-burger {
+      color: #fff; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-info .navbar-start > .navbar-item,
+      .navbar.is-info .navbar-start .navbar-link,
+      .navbar.is-info .navbar-end > .navbar-item,
+      .navbar.is-info .navbar-end .navbar-link {
+        color: #fff; }
+      .navbar.is-info .navbar-start > a.navbar-item:focus, .navbar.is-info .navbar-start > a.navbar-item:hover, .navbar.is-info .navbar-start > a.navbar-item.is-active,
+      .navbar.is-info .navbar-start .navbar-link:focus,
+      .navbar.is-info .navbar-start .navbar-link:hover,
+      .navbar.is-info .navbar-start .navbar-link.is-active,
+      .navbar.is-info .navbar-end > a.navbar-item:focus,
+      .navbar.is-info .navbar-end > a.navbar-item:hover,
+      .navbar.is-info .navbar-end > a.navbar-item.is-active,
+      .navbar.is-info .navbar-end .navbar-link:focus,
+      .navbar.is-info .navbar-end .navbar-link:hover,
+      .navbar.is-info .navbar-end .navbar-link.is-active {
+        background-color: #118fe4;
+        color: #fff; }
+      .navbar.is-info .navbar-start .navbar-link::after,
+      .navbar.is-info .navbar-end .navbar-link::after {
+        border-color: #fff; }
+      .navbar.is-info .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-info .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-info .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #118fe4;
+        color: #fff; }
+      .navbar.is-info .navbar-dropdown a.navbar-item.is-active {
+        background-color: #209cee;
+        color: #fff; } }
+  .navbar.is-success {
+    background-color: #22c35b;
+    color: #fff; }
+    .navbar.is-success .navbar-brand > .navbar-item,
+    .navbar.is-success .navbar-brand .navbar-link {
+      color: #fff; }
+    .navbar.is-success .navbar-brand > a.navbar-item:focus, .navbar.is-success .navbar-brand > a.navbar-item:hover, .navbar.is-success .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-success .navbar-brand .navbar-link:focus,
+    .navbar.is-success .navbar-brand .navbar-link:hover,
+    .navbar.is-success .navbar-brand .navbar-link.is-active {
+      background-color: #1ead51;
+      color: #fff; }
+    .navbar.is-success .navbar-brand .navbar-link::after {
+      border-color: #fff; }
+    .navbar.is-success .navbar-burger {
+      color: #fff; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-success .navbar-start > .navbar-item,
+      .navbar.is-success .navbar-start .navbar-link,
+      .navbar.is-success .navbar-end > .navbar-item,
+      .navbar.is-success .navbar-end .navbar-link {
+        color: #fff; }
+      .navbar.is-success .navbar-start > a.navbar-item:focus, .navbar.is-success .navbar-start > a.navbar-item:hover, .navbar.is-success .navbar-start > a.navbar-item.is-active,
+      .navbar.is-success .navbar-start .navbar-link:focus,
+      .navbar.is-success .navbar-start .navbar-link:hover,
+      .navbar.is-success .navbar-start .navbar-link.is-active,
+      .navbar.is-success .navbar-end > a.navbar-item:focus,
+      .navbar.is-success .navbar-end > a.navbar-item:hover,
+      .navbar.is-success .navbar-end > a.navbar-item.is-active,
+      .navbar.is-success .navbar-end .navbar-link:focus,
+      .navbar.is-success .navbar-end .navbar-link:hover,
+      .navbar.is-success .navbar-end .navbar-link.is-active {
+        background-color: #1ead51;
+        color: #fff; }
+      .navbar.is-success .navbar-start .navbar-link::after,
+      .navbar.is-success .navbar-end .navbar-link::after {
+        border-color: #fff; }
+      .navbar.is-success .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-success .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-success .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #1ead51;
+        color: #fff; }
+      .navbar.is-success .navbar-dropdown a.navbar-item.is-active {
+        background-color: #22c35b;
+        color: #fff; } }
+  .navbar.is-warning {
+    background-color: #ffdd57;
+    color: rgba(0, 0, 0, 0.7); }
+    .navbar.is-warning .navbar-brand > .navbar-item,
+    .navbar.is-warning .navbar-brand .navbar-link {
+      color: rgba(0, 0, 0, 0.7); }
+    .navbar.is-warning .navbar-brand > a.navbar-item:focus, .navbar.is-warning .navbar-brand > a.navbar-item:hover, .navbar.is-warning .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-warning .navbar-brand .navbar-link:focus,
+    .navbar.is-warning .navbar-brand .navbar-link:hover,
+    .navbar.is-warning .navbar-brand .navbar-link.is-active {
+      background-color: #ffd83d;
+      color: rgba(0, 0, 0, 0.7); }
+    .navbar.is-warning .navbar-brand .navbar-link::after {
+      border-color: rgba(0, 0, 0, 0.7); }
+    .navbar.is-warning .navbar-burger {
+      color: rgba(0, 0, 0, 0.7); }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-warning .navbar-start > .navbar-item,
+      .navbar.is-warning .navbar-start .navbar-link,
+      .navbar.is-warning .navbar-end > .navbar-item,
+      .navbar.is-warning .navbar-end .navbar-link {
+        color: rgba(0, 0, 0, 0.7); }
+      .navbar.is-warning .navbar-start > a.navbar-item:focus, .navbar.is-warning .navbar-start > a.navbar-item:hover, .navbar.is-warning .navbar-start > a.navbar-item.is-active,
+      .navbar.is-warning .navbar-start .navbar-link:focus,
+      .navbar.is-warning .navbar-start .navbar-link:hover,
+      .navbar.is-warning .navbar-start .navbar-link.is-active,
+      .navbar.is-warning .navbar-end > a.navbar-item:focus,
+      .navbar.is-warning .navbar-end > a.navbar-item:hover,
+      .navbar.is-warning .navbar-end > a.navbar-item.is-active,
+      .navbar.is-warning .navbar-end .navbar-link:focus,
+      .navbar.is-warning .navbar-end .navbar-link:hover,
+      .navbar.is-warning .navbar-end .navbar-link.is-active {
+        background-color: #ffd83d;
+        color: rgba(0, 0, 0, 0.7); }
+      .navbar.is-warning .navbar-start .navbar-link::after,
+      .navbar.is-warning .navbar-end .navbar-link::after {
+        border-color: rgba(0, 0, 0, 0.7); }
+      .navbar.is-warning .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-warning .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-warning .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #ffd83d;
+        color: rgba(0, 0, 0, 0.7); }
+      .navbar.is-warning .navbar-dropdown a.navbar-item.is-active {
+        background-color: #ffdd57;
+        color: rgba(0, 0, 0, 0.7); } }
+  .navbar.is-danger {
+    background-color: #da0b00;
+    color: #fff; }
+    .navbar.is-danger .navbar-brand > .navbar-item,
+    .navbar.is-danger .navbar-brand .navbar-link {
+      color: #fff; }
+    .navbar.is-danger .navbar-brand > a.navbar-item:focus, .navbar.is-danger .navbar-brand > a.navbar-item:hover, .navbar.is-danger .navbar-brand > a.navbar-item.is-active,
+    .navbar.is-danger .navbar-brand .navbar-link:focus,
+    .navbar.is-danger .navbar-brand .navbar-link:hover,
+    .navbar.is-danger .navbar-brand .navbar-link.is-active {
+      background-color: #c10a00;
+      color: #fff; }
+    .navbar.is-danger .navbar-brand .navbar-link::after {
+      border-color: #fff; }
+    .navbar.is-danger .navbar-burger {
+      color: #fff; }
+    @media screen and (min-width: 1056px) {
+      .navbar.is-danger .navbar-start > .navbar-item,
+      .navbar.is-danger .navbar-start .navbar-link,
+      .navbar.is-danger .navbar-end > .navbar-item,
+      .navbar.is-danger .navbar-end .navbar-link {
+        color: #fff; }
+      .navbar.is-danger .navbar-start > a.navbar-item:focus, .navbar.is-danger .navbar-start > a.navbar-item:hover, .navbar.is-danger .navbar-start > a.navbar-item.is-active,
+      .navbar.is-danger .navbar-start .navbar-link:focus,
+      .navbar.is-danger .navbar-start .navbar-link:hover,
+      .navbar.is-danger .navbar-start .navbar-link.is-active,
+      .navbar.is-danger .navbar-end > a.navbar-item:focus,
+      .navbar.is-danger .navbar-end > a.navbar-item:hover,
+      .navbar.is-danger .navbar-end > a.navbar-item.is-active,
+      .navbar.is-danger .navbar-end .navbar-link:focus,
+      .navbar.is-danger .navbar-end .navbar-link:hover,
+      .navbar.is-danger .navbar-end .navbar-link.is-active {
+        background-color: #c10a00;
+        color: #fff; }
+      .navbar.is-danger .navbar-start .navbar-link::after,
+      .navbar.is-danger .navbar-end .navbar-link::after {
+        border-color: #fff; }
+      .navbar.is-danger .navbar-item.has-dropdown:focus .navbar-link,
+      .navbar.is-danger .navbar-item.has-dropdown:hover .navbar-link,
+      .navbar.is-danger .navbar-item.has-dropdown.is-active .navbar-link {
+        background-color: #c10a00;
+        color: #fff; }
+      .navbar.is-danger .navbar-dropdown a.navbar-item.is-active {
+        background-color: #da0b00;
+        color: #fff; } }
+  .navbar > .container {
+    align-items: stretch;
+    display: flex;
+    min-height: 3.25rem;
+    width: 100%; }
+  .navbar.has-shadow {
+    box-shadow: 0 2px 0 0 whitesmoke; }
+  .navbar.is-fixed-bottom, .navbar.is-fixed-top {
+    left: 0;
+    position: fixed;
+    right: 0;
+    z-index: 30; }
+  .navbar.is-fixed-bottom {
+    bottom: 0; }
+    .navbar.is-fixed-bottom.has-shadow {
+      box-shadow: 0 -2px 0 0 whitesmoke; }
+  .navbar.is-fixed-top {
+    top: 0; }
+
+html.has-navbar-fixed-top,
+body.has-navbar-fixed-top {
+  padding-top: 3.25rem; }
+
+html.has-navbar-fixed-bottom,
+body.has-navbar-fixed-bottom {
+  padding-bottom: 3.25rem; }
+
+.navbar-brand,
+.navbar-tabs {
+  align-items: stretch;
+  display: flex;
+  flex-shrink: 0;
+  min-height: 3.25rem; }
+
+.navbar-brand a.navbar-item:focus, .navbar-brand a.navbar-item:hover {
+  background-color: transparent; }
+
+.navbar-tabs {
+  -webkit-overflow-scrolling: touch;
+  max-width: 100vw;
+  overflow-x: auto;
+  overflow-y: hidden; }
+
+.navbar-burger {
+  color: #4a4a4a;
+  cursor: pointer;
+  display: block;
+  height: 3.25rem;
+  position: relative;
+  width: 3.25rem;
+  margin-left: auto; }
+  .navbar-burger span {
+    background-color: currentColor;
+    display: block;
+    height: 1px;
+    left: calc(50% - 8px);
+    position: absolute;
+    transform-origin: center;
+    transition-duration: 86ms;
+    transition-property: background-color, opacity, transform;
+    transition-timing-function: ease-out;
+    width: 16px; }
+    .navbar-burger span:nth-child(1) {
+      top: calc(50% - 6px); }
+    .navbar-burger span:nth-child(2) {
+      top: calc(50% - 1px); }
+    .navbar-burger span:nth-child(3) {
+      top: calc(50% + 4px); }
+  .navbar-burger:hover {
+    background-color: rgba(0, 0, 0, 0.05); }
+  .navbar-burger.is-active span:nth-child(1) {
+    transform: translateY(5px) rotate(45deg); }
+  .navbar-burger.is-active span:nth-child(2) {
+    opacity: 0; }
+  .navbar-burger.is-active span:nth-child(3) {
+    transform: translateY(-5px) rotate(-45deg); }
+
+.navbar-menu {
+  display: none; }
+
+.navbar-item,
+.navbar-link {
+  color: #4a4a4a;
+  display: block;
+  line-height: 1.5;
+  padding: 0.5rem 0.75rem;
+  position: relative; }
+  .navbar-item .icon:only-child,
+  .navbar-link .icon:only-child {
+    margin-left: -0.25rem;
+    margin-right: -0.25rem; }
+
+a.navbar-item,
+.navbar-link {
+  cursor: pointer; }
+  a.navbar-item:focus, a.navbar-item:focus-within, a.navbar-item:hover, a.navbar-item.is-active,
+  .navbar-link:focus,
+  .navbar-link:focus-within,
+  .navbar-link:hover,
+  .navbar-link.is-active {
+    background-color: #fafafa;
+    color: #2e63b8; }
+
+.navbar-item {
+  display: block;
+  flex-grow: 0;
+  flex-shrink: 0; }
+  .navbar-item img {
+    max-height: 1.75rem; }
+  .navbar-item.has-dropdown {
+    padding: 0; }
+  .navbar-item.is-expanded {
+    flex-grow: 1;
+    flex-shrink: 1; }
+  .navbar-item.is-tab {
+    border-bottom: 1px solid transparent;
+    min-height: 3.25rem;
+    padding-bottom: calc(0.5rem - 1px); }
+    .navbar-item.is-tab:focus, .navbar-item.is-tab:hover {
+      background-color: transparent;
+      border-bottom-color: #2e63b8; }
+    .navbar-item.is-tab.is-active {
+      background-color: transparent;
+      border-bottom-color: #2e63b8;
+      border-bottom-style: solid;
+      border-bottom-width: 3px;
+      color: #2e63b8;
+      padding-bottom: calc(0.5rem - 3px); }
+
+.navbar-content {
+  flex-grow: 1;
+  flex-shrink: 1; }
+
+.navbar-link:not(.is-arrowless) {
+  padding-right: 2.5em; }
+  .navbar-link:not(.is-arrowless)::after {
+    border-color: #2e63b8;
+    margin-top: -0.375em;
+    right: 1.125em; }
+
+.navbar-dropdown {
+  font-size: 0.875rem;
+  padding-bottom: 0.5rem;
+  padding-top: 0.5rem; }
+  .navbar-dropdown .navbar-item {
+    padding-left: 1.5rem;
+    padding-right: 1.5rem; }
+
+.navbar-divider {
+  background-color: whitesmoke;
+  border: none;
+  display: none;
+  height: 2px;
+  margin: 0.5rem 0; }
+
+@media screen and (max-width: 1055px) {
+  .navbar > .container {
+    display: block; }
+  .navbar-brand .navbar-item,
+  .navbar-tabs .navbar-item {
+    align-items: center;
+    display: flex; }
+  .navbar-link::after {
+    display: none; }
+  .navbar-menu {
+    background-color: white;
+    box-shadow: 0 8px 16px rgba(10, 10, 10, 0.1);
+    padding: 0.5rem 0; }
+    .navbar-menu.is-active {
+      display: block; }
+  .navbar.is-fixed-bottom-touch, .navbar.is-fixed-top-touch {
+    left: 0;
+    position: fixed;
+    right: 0;
+    z-index: 30; }
+  .navbar.is-fixed-bottom-touch {
+    bottom: 0; }
+    .navbar.is-fixed-bottom-touch.has-shadow {
+      box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }
+  .navbar.is-fixed-top-touch {
+    top: 0; }
+  .navbar.is-fixed-top .navbar-menu, .navbar.is-fixed-top-touch .navbar-menu {
+    -webkit-overflow-scrolling: touch;
+    max-height: calc(100vh - 3.25rem);
+    overflow: auto; }
+  html.has-navbar-fixed-top-touch,
+  body.has-navbar-fixed-top-touch {
+    padding-top: 3.25rem; }
+  html.has-navbar-fixed-bottom-touch,
+  body.has-navbar-fixed-bottom-touch {
+    padding-bottom: 3.25rem; } }
+
+@media screen and (min-width: 1056px) {
+  .navbar,
+  .navbar-menu,
+  .navbar-start,
+  .navbar-end {
+    align-items: stretch;
+    display: flex; }
+  .navbar {
+    min-height: 3.25rem; }
+    .navbar.is-spaced {
+      padding: 1rem 2rem; }
+      .navbar.is-spaced .navbar-start,
+      .navbar.is-spaced .navbar-end {
+        align-items: center; }
+      .navbar.is-spaced a.navbar-item,
+      .navbar.is-spaced .navbar-link {
+        border-radius: 4px; }
+    .navbar.is-transparent a.navbar-item:focus, .navbar.is-transparent a.navbar-item:hover, .navbar.is-transparent a.navbar-item.is-active,
+    .navbar.is-transparent .navbar-link:focus,
+    .navbar.is-transparent .navbar-link:hover,
+    .navbar.is-transparent .navbar-link.is-active {
+      background-color: transparent !important; }
+    .navbar.is-transparent .navbar-item.has-dropdown.is-active .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:focus-within .navbar-link, .navbar.is-transparent .navbar-item.has-dropdown.is-hoverable:hover .navbar-link {
+      background-color: transparent !important; }
+    .navbar.is-transparent .navbar-dropdown a.navbar-item:focus, .navbar.is-transparent .navbar-dropdown a.navbar-item:hover {
+      background-color: whitesmoke;
+      color: #0a0a0a; }
+    .navbar.is-transparent .navbar-dropdown a.navbar-item.is-active {
+      background-color: whitesmoke;
+      color: #2e63b8; }
+  .navbar-burger {
+    display: none; }
+  .navbar-item,
+  .navbar-link {
+    align-items: center;
+    display: flex; }
+  .navbar-item {
+    display: flex; }
+    .navbar-item.has-dropdown {
+      align-items: stretch; }
+    .navbar-item.has-dropdown-up .navbar-link::after {
+      transform: rotate(135deg) translate(0.25em, -0.25em); }
+    .navbar-item.has-dropdown-up .navbar-dropdown {
+      border-bottom: 2px solid #dbdbdb;
+      border-radius: 6px 6px 0 0;
+      border-top: none;
+      bottom: 100%;
+      box-shadow: 0 -8px 8px rgba(10, 10, 10, 0.1);
+      top: auto; }
+    .navbar-item.is-active .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown {
+      display: block; }
+      .navbar.is-spaced .navbar-item.is-active .navbar-dropdown, .navbar-item.is-active .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus .navbar-dropdown, .navbar-item.is-hoverable:focus .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:focus-within .navbar-dropdown, .navbar-item.is-hoverable:focus-within .navbar-dropdown.is-boxed, .navbar.is-spaced .navbar-item.is-hoverable:hover .navbar-dropdown, .navbar-item.is-hoverable:hover .navbar-dropdown.is-boxed {
+        opacity: 1;
+        pointer-events: auto;
+        transform: translateY(0); }
+  .navbar-menu {
+    flex-grow: 1;
+    flex-shrink: 0; }
+  .navbar-start {
+    justify-content: flex-start;
+    margin-right: auto; }
+  .navbar-end {
+    justify-content: flex-end;
+    margin-left: auto; }
+  .navbar-dropdown {
+    background-color: white;
+    border-bottom-left-radius: 6px;
+    border-bottom-right-radius: 6px;
+    border-top: 2px solid #dbdbdb;
+    box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1);
+    display: none;
+    font-size: 0.875rem;
+    left: 0;
+    min-width: 100%;
+    position: absolute;
+    top: 100%;
+    z-index: 20; }
+    .navbar-dropdown .navbar-item {
+      padding: 0.375rem 1rem;
+      white-space: nowrap; }
+    .navbar-dropdown a.navbar-item {
+      padding-right: 3rem; }
+      .navbar-dropdown a.navbar-item:focus, .navbar-dropdown a.navbar-item:hover {
+        background-color: whitesmoke;
+        color: #0a0a0a; }
+      .navbar-dropdown a.navbar-item.is-active {
+        background-color: whitesmoke;
+        color: #2e63b8; }
+    .navbar.is-spaced .navbar-dropdown, .navbar-dropdown.is-boxed {
+      border-radius: 6px;
+      border-top: none;
+      box-shadow: 0 8px 8px rgba(10, 10, 10, 0.1), 0 0 0 1px rgba(10, 10, 10, 0.1);
+      display: block;
+      opacity: 0;
+      pointer-events: none;
+      top: calc(100% + (-4px));
+      transform: translateY(-5px);
+      transition-duration: 86ms;
+      transition-property: opacity, transform; }
+    .navbar-dropdown.is-right {
+      left: auto;
+      right: 0; }
+  .navbar-divider {
+    display: block; }
+  .navbar > .container .navbar-brand,
+  .container > .navbar .navbar-brand {
+    margin-left: -.75rem; }
+  .navbar > .container .navbar-menu,
+  .container > .navbar .navbar-menu {
+    margin-right: -.75rem; }
+  .navbar.is-fixed-bottom-desktop, .navbar.is-fixed-top-desktop {
+    left: 0;
+    position: fixed;
+    right: 0;
+    z-index: 30; }
+  .navbar.is-fixed-bottom-desktop {
+    bottom: 0; }
+    .navbar.is-fixed-bottom-desktop.has-shadow {
+      box-shadow: 0 -2px 3px rgba(10, 10, 10, 0.1); }
+  .navbar.is-fixed-top-desktop {
+    top: 0; }
+  html.has-navbar-fixed-top-desktop,
+  body.has-navbar-fixed-top-desktop {
+    padding-top: 3.25rem; }
+  html.has-navbar-fixed-bottom-desktop,
+  body.has-navbar-fixed-bottom-desktop {
+    padding-bottom: 3.25rem; }
+  html.has-spaced-navbar-fixed-top,
+  body.has-spaced-navbar-fixed-top {
+    padding-top: 5.25rem; }
+  html.has-spaced-navbar-fixed-bottom,
+  body.has-spaced-navbar-fixed-bottom {
+    padding-bottom: 5.25rem; }
+  a.navbar-item.is-active,
+  .navbar-link.is-active {
+    color: #0a0a0a; }
+  a.navbar-item.is-active:not(:focus):not(:hover),
+  .navbar-link.is-active:not(:focus):not(:hover) {
+    background-color: transparent; }
+  .navbar-item.has-dropdown:focus .navbar-link, .navbar-item.has-dropdown:hover .navbar-link, .navbar-item.has-dropdown.is-active .navbar-link {
+    background-color: #fafafa; } }
+
+.hero.is-fullheight-with-navbar {
+  min-height: calc(100vh - 3.25rem); }
+
+.pagination {
+  font-size: 1rem;
+  margin: -0.25rem; }
+  .pagination.is-small, #documenter .docs-sidebar form.docs-search > input.pagination {
+    font-size: 0.75rem; }
+  .pagination.is-medium {
+    font-size: 1.25rem; }
+  .pagination.is-large {
+    font-size: 1.5rem; }
+  .pagination.is-rounded .pagination-previous, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-previous,
+  .pagination.is-rounded .pagination-next,
+  #documenter .docs-sidebar form.docs-search > input.pagination .pagination-next {
+    padding-left: 1em;
+    padding-right: 1em;
+    border-radius: 290486px; }
+  .pagination.is-rounded .pagination-link, #documenter .docs-sidebar form.docs-search > input.pagination .pagination-link {
+    border-radius: 290486px; }
+
+.pagination,
+.pagination-list {
+  align-items: center;
+  display: flex;
+  justify-content: center;
+  text-align: center; }
+
+.pagination-previous,
+.pagination-next,
+.pagination-link,
+.pagination-ellipsis {
+  font-size: 1em;
+  justify-content: center;
+  margin: 0.25rem;
+  padding-left: 0.5em;
+  padding-right: 0.5em;
+  text-align: center; }
+
+.pagination-previous,
+.pagination-next,
+.pagination-link {
+  border-color: #dbdbdb;
+  color: #363636;
+  min-width: 2.25em; }
+  .pagination-previous:hover,
+  .pagination-next:hover,
+  .pagination-link:hover {
+    border-color: #b5b5b5;
+    color: #363636; }
+  .pagination-previous:focus,
+  .pagination-next:focus,
+  .pagination-link:focus {
+    border-color: #2e63b8; }
+  .pagination-previous:active,
+  .pagination-next:active,
+  .pagination-link:active {
+    box-shadow: inset 0 1px 2px rgba(10, 10, 10, 0.2); }
+  .pagination-previous[disabled],
+  .pagination-next[disabled],
+  .pagination-link[disabled] {
+    background-color: #dbdbdb;
+    border-color: #dbdbdb;
+    box-shadow: none;
+    color: #7a7a7a;
+    opacity: 0.5; }
+
+.pagination-previous,
+.pagination-next {
+  padding-left: 0.75em;
+  padding-right: 0.75em;
+  white-space: nowrap; }
+
+.pagination-link.is-current {
+  background-color: #2e63b8;
+  border-color: #2e63b8;
+  color: #fff; }
+
+.pagination-ellipsis {
+  color: #b5b5b5;
+  pointer-events: none; }
+
+.pagination-list {
+  flex-wrap: wrap; }
+
+@media screen and (max-width: 768px) {
+  .pagination {
+    flex-wrap: wrap; }
+  .pagination-previous,
+  .pagination-next {
+    flex-grow: 1;
+    flex-shrink: 1; }
+  .pagination-list li {
+    flex-grow: 1;
+    flex-shrink: 1; } }
+
+@media screen and (min-width: 769px), print {
+  .pagination-list {
+    flex-grow: 1;
+    flex-shrink: 1;
+    justify-content: flex-start;
+    order: 1; }
+  .pagination-previous {
+    order: 2; }
+  .pagination-next {
+    order: 3; }
+  .pagination {
+    justify-content: space-between; }
+    .pagination.is-centered .pagination-previous {
+      order: 1; }
+    .pagination.is-centered .pagination-list {
+      justify-content: center;
+      order: 2; }
+    .pagination.is-centered .pagination-next {
+      order: 3; }
+    .pagination.is-right .pagination-previous {
+      order: 1; }
+    .pagination.is-right .pagination-next {
+      order: 2; }
+    .pagination.is-right .pagination-list {
+      justify-content: flex-end;
+      order: 3; } }
+
+.panel {
+  font-size: 1rem; }
+  .panel:not(:last-child) {
+    margin-bottom: 1.5rem; }
+
+.panel-heading,
+.panel-tabs,
+.panel-block {
+  border-bottom: 1px solid #dbdbdb;
+  border-left: 1px solid #dbdbdb;
+  border-right: 1px solid #dbdbdb; }
+  .panel-heading:first-child,
+  .panel-tabs:first-child,
+  .panel-block:first-child {
+    border-top: 1px solid #dbdbdb; }
+
+.panel-heading {
+  background-color: whitesmoke;
+  border-radius: 4px 4px 0 0;
+  color: #222222;
+  font-size: 1.25em;
+  font-weight: 300;
+  line-height: 1.25;
+  padding: 0.5em 0.75em; }
+
+.panel-tabs {
+  align-items: flex-end;
+  display: flex;
+  font-size: 0.875em;
+  justify-content: center; }
+  .panel-tabs a {
+    border-bottom: 1px solid #dbdbdb;
+    margin-bottom: -1px;
+    padding: 0.5em; }
+    .panel-tabs a.is-active {
+      border-bottom-color: #4a4a4a;
+      color: #363636; }
+
+.panel-list a {
+  color: #222222; }
+  .panel-list a:hover {
+    color: #2e63b8; }
+
+.panel-block {
+  align-items: center;
+  color: #222222;
+  display: flex;
+  justify-content: flex-start;
+  padding: 0.5em 0.75em; }
+  .panel-block input[type="checkbox"] {
+    margin-right: 0.75em; }
+  .panel-block > .control {
+    flex-grow: 1;
+    flex-shrink: 1;
+    width: 100%; }
+  .panel-block.is-wrapped {
+    flex-wrap: wrap; }
+  .panel-block.is-active {
+    border-left-color: #2e63b8;
+    color: #363636; }
+    .panel-block.is-active .panel-icon {
+      color: #2e63b8; }
+
+a.panel-block,
+label.panel-block {
+  cursor: pointer; }
+  a.panel-block:hover,
+  label.panel-block:hover {
+    background-color: whitesmoke; }
+
+.panel-icon {
+  display: inline-block;
+  font-size: 14px;
+  height: 1em;
+  line-height: 1em;
+  text-align: center;
+  vertical-align: top;
+  width: 1em;
+  color: #7a7a7a;
+  margin-right: 0.75em; }
+  .panel-icon .fa {
+    font-size: inherit;
+    line-height: inherit; }
+
+.tabs {
+  -webkit-overflow-scrolling: touch;
+  align-items: stretch;
+  display: flex;
+  font-size: 1rem;
+  justify-content: space-between;
+  overflow: hidden;
+  overflow-x: auto;
+  white-space: nowrap; }
+  .tabs a {
+    align-items: center;
+    border-bottom-color: #dbdbdb;
+    border-bottom-style: solid;
+    border-bottom-width: 1px;
+    color: #222222;
+    display: flex;
+    justify-content: center;
+    margin-bottom: -1px;
+    padding: 0.5em 1em;
+    vertical-align: top; }
+    .tabs a:hover {
+      border-bottom-color: #222222;
+      color: #222222; }
+  .tabs li {
+    display: block; }
+    .tabs li.is-active a {
+      border-bottom-color: #2e63b8;
+      color: #2e63b8; }
+  .tabs ul {
+    align-items: center;
+    border-bottom-color: #dbdbdb;
+    border-bottom-style: solid;
+    border-bottom-width: 1px;
+    display: flex;
+    flex-grow: 1;
+    flex-shrink: 0;
+    justify-content: flex-start; }
+    .tabs ul.is-left {
+      padding-right: 0.75em; }
+    .tabs ul.is-center {
+      flex: none;
+      justify-content: center;
+      padding-left: 0.75em;
+      padding-right: 0.75em; }
+    .tabs ul.is-right {
+      justify-content: flex-end;
+      padding-left: 0.75em; }
+  .tabs .icon:first-child {
+    margin-right: 0.5em; }
+  .tabs .icon:last-child {
+    margin-left: 0.5em; }
+  .tabs.is-centered ul {
+    justify-content: center; }
+  .tabs.is-right ul {
+    justify-content: flex-end; }
+  .tabs.is-boxed a {
+    border: 1px solid transparent;
+    border-radius: 4px 4px 0 0; }
+    .tabs.is-boxed a:hover {
+      background-color: whitesmoke;
+      border-bottom-color: #dbdbdb; }
+  .tabs.is-boxed li.is-active a {
+    background-color: white;
+    border-color: #dbdbdb;
+    border-bottom-color: transparent !important; }
+  .tabs.is-fullwidth li {
+    flex-grow: 1;
+    flex-shrink: 0; }
+  .tabs.is-toggle a {
+    border-color: #dbdbdb;
+    border-style: solid;
+    border-width: 1px;
+    margin-bottom: 0;
+    position: relative; }
+    .tabs.is-toggle a:hover {
+      background-color: whitesmoke;
+      border-color: #b5b5b5;
+      z-index: 2; }
+  .tabs.is-toggle li + li {
+    margin-left: -1px; }
+  .tabs.is-toggle li:first-child a {
+    border-radius: 4px 0 0 4px; }
+  .tabs.is-toggle li:last-child a {
+    border-radius: 0 4px 4px 0; }
+  .tabs.is-toggle li.is-active a {
+    background-color: #2e63b8;
+    border-color: #2e63b8;
+    color: #fff;
+    z-index: 1; }
+  .tabs.is-toggle ul {
+    border-bottom: none; }
+  .tabs.is-toggle.is-toggle-rounded li:first-child a {
+    border-bottom-left-radius: 290486px;
+    border-top-left-radius: 290486px;
+    padding-left: 1.25em; }
+  .tabs.is-toggle.is-toggle-rounded li:last-child a {
+    border-bottom-right-radius: 290486px;
+    border-top-right-radius: 290486px;
+    padding-right: 1.25em; }
+  .tabs.is-small, #documenter .docs-sidebar form.docs-search > input.tabs {
+    font-size: 0.75rem; }
+  .tabs.is-medium {
+    font-size: 1.25rem; }
+  .tabs.is-large {
+    font-size: 1.5rem; }
+
+.column {
+  display: block;
+  flex-basis: 0;
+  flex-grow: 1;
+  flex-shrink: 1;
+  padding: 0.75rem; }
+  .columns.is-mobile > .column.is-narrow {
+    flex: none; }
+  .columns.is-mobile > .column.is-full {
+    flex: none;
+    width: 100%; }
+  .columns.is-mobile > .column.is-three-quarters {
+    flex: none;
+    width: 75%; }
+  .columns.is-mobile > .column.is-two-thirds {
+    flex: none;
+    width: 66.6666%; }
+  .columns.is-mobile > .column.is-half {
+    flex: none;
+    width: 50%; }
+  .columns.is-mobile > .column.is-one-third {
+    flex: none;
+    width: 33.3333%; }
+  .columns.is-mobile > .column.is-one-quarter {
+    flex: none;
+    width: 25%; }
+  .columns.is-mobile > .column.is-one-fifth {
+    flex: none;
+    width: 20%; }
+  .columns.is-mobile > .column.is-two-fifths {
+    flex: none;
+    width: 40%; }
+  .columns.is-mobile > .column.is-three-fifths {
+    flex: none;
+    width: 60%; }
+  .columns.is-mobile > .column.is-four-fifths {
+    flex: none;
+    width: 80%; }
+  .columns.is-mobile > .column.is-offset-three-quarters {
+    margin-left: 75%; }
+  .columns.is-mobile > .column.is-offset-two-thirds {
+    margin-left: 66.6666%; }
+  .columns.is-mobile > .column.is-offset-half {
+    margin-left: 50%; }
+  .columns.is-mobile > .column.is-offset-one-third {
+    margin-left: 33.3333%; }
+  .columns.is-mobile > .column.is-offset-one-quarter {
+    margin-left: 25%; }
+  .columns.is-mobile > .column.is-offset-one-fifth {
+    margin-left: 20%; }
+  .columns.is-mobile > .column.is-offset-two-fifths {
+    margin-left: 40%; }
+  .columns.is-mobile > .column.is-offset-three-fifths {
+    margin-left: 60%; }
+  .columns.is-mobile > .column.is-offset-four-fifths {
+    margin-left: 80%; }
+  .columns.is-mobile > .column.is-0 {
+    flex: none;
+    width: 0%; }
+  .columns.is-mobile > .column.is-offset-0 {
+    margin-left: 0%; }
+  .columns.is-mobile > .column.is-1 {
+    flex: none;
+    width: 8.33333%; }
+  .columns.is-mobile > .column.is-offset-1 {
+    margin-left: 8.33333%; }
+  .columns.is-mobile > .column.is-2 {
+    flex: none;
+    width: 16.66667%; }
+  .columns.is-mobile > .column.is-offset-2 {
+    margin-left: 16.66667%; }
+  .columns.is-mobile > .column.is-3 {
+    flex: none;
+    width: 25%; }
+  .columns.is-mobile > .column.is-offset-3 {
+    margin-left: 25%; }
+  .columns.is-mobile > .column.is-4 {
+    flex: none;
+    width: 33.33333%; }
+  .columns.is-mobile > .column.is-offset-4 {
+    margin-left: 33.33333%; }
+  .columns.is-mobile > .column.is-5 {
+    flex: none;
+    width: 41.66667%; }
+  .columns.is-mobile > .column.is-offset-5 {
+    margin-left: 41.66667%; }
+  .columns.is-mobile > .column.is-6 {
+    flex: none;
+    width: 50%; }
+  .columns.is-mobile > .column.is-offset-6 {
+    margin-left: 50%; }
+  .columns.is-mobile > .column.is-7 {
+    flex: none;
+    width: 58.33333%; }
+  .columns.is-mobile > .column.is-offset-7 {
+    margin-left: 58.33333%; }
+  .columns.is-mobile > .column.is-8 {
+    flex: none;
+    width: 66.66667%; }
+  .columns.is-mobile > .column.is-offset-8 {
+    margin-left: 66.66667%; }
+  .columns.is-mobile > .column.is-9 {
+    flex: none;
+    width: 75%; }
+  .columns.is-mobile > .column.is-offset-9 {
+    margin-left: 75%; }
+  .columns.is-mobile > .column.is-10 {
+    flex: none;
+    width: 83.33333%; }
+  .columns.is-mobile > .column.is-offset-10 {
+    margin-left: 83.33333%; }
+  .columns.is-mobile > .column.is-11 {
+    flex: none;
+    width: 91.66667%; }
+  .columns.is-mobile > .column.is-offset-11 {
+    margin-left: 91.66667%; }
+  .columns.is-mobile > .column.is-12 {
+    flex: none;
+    width: 100%; }
+  .columns.is-mobile > .column.is-offset-12 {
+    margin-left: 100%; }
+  @media screen and (max-width: 768px) {
+    .column.is-narrow-mobile {
+      flex: none; }
+    .column.is-full-mobile {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters-mobile {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds-mobile {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half-mobile {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third-mobile {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter-mobile {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth-mobile {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths-mobile {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths-mobile {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths-mobile {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters-mobile {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds-mobile {
+      margin-left: 66.6666%; }
+    .column.is-offset-half-mobile {
+      margin-left: 50%; }
+    .column.is-offset-one-third-mobile {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter-mobile {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth-mobile {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths-mobile {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths-mobile {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths-mobile {
+      margin-left: 80%; }
+    .column.is-0-mobile {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0-mobile {
+      margin-left: 0%; }
+    .column.is-1-mobile {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1-mobile {
+      margin-left: 8.33333%; }
+    .column.is-2-mobile {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2-mobile {
+      margin-left: 16.66667%; }
+    .column.is-3-mobile {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3-mobile {
+      margin-left: 25%; }
+    .column.is-4-mobile {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4-mobile {
+      margin-left: 33.33333%; }
+    .column.is-5-mobile {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5-mobile {
+      margin-left: 41.66667%; }
+    .column.is-6-mobile {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6-mobile {
+      margin-left: 50%; }
+    .column.is-7-mobile {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7-mobile {
+      margin-left: 58.33333%; }
+    .column.is-8-mobile {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8-mobile {
+      margin-left: 66.66667%; }
+    .column.is-9-mobile {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9-mobile {
+      margin-left: 75%; }
+    .column.is-10-mobile {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10-mobile {
+      margin-left: 83.33333%; }
+    .column.is-11-mobile {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11-mobile {
+      margin-left: 91.66667%; }
+    .column.is-12-mobile {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12-mobile {
+      margin-left: 100%; } }
+  @media screen and (min-width: 769px), print {
+    .column.is-narrow, .column.is-narrow-tablet {
+      flex: none; }
+    .column.is-full, .column.is-full-tablet {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters, .column.is-three-quarters-tablet {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds, .column.is-two-thirds-tablet {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half, .column.is-half-tablet {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third, .column.is-one-third-tablet {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter, .column.is-one-quarter-tablet {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth, .column.is-one-fifth-tablet {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths, .column.is-two-fifths-tablet {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths, .column.is-three-fifths-tablet {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths, .column.is-four-fifths-tablet {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters, .column.is-offset-three-quarters-tablet {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds, .column.is-offset-two-thirds-tablet {
+      margin-left: 66.6666%; }
+    .column.is-offset-half, .column.is-offset-half-tablet {
+      margin-left: 50%; }
+    .column.is-offset-one-third, .column.is-offset-one-third-tablet {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter, .column.is-offset-one-quarter-tablet {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth, .column.is-offset-one-fifth-tablet {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths, .column.is-offset-two-fifths-tablet {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths, .column.is-offset-three-fifths-tablet {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths, .column.is-offset-four-fifths-tablet {
+      margin-left: 80%; }
+    .column.is-0, .column.is-0-tablet {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0, .column.is-offset-0-tablet {
+      margin-left: 0%; }
+    .column.is-1, .column.is-1-tablet {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1, .column.is-offset-1-tablet {
+      margin-left: 8.33333%; }
+    .column.is-2, .column.is-2-tablet {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2, .column.is-offset-2-tablet {
+      margin-left: 16.66667%; }
+    .column.is-3, .column.is-3-tablet {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3, .column.is-offset-3-tablet {
+      margin-left: 25%; }
+    .column.is-4, .column.is-4-tablet {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4, .column.is-offset-4-tablet {
+      margin-left: 33.33333%; }
+    .column.is-5, .column.is-5-tablet {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5, .column.is-offset-5-tablet {
+      margin-left: 41.66667%; }
+    .column.is-6, .column.is-6-tablet {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6, .column.is-offset-6-tablet {
+      margin-left: 50%; }
+    .column.is-7, .column.is-7-tablet {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7, .column.is-offset-7-tablet {
+      margin-left: 58.33333%; }
+    .column.is-8, .column.is-8-tablet {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8, .column.is-offset-8-tablet {
+      margin-left: 66.66667%; }
+    .column.is-9, .column.is-9-tablet {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9, .column.is-offset-9-tablet {
+      margin-left: 75%; }
+    .column.is-10, .column.is-10-tablet {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10, .column.is-offset-10-tablet {
+      margin-left: 83.33333%; }
+    .column.is-11, .column.is-11-tablet {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11, .column.is-offset-11-tablet {
+      margin-left: 91.66667%; }
+    .column.is-12, .column.is-12-tablet {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12, .column.is-offset-12-tablet {
+      margin-left: 100%; } }
+  @media screen and (max-width: 1055px) {
+    .column.is-narrow-touch {
+      flex: none; }
+    .column.is-full-touch {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters-touch {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds-touch {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half-touch {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third-touch {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter-touch {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth-touch {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths-touch {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths-touch {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths-touch {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters-touch {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds-touch {
+      margin-left: 66.6666%; }
+    .column.is-offset-half-touch {
+      margin-left: 50%; }
+    .column.is-offset-one-third-touch {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter-touch {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth-touch {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths-touch {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths-touch {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths-touch {
+      margin-left: 80%; }
+    .column.is-0-touch {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0-touch {
+      margin-left: 0%; }
+    .column.is-1-touch {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1-touch {
+      margin-left: 8.33333%; }
+    .column.is-2-touch {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2-touch {
+      margin-left: 16.66667%; }
+    .column.is-3-touch {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3-touch {
+      margin-left: 25%; }
+    .column.is-4-touch {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4-touch {
+      margin-left: 33.33333%; }
+    .column.is-5-touch {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5-touch {
+      margin-left: 41.66667%; }
+    .column.is-6-touch {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6-touch {
+      margin-left: 50%; }
+    .column.is-7-touch {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7-touch {
+      margin-left: 58.33333%; }
+    .column.is-8-touch {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8-touch {
+      margin-left: 66.66667%; }
+    .column.is-9-touch {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9-touch {
+      margin-left: 75%; }
+    .column.is-10-touch {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10-touch {
+      margin-left: 83.33333%; }
+    .column.is-11-touch {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11-touch {
+      margin-left: 91.66667%; }
+    .column.is-12-touch {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12-touch {
+      margin-left: 100%; } }
+  @media screen and (min-width: 1056px) {
+    .column.is-narrow-desktop {
+      flex: none; }
+    .column.is-full-desktop {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters-desktop {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds-desktop {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half-desktop {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third-desktop {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter-desktop {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth-desktop {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths-desktop {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths-desktop {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths-desktop {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters-desktop {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds-desktop {
+      margin-left: 66.6666%; }
+    .column.is-offset-half-desktop {
+      margin-left: 50%; }
+    .column.is-offset-one-third-desktop {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter-desktop {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth-desktop {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths-desktop {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths-desktop {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths-desktop {
+      margin-left: 80%; }
+    .column.is-0-desktop {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0-desktop {
+      margin-left: 0%; }
+    .column.is-1-desktop {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1-desktop {
+      margin-left: 8.33333%; }
+    .column.is-2-desktop {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2-desktop {
+      margin-left: 16.66667%; }
+    .column.is-3-desktop {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3-desktop {
+      margin-left: 25%; }
+    .column.is-4-desktop {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4-desktop {
+      margin-left: 33.33333%; }
+    .column.is-5-desktop {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5-desktop {
+      margin-left: 41.66667%; }
+    .column.is-6-desktop {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6-desktop {
+      margin-left: 50%; }
+    .column.is-7-desktop {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7-desktop {
+      margin-left: 58.33333%; }
+    .column.is-8-desktop {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8-desktop {
+      margin-left: 66.66667%; }
+    .column.is-9-desktop {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9-desktop {
+      margin-left: 75%; }
+    .column.is-10-desktop {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10-desktop {
+      margin-left: 83.33333%; }
+    .column.is-11-desktop {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11-desktop {
+      margin-left: 91.66667%; }
+    .column.is-12-desktop {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12-desktop {
+      margin-left: 100%; } }
+  @media screen and (min-width: 1216px) {
+    .column.is-narrow-widescreen {
+      flex: none; }
+    .column.is-full-widescreen {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters-widescreen {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds-widescreen {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half-widescreen {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third-widescreen {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter-widescreen {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth-widescreen {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths-widescreen {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths-widescreen {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths-widescreen {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters-widescreen {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds-widescreen {
+      margin-left: 66.6666%; }
+    .column.is-offset-half-widescreen {
+      margin-left: 50%; }
+    .column.is-offset-one-third-widescreen {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter-widescreen {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth-widescreen {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths-widescreen {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths-widescreen {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths-widescreen {
+      margin-left: 80%; }
+    .column.is-0-widescreen {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0-widescreen {
+      margin-left: 0%; }
+    .column.is-1-widescreen {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1-widescreen {
+      margin-left: 8.33333%; }
+    .column.is-2-widescreen {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2-widescreen {
+      margin-left: 16.66667%; }
+    .column.is-3-widescreen {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3-widescreen {
+      margin-left: 25%; }
+    .column.is-4-widescreen {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4-widescreen {
+      margin-left: 33.33333%; }
+    .column.is-5-widescreen {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5-widescreen {
+      margin-left: 41.66667%; }
+    .column.is-6-widescreen {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6-widescreen {
+      margin-left: 50%; }
+    .column.is-7-widescreen {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7-widescreen {
+      margin-left: 58.33333%; }
+    .column.is-8-widescreen {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8-widescreen {
+      margin-left: 66.66667%; }
+    .column.is-9-widescreen {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9-widescreen {
+      margin-left: 75%; }
+    .column.is-10-widescreen {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10-widescreen {
+      margin-left: 83.33333%; }
+    .column.is-11-widescreen {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11-widescreen {
+      margin-left: 91.66667%; }
+    .column.is-12-widescreen {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12-widescreen {
+      margin-left: 100%; } }
+  @media screen and (min-width: 1408px) {
+    .column.is-narrow-fullhd {
+      flex: none; }
+    .column.is-full-fullhd {
+      flex: none;
+      width: 100%; }
+    .column.is-three-quarters-fullhd {
+      flex: none;
+      width: 75%; }
+    .column.is-two-thirds-fullhd {
+      flex: none;
+      width: 66.6666%; }
+    .column.is-half-fullhd {
+      flex: none;
+      width: 50%; }
+    .column.is-one-third-fullhd {
+      flex: none;
+      width: 33.3333%; }
+    .column.is-one-quarter-fullhd {
+      flex: none;
+      width: 25%; }
+    .column.is-one-fifth-fullhd {
+      flex: none;
+      width: 20%; }
+    .column.is-two-fifths-fullhd {
+      flex: none;
+      width: 40%; }
+    .column.is-three-fifths-fullhd {
+      flex: none;
+      width: 60%; }
+    .column.is-four-fifths-fullhd {
+      flex: none;
+      width: 80%; }
+    .column.is-offset-three-quarters-fullhd {
+      margin-left: 75%; }
+    .column.is-offset-two-thirds-fullhd {
+      margin-left: 66.6666%; }
+    .column.is-offset-half-fullhd {
+      margin-left: 50%; }
+    .column.is-offset-one-third-fullhd {
+      margin-left: 33.3333%; }
+    .column.is-offset-one-quarter-fullhd {
+      margin-left: 25%; }
+    .column.is-offset-one-fifth-fullhd {
+      margin-left: 20%; }
+    .column.is-offset-two-fifths-fullhd {
+      margin-left: 40%; }
+    .column.is-offset-three-fifths-fullhd {
+      margin-left: 60%; }
+    .column.is-offset-four-fifths-fullhd {
+      margin-left: 80%; }
+    .column.is-0-fullhd {
+      flex: none;
+      width: 0%; }
+    .column.is-offset-0-fullhd {
+      margin-left: 0%; }
+    .column.is-1-fullhd {
+      flex: none;
+      width: 8.33333%; }
+    .column.is-offset-1-fullhd {
+      margin-left: 8.33333%; }
+    .column.is-2-fullhd {
+      flex: none;
+      width: 16.66667%; }
+    .column.is-offset-2-fullhd {
+      margin-left: 16.66667%; }
+    .column.is-3-fullhd {
+      flex: none;
+      width: 25%; }
+    .column.is-offset-3-fullhd {
+      margin-left: 25%; }
+    .column.is-4-fullhd {
+      flex: none;
+      width: 33.33333%; }
+    .column.is-offset-4-fullhd {
+      margin-left: 33.33333%; }
+    .column.is-5-fullhd {
+      flex: none;
+      width: 41.66667%; }
+    .column.is-offset-5-fullhd {
+      margin-left: 41.66667%; }
+    .column.is-6-fullhd {
+      flex: none;
+      width: 50%; }
+    .column.is-offset-6-fullhd {
+      margin-left: 50%; }
+    .column.is-7-fullhd {
+      flex: none;
+      width: 58.33333%; }
+    .column.is-offset-7-fullhd {
+      margin-left: 58.33333%; }
+    .column.is-8-fullhd {
+      flex: none;
+      width: 66.66667%; }
+    .column.is-offset-8-fullhd {
+      margin-left: 66.66667%; }
+    .column.is-9-fullhd {
+      flex: none;
+      width: 75%; }
+    .column.is-offset-9-fullhd {
+      margin-left: 75%; }
+    .column.is-10-fullhd {
+      flex: none;
+      width: 83.33333%; }
+    .column.is-offset-10-fullhd {
+      margin-left: 83.33333%; }
+    .column.is-11-fullhd {
+      flex: none;
+      width: 91.66667%; }
+    .column.is-offset-11-fullhd {
+      margin-left: 91.66667%; }
+    .column.is-12-fullhd {
+      flex: none;
+      width: 100%; }
+    .column.is-offset-12-fullhd {
+      margin-left: 100%; } }
+
+.columns {
+  margin-left: -0.75rem;
+  margin-right: -0.75rem;
+  margin-top: -0.75rem; }
+  .columns:last-child {
+    margin-bottom: -0.75rem; }
+  .columns:not(:last-child) {
+    margin-bottom: calc(1.5rem - 0.75rem); }
+  .columns.is-centered {
+    justify-content: center; }
+  .columns.is-gapless {
+    margin-left: 0;
+    margin-right: 0;
+    margin-top: 0; }
+    .columns.is-gapless > .column {
+      margin: 0;
+      padding: 0 !important; }
+    .columns.is-gapless:not(:last-child) {
+      margin-bottom: 1.5rem; }
+    .columns.is-gapless:last-child {
+      margin-bottom: 0; }
+  .columns.is-mobile {
+    display: flex; }
+  .columns.is-multiline {
+    flex-wrap: wrap; }
+  .columns.is-vcentered {
+    align-items: center; }
+  @media screen and (min-width: 769px), print {
+    .columns:not(.is-desktop) {
+      display: flex; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-desktop {
+      display: flex; } }
+
+.columns.is-variable {
+  --columnGap: 0.75rem;
+  margin-left: calc(-1 * var(--columnGap));
+  margin-right: calc(-1 * var(--columnGap)); }
+  .columns.is-variable .column {
+    padding-left: var(--columnGap);
+    padding-right: var(--columnGap); }
+  .columns.is-variable.is-0 {
+    --columnGap: 0rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-0-mobile {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-0-tablet {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-0-tablet-only {
+      --columnGap: 0rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-0-touch {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-0-desktop {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-0-desktop-only {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-0-widescreen {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-0-widescreen-only {
+      --columnGap: 0rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-0-fullhd {
+      --columnGap: 0rem; } }
+  .columns.is-variable.is-1 {
+    --columnGap: 0.25rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-1-mobile {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-1-tablet {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-1-tablet-only {
+      --columnGap: 0.25rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-1-touch {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-1-desktop {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-1-desktop-only {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-1-widescreen {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-1-widescreen-only {
+      --columnGap: 0.25rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-1-fullhd {
+      --columnGap: 0.25rem; } }
+  .columns.is-variable.is-2 {
+    --columnGap: 0.5rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-2-mobile {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-2-tablet {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-2-tablet-only {
+      --columnGap: 0.5rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-2-touch {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-2-desktop {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-2-desktop-only {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-2-widescreen {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-2-widescreen-only {
+      --columnGap: 0.5rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-2-fullhd {
+      --columnGap: 0.5rem; } }
+  .columns.is-variable.is-3 {
+    --columnGap: 0.75rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-3-mobile {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-3-tablet {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-3-tablet-only {
+      --columnGap: 0.75rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-3-touch {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-3-desktop {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-3-desktop-only {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-3-widescreen {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-3-widescreen-only {
+      --columnGap: 0.75rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-3-fullhd {
+      --columnGap: 0.75rem; } }
+  .columns.is-variable.is-4 {
+    --columnGap: 1rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-4-mobile {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-4-tablet {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-4-tablet-only {
+      --columnGap: 1rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-4-touch {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-4-desktop {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-4-desktop-only {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-4-widescreen {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-4-widescreen-only {
+      --columnGap: 1rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-4-fullhd {
+      --columnGap: 1rem; } }
+  .columns.is-variable.is-5 {
+    --columnGap: 1.25rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-5-mobile {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-5-tablet {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-5-tablet-only {
+      --columnGap: 1.25rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-5-touch {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-5-desktop {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-5-desktop-only {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-5-widescreen {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-5-widescreen-only {
+      --columnGap: 1.25rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-5-fullhd {
+      --columnGap: 1.25rem; } }
+  .columns.is-variable.is-6 {
+    --columnGap: 1.5rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-6-mobile {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-6-tablet {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-6-tablet-only {
+      --columnGap: 1.5rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-6-touch {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-6-desktop {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-6-desktop-only {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-6-widescreen {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-6-widescreen-only {
+      --columnGap: 1.5rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-6-fullhd {
+      --columnGap: 1.5rem; } }
+  .columns.is-variable.is-7 {
+    --columnGap: 1.75rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-7-mobile {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-7-tablet {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-7-tablet-only {
+      --columnGap: 1.75rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-7-touch {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-7-desktop {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-7-desktop-only {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-7-widescreen {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-7-widescreen-only {
+      --columnGap: 1.75rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-7-fullhd {
+      --columnGap: 1.75rem; } }
+  .columns.is-variable.is-8 {
+    --columnGap: 2rem; }
+  @media screen and (max-width: 768px) {
+    .columns.is-variable.is-8-mobile {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 769px), print {
+    .columns.is-variable.is-8-tablet {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 769px) and (max-width: 1055px) {
+    .columns.is-variable.is-8-tablet-only {
+      --columnGap: 2rem; } }
+  @media screen and (max-width: 1055px) {
+    .columns.is-variable.is-8-touch {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 1056px) {
+    .columns.is-variable.is-8-desktop {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 1056px) and (max-width: 1215px) {
+    .columns.is-variable.is-8-desktop-only {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 1216px) {
+    .columns.is-variable.is-8-widescreen {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 1216px) and (max-width: 1407px) {
+    .columns.is-variable.is-8-widescreen-only {
+      --columnGap: 2rem; } }
+  @media screen and (min-width: 1408px) {
+    .columns.is-variable.is-8-fullhd {
+      --columnGap: 2rem; } }
+
+.tile {
+  align-items: stretch;
+  display: block;
+  flex-basis: 0;
+  flex-grow: 1;
+  flex-shrink: 1;
+  min-height: min-content; }
+  .tile.is-ancestor {
+    margin-left: -0.75rem;
+    margin-right: -0.75rem;
+    margin-top: -0.75rem; }
+    .tile.is-ancestor:last-child {
+      margin-bottom: -0.75rem; }
+    .tile.is-ancestor:not(:last-child) {
+      margin-bottom: 0.75rem; }
+  .tile.is-child {
+    margin: 0 !important; }
+  .tile.is-parent {
+    padding: 0.75rem; }
+  .tile.is-vertical {
+    flex-direction: column; }
+    .tile.is-vertical > .tile.is-child:not(:last-child) {
+      margin-bottom: 1.5rem !important; }
+  @media screen and (min-width: 769px), print {
+    .tile:not(.is-child) {
+      display: flex; }
+    .tile.is-1 {
+      flex: none;
+      width: 8.33333%; }
+    .tile.is-2 {
+      flex: none;
+      width: 16.66667%; }
+    .tile.is-3 {
+      flex: none;
+      width: 25%; }
+    .tile.is-4 {
+      flex: none;
+      width: 33.33333%; }
+    .tile.is-5 {
+      flex: none;
+      width: 41.66667%; }
+    .tile.is-6 {
+      flex: none;
+      width: 50%; }
+    .tile.is-7 {
+      flex: none;
+      width: 58.33333%; }
+    .tile.is-8 {
+      flex: none;
+      width: 66.66667%; }
+    .tile.is-9 {
+      flex: none;
+      width: 75%; }
+    .tile.is-10 {
+      flex: none;
+      width: 83.33333%; }
+    .tile.is-11 {
+      flex: none;
+      width: 91.66667%; }
+    .tile.is-12 {
+      flex: none;
+      width: 100%; } }
+
+.hero {
+  align-items: stretch;
+  display: flex;
+  flex-direction: column;
+  justify-content: space-between; }
+  .hero .navbar {
+    background: none; }
+  .hero .tabs ul {
+    border-bottom: none; }
+  .hero.is-white {
+    background-color: white;
+    color: #0a0a0a; }
+    .hero.is-white a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-white strong {
+      color: inherit; }
+    .hero.is-white .title {
+      color: #0a0a0a; }
+    .hero.is-white .subtitle {
+      color: rgba(10, 10, 10, 0.9); }
+      .hero.is-white .subtitle a:not(.button),
+      .hero.is-white .subtitle strong {
+        color: #0a0a0a; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-white .navbar-menu {
+        background-color: white; } }
+    .hero.is-white .navbar-item,
+    .hero.is-white .navbar-link {
+      color: rgba(10, 10, 10, 0.7); }
+    .hero.is-white a.navbar-item:hover, .hero.is-white a.navbar-item.is-active,
+    .hero.is-white .navbar-link:hover,
+    .hero.is-white .navbar-link.is-active {
+      background-color: #f2f2f2;
+      color: #0a0a0a; }
+    .hero.is-white .tabs a {
+      color: #0a0a0a;
+      opacity: 0.9; }
+      .hero.is-white .tabs a:hover {
+        opacity: 1; }
+    .hero.is-white .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-white .tabs.is-boxed a, .hero.is-white .tabs.is-toggle a {
+      color: #0a0a0a; }
+      .hero.is-white .tabs.is-boxed a:hover, .hero.is-white .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-white .tabs.is-boxed li.is-active a, .hero.is-white .tabs.is-boxed li.is-active a:hover, .hero.is-white .tabs.is-toggle li.is-active a, .hero.is-white .tabs.is-toggle li.is-active a:hover {
+      background-color: #0a0a0a;
+      border-color: #0a0a0a;
+      color: white; }
+    .hero.is-white.is-bold {
+      background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-white.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #e6e6e6 0%, white 71%, white 100%); } }
+  .hero.is-black {
+    background-color: #0a0a0a;
+    color: white; }
+    .hero.is-black a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-black strong {
+      color: inherit; }
+    .hero.is-black .title {
+      color: white; }
+    .hero.is-black .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-black .subtitle a:not(.button),
+      .hero.is-black .subtitle strong {
+        color: white; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-black .navbar-menu {
+        background-color: #0a0a0a; } }
+    .hero.is-black .navbar-item,
+    .hero.is-black .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-black a.navbar-item:hover, .hero.is-black a.navbar-item.is-active,
+    .hero.is-black .navbar-link:hover,
+    .hero.is-black .navbar-link.is-active {
+      background-color: black;
+      color: white; }
+    .hero.is-black .tabs a {
+      color: white;
+      opacity: 0.9; }
+      .hero.is-black .tabs a:hover {
+        opacity: 1; }
+    .hero.is-black .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-black .tabs.is-boxed a, .hero.is-black .tabs.is-toggle a {
+      color: white; }
+      .hero.is-black .tabs.is-boxed a:hover, .hero.is-black .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-black .tabs.is-boxed li.is-active a, .hero.is-black .tabs.is-boxed li.is-active a:hover, .hero.is-black .tabs.is-toggle li.is-active a, .hero.is-black .tabs.is-toggle li.is-active a:hover {
+      background-color: white;
+      border-color: white;
+      color: #0a0a0a; }
+    .hero.is-black.is-bold {
+      background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-black.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, black 0%, #0a0a0a 71%, #181616 100%); } }
+  .hero.is-light {
+    background-color: whitesmoke;
+    color: #363636; }
+    .hero.is-light a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-light strong {
+      color: inherit; }
+    .hero.is-light .title {
+      color: #363636; }
+    .hero.is-light .subtitle {
+      color: rgba(54, 54, 54, 0.9); }
+      .hero.is-light .subtitle a:not(.button),
+      .hero.is-light .subtitle strong {
+        color: #363636; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-light .navbar-menu {
+        background-color: whitesmoke; } }
+    .hero.is-light .navbar-item,
+    .hero.is-light .navbar-link {
+      color: rgba(54, 54, 54, 0.7); }
+    .hero.is-light a.navbar-item:hover, .hero.is-light a.navbar-item.is-active,
+    .hero.is-light .navbar-link:hover,
+    .hero.is-light .navbar-link.is-active {
+      background-color: #e8e8e8;
+      color: #363636; }
+    .hero.is-light .tabs a {
+      color: #363636;
+      opacity: 0.9; }
+      .hero.is-light .tabs a:hover {
+        opacity: 1; }
+    .hero.is-light .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-light .tabs.is-boxed a, .hero.is-light .tabs.is-toggle a {
+      color: #363636; }
+      .hero.is-light .tabs.is-boxed a:hover, .hero.is-light .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-light .tabs.is-boxed li.is-active a, .hero.is-light .tabs.is-boxed li.is-active a:hover, .hero.is-light .tabs.is-toggle li.is-active a, .hero.is-light .tabs.is-toggle li.is-active a:hover {
+      background-color: #363636;
+      border-color: #363636;
+      color: whitesmoke; }
+    .hero.is-light.is-bold {
+      background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-light.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #dfd8d9 0%, whitesmoke 71%, white 100%); } }
+  .hero.is-dark, .content kbd.hero {
+    background-color: #363636;
+    color: whitesmoke; }
+    .hero.is-dark a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .content kbd.hero a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-dark strong,
+    .content kbd.hero strong {
+      color: inherit; }
+    .hero.is-dark .title, .content kbd.hero .title {
+      color: whitesmoke; }
+    .hero.is-dark .subtitle, .content kbd.hero .subtitle {
+      color: rgba(245, 245, 245, 0.9); }
+      .hero.is-dark .subtitle a:not(.button), .content kbd.hero .subtitle a:not(.button),
+      .hero.is-dark .subtitle strong,
+      .content kbd.hero .subtitle strong {
+        color: whitesmoke; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-dark .navbar-menu, .content kbd.hero .navbar-menu {
+        background-color: #363636; } }
+    .hero.is-dark .navbar-item, .content kbd.hero .navbar-item,
+    .hero.is-dark .navbar-link,
+    .content kbd.hero .navbar-link {
+      color: rgba(245, 245, 245, 0.7); }
+    .hero.is-dark a.navbar-item:hover, .content kbd.hero a.navbar-item:hover, .hero.is-dark a.navbar-item.is-active, .content kbd.hero a.navbar-item.is-active,
+    .hero.is-dark .navbar-link:hover,
+    .content kbd.hero .navbar-link:hover,
+    .hero.is-dark .navbar-link.is-active,
+    .content kbd.hero .navbar-link.is-active {
+      background-color: #292929;
+      color: whitesmoke; }
+    .hero.is-dark .tabs a, .content kbd.hero .tabs a {
+      color: whitesmoke;
+      opacity: 0.9; }
+      .hero.is-dark .tabs a:hover, .content kbd.hero .tabs a:hover {
+        opacity: 1; }
+    .hero.is-dark .tabs li.is-active a, .content kbd.hero .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-dark .tabs.is-boxed a, .content kbd.hero .tabs.is-boxed a, .hero.is-dark .tabs.is-toggle a, .content kbd.hero .tabs.is-toggle a {
+      color: whitesmoke; }
+      .hero.is-dark .tabs.is-boxed a:hover, .content kbd.hero .tabs.is-boxed a:hover, .hero.is-dark .tabs.is-toggle a:hover, .content kbd.hero .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-dark .tabs.is-boxed li.is-active a, .content kbd.hero .tabs.is-boxed li.is-active a, .hero.is-dark .tabs.is-boxed li.is-active a:hover, .content kbd.hero .tabs.is-boxed li.is-active a:hover, .hero.is-dark .tabs.is-toggle li.is-active a, .content kbd.hero .tabs.is-toggle li.is-active a, .hero.is-dark .tabs.is-toggle li.is-active a:hover, .content kbd.hero .tabs.is-toggle li.is-active a:hover {
+      background-color: whitesmoke;
+      border-color: whitesmoke;
+      color: #363636; }
+    .hero.is-dark.is-bold, .content kbd.hero.is-bold {
+      background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-dark.is-bold .navbar-menu, .content kbd.hero.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #1f191a 0%, #363636 71%, #46403f 100%); } }
+  .hero.is-primary, .docstring > section > a.hero.docs-sourcelink {
+    background-color: #4eb5de;
+    color: #fff; }
+    .hero.is-primary a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current), .docstring > section > a.hero.docs-sourcelink a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-primary strong,
+    .docstring > section > a.hero.docs-sourcelink strong {
+      color: inherit; }
+    .hero.is-primary .title, .docstring > section > a.hero.docs-sourcelink .title {
+      color: #fff; }
+    .hero.is-primary .subtitle, .docstring > section > a.hero.docs-sourcelink .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-primary .subtitle a:not(.button), .docstring > section > a.hero.docs-sourcelink .subtitle a:not(.button),
+      .hero.is-primary .subtitle strong,
+      .docstring > section > a.hero.docs-sourcelink .subtitle strong {
+        color: #fff; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-primary .navbar-menu, .docstring > section > a.hero.docs-sourcelink .navbar-menu {
+        background-color: #4eb5de; } }
+    .hero.is-primary .navbar-item, .docstring > section > a.hero.docs-sourcelink .navbar-item,
+    .hero.is-primary .navbar-link,
+    .docstring > section > a.hero.docs-sourcelink .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-primary a.navbar-item:hover, .docstring > section > a.hero.docs-sourcelink a.navbar-item:hover, .hero.is-primary a.navbar-item.is-active, .docstring > section > a.hero.docs-sourcelink a.navbar-item.is-active,
+    .hero.is-primary .navbar-link:hover,
+    .docstring > section > a.hero.docs-sourcelink .navbar-link:hover,
+    .hero.is-primary .navbar-link.is-active,
+    .docstring > section > a.hero.docs-sourcelink .navbar-link.is-active {
+      background-color: #39acda;
+      color: #fff; }
+    .hero.is-primary .tabs a, .docstring > section > a.hero.docs-sourcelink .tabs a {
+      color: #fff;
+      opacity: 0.9; }
+      .hero.is-primary .tabs a:hover, .docstring > section > a.hero.docs-sourcelink .tabs a:hover {
+        opacity: 1; }
+    .hero.is-primary .tabs li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-primary .tabs.is-boxed a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a, .hero.is-primary .tabs.is-toggle a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a {
+      color: #fff; }
+      .hero.is-primary .tabs.is-boxed a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed a:hover, .hero.is-primary .tabs.is-toggle a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-primary .tabs.is-boxed li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a, .hero.is-primary .tabs.is-boxed li.is-active a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-boxed li.is-active a:hover, .hero.is-primary .tabs.is-toggle li.is-active a, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a, .hero.is-primary .tabs.is-toggle li.is-active a:hover, .docstring > section > a.hero.docs-sourcelink .tabs.is-toggle li.is-active a:hover {
+      background-color: #fff;
+      border-color: #fff;
+      color: #4eb5de; }
+    .hero.is-primary.is-bold, .docstring > section > a.hero.is-bold.docs-sourcelink {
+      background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-primary.is-bold .navbar-menu, .docstring > section > a.hero.is-bold.docs-sourcelink .navbar-menu {
+          background-image: linear-gradient(141deg, #1bc7de 0%, #4eb5de 71%, #5fa9e7 100%); } }
+  .hero.is-link {
+    background-color: #2e63b8;
+    color: #fff; }
+    .hero.is-link a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-link strong {
+      color: inherit; }
+    .hero.is-link .title {
+      color: #fff; }
+    .hero.is-link .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-link .subtitle a:not(.button),
+      .hero.is-link .subtitle strong {
+        color: #fff; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-link .navbar-menu {
+        background-color: #2e63b8; } }
+    .hero.is-link .navbar-item,
+    .hero.is-link .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-link a.navbar-item:hover, .hero.is-link a.navbar-item.is-active,
+    .hero.is-link .navbar-link:hover,
+    .hero.is-link .navbar-link.is-active {
+      background-color: #2958a4;
+      color: #fff; }
+    .hero.is-link .tabs a {
+      color: #fff;
+      opacity: 0.9; }
+      .hero.is-link .tabs a:hover {
+        opacity: 1; }
+    .hero.is-link .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-link .tabs.is-boxed a, .hero.is-link .tabs.is-toggle a {
+      color: #fff; }
+      .hero.is-link .tabs.is-boxed a:hover, .hero.is-link .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-link .tabs.is-boxed li.is-active a, .hero.is-link .tabs.is-boxed li.is-active a:hover, .hero.is-link .tabs.is-toggle li.is-active a, .hero.is-link .tabs.is-toggle li.is-active a:hover {
+      background-color: #fff;
+      border-color: #fff;
+      color: #2e63b8; }
+    .hero.is-link.is-bold {
+      background-image: linear-gradient(141deg, #1b6098 0%, #2e63b8 71%, #2d51d2 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-link.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #1b6098 0%, #2e63b8 71%, #2d51d2 100%); } }
+  .hero.is-info {
+    background-color: #209cee;
+    color: #fff; }
+    .hero.is-info a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-info strong {
+      color: inherit; }
+    .hero.is-info .title {
+      color: #fff; }
+    .hero.is-info .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-info .subtitle a:not(.button),
+      .hero.is-info .subtitle strong {
+        color: #fff; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-info .navbar-menu {
+        background-color: #209cee; } }
+    .hero.is-info .navbar-item,
+    .hero.is-info .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-info a.navbar-item:hover, .hero.is-info a.navbar-item.is-active,
+    .hero.is-info .navbar-link:hover,
+    .hero.is-info .navbar-link.is-active {
+      background-color: #118fe4;
+      color: #fff; }
+    .hero.is-info .tabs a {
+      color: #fff;
+      opacity: 0.9; }
+      .hero.is-info .tabs a:hover {
+        opacity: 1; }
+    .hero.is-info .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-info .tabs.is-boxed a, .hero.is-info .tabs.is-toggle a {
+      color: #fff; }
+      .hero.is-info .tabs.is-boxed a:hover, .hero.is-info .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-info .tabs.is-boxed li.is-active a, .hero.is-info .tabs.is-boxed li.is-active a:hover, .hero.is-info .tabs.is-toggle li.is-active a, .hero.is-info .tabs.is-toggle li.is-active a:hover {
+      background-color: #fff;
+      border-color: #fff;
+      color: #209cee; }
+    .hero.is-info.is-bold {
+      background-image: linear-gradient(141deg, #04a6d7 0%, #209cee 71%, #3287f5 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-info.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #04a6d7 0%, #209cee 71%, #3287f5 100%); } }
+  .hero.is-success {
+    background-color: #22c35b;
+    color: #fff; }
+    .hero.is-success a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-success strong {
+      color: inherit; }
+    .hero.is-success .title {
+      color: #fff; }
+    .hero.is-success .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-success .subtitle a:not(.button),
+      .hero.is-success .subtitle strong {
+        color: #fff; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-success .navbar-menu {
+        background-color: #22c35b; } }
+    .hero.is-success .navbar-item,
+    .hero.is-success .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-success a.navbar-item:hover, .hero.is-success a.navbar-item.is-active,
+    .hero.is-success .navbar-link:hover,
+    .hero.is-success .navbar-link.is-active {
+      background-color: #1ead51;
+      color: #fff; }
+    .hero.is-success .tabs a {
+      color: #fff;
+      opacity: 0.9; }
+      .hero.is-success .tabs a:hover {
+        opacity: 1; }
+    .hero.is-success .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-success .tabs.is-boxed a, .hero.is-success .tabs.is-toggle a {
+      color: #fff; }
+      .hero.is-success .tabs.is-boxed a:hover, .hero.is-success .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-success .tabs.is-boxed li.is-active a, .hero.is-success .tabs.is-boxed li.is-active a:hover, .hero.is-success .tabs.is-toggle li.is-active a, .hero.is-success .tabs.is-toggle li.is-active a:hover {
+      background-color: #fff;
+      border-color: #fff;
+      color: #22c35b; }
+    .hero.is-success.is-bold {
+      background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-success.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #12a02c 0%, #22c35b 71%, #1fdf83 100%); } }
+  .hero.is-warning {
+    background-color: #ffdd57;
+    color: rgba(0, 0, 0, 0.7); }
+    .hero.is-warning a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-warning strong {
+      color: inherit; }
+    .hero.is-warning .title {
+      color: rgba(0, 0, 0, 0.7); }
+    .hero.is-warning .subtitle {
+      color: rgba(0, 0, 0, 0.9); }
+      .hero.is-warning .subtitle a:not(.button),
+      .hero.is-warning .subtitle strong {
+        color: rgba(0, 0, 0, 0.7); }
+    @media screen and (max-width: 1055px) {
+      .hero.is-warning .navbar-menu {
+        background-color: #ffdd57; } }
+    .hero.is-warning .navbar-item,
+    .hero.is-warning .navbar-link {
+      color: rgba(0, 0, 0, 0.7); }
+    .hero.is-warning a.navbar-item:hover, .hero.is-warning a.navbar-item.is-active,
+    .hero.is-warning .navbar-link:hover,
+    .hero.is-warning .navbar-link.is-active {
+      background-color: #ffd83d;
+      color: rgba(0, 0, 0, 0.7); }
+    .hero.is-warning .tabs a {
+      color: rgba(0, 0, 0, 0.7);
+      opacity: 0.9; }
+      .hero.is-warning .tabs a:hover {
+        opacity: 1; }
+    .hero.is-warning .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-warning .tabs.is-boxed a, .hero.is-warning .tabs.is-toggle a {
+      color: rgba(0, 0, 0, 0.7); }
+      .hero.is-warning .tabs.is-boxed a:hover, .hero.is-warning .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-warning .tabs.is-boxed li.is-active a, .hero.is-warning .tabs.is-boxed li.is-active a:hover, .hero.is-warning .tabs.is-toggle li.is-active a, .hero.is-warning .tabs.is-toggle li.is-active a:hover {
+      background-color: rgba(0, 0, 0, 0.7);
+      border-color: rgba(0, 0, 0, 0.7);
+      color: #ffdd57; }
+    .hero.is-warning.is-bold {
+      background-image: linear-gradient(141deg, #ffaf24 0%, #ffdd57 71%, #fffa70 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-warning.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #ffaf24 0%, #ffdd57 71%, #fffa70 100%); } }
+  .hero.is-danger {
+    background-color: #da0b00;
+    color: #fff; }
+    .hero.is-danger a:not(.button):not(.dropdown-item):not(.tag):not(.pagination-link.is-current),
+    .hero.is-danger strong {
+      color: inherit; }
+    .hero.is-danger .title {
+      color: #fff; }
+    .hero.is-danger .subtitle {
+      color: rgba(255, 255, 255, 0.9); }
+      .hero.is-danger .subtitle a:not(.button),
+      .hero.is-danger .subtitle strong {
+        color: #fff; }
+    @media screen and (max-width: 1055px) {
+      .hero.is-danger .navbar-menu {
+        background-color: #da0b00; } }
+    .hero.is-danger .navbar-item,
+    .hero.is-danger .navbar-link {
+      color: rgba(255, 255, 255, 0.7); }
+    .hero.is-danger a.navbar-item:hover, .hero.is-danger a.navbar-item.is-active,
+    .hero.is-danger .navbar-link:hover,
+    .hero.is-danger .navbar-link.is-active {
+      background-color: #c10a00;
+      color: #fff; }
+    .hero.is-danger .tabs a {
+      color: #fff;
+      opacity: 0.9; }
+      .hero.is-danger .tabs a:hover {
+        opacity: 1; }
+    .hero.is-danger .tabs li.is-active a {
+      opacity: 1; }
+    .hero.is-danger .tabs.is-boxed a, .hero.is-danger .tabs.is-toggle a {
+      color: #fff; }
+      .hero.is-danger .tabs.is-boxed a:hover, .hero.is-danger .tabs.is-toggle a:hover {
+        background-color: rgba(10, 10, 10, 0.1); }
+    .hero.is-danger .tabs.is-boxed li.is-active a, .hero.is-danger .tabs.is-boxed li.is-active a:hover, .hero.is-danger .tabs.is-toggle li.is-active a, .hero.is-danger .tabs.is-toggle li.is-active a:hover {
+      background-color: #fff;
+      border-color: #fff;
+      color: #da0b00; }
+    .hero.is-danger.is-bold {
+      background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); }
+      @media screen and (max-width: 768px) {
+        .hero.is-danger.is-bold .navbar-menu {
+          background-image: linear-gradient(141deg, #a70013 0%, #da0b00 71%, #f43500 100%); } }
+  .hero.is-small .hero-body, #documenter .docs-sidebar form.docs-search > input.hero .hero-body {
+    padding-bottom: 1.5rem;
+    padding-top: 1.5rem; }
+  @media screen and (min-width: 769px), print {
+    .hero.is-medium .hero-body {
+      padding-bottom: 9rem;
+      padding-top: 9rem; } }
+  @media screen and (min-width: 769px), print {
+    .hero.is-large .hero-body {
+      padding-bottom: 18rem;
+      padding-top: 18rem; } }
+  .hero.is-halfheight .hero-body, .hero.is-fullheight .hero-body, .hero.is-fullheight-with-navbar .hero-body {
+    align-items: center;
+    display: flex; }
+    .hero.is-halfheight .hero-body > .container, .hero.is-fullheight .hero-body > .container, .hero.is-fullheight-with-navbar .hero-body > .container {
+      flex-grow: 1;
+      flex-shrink: 1; }
+  .hero.is-halfheight {
+    min-height: 50vh; }
+  .hero.is-fullheight {
+    min-height: 100vh; }
+
+.hero-video {
+  overflow: hidden; }
+  .hero-video video {
+    left: 50%;
+    min-height: 100%;
+    min-width: 100%;
+    position: absolute;
+    top: 50%;
+    transform: translate3d(-50%, -50%, 0); }
+  .hero-video.is-transparent {
+    opacity: 0.3; }
+  @media screen and (max-width: 768px) {
+    .hero-video {
+      display: none; } }
+
+.hero-buttons {
+  margin-top: 1.5rem; }
+  @media screen and (max-width: 768px) {
+    .hero-buttons .button {
+      display: flex; }
+      .hero-buttons .button:not(:last-child) {
+        margin-bottom: 0.75rem; } }
+  @media screen and (min-width: 769px), print {
+    .hero-buttons {
+      display: flex;
+      justify-content: center; }
+      .hero-buttons .button:not(:last-child) {
+        margin-right: 1.5rem; } }
+
+.hero-head,
+.hero-foot {
+  flex-grow: 0;
+  flex-shrink: 0; }
+
+.hero-body {
+  flex-grow: 1;
+  flex-shrink: 0;
+  padding: 3rem 1.5rem; }
+
+.section {
+  padding: 3rem 1.5rem; }
+  @media screen and (min-width: 1056px) {
+    .section.is-medium {
+      padding: 9rem 1.5rem; }
+    .section.is-large {
+      padding: 18rem 1.5rem; } }
+
+.footer {
+  background-color: #fafafa;
+  padding: 3rem 1.5rem 6rem; }
+
+h1 .docs-heading-anchor, h1 .docs-heading-anchor:hover, h1 .docs-heading-anchor:visited, h2 .docs-heading-anchor, h2 .docs-heading-anchor:hover, h2 .docs-heading-anchor:visited, h3 .docs-heading-anchor, h3 .docs-heading-anchor:hover, h3 .docs-heading-anchor:visited, h4 .docs-heading-anchor, h4 .docs-heading-anchor:hover, h4 .docs-heading-anchor:visited, h5 .docs-heading-anchor, h5 .docs-heading-anchor:hover, h5 .docs-heading-anchor:visited, h6 .docs-heading-anchor, h6 .docs-heading-anchor:hover, h6 .docs-heading-anchor:visited {
+  color: #222222; }
+
+h1 .docs-heading-anchor-permalink, h2 .docs-heading-anchor-permalink, h3 .docs-heading-anchor-permalink, h4 .docs-heading-anchor-permalink, h5 .docs-heading-anchor-permalink, h6 .docs-heading-anchor-permalink {
+  visibility: hidden;
+  vertical-align: middle;
+  margin-left: 0.5em;
+  font-size: 0.7rem; }
+  h1 .docs-heading-anchor-permalink::before, h2 .docs-heading-anchor-permalink::before, h3 .docs-heading-anchor-permalink::before, h4 .docs-heading-anchor-permalink::before, h5 .docs-heading-anchor-permalink::before, h6 .docs-heading-anchor-permalink::before {
+    font-family: "Font Awesome 5 Free";
+    font-weight: 900;
+    content: "\f0c1"; }
+
+h1:hover .docs-heading-anchor-permalink, h2:hover .docs-heading-anchor-permalink, h3:hover .docs-heading-anchor-permalink, h4:hover .docs-heading-anchor-permalink, h5:hover .docs-heading-anchor-permalink, h6:hover .docs-heading-anchor-permalink {
+  visibility: visible; }
+
+.docs-dark-only {
+  display: none !important; }
+
+.admonition {
+  background-color: #b5b5b5;
+  border-style: solid;
+  border-width: 1px;
+  border-color: #363636;
+  border-radius: 4px;
+  font-size: 1rem; }
+  .admonition strong {
+    color: currentColor; }
+  .admonition.is-small, #documenter .docs-sidebar form.docs-search > input.admonition {
+    font-size: 0.75rem; }
+  .admonition.is-medium {
+    font-size: 1.25rem; }
+  .admonition.is-large {
+    font-size: 1.5rem; }
+  .admonition.is-default {
+    background-color: #b5b5b5;
+    border-color: #363636; }
+    .admonition.is-default > .admonition-header {
+      background-color: #363636;
+      color: #fff; }
+    .admonition.is-default > .admonition-body {
+      color: #fff; }
+  .admonition.is-info {
+    background-color: #b8dffa;
+    border-color: #209cee; }
+    .admonition.is-info > .admonition-header {
+      background-color: #209cee;
+      color: #fff; }
+    .admonition.is-info > .admonition-body {
+      color: rgba(0, 0, 0, 0.7); }
+  .admonition.is-success {
+    background-color: #9beeb8;
+    border-color: #22c35b; }
+    .admonition.is-success > .admonition-header {
+      background-color: #22c35b;
+      color: #fff; }
+    .admonition.is-success > .admonition-body {
+      color: rgba(0, 0, 0, 0.7); }
+  .admonition.is-warning {
+    background-color: #fff3c5;
+    border-color: #ffdd57; }
+    .admonition.is-warning > .admonition-header {
+      background-color: #ffdd57;
+      color: rgba(0, 0, 0, 0.7); }
+    .admonition.is-warning > .admonition-body {
+      color: rgba(0, 0, 0, 0.7); }
+  .admonition.is-danger {
+    background-color: #ff857e;
+    border-color: #da0b00; }
+    .admonition.is-danger > .admonition-header {
+      background-color: #da0b00;
+      color: #fff; }
+    .admonition.is-danger > .admonition-body {
+      color: #fff; }
+  .admonition.is-compat {
+    background-color: #99e6f0;
+    border-color: #1db5c9; }
+    .admonition.is-compat > .admonition-header {
+      background-color: #1db5c9;
+      color: #fff; }
+    .admonition.is-compat > .admonition-body {
+      color: rgba(0, 0, 0, 0.7); }
+
+.admonition-header {
+  color: #fff;
+  background-color: #363636;
+  align-items: center;
+  font-weight: 700;
+  justify-content: space-between;
+  line-height: 1.25;
+  padding: 0.75em;
+  position: relative; }
+  .admonition-header:before {
+    font-family: "Font Awesome 5 Free";
+    font-weight: 900;
+    margin-right: 0.75em;
+    content: "\f06a"; }
+
+.admonition-body {
+  color: #222222;
+  padding: 1em 1.25em; }
+  .admonition-body pre {
+    background-color: whitesmoke; }
+  .admonition-body code {
+    background-color: rgba(0, 0, 0, 0.05); }
+
+.docstring {
+  margin-bottom: 1em;
+  background-color: transparent;
+  border: 1px solid #dbdbdb;
+  box-shadow: 2px 2px 3px rgba(10, 10, 10, 0.1);
+  max-width: 100%; }
+  .docstring > header {
+    display: flex;
+    flex-grow: 1;
+    align-items: stretch;
+    padding: 0.75rem;
+    background-color: whitesmoke;
+    box-shadow: 0 1px 2px rgba(10, 10, 10, 0.1);
+    box-shadow: none;
+    border-bottom: 1px solid #dbdbdb; }
+    .docstring > header code {
+      background-color: transparent; }
+    .docstring > header .docstring-binding {
+      margin-right: 0.3em; }
+    .docstring > header .docstring-category {
+      margin-left: 0.3em; }
+  .docstring > section {
+    position: relative;
+    padding: 1rem 1.25rem;
+    border-bottom: 1px solid #dbdbdb; }
+    .docstring > section:last-child {
+      border-bottom: none; }
+    .docstring > section > a.docs-sourcelink {
+      transition: opacity 0.3s;
+      opacity: 0;
+      position: absolute;
+      right: 0.625rem;
+      bottom: 0.5rem; }
+  .docstring:hover > section > a.docs-sourcelink {
+    opacity: 0.2; }
+  .docstring > section:hover a.docs-sourcelink {
+    opacity: 1; }
+
+.content pre {
+  border: 1px solid #dbdbdb; }
+
+.content code {
+  font-weight: inherit; }
+
+.content a code {
+  color: #2e63b8; }
+
+.content h1 code, .content h2 code, .content h3 code, .content h4 code, .content h5 code, .content h6 code {
+  color: #222222; }
+
+.content table {
+  display: block;
+  width: initial;
+  max-width: 100%;
+  overflow-x: auto; }
+
+.content blockquote > ul:first-child, .content blockquote > ol:first-child, .content .admonition-body > ul:first-child, .content .admonition-body > ol:first-child {
+  margin-top: 0; }
+
+.breadcrumb a.is-disabled {
+  cursor: default;
+  pointer-events: none; }
+  .breadcrumb a.is-disabled, .breadcrumb a.is-disabled:hover {
+    color: #222222; }
+
+.hljs {
+  background: initial !important;
+  padding: initial !important; }
+
+.katex .katex-mathml {
+  top: 0;
+  right: 0; }
+
+html {
+  -moz-osx-font-smoothing: auto;
+  -webkit-font-smoothing: auto; }
+
+/* This file contain the overall layout.
+ *
+ * The main container is <div> that is identified by id #documenter.
+ */
+#documenter .docs-main > article {
+  overflow-wrap: break-word; }
+
+@media screen and (min-width: 1056px) {
+  #documenter .docs-main {
+    max-width: 52rem;
+    margin-left: 20rem;
+    padding-right: 1rem; } }
+
+@media screen and (max-width: 1055px) {
+  #documenter .docs-main {
+    width: 100%; }
+    #documenter .docs-main > article {
+      max-width: 52rem;
+      margin-left: auto;
+      margin-right: auto;
+      margin-bottom: 1rem;
+      padding: 0 1rem; }
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diff --git a/v0.15.15/assets/themeswap.js b/v0.15.15/assets/themeswap.js
new file mode 100644
index 00000000..d4666841
--- /dev/null
+++ b/v0.15.15/assets/themeswap.js
@@ -0,0 +1,42 @@
+// Small function to quickly swap out themes. Gets put into the <head> tag..
+function set_theme_from_local_storage() {
+  // Browser does not support Web Storage, bail early.
+  if(typeof(window.localStorage) === "undefined") return;
+  // Get the user-picked theme from localStorage. May be `null`, which means the default
+  // theme.
+  var theme =  window.localStorage.getItem("documenter-theme");
+  // Initialize a few variables for the loop:
+  //
+  //  - active: will contain the index of the theme that should be active. Note that there
+  //    is no guarantee that localStorage contains sane values. If `active` stays `null`
+  //    we either could not find the theme or it is the default (primary) theme anyway.
+  //    Either way, we then need to stick to the primary theme.
+  //
+  //  - disabled: style sheets that should be disabled (i.e. all the theme style sheets
+  //    that are not the currently active theme)
+  var active = null; var disabled = [];
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+    var ss = document.styleSheets[i];
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+    // which must contain the name of the theme. The names in localStorage much match this.
+    var themename = ss.ownerNode.getAttribute("data-theme-name");
+    // attribute not set => non-theme stylesheet => ignore
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+    // To distinguish the default (primary) theme, it needs to have the data-theme-primary
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+}
+set_theme_from_local_storage();
diff --git a/v0.15.15/dev/index.html b/v0.15.15/dev/index.html
new file mode 100644
index 00000000..c0b6a74f
--- /dev/null
+++ b/v0.15.15/dev/index.html
@@ -0,0 +1,37 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Development · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li class="is-active"><a class="tocitem" href>Development</a><ul class="internal"><li><a class="tocitem" href="#Why-two-packages?-1"><span>Why two packages?</span></a></li><li><a class="tocitem" href="#The-developer&#39;s-right-to-build-from-source-1"><span>The developer&#39;s right to build from source</span></a></li><li><a class="tocitem" href="#From-release-to-release-to-release-1"><span>From release to release to release</span></a></li></ul></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../generated/annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../generated/automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../generated/chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../generated/disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../generated/nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../generated/padua/">Padua transform</a></li><li><a class="tocitem" href="../generated/sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../generated/spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../generated/subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../generated/triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Development</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Development</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/docs/src/dev.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Development-Documentation-1"><a class="docs-heading-anchor" href="#Development-Documentation-1">Development Documentation</a><a class="docs-heading-anchor-permalink" href="#Development-Documentation-1" title="Permalink"></a></h1><p>The core of <a href="https://github.com/JuliaApproximation/FastTransforms.jl"><code>FastTransforms.jl</code></a> is developed in parallel with the <a href="https://github.com/MikaelSlevinsky/FastTransforms">C library</a> of the same name. Julia and C interoperability is enhanced by the <a href="https://github.com/JuliaPackaging/BinaryBuilder.jl">BinaryBuilder</a> infrastructure, which provides the user a safe and seamless experience using a package in a different language.</p><h2 id="Why-two-packages?-1"><a class="docs-heading-anchor" href="#Why-two-packages?-1">Why two packages?</a><a class="docs-heading-anchor-permalink" href="#Why-two-packages?-1" title="Permalink"></a></h2><p>Orthogonal polynomial transforms are performance-sensitive imperative tasks. Yet, many of Julia&#39;s rich and evolving language features are simply unnecessary for defining these computational routines. Moreover, rapid language changes in Julia (as compared to C) have been more than a perturbation to this repository in the past.</p><p>The C library generates assembly for vectorized operations such as single instruction multiple data (SIMD) that is more efficient than that generated by a compiler without human intervention. It also uses OpenMP to introduce shared memory parallelism for large tasks. Finally, calling into precompiled binaries reduces the Julia package&#39;s pre-compilation and dependencies, improving the user experience. Some of these capabilities also exist in Julia, but with C there is frankly more control over performance.</p><p>C libraries are easier to call from any other language, partly explaining why the Python package manager Spack <a href="https://spack.readthedocs.io/en/latest/package_list.html#fasttransforms">already supports the C library</a> through third-party efforts.</p><p>In Julia, a parametric composite type with unrestricted type parameters is just about as big as <code>Any</code>. Such a type allows the Julia API to far exceed the C API in its ability to unify all of the orthogonal polynomial transforms and present them as linear operators. The <code>mutable struct FTPlan{T, N, K}</code>, together with <code>AdjointFTPlan</code> and <code>TransposeFTPlan</code>, are the core Julia types in this repository. Whereas <code>T</code> is understood to represent element type of the plan and <code>N</code> represents the number of leading dimensions of the array on which it operates, <code>K</code> is a mere enumeration which serves to distinguish the orthogonal polynomials at play. For example, <code>FTPlan{Float64, 1, LEG2CHEB}</code> represents the necessary pre-computations to convert 64-bit Legendre series to Chebyshev series (of the first kind). <code>N == 1</code> because Chebyshev and Legendre series are naturally represented with vectors of coefficients. However, this particular plan may operate not only on vectors but also on matrices, column-by-column.</p><h2 id="The-developer&#39;s-right-to-build-from-source-1"><a class="docs-heading-anchor" href="#The-developer&#39;s-right-to-build-from-source-1">The developer&#39;s right to build from source</a><a class="docs-heading-anchor-permalink" href="#The-developer&#39;s-right-to-build-from-source-1" title="Permalink"></a></h2><p>Precompiled binaries are important for users, but development in C may be greatly accelerated by coupling it with a dynamic language such as Julia. For this reason, the repository preserves the developer&#39;s right to build the C library from source by setting an environment variable to trigger the build script:</p><pre><code class="language-julia">julia&gt; ENV[&quot;FT_BUILD_FROM_SOURCE&quot;] = &quot;true&quot;
+&quot;true&quot;
+
+(@v1.5) pkg&gt; build FastTransforms
+   Building FFTW ──────────→ `~/.julia/packages/FFTW/ayqyZ/deps/build.log`
+   Building TimeZones ─────→ `~/.julia/packages/TimeZones/K98G0/deps/build.log`
+   Building FastTransforms → `~/.julia/dev/FastTransforms/deps/build.log`
+
+julia&gt; using FastTransforms
+[ Info: Precompiling FastTransforms [057dd010-8810-581a-b7be-e3fc3b93f78c]
+</code></pre><p>This lets the developer experiment with new features through <code>ccall</code>ing into bleeding edge source code. Customizing the build script further allows the developer to track a different branch or even a fork.</p><h2 id="From-release-to-release-to-release-1"><a class="docs-heading-anchor" href="#From-release-to-release-to-release-1">From release to release to release</a><a class="docs-heading-anchor-permalink" href="#From-release-to-release-to-release-1" title="Permalink"></a></h2><p>To get from a C library release to a Julia package release, the developer needs to update Yggdrasil&#39;s <a href="https://github.com/JuliaPackaging/Yggdrasil/blob/master/F/FastTransforms/build_tarballs.jl">build_tarballs.jl</a> script for the new version and its 256-bit SHA. On macOS, the SHA can be found by:</p><pre><code class="language-julia">shell&gt; curl https://codeload.github.com/MikaelSlevinsky/FastTransforms/tar.gz/v0.6.2 --output FastTransforms.tar.gz
+  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
+                                 Dload  Upload   Total   Spent    Left  Speed
+100  168k    0  168k    0     0   429k      0 --:--:-- --:--:-- --:--:--  429k
+
+shell&gt; shasum -a 256 FastTransforms.tar.gz
+fd00befcb0c20ba962a8744a7b9139355071ee95be70420de005b7c0f6e023aa  FastTransforms.tar.gz
+
+shell&gt; rm -f FastTransforms.tar.gz
+</code></pre><p>Using <a href="https://github.com/JuliaCrypto/SHA.jl">SHA.jl</a>, the SHA can also be found by:</p><pre><code class="language-julia">shell&gt; curl https://codeload.github.com/MikaelSlevinsky/FastTransforms/tar.gz/v0.6.2 --output FastTransforms.tar.gz
+  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current
+                                 Dload  Upload   Total   Spent    Left  Speed
+100  168k    0  168k    0     0   442k      0 --:--:-- --:--:-- --:--:--  443k
+
+julia&gt; using SHA
+
+julia&gt; open(&quot;FastTransforms.tar.gz&quot;) do f
+           bytes2hex(sha256(f))
+       end
+&quot;fd00befcb0c20ba962a8744a7b9139355071ee95be70420de005b7c0f6e023aa&quot;
+
+shell&gt; rm -f FastTransforms.tar.gz
+</code></pre><p>Then we wait for the friendly folks at <a href="https://github.com/JuliaPackaging">JuliaPackaging</a> to merge the pull request to Yggdrasil, triggering a new release of the <a href="https://github.com/JuliaBinaryWrappers/FastTransforms_jll.jl">FastTransforms_jll.jl</a> meta package that stores all precompiled binaries. With this release, we update the FastTransforms.jl <a href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/Project.toml">Project.toml</a> to point to the latest release and register the new version.</p><p>Since development of Yggdrasil is quite rapid, a fork may easily become stale. Git permits the developer to forcibly make a master branch on a fork even with upstream master:</p><pre><code class="language-none">git fetch upstream
+git checkout master
+git reset --hard upstream/master
+git push origin master --force</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../">« Home</a><a class="docs-footer-nextpage" href="../generated/annulus/">Integration on an annulus »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Integration on an annulus · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li class="is-active"><a class="tocitem" href>Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Integration on an annulus</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Integration on an annulus</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/annulus.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Integration-on-an-annulus-1"><a class="docs-heading-anchor" href="#Integration-on-an-annulus-1">Integration on an annulus</a><a class="docs-heading-anchor-permalink" href="#Integration-on-an-annulus-1" title="Permalink"></a></h1><p>In this example, we explore integration of the function:</p><div>\[  f(x,y) = \frac{x^3}{x^2+y^2-\frac{1}{4}},\]</div><p>over the annulus defined by <span>$\{(r,\theta) : \rho &lt; r &lt; 1, 0 &lt; \theta &lt; 2\pi\}$</span> with parameter <span>$\rho = \frac{2}{3}$</span>. We will calculate the integral:</p><div>\[  \int_0^{2\pi}\int_{\frac{2}{3}}^1 f(r\cos\theta,r\sin\theta)^2r{\rm\,d}r{\rm\,d}\theta,\]</div><p>by analyzing the function in an annulus polynomial series. We analyze the function on an <span>$N\times M$</span> tensor product grid defined by:</p><div>\[\begin{aligned}
+r_n &amp; = \sqrt{\cos^2\left[(n+\tfrac{1}{2})\pi/2N\right] + \rho^2 \sin^2\left[(n+\tfrac{1}{2})\pi/2N\right]},\quad{\rm for}\quad 0\le n &lt; N,\quad{\rm and}\\
+\theta_m &amp; = 2\pi m/M,\quad{\rm for}\quad 0\le m &lt; M;
+\end{aligned}\]</div><p>we convert the function samples to Chebyshev×Fourier coefficients using <code>plan_annulus_analysis</code>; and finally, we transform the Chebyshev×Fourier coefficients to annulus polynomial coefficients using <code>plan_ann2cxf</code>.</p><p>For the storage pattern of the arrays, please consult the <a href="https://MikaelSlevinsky.github.io/FastTransforms">documentation</a>.</p><pre><code class="language-julia">using FastTransforms, LinearAlgebra, Plots
+const GENFIGS = joinpath(pkgdir(FastTransforms), &quot;docs/src/generated&quot;)
+!isdir(GENFIGS) &amp;&amp; mkdir(GENFIGS)
+plotlyjs()</code></pre><pre><code class="language-none">Plots.PlotlyJSBackend()</code></pre><p>Our function <span>$f$</span> on the annulus:</p><pre><code class="language-julia">f = (x,y) -&gt; x^3/(x^2+y^2-1/4)</code></pre><pre><code class="language-none">#1 (generic function with 1 method)</code></pre><p>The annulus polynomial degree:</p><pre><code class="language-julia">N = 8
+M = 4N-3</code></pre><pre><code class="language-none">29</code></pre><p>The annulus inner radius:</p><pre><code class="language-julia">ρ = 2/3</code></pre><pre><code class="language-none">0.6666666666666666</code></pre><p>The radial grid:</p><pre><code class="language-julia">r = [begin t = (N-n-0.5)/(2N); ct = sinpi(t); st = cospi(t); sqrt(ct^2+ρ^2*st^2) end for n in 0:N-1]</code></pre><pre><code class="language-none">8-element Vector{Float64}:
+ 0.9973277184004194
+ 0.9763124517373388
+ 0.9362410410518701
+ 0.8811435628419545
+ 0.8173313074308551
+ 0.7535895152498838
+ 0.7008983100472356
+ 0.6706577864713554</code></pre><p>The angular grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">θ = (0:M-1)*2/M</code></pre><pre><code class="language-none">0.0:0.06896551724137931:1.9310344827586206</code></pre><p>On the mapped tensor product grid, our function samples are:</p><pre><code class="language-julia">F = [f(r*cospi(θ), r*sinpi(θ)) for r in r, θ in θ]</code></pre><pre><code class="language-none">8×29 Matrix{Float64}:
+ 1.33215  1.24089  0.995869  0.672118  0.361447  0.136908  0.0255072  0.000211389  -0.00564085  -0.0675532  -0.235438  -0.509748  -0.838068  -1.13371  -1.30886  -1.30886  -1.13371  -0.838068  -0.509748  -0.235438  -0.0675532  -0.00564085  0.000211389  0.0255072  0.136908  0.361447  0.672118  0.995869  1.24089
+ 1.32342  1.23275  0.989337  0.66771   0.359076  0.13601   0.0253399  0.000210003  -0.00560385  -0.0671101  -0.233894  -0.506405  -0.832572  -1.12628  -1.30028  -1.30028  -1.12628  -0.832572  -0.506405  -0.233894  -0.0671101  -0.00560385  0.000210003  0.0253399  0.13601   0.359076  0.66771   0.989337  1.23275
+ 1.30981  1.22008  0.979168  0.660847  0.355385  0.134612  0.0250795  0.000207844  -0.00554625  -0.0664203  -0.23149   -0.5012    -0.824014  -1.1147   -1.28691  -1.28691  -1.1147   -0.824014  -0.5012    -0.23149   -0.0664203  -0.00554625  0.000207844  0.0250795  0.134612  0.355385  0.660847  0.979168  1.22008
+ 1.29961  1.21057  0.97154   0.655698  0.352617  0.133563  0.0248841  0.000206225  -0.00550305  -0.0659028  -0.229687  -0.497295  -0.817594  -1.10601  -1.27689  -1.27689  -1.10601  -0.817594  -0.497295  -0.229687  -0.0659028  -0.00550305  0.000206225  0.0248841  0.133563  0.352617  0.655698  0.97154   1.21057
+ 1.30613  1.21665  0.976415  0.658989  0.354386  0.134233  0.025009   0.00020726   -0.00553066  -0.0662336  -0.230839  -0.499791  -0.821697  -1.11156  -1.28329  -1.28329  -1.11156  -0.821697  -0.499791  -0.230839  -0.0662336  -0.00553066  0.00020726   0.025009   0.134233  0.354386  0.658989  0.976415  1.21665
+ 1.34623  1.25399  1.00639   0.679218  0.365265  0.138354  0.0257767  0.000213622  -0.00570044  -0.0682668  -0.237925  -0.515133  -0.846922  -1.14569  -1.32269  -1.32269  -1.14569  -0.846922  -0.515133  -0.237925  -0.0682668  -0.00570044  0.000213622  0.0257767  0.138354  0.365265  0.679218  1.00639   1.25399
+ 1.42719  1.32941  1.06692   0.720069  0.387234  0.146675  0.027327   0.00022647   -0.00604329  -0.0723726  -0.252235  -0.546115  -0.897858  -1.21459  -1.40224  -1.40224  -1.21459  -0.897858  -0.546115  -0.252235  -0.0723726  -0.00604329  0.00022647   0.027327   0.146675  0.387234  0.720069  1.06692   1.32941
+ 1.5099   1.40645  1.12874   0.761795  0.409673  0.155175  0.0289105  0.000239594  -0.00639348  -0.0765664  -0.266852  -0.577762  -0.949887  -1.28498  -1.4835   -1.4835   -1.28498  -0.949887  -0.577762  -0.266852  -0.0765664  -0.00639348  0.000239594  0.0289105  0.155175  0.409673  0.761795  1.12874   1.40645</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">X = [r*cospi(θ) for r in r, θ in θ]
+Y = [r*sinpi(θ) for r in r, θ in θ]
+scatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:red)
+surface!(X, Y, F; legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;annulus.html&quot;))</code></pre><object type="text/html" data="../annulus.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/annulus.html&quot;</code></pre><p>We precompute an Annulus–Chebyshev×Fourier plan:</p><pre><code class="language-julia">α, β, γ = 0, 0, 0
+P = plan_ann2cxf(F, α, β, γ, ρ)</code></pre><pre><code class="language-none">FastTransforms Annulus--Chebyshev×Fourier plan for 8×29-element array of Float64</code></pre><p>And an FFTW Chebyshev×Fourier analysis plan on the annulus:</p><pre><code class="language-julia">PA = plan_annulus_analysis(F, ρ)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Chebyshev×Fourier analysis on the annulus for 8×29-element array of Float64</code></pre><p>Its annulus coefficients are:</p><pre><code class="language-julia">U = P\(PA*F)</code></pre><pre><code class="language-none">8×29 Matrix{Float64}:
+ -2.45849e-17   2.92896e-17   0.926725      2.04896e-17  -7.722e-18     6.1888e-17    0.29418      -1.81602e-17   2.67464e-17   1.20498e-17  -6.62939e-18   1.11857e-17  -1.67703e-17  -6.13512e-19  -3.42122e-17   6.23458e-17   1.8968e-17    3.12444e-17   4.92041e-18   3.83711e-17   7.86308e-17  -1.08653e-17   5.78808e-17  -1.56088e-17  -3.34631e-17  -8.2245e-18    3.76837e-17  -3.30615e-17  -4.36512e-17
+ -9.36993e-18  -2.254e-18    -0.124037     -5.91733e-18   3.70137e-17  -1.89099e-17  -0.0976704     1.024e-18    -2.32787e-17  -9.77876e-18   2.00575e-17  -1.04302e-17   7.97476e-19  -5.50321e-18   4.69595e-17  -4.01755e-17  -1.55142e-18  -2.52689e-17   1.02515e-18  -2.67731e-17  -6.90711e-17   5.4336e-18   -5.62647e-17   1.0013e-17    1.53665e-17   7.96412e-18  -4.27121e-17   2.50418e-17   4.09539e-17
+ -2.1258e-17    1.12715e-18   0.042116      9.94105e-19  -1.44328e-17   9.15449e-18   0.0336531     3.6262e-19    1.41794e-17   7.39131e-18  -9.39246e-18   6.73552e-18   7.9017e-18    1.31493e-18  -1.74808e-17   2.30498e-17  -4.92523e-18   1.03454e-17  -1.03774e-17   1.67754e-17   1.97933e-17  -8.57e-18      3.57962e-17  -1.14124e-17  -3.35749e-17  -5.45601e-18   2.98569e-17  -2.14064e-17  -3.95395e-17
+ -5.78545e-18   4.00391e-18  -0.0139459     3.14722e-18  -1.97145e-18   5.82968e-18  -0.011224      6.26797e-18   2.25101e-17   6.88701e-18  -1.706e-18     7.40166e-18   3.44473e-18   9.55486e-18   5.33772e-18   2.9721e-18   -8.00488e-18   3.40533e-18   4.2453e-18    2.2961e-19   -1.44173e-17   7.73146e-18  -2.06172e-17   5.91455e-18   1.1306e-17    3.25478e-18  -1.21454e-17   8.18752e-18   4.67076e-18
+ -2.40148e-17   7.71573e-19   0.00458845   -2.03822e-18   1.86344e-17   3.19547e-18   0.00369818   -1.86152e-18  -1.04804e-17   8.11326e-19   1.0092e-17   -1.77139e-18  -1.80973e-18  -6.8012e-18    1.80129e-18  -4.24712e-18   6.46529e-18  -7.2048e-18    7.11746e-18  -4.72462e-18   1.73345e-17  -5.27319e-18   1.40121e-17  -1.67467e-18  -4.79598e-19   8.00009e-19   6.60738e-18  -3.34661e-18  -2.0813e-18
+  2.61466e-17   1.71852e-19  -0.00150441    7.97602e-19  -9.38596e-18  -3.21855e-18  -0.00121128   -4.47164e-19  -8.79109e-18  -4.83245e-18   2.65743e-18  -5.47568e-18  -5.50836e-19  -2.9175e-18    7.42411e-18  -5.70705e-18  -3.31104e-18  -3.85137e-19   2.72442e-18  -5.31797e-19  -2.48579e-18   3.59849e-18   7.3637e-19    3.4972e-18    6.6109e-18    1.53405e-18   6.20867e-18   4.33464e-18   7.06298e-18
+  6.05256e-17  -4.20047e-18   0.000517281  -2.62968e-18   1.29799e-17  -9.06153e-18   0.000424358  -4.57265e-18   3.91183e-18  -6.80939e-18  -9.8607e-18   -2.399e-18     2.87152e-18   6.6648e-19   -2.13866e-17   1.69496e-20   4.87425e-18   5.37575e-18  -1.38669e-17   3.57204e-19  -5.42692e-18   2.48838e-18  -1.15939e-17   4.39475e-19   3.73151e-18  -1.63971e-18   2.61275e-18   1.39577e-18   8.50526e-18
+ -1.16089e-17   6.39707e-19  -0.000162126   3.55753e-18   7.44168e-18   4.28763e-18  -5.40419e-5    5.16629e-18   7.08965e-18   5.4486e-18    6.55323e-18   4.64571e-18   2.63303e-18   6.04678e-19   6.15346e-19  -2.13942e-18  -1.32656e-17  -3.57457e-18   1.16079e-17  -5.67995e-18  -1.01101e-17  -4.98049e-18   1.02985e-17  -2.89642e-18  -1.8487e-17   -2.30036e-18   2.95997e-18  -1.26575e-18  -1.033e-17</code></pre><p>The annulus coefficients are useful for integration. The integral of <span>$[f(x,y)]^2$</span> over the annulus is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, 5π/8*(1675/4536+9*log(3)/32-3*log(7)/32)</code></pre><pre><code class="language-none">(0.9735516844404255, 0.973547572736036)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../dev/">« Development</a><a class="docs-footer-nextpage" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/generated/automaticdifferentiation/index.html b/v0.15.15/generated/automaticdifferentiation/index.html
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@@ -0,0 +1,19 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Automatic differentiation through spherical harmonic transforms · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li class="is-active"><a class="tocitem" href>Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Automatic differentiation through spherical harmonic transforms</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Automatic differentiation through spherical harmonic transforms</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/automaticdifferentiation.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Automatic-differentiation-through-spherical-harmonic-transforms-1"><a class="docs-heading-anchor" href="#Automatic-differentiation-through-spherical-harmonic-transforms-1">Automatic differentiation through spherical harmonic transforms</a><a class="docs-heading-anchor-permalink" href="#Automatic-differentiation-through-spherical-harmonic-transforms-1" title="Permalink"></a></h1><p>This example finds a positive value of <span>$\lambda$</span> in:</p><div>\[f(r) = \sin[\lambda (k\cdot r)],\]</div><p>for some <span>$k,r\in\mathbb{S}^2$</span> such that <span>$\int_{\mathbb{S}^2} f^2 {\rm\,d}\Omega = 1$</span>. We do this by using derivative information through:</p><div>\[\dfrac{\partial f}{\partial \lambda} = (k\cdot r) \cos[\lambda (k\cdot r)].\]</div><pre><code class="language-julia">using FastTransforms, LinearAlgebra</code></pre><p>The colatitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">N = 15
+θ = (0.5:N-0.5)/N</code></pre><pre><code class="language-none">0.03333333333333333:0.06666666666666667:0.9666666666666667</code></pre><p>The longitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">M = 2*N-1
+φ = (0:M-1)*2/M</code></pre><pre><code class="language-none">0.0:0.06896551724137931:1.9310344827586206</code></pre><p>We precompute a spherical harmonic–Fourier plan:</p><pre><code class="language-julia">P = plan_sph2fourier(Float64, N)</code></pre><pre><code class="language-none">FastTransforms Spherical harmonic--Fourier plan for 15×29-element array of Float64</code></pre><p>And an FFTW Fourier analysis plan on <span>$\mathbb{S}^2$</span>:</p><pre><code class="language-julia">PA = plan_sph_analysis(Float64, N, M)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Fourier analysis on the sphere for 15×29-element array of Float64</code></pre><p>Our choice of <span>$k$</span> and angular parametrization of <span>$r$</span>:</p><pre><code class="language-julia">k = [2/7, 3/7, 6/7]
+r = (θ,φ) -&gt; [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]</code></pre><pre><code class="language-none">#1 (generic function with 1 method)</code></pre><p>Our initial guess for <span>$\lambda$</span>:</p><pre><code class="language-julia">λ = 1.0</code></pre><pre><code class="language-none">1.0</code></pre><p>Then we run Newton iteration and grab an espresso:</p><pre><code class="language-julia">for _ in 1:7
+    F = [sin(λ*(k⋅r(θ,φ))) for θ in θ, φ in φ]
+    Fλ = [(k⋅r(θ,φ))*cos(λ*(k⋅r(θ,φ))) for θ in θ, φ in φ]
+    U = P\(PA*F)
+    Uλ = P\(PA*Fλ)
+    global λ = λ - (norm(U)^2-1)/(2*sum(U.*Uλ))
+    println(&quot;λ: $(rpad(λ, 18)) and the 2-norm: $(rpad(norm(U), 18))&quot;)
+end</code></pre><pre><code class="language-none">λ: 0.5565017029393282 and the 2-norm: 1.8510924318185522
+λ: 0.5031571262839711 and the 2-norm: 1.1041845914870363
+λ: 0.5010418434316174 and the 2-norm: 1.0040147091934821
+λ: 0.5010383094266805 and the 2-norm: 1.0000066984258869
+λ: 0.5010383094167955 and the 2-norm: 1.0000000000187361
+λ: 0.5010383094167954 and the 2-norm: 1.0000000000000002
+λ: 0.5010383094167955 and the 2-norm: 0.9999999999999999
+</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../annulus/">« Integration on an annulus</a><a class="docs-footer-nextpage" href="../chebyshev/">Chebyshev transform »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/generated/chebyshev/index.html b/v0.15.15/generated/chebyshev/index.html
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Chebyshev transform · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li class="is-active"><a class="tocitem" href>Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Chebyshev transform</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Chebyshev transform</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/chebyshev.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Chebyshev-transform-1"><a class="docs-heading-anchor" href="#Chebyshev-transform-1">Chebyshev transform</a><a class="docs-heading-anchor-permalink" href="#Chebyshev-transform-1" title="Permalink"></a></h1><p>This demonstrates the Chebyshev transform and inverse transform, explaining precisely the normalization and points</p><pre><code class="language-julia">using FastTransforms
+n = 20</code></pre><pre><code class="language-none">20</code></pre><p>First kind points <span>$\to$</span> first kind polynomials</p><pre><code class="language-julia">p_1 = chebyshevpoints(Float64, n, Val(1))
+f = exp.(p_1)
+f̌ = chebyshevtransform(f, Val(1))
+f̃ = x -&gt; [cos(k*acos(x)) for k=0:n-1]&#39; * f̌
+f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>First kind polynomials <span>$\to$</span> first kind points</p><pre><code class="language-julia">ichebyshevtransform(f̌, Val(1)) ≈ exp.(p_1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind points <span>$\to$</span> first kind polynomials</p><pre><code class="language-julia">p_2 = chebyshevpoints(Float64, n, Val(2))
+f = exp.(p_2)
+f̌ = chebyshevtransform(f, Val(2))
+f̃ = x -&gt; [cos(k*acos(x)) for k=0:n-1]&#39; * f̌
+f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>First kind polynomials <span>$\to$</span> second kind points</p><pre><code class="language-julia">ichebyshevtransform(f̌, Val(2)) ≈ exp.(p_2)</code></pre><pre><code class="language-none">true</code></pre><p>First kind points <span>$\to$</span> second kind polynomials</p><pre><code class="language-julia">p_1 = chebyshevpoints(Float64, n, Val(1))
+f = exp.(p_1)
+f̌ = chebyshevutransform(f, Val(1))
+f̃ = x -&gt; [sin((k+1)*acos(x))/sin(acos(x)) for k=0:n-1]&#39; * f̌
+f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind polynomials <span>$\to$</span> first kind points</p><pre><code class="language-julia">ichebyshevutransform(f̌, Val(1)) ≈ exp.(p_1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind points <span>$\to$</span> second kind polynomials</p><pre><code class="language-julia">p_2 = chebyshevpoints(Float64, n, Val(2))[2:n-1]
+f = exp.(p_2)
+f̌ = chebyshevutransform(f, Val(2))
+f̃ = x -&gt; [sin((k+1)*acos(x))/sin(acos(x)) for k=0:n-3]&#39; * f̌
+f̃(0.1) ≈ exp(0.1)</code></pre><pre><code class="language-none">true</code></pre><p>Second kind polynomials <span>$\to$</span> second kind points</p><pre><code class="language-julia">ichebyshevutransform(f̌, Val(2)) ≈ exp.(p_2)</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../automaticdifferentiation/">« Automatic differentiation through spherical harmonic transforms</a><a class="docs-footer-nextpage" href="../disk/">Holomorphic integration on the unit disk »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/generated/disk/index.html b/v0.15.15/generated/disk/index.html
new file mode 100644
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Holomorphic integration on the unit disk · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li class="is-active"><a class="tocitem" href>Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Holomorphic integration on the unit disk</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Holomorphic integration on the unit disk</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/disk.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Holomorphic-integration-on-the-unit-disk-1"><a class="docs-heading-anchor" href="#Holomorphic-integration-on-the-unit-disk-1">Holomorphic integration on the unit disk</a><a class="docs-heading-anchor-permalink" href="#Holomorphic-integration-on-the-unit-disk-1" title="Permalink"></a></h1><p>In this example, we explore integration of a harmonic function:</p><div>\[  f(x,y) = \frac{x^2-y^2+1}{(x^2-y^2+1)^2+(2xy+1)^2},\]</div><p>over the unit disk. In this case, we know from complex analysis that the integral of a holomorphic function is equal to <span>$\pi \times f(0,0)$</span>. We analyze the function on an <span>$N\times M$</span> tensor product grid defined by:</p><div>\[\begin{aligned}
+r_n &amp; = \cos\left[(n+\tfrac{1}{2})\pi/2N\right],\quad{\rm for}\quad 0\le n &lt; N,\quad{\rm and}\\
+\theta_m &amp; = 2\pi m/M,\quad{\rm for}\quad 0\le m &lt; M;
+\end{aligned}\]</div><p>we convert the function samples to Chebyshev×Fourier coefficients using <code>plan_disk_analysis</code>; and finally, we transform the Chebyshev×Fourier coefficients to Zernike polynomial coefficients using <code>plan_disk2cxf</code>.</p><p>For the storage pattern of the arrays, please consult the <a href="https://MikaelSlevinsky.github.io/FastTransforms">documentation</a>.</p><pre><code class="language-julia">using FastTransforms, LinearAlgebra, Plots
+const GENFIGS = joinpath(pkgdir(FastTransforms), &quot;docs/src/generated&quot;)
+!isdir(GENFIGS) &amp;&amp; mkdir(GENFIGS)
+plotlyjs()</code></pre><pre><code class="language-none">Plots.PlotlyJSBackend()</code></pre><p>Our function <span>$f$</span> on the disk:</p><pre><code class="language-julia">f = (x,y) -&gt; (x^2-y^2+1)/((x^2-y^2+1)^2+(2x*y+1)^2)</code></pre><pre><code class="language-none">#1 (generic function with 1 method)</code></pre><p>The Zernike polynomial degree:</p><pre><code class="language-julia">N = 15
+M = 4N-3</code></pre><pre><code class="language-none">57</code></pre><p>The radial grid:</p><pre><code class="language-julia">r = [sinpi((N-n-0.5)/(2N)) for n in 0:N-1]</code></pre><pre><code class="language-none">15-element Vector{Float64}:
+ 0.9986295347545738
+ 0.9876883405951378
+ 0.9659258262890683
+ 0.9335804264972017
+ 0.8910065241883678
+ 0.838670567945424
+ 0.7771459614569709
+ 0.7071067811865476
+ 0.6293203910498375
+ 0.5446390350150271
+ 0.45399049973954675
+ 0.35836794954530027
+ 0.25881904510252074
+ 0.15643446504023087
+ 0.052335956242943835</code></pre><p>The angular grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">θ = (0:M-1)*2/M</code></pre><pre><code class="language-none">0.0:0.03508771929824561:1.9649122807017543</code></pre><p>On the mapped tensor product grid, our function samples are:</p><pre><code class="language-julia">F = [f(r*cospi(θ), r*sinpi(θ)) for r in r, θ in θ]</code></pre><pre><code class="language-none">15×57 Matrix{Float64}:
+ 0.400329  0.36696   0.336645  0.308443  0.281619  0.25557   0.22977   0.203733  0.176996  0.149111  0.119689  0.0885456  0.0561428  0.0249494  0.00382185  0.0233794  0.192001  0.82415   1.84146   1.85719   1.41721   1.08969   0.879424  0.739148  0.639757  0.565314  0.506844  0.459027  0.418538  0.383193  0.351486  0.32233   0.294899  0.268532  0.24267   0.216811  0.190481  0.163223  0.134611  0.104328  0.0724218  0.0400826  0.0120549  0.00476215  0.075801  0.422295  1.37342   1.98551   1.63411   1.23553   0.973247  0.802761  0.685557  0.600091  0.534475  0.481845  0.438023
+ 0.402946  0.369531  0.339215  0.31106   0.284337  0.258454  0.232899  0.207211  0.180965  0.153777  0.125364  0.0957188  0.0656309  0.0381784  0.0233592   0.0535023  0.23469   0.838287  1.74173   1.78814   1.39763   1.08662   0.881061  0.742049  0.642889  0.56837   0.509752  0.461793  0.421195  0.385781  0.35405   0.324917  0.297559  0.271324  0.245665  0.220098  0.194183  0.16751   0.139734  0.110675  0.0806214  0.0512076  0.0280171  0.0289628   0.112787  0.46247   1.32844   1.88443   1.59532   1.22668   0.973254  0.805245  0.688639  0.603204  0.53746   0.48468   0.44073
+ 0.408107  0.374635  0.344345  0.316308  0.289809  0.264275  0.239228  0.214259  0.189018  0.16325   0.136874  0.110236   0.0847405  0.0645701  0.0616188   0.110283   0.308499  0.852043  1.57431   1.65952   1.35481   1.07725   0.882418  0.74674   0.648492  0.574076  0.515313  0.467166  0.426411  0.390904  0.359157  0.330094  0.302904  0.276953  0.251718  0.226757  0.201691  0.176211  0.150131  0.123537  0.0971828  0.0735249  0.059617   0.0756242   0.180187  0.525812  1.24639   1.70902   1.5172    1.20513   0.970751  0.808756  0.693948  0.608911  0.543108  0.490146  0.446017
+ 0.415648  0.382189  0.352011  0.324209  0.298096  0.273134  0.248897  0.225051  0.201367  0.177773  0.154485  0.132336   0.113545   0.103633   0.116351    0.186253   0.393918  0.849832  1.38148   1.49082   1.28527   1.05638   0.879972  0.751049  0.655222  0.581588  0.52299   0.474802  0.433974  0.398441  0.366752  0.33786   0.310977  0.2855    0.260948  0.236942  0.213198  0.189555  0.166059  0.143176  0.122289   0.106906   0.105724   0.140558    0.26534   0.588182  1.1413    1.4992    1.40336   1.16548   0.961348  0.810521  0.699782  0.616152  0.550745  0.497814  0.453615
+ 0.425289  0.392035  0.362148  0.334773  0.309271  0.285158  0.262081  0.239809  0.218269  0.197619  0.178435  0.162105   0.151689   0.153844   0.183081    0.270225   0.470832  0.826183  1.19548   1.30726   1.19053   1.01926   0.869418  0.751971  0.661094  0.589601  0.531924  0.48414   0.443527  0.408177  0.376729  0.348191  0.321822  0.297066  0.273507  0.250853  0.228945  0.20781   0.187783  0.169776  0.15586    0.150546   0.163666   0.216532    0.352149  0.631169  1.0287    1.29056   1.26502   1.10458   0.940232  0.806897  0.703689  0.623316  0.559314  0.506989  0.463072
+ 0.436597  0.403911  0.374626  0.347975  0.323392  0.300472  0.278957  0.258746  0.239942  0.222959  0.208736  0.199165   0.19792    0.212076   0.254963    0.349717   0.526163  0.785631  1.03278   1.13127   1.07899   0.964458  0.847102  0.746235  0.663661  0.596384  0.540917  0.494365  0.454527  0.419771  0.388896  0.361011  0.335454  0.311744  0.289549  0.268688  0.249152  0.23118   0.215414  0.203195  0.197165   0.20243    0.228745   0.293986    0.426183  0.648643  0.920719  1.10477   1.11859   1.02459   0.904279  0.794291  0.702811  0.628337  0.567372  0.51668   0.47372
+ 0.448951  0.417414  0.389209  0.363706  0.340449  0.319139  0.299632  0.28197   0.266434  0.253672  0.244908  0.242329   0.249735   0.273549   0.32399     0.414856   0.556748  0.73654   0.898135  0.976631  0.96284   0.895308  0.811683  0.731268  0.660475  0.599969  0.54849   0.504405  0.466222  0.432719  0.402938  0.376152  0.351819  0.329563  0.309162  0.29056   0.273906  0.259647  0.248682  0.242655  0.244458   0.259053   0.294635   0.36347     0.47935   0.644419  0.824368  0.950029  0.979333  0.933025  0.853895  0.770471  0.694553  0.628995  0.573203  0.525623  0.484659
+ 0.461538  0.431966  0.405508  0.381723  0.360304  0.341079  0.324035  0.309345  0.297441  0.289121  0.285721  0.289387   0.303423   0.332641   0.383252    0.461146   0.566675  0.686278  0.79016   0.848441  0.853234  0.818825  0.765072  0.706268  0.649804  0.598546  0.553073  0.513009  0.477665  0.446331  0.418379  0.393304  0.370732  0.350422  0.332279  0.316375  0.303005  0.292765  0.286694  0.286496  0.294846   0.315771   0.354858   0.418544    0.510882  0.626287  0.742362  0.826153  0.856971  0.839629  0.793294  0.735701  0.677489  0.623454  0.575098  0.532405  0.494793
+ 0.473406  0.446815  0.422943  0.401579  0.382592  0.365953  0.35177   0.340321  0.332115  0.327962  0.329086  0.337225   0.354715   0.384367   0.428886    0.489368   0.562769  0.639621  0.705232  0.746138  0.75726   0.742897  0.711918  0.672777  0.631361  0.591026  0.553364  0.51894   0.487799  0.459755  0.434554  0.411958  0.391793  0.373976  0.358542  0.345678  0.33577   0.329466  0.327769  0.332147  0.344633   0.367837   0.404636   0.457191    0.524883  0.601613  0.674803  0.729338  0.755332  0.752747  0.728907  0.692933  0.652092  0.610928  0.571808  0.535736  0.502968
+ 0.483592  0.461074  0.44072   0.422552  0.406616  0.393018  0.381958  0.373761  0.368913  0.368096  0.372211  0.382374   0.399829   0.425704   0.460521    0.503436   0.551426  0.599039  0.639428  0.66664   0.677821  0.673802  0.657934  0.634338  0.606657  0.577562  0.548776  0.521299  0.49565   0.472064  0.450625  0.431361  0.4143    0.399515  0.387153  0.377475  0.370881  0.36795   0.369472  0.37646   0.390112   0.411659   0.442005   0.481097    0.527085  0.575698  0.62056   0.654949  0.674261  0.67754   0.667091  0.646854  0.620817  0.592158  0.563054  0.534833  0.508227
+ 0.491347  0.47384   0.457857  0.443596  0.43124   0.420991  0.413088  0.407835  0.405607  0.406854  0.41208   0.421791   0.436393   0.456016   0.480289    0.508089   0.537411  0.565495  0.589313  0.606297  0.614986  0.615273  0.608182  0.595383  0.578689  0.55973   0.539808  0.519875  0.500596  0.482417  0.465645  0.450499  0.437168  0.425839  0.416729  0.410109  0.406316  0.405766  0.408937  0.416345  0.428463   0.445585   0.467622   0.493853    0.522719  0.551798  0.578117  0.598782  0.611716  0.616137  0.612554  0.602381  0.587414  0.569403  0.549822  0.529795  0.510121
+ 0.496372  0.484362  0.473263  0.463344  0.454844  0.447987  0.442992  0.440085  0.43949   0.441422  0.446059  0.453506   0.463734   0.476516   0.491364    0.507491   0.523832  0.539138  0.552155  0.561824  0.567461  0.568845  0.566188  0.560036  0.551118  0.54022   0.528088  0.515374  0.502621  0.490272  0.478681  0.468141  0.458903  0.451197  0.445243  0.441264  0.439485  0.440128  0.443394  0.44943   0.458281   0.469829   0.483724   0.499329    0.51571   0.531695  0.546006  0.557461  0.565171  0.568681  0.567994  0.563506  0.555873  0.545868  0.534265  0.521767  0.508973
+ 0.498951  0.492196  0.485875  0.480211  0.475399  0.471612  0.469002  0.467693  0.467782  0.469331  0.472348  0.476782   0.482503   0.489293   0.496841    0.504746   0.512549  0.519761  0.525915  0.530618  0.533588  0.534687  0.533917  0.531408  0.527389  0.522155  0.516029  0.509344  0.502414  0.495534  0.488967  0.482948  0.477687  0.473367  0.470152  0.468178  0.467558  0.468372  0.470657  0.474394  0.479493   0.485782   0.492995   0.500776    0.508691  0.516259  0.522997  0.528468  0.532332  0.534375  0.53453   0.532867  0.52957   0.524904  0.519183  0.512736  0.505891
+ 0.499854  0.497256  0.494799  0.492592  0.490727  0.489288  0.488339  0.487926  0.488075  0.488789  0.490046  0.491797   0.493969   0.496462   0.499157    0.501918   0.5046    0.507061  0.509167  0.510805  0.511889  0.512367  0.512222  0.51147   0.510163  0.508376  0.506206  0.503765  0.501171  0.498544  0.496003  0.493658  0.491611  0.48995   0.488749  0.488063  0.48793   0.488363  0.489352  0.490864  0.492836   0.495182   0.497793   0.500538    0.503278  0.505867  0.508166  0.51005   0.51142   0.512206  0.512372  0.511919  0.510882  0.509324  0.507332  0.505012  0.502479
+ 0.499998  0.4997    0.499416  0.49916   0.498945  0.498781  0.498675  0.498633  0.498657  0.498746  0.498895  0.499098   0.499346   0.499625   0.499922    0.500224   0.500515  0.500781  0.50101   0.501189  0.50131   0.501367  0.501358  0.501283  0.501146  0.500953  0.500715  0.500442  0.500148  0.499848  0.499555  0.499284  0.499047  0.498856  0.49872   0.498646  0.498637  0.498693  0.498813  0.498991  0.499217   0.499482   0.499772   0.500074    0.500372  0.500652  0.500901  0.501106  0.501257  0.501347  0.501371  0.501328  0.501222  0.501056  0.500839  0.500582  0.500297</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">X = [r*cospi(θ) for r in r, θ in θ]
+Y = [r*sinpi(θ) for r in r, θ in θ]
+scatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:red)
+surface!(X, Y, F; legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;zernike.html&quot;))</code></pre><object type="text/html" data="../zernike.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/zernike.html&quot;</code></pre><p>We precompute a (generalized) Zernike–Chebyshev×Fourier plan:</p><pre><code class="language-julia">α, β = 0, 0
+P = plan_disk2cxf(F, α, β)</code></pre><pre><code class="language-none">FastTransforms Zernike--Chebyshev×Fourier plan for 15×57-element array of Float64</code></pre><p>And an FFTW Chebyshev×Fourier analysis plan on the disk:</p><pre><code class="language-julia">PA = plan_disk_analysis(F)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Chebyshev×Fourier analysis on the disk for 15×57-element array of Float64</code></pre><p>Its Zernike coefficients are:</p><pre><code class="language-julia">U = P\(PA*F)</code></pre><pre><code class="language-none">15×57 Matrix{Float64}:
+  0.886227     3.60709e-6  -1.8336e-6   -0.361801     3.60559e-11  -1.17688e-6   6.36308e-6   0.140125     -0.140125     -6.35177e-6   -7.70959e-6  1.89039e-10  0.118427     1.54098e-5  7.4099e-7    -0.0522214    -0.0522214    -1.71856e-5  1.64002e-5   0.0472361    -5.20197e-10  4.08953e-7   -3.63399e-5  -0.0217254    0.0217254    3.88099e-5   3.92308e-5  -1.24018e-9   -0.0202253    -8.31939e-5  -2.14893e-7   0.00949917    0.00949917   8.82306e-5   -8.80125e-5   -0.00898531   2.80468e-9   -1.10226e-7   0.000185657   0.00427337   -0.00427337   -0.000194603  -0.000194714  6.17793e-9   0.00408335   0.000406568  5.5777e-8    -0.00195832   -0.0019583    -0.000423167  0.000423111  0.00188439   -1.33894e-8   2.79926e-8   -0.000878195  -0.00090912   0.000909147
+  3.08825e-17  4.60728e-6  -2.33805e-6  -4.33e-11     4.33e-11     -1.22625e-6   6.53675e-6   2.91135e-17  -1.46429e-10  -5.65109e-6   -6.90982e-6  1.84987e-10  1.84987e-10  1.21904e-5  6.29629e-7   -4.19031e-10  -7.40235e-18  -1.21069e-5  1.14861e-5   4.50193e-10  -4.50193e-10  3.03358e-7   -2.25713e-5   1.03258e-17  9.39347e-10  2.10848e-5   2.13797e-5  -9.62216e-10  -9.62216e-10  -3.90991e-5  -1.42777e-7   1.94644e-9    2.80911e-17  3.51181e-5   -3.49801e-5   -1.94972e-9   1.94972e-9   -6.65696e-8   6.06806e-5    1.30586e-17  -3.87473e-9   -4.9981e-5    -5.00452e-5   3.82278e-9   3.82278e-9   7.63297e-5   3.09339e-8   -7.49277e-9    1.61027e-18  -5.04164e-5   5.03866e-5   7.2952e-9    -7.2952e-9    1.38574e-8   -4.45519e-5    2.60005e-17  1.36316e-8
+  3.54191e-17  4.76065e-6  -2.40899e-6  -4.59639e-11  4.59638e-11  -1.12866e-6   5.89804e-6   6.18124e-18  -1.43511e-10  -4.51295e-6   -5.57325e-6  1.70088e-10  1.70088e-10  8.73447e-6  4.92668e-7   -3.63967e-10  -2.11966e-17  -7.74165e-6  7.28634e-6   3.70513e-10  -3.70513e-10  2.09854e-7   -1.26794e-5  -9.92069e-18  7.33255e-10  1.02945e-5   1.04878e-5  -7.12279e-10  -7.12279e-10  -1.63841e-5  -8.90173e-8   1.36506e-9   -1.87551e-17  1.23112e-5   -1.22292e-5   -1.29344e-9   1.29344e-9   -3.78749e-8   1.71213e-5   -9.44761e-18  -2.42653e-9   -1.07347e-5   -1.07697e-5   2.25423e-9   2.25423e-9   1.13275e-5   1.62097e-8   -4.14789e-9    7.15519e-18  -4.10621e-6   4.09201e-6   3.57033e-9   -3.57033e-9   7.2136e-9    -3.89728e-6    8.38482e-18  7.03625e-9
+  3.7535e-19   4.3306e-6   -2.18254e-6  -4.50915e-11  4.50915e-11  -9.41975e-7   4.79767e-6   2.32655e-17  -1.3221e-10   -3.27045e-6   -4.09126e-6  1.48194e-10  1.48194e-10  5.69834e-6  3.57019e-7   -3.00851e-10   4.15138e-18  -4.50516e-6  4.19432e-6   2.90868e-10  -2.90868e-10  1.35612e-7   -6.44339e-6   6.75322e-18  5.46652e-10  4.50749e-6   4.62617e-6  -5.03847e-10  -5.03847e-10  -6.09951e-6  -5.21037e-8   9.1491e-10    2.51335e-18  3.77955e-6   -3.73364e-6   -8.19854e-10  8.19854e-10  -2.03036e-8   4.12363e-6    2.10797e-17  -1.45125e-9   -1.88522e-6   -1.90324e-6   1.26862e-9   1.26862e-9   1.23872e-6   7.40728e-9   -2.01666e-9    5.16575e-18  -6.4875e-7    6.41095e-7   1.96336e-9   -1.96336e-9   3.94603e-9   -4.95856e-7    9.84193e-18  3.81545e-9
+ -1.18289e-17  3.55971e-6  -1.7846e-6   -4.1593e-11   4.1593e-11   -7.20914e-7   3.55774e-6  -5.44669e-18  -1.15465e-10  -2.16169e-6   -2.74892e-6  1.22948e-10  1.22948e-10  3.3937e-6   2.40326e-7   -2.37394e-10   8.29477e-18  -2.38904e-6  2.19119e-6   2.18301e-10  -2.18301e-10  8.19355e-8   -2.95988e-6  -1.46774e-18  3.89943e-10  1.76401e-6   1.8323e-6   -3.41184e-10  -3.41184e-10  -2.0084e-6   -2.86395e-8   5.87175e-10  -3.7024e-18   1.01021e-6   -9.86038e-7   -4.97705e-10  4.97705e-10  -1.02636e-8   8.36501e-7   -1.91606e-17  -8.31421e-10  -2.51578e-7   -2.59455e-7   6.11155e-10  6.11155e-10  2.81636e-7   4.14107e-9   -1.17835e-9    6.44999e-18  -1.31206e-7   1.26866e-7   1.1332e-9    -1.1332e-9    2.26757e-9   -8.50354e-8    4.13504e-18  2.17398e-9
+  2.9532e-17   2.67365e-6  -1.33163e-6  -3.63778e-11  3.63778e-11  -5.08751e-7   2.4183e-6   -1.47781e-17  -9.60672e-11  -1.3062e-6    -1.69561e-6  9.74399e-11  9.74399e-11  1.84711e-6  1.50509e-7   -1.79257e-10   8.4605e-19   -1.15523e-6  1.03773e-6   1.56975e-10  -1.56975e-10  4.63055e-8   -1.22747e-6  -7.64459e-19  2.66772e-10  6.14181e-7   6.51026e-7  -2.21796e-10  -2.21796e-10  -5.82251e-7  -1.47961e-8   3.62177e-10   4.04991e-18  2.3447e-7    -2.22474e-7   -2.90765e-10  2.90765e-10  -4.27394e-9   1.32135e-7    1.10407e-18  -3.9572e-10   -7.37753e-8   -7.83499e-8   3.78556e-10  3.78556e-10  7.69466e-8   2.43764e-9   -7.22143e-10  -2.20019e-18  -3.3267e-8    3.06793e-8   6.86748e-10  -6.86748e-10  1.36854e-9   -1.89956e-8    5.29828e-18  1.30213e-9
+  4.8454e-18   1.84493e-6  -9.11632e-7  -3.03234e-11  3.03234e-11  -3.31998e-7   1.51086e-6   9.13653e-18  -7.63919e-11  -7.22019e-7   -9.61716e-7  7.39635e-11  7.39635e-11  9.19025e-7  8.7759e-8    -1.29855e-10  -1.00058e-17  -5.0973e-7   4.44593e-7   1.08464e-10  -1.08464e-10  2.44943e-8   -4.5896e-7   -7.25056e-18  1.75682e-10  1.89131e-7   2.07797e-7  -1.3908e-10   -1.3908e-10   -1.48285e-7  -7.20906e-9   2.15876e-10  -9.44039e-18  4.31232e-8   -3.83843e-8   -1.35983e-10  1.35983e-10  -2.58242e-9   4.86298e-8   -3.52213e-18  -2.58784e-10  -2.49419e-8   -2.77411e-8   2.45364e-10  2.45364e-10  2.49291e-8   1.50968e-9   -4.63692e-10   6.50763e-18  -1.04761e-8   8.85511e-9   4.36633e-10  -4.36633e-10  8.66632e-10  -5.46345e-9    2.04425e-18  8.19335e-10
+ -2.37746e-17  1.17276e-6  -5.74087e-7  -2.41606e-11  2.41606e-11  -2.00616e-7   8.68671e-7  -1.72499e-18  -5.82253e-11  -3.64941e-7   -5.01985e-7  5.39205e-11  5.39205e-11  4.17975e-7  4.76625e-8   -9.05511e-11  -4.9981e-18   -2.05562e-7  1.71822e-7   7.23176e-11  -7.23176e-11  1.21586e-8   -1.5476e-7    2.16322e-18  1.11916e-10  5.11842e-8   6.01101e-8  -8.43279e-11  -8.43279e-11  -2.90142e-8  -2.68449e-9   9.8079e-11   -4.79653e-18  1.93294e-8   -1.63497e-8   -9.30964e-11  9.30964e-11  -1.64272e-9   2.0359e-8    -2.13593e-18  -1.75944e-10  -9.61519e-9   -1.14155e-8   1.65598e-10  1.65598e-10  9.47999e-9   9.81067e-10  -3.10521e-10  -2.38645e-18  -4.06062e-9   2.99682e-9   2.90001e-10  -2.90001e-10  5.7406e-10   -2.00747e-9   -3.59072e-18  5.39466e-10
+  8.95539e-18  6.87558e-7  -3.32907e-7  -1.84685e-11  1.84685e-11  -1.12306e-7   4.59773e-7  -2.97799e-18  -4.265e-11    -1.68481e-7   -2.41286e-7  3.78985e-11  3.78985e-11  1.73828e-7  2.4139e-8    -6.10346e-11  -1.33435e-18  -7.61356e-8  5.9745e-8    4.66938e-11  -4.66938e-11  5.69883e-9   -4.73542e-8  -2.61397e-18  6.84382e-11  1.00798e-8   1.31808e-8  -3.64534e-11  -3.64534e-11  -1.46721e-8  -1.7526e-9    6.92775e-11  -5.64422e-18  9.70857e-9   -7.74328e-9   -6.54378e-11  6.54378e-11  -1.09391e-9   9.61505e-9    2.81389e-19  -1.23027e-10  -4.18802e-9   -5.39773e-9   1.15147e-10  1.15147e-10  4.18575e-9   6.64834e-10  -2.1464e-10    7.04116e-18  -1.89907e-9   1.17239e-9   1.99193e-10  -1.99193e-10  3.95103e-10  -9.19881e-10   1.86274e-18  3.68061e-10
+  2.15782e-17  3.71865e-7  -1.77783e-7  -1.35612e-11  1.35612e-11  -5.82608e-8   2.24022e-7   3.72333e-18  -3.01692e-11  -7.09608e-8   -1.06944e-7  2.57607e-11  2.57607e-11  6.63405e-8  1.14574e-8   -3.98083e-11   1.83302e-17  -2.62265e-8  1.87191e-8   2.83655e-11  -2.83655e-11  1.81554e-9   -1.02616e-8   1.27257e-18  2.72302e-11  5.57557e-9   7.66477e-9  -2.60181e-11  -2.60181e-11  -8.14921e-9  -1.19076e-9   4.92954e-11   1.47536e-17  5.39512e-9   -4.04931e-9   -4.64096e-11  4.64096e-11  -7.54615e-10  5.0669e-9     1.0689e-17   -8.69428e-11  -2.04308e-9   -2.88332e-9   8.10649e-11  8.10649e-11  2.11288e-9   4.64752e-10  -1.50494e-10   5.16894e-18  -1.03471e-9   5.23655e-10  1.39056e-10  -1.39056e-10  2.79431e-10  -5.01563e-10   5.97653e-18  2.55748e-10
+ -1.47947e-17  1.85546e-7  -8.74169e-8  -9.64281e-12  9.6428e-12   -2.80375e-8   1.00537e-7  -7.35134e-19  -2.06073e-11  -2.73295e-8   -4.39821e-8  1.69233e-11  1.69233e-11  2.34206e-8  5.10163e-9   -2.35204e-11   6.51352e-18  -5.91169e-9  3.77929e-9   9.88461e-12  -9.88462e-12  1.24842e-9   -6.38622e-9   4.02236e-18  1.91141e-11  3.32832e-9   4.77417e-9  -1.82332e-11  -1.82332e-11  -4.89671e-9  -8.28984e-10  3.44828e-11   7.48581e-18  3.25458e-9   -2.31249e-9   -3.24e-11     3.24e-11     -5.30949e-10  2.93011e-9   -6.11335e-18  -6.05679e-11  -1.10379e-9   -1.6978e-9    5.63435e-11  5.63436e-11  1.1914e-9    3.3001e-10   -1.04342e-10  -2.57553e-18  -6.27959e-10  2.63577e-10  9.6157e-11   -9.6157e-11   2.00002e-10  -3.071e-10     7.37827e-18  1.76348e-10
+ -3.12442e-17  8.54426e-8  -3.95787e-8  -6.58743e-12  6.58744e-12  -1.26163e-8   4.18408e-8  -1.80052e-17  -1.3631e-11   -9.62687e-9   -1.67874e-8  9.48623e-12  9.48623e-12  4.72571e-9  1.23574e-9   -6.65263e-12  -3.83785e-18  -3.91558e-9  2.44388e-9   6.57828e-12  -6.57828e-12  8.65402e-10  -4.14906e-9   2.72883e-18  1.2711e-11   2.09945e-9   3.10576e-9  -1.21149e-11  -1.21149e-11  -3.10737e-9  -5.79121e-10  2.28905e-11   6.23804e-18  2.07394e-9   -1.41354e-9   -2.1486e-11   2.1486e-11   -3.73369e-10  1.81245e-9   -1.03001e-17  -4.01214e-11  -6.48005e-10  -1.06694e-9   3.72789e-11  3.72789e-11  7.26798e-10  2.33379e-10  -6.89482e-11   4.73336e-18  -4.05112e-10  1.46777e-10  6.34527e-11  -6.34527e-11  1.42127e-10  -1.99851e-10   7.62512e-18  1.16198e-10
+  1.33271e-17  3.66259e-8  -1.66324e-8  -4.39971e-12  4.39972e-12  -5.20978e-9   1.59586e-8  -1.01503e-17  -7.0843e-12   -1.58674e-9   -2.96274e-9  1.91297e-12  1.91297e-12  3.12298e-9  8.33281e-10  -3.95183e-12  -6.31239e-18  -2.58884e-9  1.5939e-9    3.90661e-12  -3.90663e-12  5.8643e-10   -2.71374e-9   3.31823e-18  7.54633e-12  1.34984e-9   2.03322e-9  -7.18992e-12  -7.18992e-12  -2.00561e-9  -3.94051e-10  1.35798e-11  -3.88588e-18  1.34233e-9   -8.92165e-10  -1.27412e-11  1.27412e-11  -2.54934e-10  1.15296e-9   -7.65968e-18  -2.37812e-11  -3.99094e-10  -6.85581e-10  2.20855e-11  2.20855e-11  4.59097e-10  1.5982e-10   -4.0826e-11   -2.81128e-18  -2.64588e-10  8.74454e-11  3.75507e-11  -3.75507e-11  9.75761e-11  -1.31247e-10  -3.71219e-18  6.87229e-11
+ -1.29499e-17  1.42637e-8  -6.34424e-9  -2.10396e-12  2.10396e-12  -6.84193e-10  1.98342e-9   2.18678e-18  -7.77242e-13  -9.64872e-10  -1.8079e-9   8.82102e-13  8.82104e-13  1.90051e-9  5.11075e-10  -1.82214e-12   9.26204e-18  -1.57577e-9  9.64939e-10  1.80117e-12  -1.80117e-12  3.60351e-10  -1.64478e-9   5.54127e-18  3.47897e-12  8.12528e-10  1.2328e-9   -3.31434e-12  -3.31434e-12  -1.2092e-9   -2.42517e-10  6.2592e-12   -3.29227e-18  8.10242e-10  -5.33001e-10  -5.872e-12    5.872e-12    -1.57104e-10  6.91093e-10  -6.13378e-18  -1.09586e-11  -2.3601e-10   -4.12661e-10  1.01758e-11  1.01758e-11  2.74436e-10  9.85995e-11  -1.88077e-11  -5.45761e-18  -1.60322e-10  5.09818e-11  1.7296e-11   -1.7296e-11   6.02559e-11  -7.9705e-11    4.13813e-19  3.16487e-11
+ -2.57377e-17  3.5367e-9   -1.55057e-9  -5.05721e-14  5.05682e-14  -1.24617e-9   3.61129e-9  -3.1012e-18   -1.49119e-13  -1.75608e-9   -3.29176e-9  1.69228e-13  1.6923e-13   3.45928e-9  9.31108e-10  -3.49575e-13  -1.75255e-18  -2.86824e-9  1.75527e-9   3.45548e-13  -3.4555e-13   6.56655e-10  -2.99235e-9  -1.63745e-18  6.67424e-13  1.47702e-9   2.24293e-9  -6.35833e-13  -6.35832e-13  -2.1985e-9   -4.42011e-10  1.20077e-12   2.0917e-18   1.47335e-9   -9.68009e-10  -1.12648e-12  1.12649e-12  -2.86382e-10  1.25563e-9    2.55539e-19  -2.10227e-12  -4.28097e-10  -7.50132e-10  1.95208e-12  1.95208e-12  4.98453e-10  1.79759e-10  -3.60793e-12   1.51272e-18  -2.91666e-10  9.23134e-11  3.31791e-12  -3.31791e-12  1.09866e-10  -1.45042e-10  -9.98777e-19  6.07111e-12</code></pre><p>The Zernike coefficients are useful for integration. The integral of <span>$f(x,y)$</span> over the disk should be <span>$\pi/2$</span> by harmonicity. The coefficient of <span>$Z_{0,0}$</span> multiplied by <code>√π</code> is:</p><pre><code class="language-julia">U[1, 1]*sqrt(π)</code></pre><pre><code class="language-none">1.5707963267948968</code></pre><p>Using an orthonormal basis, the integral of <span>$[f(x,y)]^2$</span> over the disk is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))</code></pre><pre><code class="language-none">(0.9789599193439185, 0.9789599179781414)</code></pre><p>But there&#39;s more! Next, we repeat the experiment using the Dunkl-Xu orthonormal polynomials supported on the rectangularized disk.</p><pre><code class="language-julia">N = 2N
+M = N</code></pre><pre><code class="language-none">30</code></pre><p>We analyze the function on an <span>$N\times M$</span> mapped tensor product <span>$xy$</span>-grid defined by:</p><div>\[\begin{aligned}
+x_n &amp; = \cos\left(\frac{2n+1}{2N}\pi\right) = \sin\left(\frac{N-2n-1}{2N}\pi\right),\quad {\rm for} \quad 0 \le n &lt; N,\quad{\rm and}\\
+z_m &amp; = \cos\left(\frac{2m+1}{2M}\pi\right) = \sin\left(\frac{M-2m-1}{2M}\pi\right),\quad {\rm for} \quad 0 \le m &lt; M,\\
+y_{n,m} &amp; = \sqrt{1-x_n^2}z_m.
+\end{aligned}\]</div><p>Slightly more accuracy can be expected by using an auxiliary array:</p><div>\[  w_n = \sin\left(\frac{2n+1}{2N}\pi\right),\quad {\rm for} \quad 0 \le n &lt; N,\]</div><p>so that <span>$y_{n,m} = w_nz_m$</span>.</p><p>The x grid</p><pre><code class="language-julia">w = [sinpi((n+0.5)/N) for n in 0:N-1]
+x = [sinpi((N-2n-1)/(2N)) for n in 0:N-1]</code></pre><pre><code class="language-none">30-element Vector{Float64}:
+  0.9986295347545738
+  0.9876883405951378
+  0.9659258262890683
+  0.9335804264972017
+  0.8910065241883678
+  0.838670567945424
+  0.7771459614569709
+  0.7071067811865476
+  0.6293203910498375
+  0.5446390350150271
+  0.45399049973954675
+  0.35836794954530027
+  0.25881904510252074
+  0.15643446504023087
+  0.052335956242943835
+ -0.052335956242943835
+ -0.15643446504023087
+ -0.25881904510252074
+ -0.35836794954530027
+ -0.45399049973954675
+ -0.5446390350150271
+ -0.6293203910498375
+ -0.7071067811865476
+ -0.7771459614569709
+ -0.838670567945424
+ -0.8910065241883678
+ -0.9335804264972017
+ -0.9659258262890683
+ -0.9876883405951378
+ -0.9986295347545738</code></pre><p>The z grid</p><pre><code class="language-julia">z = [sinpi((M-2m-1)/(2M)) for m in 0:M-1]</code></pre><pre><code class="language-none">30-element Vector{Float64}:
+  0.9986295347545738
+  0.9876883405951378
+  0.9659258262890683
+  0.9335804264972017
+  0.8910065241883678
+  0.838670567945424
+  0.7771459614569709
+  0.7071067811865476
+  0.6293203910498375
+  0.5446390350150271
+  0.45399049973954675
+  0.35836794954530027
+  0.25881904510252074
+  0.15643446504023087
+  0.052335956242943835
+ -0.052335956242943835
+ -0.15643446504023087
+ -0.25881904510252074
+ -0.35836794954530027
+ -0.45399049973954675
+ -0.5446390350150271
+ -0.6293203910498375
+ -0.7071067811865476
+ -0.7771459614569709
+ -0.838670567945424
+ -0.8910065241883678
+ -0.9335804264972017
+ -0.9659258262890683
+ -0.9876883405951378
+ -0.9986295347545738</code></pre><p>On the mapped tensor product grid, our function samples are:</p><pre><code class="language-julia">F = [f(x[n], w[n]*z) for n in 1:N, z in z]</code></pre><pre><code class="language-none">30×30 Matrix{Float64}:
+ 0.383725    0.383905   0.384264   0.384798  0.3855    0.386365  0.387383  0.388542  0.389832  0.391237  0.392744  0.394337  0.395997  0.397708  0.399451  0.401207  0.402957  0.404681  0.406361  0.407977  0.409512  0.410949  0.41227   0.413462  0.41451   0.415403  0.41613   0.416683   0.417055   0.417242
+ 0.353509    0.354039   0.355094   0.356664  0.358732  0.36128   0.364281  0.367707  0.371524  0.375695  0.380177  0.384927  0.389897  0.395036  0.400292  0.405609  0.41093   0.416197  0.421352  0.426336  0.431089  0.435556  0.439683  0.443417  0.446713  0.449527  0.451824  0.453573   0.454752   0.455346
+ 0.325652    0.32653    0.328275   0.330873  0.334296  0.338513  0.343483  0.349158  0.355488  0.362412  0.36987   0.377792  0.386108  0.394741  0.40361   0.412629  0.421708  0.43075   0.439655  0.44832   0.456637  0.464501  0.471805  0.478449  0.484336  0.489382  0.493512  0.496665   0.498793   0.499866
+ 0.29943     0.300665   0.303122   0.306774  0.311585  0.317506  0.324478  0.332436  0.341308  0.351018  0.361484  0.372625  0.384354  0.396582  0.409213  0.422145  0.435264  0.448446  0.461551  0.474426  0.486904  0.498809  0.50996   0.520175  0.529284  0.537127  0.54357   0.548501   0.551834   0.553515
+ 0.274261    0.275876   0.279088   0.283858  0.290132  0.297838  0.306895  0.317212  0.328692  0.341239  0.354758  0.36916   0.384358  0.400269  0.416811  0.43389   0.451401  0.469213  0.487163  0.505054  0.522647  0.539669  0.555819  0.570781  0.584246  0.595923  0.605564  0.612965   0.617979   0.620509
+ 0.249651    0.251685   0.255724   0.261714  0.269574  0.279203  0.290482  0.303282  0.31747   0.332923  0.349529  0.367198  0.385862  0.405474  0.426001  0.44741   0.469656  0.492656  0.516277  0.540305  0.564443  0.588294  0.611378  0.633149  0.653036  0.670489  0.685018  0.696234   0.703855   0.707707
+ 0.225163    0.227669   0.232643   0.240006  0.249642  0.261402  0.275112  0.290582  0.307622  0.326061  0.345762  0.366637  0.388654  0.411835  0.43625   0.461998  0.489179  0.517862  0.548041  0.579594  0.612236  0.645481  0.678629  0.710777  0.740882  0.76785   0.790662  0.808467   0.820649   0.826828
+ 0.200384    0.203443   0.209507   0.218467  0.230156  0.244357  0.260808  0.279223  0.299317  0.32084   0.343606  0.367524  0.392611  0.418996  0.446912  0.47667   0.508629  0.543152  0.580544  0.620979  0.664413  0.710473  0.758363  0.806792  0.853985  0.897808  0.936015  0.966541   0.987766   0.99863
+ 0.174918    0.178645   0.186025   0.196908  0.211057  0.228154  0.247802  0.269562  0.292995  0.317717  0.343461  0.370116  0.397762  0.426667  0.457278  0.490195  0.526141  0.565917  0.610353  0.660232  0.716173  0.778452  0.846763  0.919914  0.995547  1.07001   1.13854   1.19588    1.23718    1.25878
+ 0.148385    0.152947   0.161975   0.175262  0.192474  0.213137  0.23665   0.262328  0.289486  0.317533  0.346071  0.374964  0.404363  0.43471   0.4667    0.501255  0.539494  0.582713  0.632375  0.690092  0.75756   0.836429  0.928002  1.03272   1.1493    1.27371   1.39809   1.51064    1.59716    1.64443
+ 0.120453    0.126104   0.137278   0.153696  0.174875  0.200102  0.228448  0.258839  0.290208  0.321663  0.352638  0.382979  0.41296   0.443231  0.47475   0.508726  0.546578  0.589942  0.640699  0.701019  0.773401  0.860651  0.965732  1.0913    1.23871   1.40612   1.58568   1.76048    1.90408    1.98636
+ 0.0909577   0.098092   0.112194   0.132868  0.159398  0.19068   0.225238  0.261383  0.297474  0.332223  0.364913  0.395469  0.424393  0.452621  0.481372  0.512033  0.546102  0.585165  0.630904  0.685083  0.749484  0.825684  0.914588  1.01552   1.12484   1.23449   1.33202   1.40445    1.44601    1.46226
+ 0.0602361   0.0695018  0.0877988  0.114536  0.148582  0.188133  0.230785  0.273857  0.314915  0.352268  0.385224  0.414044  0.439685  0.46349   0.486923  0.511411  0.53824   0.568495  0.60296   0.641919  0.684785  0.729453  0.77136   0.802572  0.811931  0.788253  0.727788  0.642222   0.558465   0.506932
+ 0.0300951   0.0426105  0.0672646  0.103059  0.148022  0.199015  0.251986  0.302743  0.347947  0.385818  0.416228  0.440285  0.45973   0.476426  0.492035  0.507855  0.524738  0.542996  0.562232  0.581051  0.596627  0.604238  0.597148  0.56764   0.510053  0.425442  0.32469   0.226238   0.149204   0.107374
+ 0.00673069  0.0245336  0.0593763  0.109244  0.17025   0.236535  0.301213  0.358181  0.403763  0.437224  0.460093  0.47501   0.484736  0.491598  0.497272  0.502743  0.508304  0.513517  0.517087  0.516699  0.508899  0.489293  0.453432  0.398651  0.326385  0.243411  0.160485  0.0888546  0.0371183  0.010234
+ 0.010234    0.0371183  0.0888546  0.160485  0.243411  0.326385  0.398651  0.453432  0.489293  0.508899  0.516699  0.517087  0.513517  0.508304  0.502743  0.497272  0.491598  0.484736  0.47501   0.460093  0.437224  0.403763  0.358181  0.301213  0.236535  0.17025   0.109244  0.0593763  0.0245336  0.00673069
+ 0.107374    0.149204   0.226238   0.32469   0.425442  0.510053  0.56764   0.597148  0.604238  0.596627  0.581051  0.562232  0.542996  0.524738  0.507855  0.492035  0.476426  0.45973   0.440285  0.416228  0.385818  0.347947  0.302743  0.251986  0.199015  0.148022  0.103059  0.0672646  0.0426105  0.0300951
+ 0.506932    0.558465   0.642222   0.727788  0.788253  0.811931  0.802572  0.77136   0.729453  0.684785  0.641919  0.60296   0.568495  0.53824   0.511411  0.486923  0.46349   0.439685  0.414044  0.385224  0.352268  0.314915  0.273857  0.230785  0.188133  0.148582  0.114536  0.0877988  0.0695018  0.0602361
+ 1.46226     1.44601    1.40445    1.33202   1.23449   1.12484   1.01552   0.914588  0.825684  0.749484  0.685083  0.630904  0.585165  0.546102  0.512033  0.481372  0.452621  0.424393  0.395469  0.364913  0.332223  0.297474  0.261383  0.225238  0.19068   0.159398  0.132868  0.112194   0.098092   0.0909577
+ 1.98636     1.90408    1.76048    1.58568   1.40612   1.23871   1.0913    0.965732  0.860651  0.773401  0.701019  0.640699  0.589942  0.546578  0.508726  0.47475   0.443231  0.41296   0.382979  0.352638  0.321663  0.290208  0.258839  0.228448  0.200102  0.174875  0.153696  0.137278   0.126104   0.120453
+ 1.64443     1.59716    1.51064    1.39809   1.27371   1.1493    1.03272   0.928002  0.836429  0.75756   0.690092  0.632375  0.582713  0.539494  0.501255  0.4667    0.43471   0.404363  0.374964  0.346071  0.317533  0.289486  0.262328  0.23665   0.213137  0.192474  0.175262  0.161975   0.152947   0.148385
+ 1.25878     1.23718    1.19588    1.13854   1.07001   0.995547  0.919914  0.846763  0.778452  0.716173  0.660232  0.610353  0.565917  0.526141  0.490195  0.457278  0.426667  0.397762  0.370116  0.343461  0.317717  0.292995  0.269562  0.247802  0.228154  0.211057  0.196908  0.186025   0.178645   0.174918
+ 0.99863     0.987766   0.966541   0.936015  0.897808  0.853985  0.806792  0.758363  0.710473  0.664413  0.620979  0.580544  0.543152  0.508629  0.47667   0.446912  0.418996  0.392611  0.367524  0.343606  0.32084   0.299317  0.279223  0.260808  0.244357  0.230156  0.218467  0.209507   0.203443   0.200384
+ 0.826828    0.820649   0.808467   0.790662  0.76785   0.740882  0.710777  0.678629  0.645481  0.612236  0.579594  0.548041  0.517862  0.489179  0.461998  0.43625   0.411835  0.388654  0.366637  0.345762  0.326061  0.307622  0.290582  0.275112  0.261402  0.249642  0.240006  0.232643   0.227669   0.225163
+ 0.707707    0.703855   0.696234   0.685018  0.670489  0.653036  0.633149  0.611378  0.588294  0.564443  0.540305  0.516277  0.492656  0.469656  0.44741   0.426001  0.405474  0.385862  0.367198  0.349529  0.332923  0.31747   0.303282  0.290482  0.279203  0.269574  0.261714  0.255724   0.251685   0.249651
+ 0.620509    0.617979   0.612965   0.605564  0.595923  0.584246  0.570781  0.555819  0.539669  0.522647  0.505054  0.487163  0.469213  0.451401  0.43389   0.416811  0.400269  0.384358  0.36916   0.354758  0.341239  0.328692  0.317212  0.306895  0.297838  0.290132  0.283858  0.279088   0.275876   0.274261
+ 0.553515    0.551834   0.548501   0.54357   0.537127  0.529284  0.520175  0.50996   0.498809  0.486904  0.474426  0.461551  0.448446  0.435264  0.422145  0.409213  0.396582  0.384354  0.372625  0.361484  0.351018  0.341308  0.332436  0.324478  0.317506  0.311585  0.306774  0.303122   0.300665   0.29943
+ 0.499866    0.498793   0.496665   0.493512  0.489382  0.484336  0.478449  0.471805  0.464501  0.456637  0.44832   0.439655  0.43075   0.421708  0.412629  0.40361   0.394741  0.386108  0.377792  0.36987   0.362412  0.355488  0.349158  0.343483  0.338513  0.334296  0.330873  0.328275   0.32653    0.325652
+ 0.455346    0.454752   0.453573   0.451824  0.449527  0.446713  0.443417  0.439683  0.435556  0.431089  0.426336  0.421352  0.416197  0.41093   0.405609  0.400292  0.395036  0.389897  0.384927  0.380177  0.375695  0.371524  0.367707  0.364281  0.36128   0.358732  0.356664  0.355094   0.354039   0.353509
+ 0.417242    0.417055   0.416683   0.41613   0.415403  0.41451   0.413462  0.41227   0.410949  0.409512  0.407977  0.406361  0.404681  0.402957  0.401207  0.399451  0.397708  0.395997  0.394337  0.392744  0.391237  0.389832  0.388542  0.387383  0.386365  0.3855    0.384798  0.384264   0.383905   0.383725</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">X = [x for x in x, z in z]
+Y = [w*z for w in w, z in z]
+scatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:green)
+surface!(X, Y, F; legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;dunklxu.html&quot;))</code></pre><object type="text/html" data="../dunklxu.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/dunklxu.html&quot;</code></pre><p>We precompute a Dunkl-Xu–Chebyshev plan:</p><pre><code class="language-julia">P = plan_rectdisk2cheb(F, β)</code></pre><pre><code class="language-none">FastTransforms Dunkl-Xu--Chebyshev² plan for 30×30-element array of Float64</code></pre><p>And an FFTW Chebyshev² analysis plan on the rectangularized disk:</p><pre><code class="language-julia">PA = plan_rectdisk_analysis(F)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Chebyshev analysis on the rectangularized disk for 30×30-element array of Float64</code></pre><p>Its Dunkl-Xu coefficients are:</p><pre><code class="language-julia">U = P\(PA*F)</code></pre><pre><code class="language-none">30×30 Matrix{Float64}:
+  0.886226      2.91482e-18  -6.09829e-7    7.46859e-18  -0.0236857    -1.03089e-18  -0.00550977    1.55635e-18  -0.000650943   5.16951e-19   2.15779e-9   -3.61345e-20   1.86065e-5    1.15602e-18   4.38992e-6    4.86495e-19   4.19398e-7   -2.36331e-18  -1.00953e-7    2.61786e-18  -8.14396e-8    1.00901e-18  -3.94076e-8   -5.05452e-19  -1.67897e-8   -9.68766e-19  -6.33162e-9   -2.79749e-18  -2.11252e-9    8.20668e-19
+ -1.82504e-18  -0.361799     -4.06548e-18  -0.062663     -1.26332e-18   2.72128e-6   -1.4716e-19    0.00252359   -1.53351e-18   0.000679258  -5.06658e-18   9.1001e-5     6.2766e-18    1.03955e-6   -6.44725e-19  -2.31664e-6    4.06045e-18  -3.11859e-7   -1.29757e-18   1.77496e-7   -4.52069e-18   1.44389e-7    4.00752e-18   6.82707e-8   -7.73146e-18   2.5634e-8     3.6454e-18    7.91583e-9   -4.99128e-19   1.6359e-9
+ -5.19659e-7    1.77123e-18   0.105921     -4.37394e-18   0.0404829     3.53441e-19   0.00663284   -7.04472e-19  -5.56102e-6   -1.76702e-19  -0.000301082   9.63513e-21  -8.77391e-5   -2.28415e-19  -1.39615e-5   -6.02861e-20  -1.31088e-6    1.21769e-19  -2.80392e-7    5.33368e-20  -2.38006e-7    9.26254e-20  -1.39444e-7   -8.23221e-20  -5.76521e-8   -2.26363e-19  -1.77475e-8   -8.51099e-19  -3.52357e-9    2.71521e-19
+ -1.32446e-18   0.125331      5.16222e-18   1.52509e-6    1.52224e-18  -0.013651      4.59065e-19  -0.00478429    1.7437e-18   -0.000775222   5.39444e-18   4.86933e-6   -6.32553e-18   4.00219e-5    6.1449e-19    1.28528e-5   -3.66863e-18   2.68143e-6    1.10971e-18   5.35246e-7    3.65472e-18   1.5728e-7    -3.05701e-18   5.72745e-8    5.55166e-18   1.62262e-8   -2.45695e-18   4.075e-10     3.06319e-19  -1.20696e-9
+ -0.0886209     5.87339e-18  -0.0913638     3.09208e-18  -0.0231032    -7.65237e-19   2.55845e-6   -3.00844e-20   0.00173316    8.97087e-22   0.000591205   3.74945e-21   9.51801e-5   -2.71771e-19  -9.67049e-7   -1.57546e-19  -5.17388e-6    9.69671e-19  -1.60228e-6   -1.2848e-18   -2.52759e-7   -5.71811e-19   9.35469e-9    3.22564e-19   2.66735e-8    6.83271e-19   1.62648e-8    1.93725e-18   7.6679e-9    -5.72686e-19
+ -2.97095e-19  -2.79797e-6   -7.50681e-18   0.0328526    -2.04986e-18   0.0160342     4.40714e-19   0.00332497   -1.61538e-18  -8.62281e-6   -4.81324e-18  -0.000228689   5.24108e-18  -7.87989e-5   -4.77978e-19  -1.43006e-5    2.61738e-18  -1.11779e-6   -7.23908e-19   2.57992e-8   -2.15228e-18  -9.03781e-8    1.59592e-18  -8.97012e-8   -2.50435e-18  -4.18139e-8    9.49482e-19  -1.37244e-8   -1.26486e-19  -2.86072e-9
+  0.0632999     3.41915e-18   0.0392743     2.04798e-19   3.65838e-6   -1.28777e-18  -0.00566089   -8.19676e-20  -0.00237159    2.32247e-19  -0.0004495    -2.03756e-20   7.81213e-6    5.90042e-19   3.39614e-5    2.90117e-19   1.24485e-5   -1.55416e-18   2.90796e-6    1.87269e-18   5.68462e-7    7.70684e-19   1.34604e-7   -4.06242e-19   3.66282e-8   -7.1747e-19    6.0499e-9    -2.08524e-18  -9.48683e-10   6.16421e-19
+  3.09716e-18  -0.0381303     6.85278e-18  -0.0305859     1.24178e-18  -0.00858298    1.57978e-18   4.65679e-6    1.48577e-18   0.000859316   3.66318e-18   0.000335164  -3.67668e-18   6.02308e-5    2.74714e-19  -1.60502e-6   -1.31714e-18  -4.61957e-6    2.8105e-19   -1.57519e-6    5.32057e-19  -2.83912e-7   -1.10903e-19   6.48665e-9   -9.75956e-20   2.64839e-8    4.45112e-20   1.29647e-8   -5.92566e-21   3.53416e-9
+ -0.0246173     1.28294e-18  -7.2626e-6    -5.42555e-19   0.0116417    -1.5197e-18    0.00624266   -1.5262e-18    0.00144602   -1.20352e-19  -1.39151e-5    7.19328e-21  -0.000132715  -7.90881e-19  -5.15476e-5   -3.3778e-19   -1.08626e-5    1.76166e-18  -1.14678e-6   -1.99294e-18  -1.60201e-8   -7.73951e-19  -6.95967e-8    3.34098e-19  -5.06628e-8    6.43971e-19  -1.89806e-8    1.87268e-18  -4.88118e-9   -5.53209e-19
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+  1.54054e-5    1.3469e-18    1.00144e-6    1.82904e-19   1.23964e-6   -8.86981e-20   1.21824e-6    5.88101e-20   9.71898e-7   -1.0139e-19    6.32656e-7   -8.23915e-20   3.38215e-7    1.52369e-19   1.49487e-7   -1.10294e-19   5.48103e-8   -2.0251e-19    1.65791e-8    6.6719e-20    4.02426e-9    1.20342e-19   7.09969e-10  -6.40354e-20   4.88112e-11  -5.32019e-20  -2.53943e-11   1.22809e-19  -1.51441e-11   7.69628e-20
+ -1.53496e-18   0.000145153   1.15554e-19   0.000143445  -5.81062e-20   6.55677e-5    2.32816e-19  -1.45469e-5    2.72345e-19  -5.3233e-5     4.51728e-20  -5.18305e-5   -3.6008e-21   -3.33247e-5   -1.62663e-19  -1.60719e-5   -4.71441e-19  -6.0251e-6     7.67245e-20  -1.74358e-6    3.53714e-20  -3.62096e-7    2.92342e-20  -3.58901e-8   -1.45255e-19   9.57958e-9   -1.47136e-20   6.5884e-9     3.52877e-19   1.80042e-9</code></pre><p>The Dunkl-Xu coefficients are useful for integration. The integral of <span>$f(x,y)$</span> over the disk should be <span>$\pi/2$</span> by harmonicity. The coefficient of <span>$P_{0,0}$</span> multiplied by <code>√π</code> is:</p><pre><code class="language-julia">U[1, 1]*sqrt(π)</code></pre><pre><code class="language-none">1.5707955409153043</code></pre><p>Using an orthonormal basis, the integral of <span>$[f(x,y)]^2$</span> over the disk is approximately the square of the 2-norm of the coefficients:</p><pre><code class="language-julia">norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))</code></pre><pre><code class="language-none">(0.978937045726087, 0.9789599179781414)</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../chebyshev/">« Chebyshev transform</a><a class="docs-footer-nextpage" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span> »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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diff --git a/v0.15.15/generated/nonlocaldiffusion/index.html b/v0.15.15/generated/nonlocaldiffusion/index.html
new file mode 100644
index 00000000..1c301811
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+++ b/v0.15.15/generated/nonlocaldiffusion/index.html
@@ -0,0 +1,69 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Nonlocal diffusion on mathbbS^2 · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li class="is-active"><a class="tocitem" href>Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/nonlocaldiffusion.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Nonlocal-diffusion-on-\\mathbb{S}2-1"><a class="docs-heading-anchor" href="#Nonlocal-diffusion-on-\\mathbb{S}2-1">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a><a class="docs-heading-anchor-permalink" href="#Nonlocal-diffusion-on-\\mathbb{S}2-1" title="Permalink"></a></h1><p>This example calculates the spectrum of the nonlocal diffusion operator:</p><div>\[\mathcal{L}_\delta u = \int_{\mathbb{S}^2} \rho_\delta(|\mathbf{x}-\mathbf{y}|)\left[u(\mathbf{x}) - u(\mathbf{y})\right] \,\mathrm{d}\Omega(\mathbf{y}),\]</div><p>defined in Eq. (2) of</p><p>R. M. Slevinsky, H. Montanelli, and Q. Du, <a href="https://doi.org/10.1016/j.jcp.2018.06.024">A spectral method for nonlocal diffusion operators on the sphere</a>, <em>J. Comp. Phys.</em>, <strong>372</strong>:893–911, 2018.</p><p>In the above, <span>$0&lt;\delta&lt;2$</span>, <span>$-1&lt;\alpha&lt;1$</span>, and the kernel:</p><div>\[\rho_\delta(|\mathbf{x}-\mathbf{y}|) = \frac{4(1+\alpha)}{\pi \delta^{2+2\alpha}} \frac{\chi_{[0,\delta]}(|\mathbf{x}-\mathbf{y}|)}{|\mathbf{x}-\mathbf{y}|^{2-2\alpha}},\]</div><p>where <span>$\chi_I(\cdot)$</span> is the indicator function on the set <span>$I$</span>.</p><p>This nonlocal operator is diagonalized by spherical harmonics:</p><div>\[\mathcal{L}_\delta Y_\ell^m(\mathbf{x}) = \lambda_\ell(\alpha, \delta) Y_\ell^m(\mathbf{x}),\]</div><p>and its eigenfunctions are given by the generalized Funk–Hecke formula:</p><div>\[\lambda_\ell(\alpha, \delta) = \frac{(1+\alpha) 2^{2+\alpha}}{\delta^{2+2\alpha}}\int_{1-\delta^2/2}^1 \left[P_\ell(t)-1\right] (1-t)^{\alpha-1} \,\mathrm{d} t.\]</div><p>In the paper, the authors use Clenshaw–Curtis quadrature and asymptotic evaluation of Legendre polynomials to achieve <span>$\mathcal{O}(n^2\log n)$</span> complexity for the evaluation of the first <span>$n$</span> eigenvalues. With a change of basis, this complexity can be reduced to <span>$\mathcal{O}(n\log n)$</span>.</p><p>First, we represent:</p><div>\[P_n(t) - 1 = \sum_{j=0}^{n-1} \left[P_{j+1}(t) - P_j(t)\right] = -\sum_{j=0}^{n-1} (1-t) P_j^{(1,0)}(t).\]</div><p>Then, we represent <span>$P_j^{(1,0)}(t)$</span> with Jacobi polynomials <span>$P_i^{(\alpha,0)}(t)$</span> and we integrate using <a href="https://dlmf.nist.gov/18.9.16">DLMF 18.9.16</a>:</p><div>\[\int_x^1 P_i^{(\alpha,0)}(t)(1-t)^\alpha\,\mathrm{d}t = \left\{ \begin{array}{cc} \frac{(1-x)^{\alpha+1}}{\alpha+1} &amp; \mathrm{for~}i=0,\\ \frac{1}{2i}(1-x)^{\alpha+1}(1+x)P_{i-1}^{(\alpha+1,1)}(x), &amp; \mathrm{for~}i&gt;0.\end{array}\right.\]</div><p>The code below implements this algorithm, making use of the Jacobi–Jacobi transform <code>plan_jac2jac</code>. For numerical stability, the conversion from Jacobi polynomials <span>$P_j^{(1,0)}(t)$</span> to <span>$P_i^{(\alpha,0)}(t)$</span> is divided into conversion from <span>$P_j^{(1,0)}(t)$</span> to <span>$P_k^{(0,0)}(t)$</span>, before conversion from <span>$P_k^{(0,0)}(t)$</span> to <span>$P_i^{(\alpha,0)}(t)$</span>.</p><pre><code class="language-julia">using FastTransforms, LinearAlgebra
+
+function oprec!(n::Integer, v::AbstractVector, alpha::Real, delta2::Real)
+    if n &gt; 0
+        v[1] = 1
+    end
+    if n &gt; 1
+        v[2] = (4*alpha+8-(alpha+4)*delta2)/4
+    end
+    for i = 1:n-2
+        v[i+2] = (((2*i+alpha+2)*(2*i+alpha+4)+alpha*(alpha+2))/(2*(i+1)*(2*i+alpha+2))*(2*i+alpha+3)/(i+alpha+3) - delta2/4*(2*i+alpha+3)/(i+1)*(2*i+alpha+4)/(i+alpha+3))*v[i+1] - (i+alpha+1)/(i+alpha+3)*(2*i+alpha+4)/(2*i+alpha+2)*v[i]
+    end
+    return v
+end
+
+function evaluate_lambda(n::Integer, alpha::T, delta::T) where T
+    delta2 = delta*delta
+    scl = (1+alpha)*(2-delta2/2)
+
+    lambda = Vector{T}(undef, n)
+
+    if n &gt; 0
+        lambda[1] = 0
+    end
+    if n &gt; 1
+        lambda[2] = -2
+    end
+
+    oprec!(n-2, view(lambda, 3:n), alpha, delta2)
+
+    for i = 2:n-1
+        lambda[i+1] *= -scl/(i-1)
+    end
+
+    p = plan_jac2jac(T, n-1, zero(T), zero(T), alpha, zero(T))
+
+    lmul!(p&#39;, view(lambda, 2:n))
+
+    for i = 2:n-1
+        lambda[i+1] = ((2i-1)*lambda[i+1] + (i-1)*lambda[i])/i
+    end
+
+    for i = 2:n-1
+        lambda[i+1] += lambda[i]
+    end
+
+    return lambda
+end</code></pre><pre><code class="language-none">evaluate_lambda (generic function with 1 method)</code></pre><p>The spectrum in <code>Float64</code>:</p><pre><code class="language-julia">lambda = evaluate_lambda(10, -0.5, 1.0)</code></pre><pre><code class="language-none">10-element Vector{Float64}:
+   0.0
+  -2.0
+  -5.5
+  -9.75
+ -14.09375
+ -18.203125
+ -22.08984375
+ -25.935546875
+ -29.8870849609375
+ -33.95416259765625</code></pre><p>The spectrum in <code>BigFloat</code>:</p><pre><code class="language-julia">lambdabf = evaluate_lambda(10, parse(BigFloat, &quot;-0.5&quot;), parse(BigFloat, &quot;1.0&quot;))</code></pre><pre><code class="language-none">10-element Vector{BigFloat}:
+   0.0
+  -2.0
+  -5.5
+  -9.75
+ -14.09375
+ -18.203125
+ -22.08984375
+ -25.935546875
+ -29.8870849609375
+ -33.95416259765625</code></pre><p>The <span>$\infty$</span>-norm relative error:</p><pre><code class="language-julia">norm(lambda-lambdabf, Inf)/norm(lambda, Inf)</code></pre><pre><code class="language-none">0.0</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../disk/">« Holomorphic integration on the unit disk</a><a class="docs-footer-nextpage" href="../padua/">Padua transform »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/generated/padua/index.html b/v0.15.15/generated/padua/index.html
new file mode 100644
index 00000000..e01920f2
--- /dev/null
+++ b/v0.15.15/generated/padua/index.html
@@ -0,0 +1,16 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Padua transform · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li class="is-active"><a class="tocitem" href>Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Padua transform</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Padua transform</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/padua.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Padua-transform-1"><a class="docs-heading-anchor" href="#Padua-transform-1">Padua transform</a><a class="docs-heading-anchor-permalink" href="#Padua-transform-1" title="Permalink"></a></h1><p>This demonstrates the Padua transform and inverse transform, explaining precisely the normalization and points</p><pre><code class="language-julia">using FastTransforms</code></pre><p>We define the Padua points and extract Cartesian components:</p><pre><code class="language-julia">N = 15
+pts = paduapoints(N)
+x = pts[:,1]
+y = pts[:,2];
+nothing #hide</code></pre><p>We take the Padua transform of the function:</p><pre><code class="language-julia">f = (x,y) -&gt; exp(x + cos(y))
+f̌ = paduatransform(f.(x , y));
+nothing #hide</code></pre><p>and use the coefficients to create an approximation to the function <span>$f$</span>:</p><pre><code class="language-julia">f̃ = (x,y) -&gt; begin
+    j = 1
+    ret = 0.0
+    for n in 0:N, k in 0:n
+        ret += f̌[j]*cos((n-k)*acos(x)) * cos(k*acos(y))
+        j += 1
+    end
+    ret
+end</code></pre><pre><code class="language-none">#3 (generic function with 1 method)</code></pre><p>At a particular point, is the function well-approximated?</p><pre><code class="language-julia">f̃(0.1,0.2) ≈ f(0.1,0.2)</code></pre><pre><code class="language-none">true</code></pre><p>Does the inverse transform bring us back to the grid?</p><pre><code class="language-julia">ipaduatransform(f̌) ≈ f̃.(x,y)</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../nonlocaldiffusion/">« Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a><a class="docs-footer-nextpage" href="../sphere/">Spherical harmonic addition theorem »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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@@ -0,0 +1,133 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Spherical harmonic addition theorem · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li class="is-active"><a class="tocitem" href>Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Spherical harmonic addition theorem</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Spherical harmonic addition theorem</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/sphere.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Spherical-harmonic-addition-theorem-1"><a class="docs-heading-anchor" href="#Spherical-harmonic-addition-theorem-1">Spherical harmonic addition theorem</a><a class="docs-heading-anchor-permalink" href="#Spherical-harmonic-addition-theorem-1" title="Permalink"></a></h1><p>This example confirms numerically that</p><div>\[f(z) = \frac{P_n(z\cdot y) - P_n(x\cdot y)}{z\cdot y - x\cdot y},\]</div><p>is actually a degree-<span>$(n-1)$</span> polynomial on <span>$\mathbb{S}^2$</span>, where <span>$P_n$</span> is the degree-<span>$n$</span> Legendre polynomial, and <span>$x,y,z \in \mathbb{S}^2$</span>. To verify, we sample the function on a <span>$N\times M$</span> equiangular grid defined by:</p><div>\[\begin{aligned}
+\theta_n &amp; = (n+\tfrac{1}{2})\pi/N,\quad{\rm for}\quad 0\le n &lt; N,\quad{\rm and}\\
+\varphi_m &amp; = 2\pi m/M,\quad{\rm for}\quad 0\le m &lt; M;
+\end{aligned}\]</div><p>we convert the function samples to Fourier coefficients using <code>plan_sph_analysis</code>; and finally, we transform the Fourier coefficients to spherical harmonic coefficients using <code>plan_sph2fourier</code>.</p><p>In the basis of spherical harmonics, it is plain to see the addition theorem in action, since <span>$P_n(x\cdot y)$</span> should only consist of exact-degree-<span>$n$</span> harmonics.</p><p>For the storage pattern of the arrays, please consult the <a href="https://MikaelSlevinsky.github.io/FastTransforms">documentation</a>.</p><pre><code class="language-julia">function threshold!(A::AbstractArray, ϵ)
+    for i in eachindex(A)
+        if abs(A[i]) &lt; ϵ A[i] = 0 end
+    end
+    A
+end
+
+using FastTransforms, LinearAlgebra, Plots
+const GENFIGS = joinpath(pkgdir(FastTransforms), &quot;docs/src/generated&quot;)
+!isdir(GENFIGS) &amp;&amp; mkdir(GENFIGS)
+plotlyjs()</code></pre><pre><code class="language-none">Plots.PlotlyJSBackend()</code></pre><p>The colatitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">N = 15
+θ = (0.5:N-0.5)/N</code></pre><pre><code class="language-none">0.03333333333333333:0.06666666666666667:0.9666666666666667</code></pre><p>The longitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">M = 2*N-1
+φ = (0:M-1)*2/M</code></pre><pre><code class="language-none">0.0:0.06896551724137931:1.9310344827586206</code></pre><p>Arbitrarily, we place <span>$x$</span> at the North pole:</p><pre><code class="language-julia">x = [0,0,1]</code></pre><pre><code class="language-none">3-element Vector{Int64}:
+ 0
+ 0
+ 1</code></pre><p>Another vector is completely free:</p><pre><code class="language-julia">y = normalize([.123,.456,.789])</code></pre><pre><code class="language-none">3-element Vector{Float64}:
+ 0.13375998748853216
+ 0.4958906853233388
+ 0.8580213831581455</code></pre><p>Thus <span>$z \in \mathbb{S}^2$</span> is our variable vector, parameterized in spherical coordinates:</p><pre><code class="language-julia">z = (θ,φ) -&gt; [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]</code></pre><pre><code class="language-none">#1 (generic function with 1 method)</code></pre><p>On the tensor product grid, the Legendre polynomial <span>$P_n(z\cdot y)$</span> is:</p><pre><code class="language-julia">A = [(2k+1)/(k+1) for k in 0:N-1]
+B = zeros(N)
+C = [k/(k+1) for k in 0:N]
+c = zeros(N); c[N] = 1
+pts = vec([z(θ, φ)⋅y for θ in θ, φ in φ])
+phi0 = ones(N*M)
+F = reshape(FastTransforms.clenshaw!(c, A, B, C, pts, phi0, zeros(N*M)), N, M)</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+  0.264259    0.299171     0.304985    0.288068    0.261038    0.237692     0.228241    0.236528     0.259192    0.286391     0.304437    0.300462     0.26755      0.207601     0.130208    0.0483744   -0.0262845   -0.0865116   -0.129804   -0.156955   -0.169985    -0.170403    -0.158265    -0.132139   -0.0899937  -0.0308858   0.0429655   0.124641    0.202756
+  0.212068    0.303332     0.129215   -0.186607   -0.387155   -0.383993    -0.338172   -0.379747    -0.392602   -0.206438     0.109443    0.299961     0.225231    -0.0101802   -0.207053   -0.258628    -0.187516    -0.070652     0.0323131   0.0988479   0.12977      0.130741     0.102005     0.0380582  -0.0627707  -0.180155   -0.256899   -0.215501   -0.0267606
+ -0.115553    0.236712     0.221776   -0.251073   -0.32857     0.421619     0.986223    0.482429    -0.299585   -0.280602     0.198511    0.253762    -0.0930651   -0.258938    -0.0793421   0.160653     0.233501     0.154045     0.0336174  -0.0560314  -0.0990238   -0.100375    -0.0604041    0.0261339   0.145985    0.231751    0.1719     -0.0610864  -0.255787
+ -0.18454    -0.186901     0.216999    0.207436   -0.278408   -0.36511     -0.189358   -0.35156     -0.304334    0.180746     0.238643   -0.165767    -0.202157     0.128252     0.217098   -0.00943667  -0.200512    -0.194373    -0.0821865   0.0208264   0.0732008    0.0748654    0.0260895   -0.074028   -0.188494   -0.206184   -0.027257    0.20837     0.147067
+  0.233218   -0.0443128   -0.25662     0.0443223   0.302577    0.209245     0.107407    0.198264     0.305263    0.0716125   -0.25045    -0.0709297    0.228915     0.0560634   -0.209167   -0.109098     0.135993     0.209367     0.121014    0.0107106  -0.049922    -0.0518826    0.00472316   0.112882    0.206906    0.148044   -0.0921222  -0.214775    0.0327421
+ -0.14959     0.176398     0.159536   -0.157586   -0.253853   -0.135785    -0.0630475  -0.127292    -0.249419   -0.174706     0.141057    0.191837    -0.130845    -0.171771     0.128955    0.181407    -0.058914    -0.206946    -0.154207   -0.0410986   0.0276329    0.029906    -0.034464    -0.146673   -0.208687   -0.0754426   0.17029     0.145612   -0.156134
+  0.03232    -0.216991    -0.0542418   0.201432    0.206916    0.0892457    0.0316764   0.0822717    0.200041    0.210302    -0.0334057  -0.219505     0.00906962   0.211107    -0.0222883  -0.209099    -0.0231776    0.189332     0.183999    0.0724419  -0.00503206  -0.00766855   0.065182     0.177672    0.19593    -0.0044746  -0.206821   -0.0443208   0.20777
+  0.0772106   0.200813    -0.0345837  -0.214416   -0.166372   -0.0543381   -0.0063074  -0.0483886   -0.158601   -0.217382    -0.0533452   0.193042     0.0976693   -0.187906    -0.085199    0.193101     0.105896    -0.154519    -0.211246   -0.107108   -0.019323    -0.0162213   -0.09921     -0.206977   -0.166608    0.0879047   0.201099   -0.0639311  -0.196895
+ -0.161616   -0.14919      0.105731    0.2116      0.130202    0.0251362   -0.0160611   0.0199531    0.122174    0.210305     0.12046    -0.134582    -0.17451      0.114917     0.174042   -0.130385    -0.182374     0.0957622    0.234753    0.148573    0.0475436    0.0437788    0.140028     0.233975    0.113813   -0.1691     -0.148371    0.159712    0.133414
+  0.208908    0.0728989   -0.161008   -0.198486   -0.0961065   0.00135321   0.037119    0.00590617  -0.0881639  -0.194067    -0.170766    0.0549875    0.211431    -0.00338118  -0.21986     0.016122     0.234375     0.00021735  -0.247537   -0.203094   -0.0836434   -0.0787903   -0.19406     -0.253043   -0.023216    0.231655    0.0407554  -0.218225   -0.0261102
+ -0.203495    0.0220031    0.200371    0.176174    0.0619327  -0.0270702   -0.058089   -0.0310551    0.0543296   0.169516     0.204695    0.0395021   -0.194934    -0.128043     0.183785    0.141369    -0.211961    -0.150004     0.2205      0.283345    0.137864     0.130789     0.275142     0.23809    -0.126501   -0.226893    0.11958     0.198142   -0.109095
+  0.12233    -0.127714    -0.219526   -0.142772   -0.0253159   0.0536809    0.080125    0.0571016   -0.0183211  -0.134724    -0.218347   -0.140698     0.10537      0.230635    -0.0169741  -0.260275     0.00868827   0.306062    -0.0323035  -0.400665   -0.252906    -0.23893     -0.40434     -0.0688019   0.303902    0.0393269  -0.259455   -0.0416906   0.225524
+  0.0533261   0.221676     0.20588     0.0928744  -0.0169863  -0.083121    -0.10464    -0.0859165   -0.0229991   0.0845139    0.199903    0.226054     0.0700661   -0.185075    -0.235303    0.0671548    0.306034     0.0030983   -0.399433   -0.020757    0.815719     0.855083     0.0350084   -0.404293   -0.0323252   0.304047    0.0929697  -0.224541   -0.198835
+ -0.251975   -0.233798    -0.13019    -0.0152352   0.0703864   0.11835      0.133806    0.120358     0.0748091  -0.00825682  -0.122061   -0.22853     -0.255028    -0.136944     0.097903    0.288106     0.247787    -0.0273998   -0.313828   -0.4047     -0.353264    -0.349855    -0.403561    -0.327222   -0.0497156   0.234981    0.294129    0.11465    -0.123547
+  0.0890404   0.00957584  -0.0584588  -0.110278   -0.145276   -0.165114    -0.171728   -0.165964    -0.14708    -0.113177    -0.062519    0.00451035   0.0834519    0.16497      0.23634     0.285407     0.305513     0.298672     0.274919    0.248139    0.230823     0.230209     0.246547     0.273036    0.297446    0.305825    0.287718    0.240496    0.170292</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">X = [sinpi(θ)*cospi(φ) for θ in θ, φ in φ]
+Y = [sinpi(θ)*sinpi(φ) for θ in θ, φ in φ]
+Z = [cospi(θ) for θ in θ, φ in φ]
+scatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)
+surface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;sphere1.html&quot;))</code></pre><object type="text/html" data="../sphere1.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere1.html&quot;</code></pre><p>We show the cut in the surface to help illustrate the definition of the grid. In particular, we do not sample the poles.</p><p>We precompute a spherical harmonic–Fourier plan:</p><pre><code class="language-julia">P = plan_sph2fourier(F)</code></pre><pre><code class="language-none">FastTransforms Spherical harmonic--Fourier plan for 15×29-element array of Float64</code></pre><p>And an FFTW Fourier analysis plan on <span>$\mathbb{S}^2$</span>:</p><pre><code class="language-julia">PA = plan_sph_analysis(F)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Fourier analysis on the sphere for 15×29-element array of Float64</code></pre><p>Its spherical harmonic coefficients demonstrate that it is exact-degree-<span>$n$</span>:</p><pre><code class="language-julia">V = PA*F
+U = threshold!(P\V, 400*eps())</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0         -1.66397e-5  2.73274e-5
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0         -0.000271538  -7.91038e-5   0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         3.29805e-5  -0.00164832   0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.00703526  -0.00174747  0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0122275  0.0220184  0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0        -0.0503776  0.0488881  0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0       -0.134224  -0.0799001   0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0729185  -0.259962   0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.337609  0.00337719  0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0610941  0.235853  0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0289877  -0.0164793  0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0         0.0        0.0       0.190197  0.192109  0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.0       0.0        -0.0788841  0.135585  0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.0       0.188313  0.0507949   0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0
+ 0.142187  0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0</code></pre><p>The <span>$L^2(\mathbb{S}^2)$</span> norm of the function is:</p><pre><code class="language-julia">nrm1 = norm(U)</code></pre><pre><code class="language-none">0.6582728344942355</code></pre><p>Similarly, on the tensor product grid, our function samples are:</p><pre><code class="language-julia">Pnxy = FastTransforms.clenshaw!(c, A, B, C, [x⋅y], [1.0], [0.0])[1]
+F = [(F[n, m] - Pnxy)/(z(θ[n], φ[m])⋅y - x⋅y) for n in 1:N, m in 1:M]</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+  5.19948      4.13834      2.99067      1.90658      1.02691     0.455272    0.249877    0.429314    0.977414    1.83893      2.91328     4.06148      5.13287      6.0026       6.60156      6.92544     7.02254     6.96965     6.84793     6.72603     6.65164      6.64905     6.71906     6.83899     6.96269     7.02276     6.93845     6.63197     6.05227
+  5.95491      2.78879     -1.44975     -4.81316     -5.93907    -5.32122    -4.74802    -5.26014    -5.93537    -4.96628     -1.72861     2.51536      5.80241      7.01649      6.35996      4.76275     3.10172     1.83264     1.03553     0.610092    0.43191      0.426508    0.591355    0.996377    1.76414     3.00054     4.64424     6.26964     7.0226
+  6.89687      5.65236      0.11585     -5.28724     -4.64181     1.51819     5.42995     1.95544    -4.33608    -5.4796      -0.331651    5.39124      6.95616      4.78949      1.90996      0.265776   -0.0679633   0.206459    0.546026    0.760489    0.851318     0.854026    0.770114    0.565133    0.231314   -0.0604333   0.208258    1.74968     4.58324
+  3.06027      6.5357       5.89997     -0.165743    -5.46592    -5.06636    -3.28816    -4.90175    -5.62054    -0.644121     5.6253      6.677        3.31846      0.440384    -0.00401181   0.652985    1.01303     0.876591    0.580633    0.35795     0.254199     0.250991    0.347269    0.561893    0.857659    1.01648     0.69514     0.0273999   0.337402
+ -0.070137     1.60923      5.43093      6.93528      3.91137    -0.131309   -1.75656    -0.336142    3.61343     6.85843      5.66343     1.83509     -0.053904     0.487406     1.01741      0.644213    0.136921    0.0101545   0.134135    0.275013    0.346961     0.349218    0.282296    0.144972    0.0138328   0.115298    0.603776    1.01615     0.548272
+  0.945078     0.135483     0.27158      2.71505      5.55048     6.82449     7.00499     6.85725     5.69314     2.92844      0.369819    0.0844295    0.912316     0.807551     0.149683     0.0509116   0.357273    0.499174    0.407141    0.269902    0.193177     0.1907      0.262329    0.397299    0.498435    0.37596     0.0666419   0.119637    0.764012
+  0.3347       0.96741      0.756526     0.0516758    0.0403323   0.667862    1.0399      0.710559    0.0718486   0.0205398    0.70939     0.987443     0.382027     0.0075432    0.314675     0.493074    0.249535    0.0255986   0.0288774   0.124344    0.187529     0.189637    0.130366    0.0344678   0.0191719   0.228563    0.486554    0.340488    0.0125441
+  0.19163      0.0244645    0.474228     0.953439     0.971777    0.756739    0.645454    0.743468    0.95977     0.969839     0.515354    0.0373859    0.165042     0.488731     0.32132      0.0219213   0.0963195   0.301654    0.329627    0.240493    0.171995     0.169627    0.234193    0.325354    0.310183    0.111448    0.0141702   0.296273    0.495085
+  0.41699      0.454012     0.154439     0.00689009   0.147415    0.349199    0.434542    0.359728    0.162073    0.00898106   0.134876    0.43942      0.434649     0.100528     0.0376636    0.284172    0.302882    0.085971   -0.0128005   0.0446154   0.109712     0.112106    0.0501911  -0.0122374   0.0727995   0.291434    0.297253    0.0501979   0.0815347
+  0.00653828   0.144506     0.416175     0.496049     0.398793    0.286378    0.242449    0.28086     0.390091    0.493228     0.429442    0.163601     0.00423886   0.186207     0.340647     0.145106   -0.0125214   0.139641    0.288402    0.253913    0.179097     0.176118    0.248108    0.291182    0.154331   -0.0106262   0.126633    0.337571    0.204303
+  0.334489     0.165749     0.014265     0.0385386    0.156172    0.253936    0.289478    0.258454    0.164306    0.0451436    0.010362    0.151498     0.32921      0.257363     0.0225829    0.0493168   0.268651    0.220231   -0.0026208  -0.0383697   0.0440181    0.047986   -0.0336588  -0.0128432   0.205569    0.277144    0.0634765   0.012466    0.242082
+  0.0666146    0.257095     0.341563     0.293211     0.203674    0.139862    0.117949    0.137043    0.198126    0.287354     0.341672    0.267702     0.0789497   -0.00992474   0.150427     0.293905    0.12293    -0.051658    0.138809    0.33873     0.255252     0.247571    0.340446    0.15898    -0.0503184   0.104503    0.292551    0.165851   -0.00643622
+  0.106032    -0.00382806   0.00704658   0.088086     0.17021     0.221457    0.238521    0.223661    0.174806    0.0942214    0.0112304  -0.00679647   0.0953468    0.252997     0.275056     0.0878466  -0.0516354   0.119191    0.338121    0.128404   -0.323093    -0.344224    0.0980961   0.340427    0.138821   -0.0504052   0.0724608   0.267888    0.261055
+  0.286625     0.280994     0.220196     0.149338     0.0951419   0.0642734   0.0542416   0.0629728   0.0923113   0.144964     0.215269    0.278062     0.288893     0.21207      0.0695276   -0.0416382  -0.0180382   0.136094    0.292814    0.340282    0.310784     0.308881    0.339519    0.300016    0.148439   -0.0107592  -0.0450601   0.0595874   0.203734
+  0.0747987    0.122395     0.163672     0.195512     0.217272    0.229726    0.233902    0.230262    0.2184      0.197306     0.166153    0.125451     0.0781262    0.0298766   -0.0118277   -0.0400996  -0.0514099  -0.0472393  -0.0335309  -0.0182388  -0.00839924  -0.0080514  -0.0173325  -0.0324517  -0.0465243  -0.0515701  -0.0414172  -0.0142377   0.0267486</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">scatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)
+surface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;sphere2.html&quot;))</code></pre><object type="text/html" data="../sphere2.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere2.html&quot;</code></pre><p>Its spherical harmonic coefficients demonstrate that it is degree-<span>$(n-1)$</span>:</p><pre><code class="language-julia">V = PA*F
+U = threshold!(P\V, 400*eps())</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+  2.07907     0.87453     0.235893    0.069594   -0.119618    0.0581001   0.0586842   0.0859934  -0.0488866  -0.015775   -0.060899   -0.0291623  -0.000291717  -0.00253358   0.00903247   0.000694039   0.000413142  -0.00117608  0.0011413   0.000780662  0.00140576  0.000942806  -0.000234181  8.63587e-6  -0.00043161  -0.000121732  -3.54626e-5  0.0  0.0
+  1.51317     0.44642     0.120416   -0.169934    0.292081    0.328839    0.332145    0.288911   -0.164244   -0.0423205  -0.163378   -0.0586349  -0.000586539  -0.00145765   0.00519666  -0.00998075   -0.00594126   -0.00862106  0.00836616  0.00369554   0.00665466  0.00342882   -0.000851678  2.16057e-5  -0.00107982   0.0           0.0         0.0  0.0
+  0.36606    -0.627659   -0.169303   -0.592046    1.0176      0.703541    0.710614    0.503834   -0.286426   -0.056082   -0.216504   -0.0224552  -0.000224625   0.0140577   -0.0501173   -0.0493515    -0.0293776    -0.0276576   0.0268398   0.00914327   0.0164645   0.00585456   -0.0014542    0.0          0.0          0.0           0.0         0.0  0.0
+ -0.225238   -1.3923     -0.375555   -0.884141    1.51965     0.893241    0.902221    0.498016   -0.283118   -0.0162747  -0.0628284   0.165928    0.00165982    0.0536982   -0.191439    -0.123087     -0.0732701    -0.0534663   0.0518855   0.0122482    0.0220556   0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.0279478  -1.24976    -0.337105   -0.80053     1.37594     0.669715    0.676448    0.113165   -0.0643333   0.096013    0.370657    0.512707    0.00512874    0.109365    -0.389897    -0.195697     -0.116493     -0.0592355   0.0574841   0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.642706   -0.460978   -0.124343   -0.408306    0.701792    0.115506    0.116667   -0.53107     0.30191     0.2422      0.935011    0.866631    0.00866913    0.145962    -0.520371    -0.183527     -0.109249      0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.924445    0.171516    0.0462641  -0.0394459   0.0677993  -0.395183   -0.399156   -1.05835     0.601662    0.335991    1.29709     0.970497    0.00970813    0.116526    -0.415426     0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.619857    0.0934262   0.0252005   0.0128822  -0.0221418  -0.505099   -0.510177   -1.1197      0.636541    0.30573     1.18027     0.65018     0.00650392    0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.0816312  -0.512221   -0.138165   -0.239451    0.411566   -0.194804   -0.196763   -0.706203    0.401471    0.16128     0.622619    0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+ -0.15003    -0.975789   -0.263206   -0.507765    0.872741    0.197111    0.199092   -0.186337    0.105931    0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.105958   -0.834521   -0.225101   -0.515565    0.886148    0.287159    0.290046    0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.530802   -0.266039   -0.0717606  -0.261012    0.448626    0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.668154    0.140073    0.0377829   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.390394    0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0
+  0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0</code></pre><p>Finally, the Legendre polynomial <span>$P_n(z\cdot x)$</span> is aligned with the grid:</p><pre><code class="language-julia">pts = vec([z(θ, φ)⋅x for θ in θ, φ in φ])
+F = reshape(FastTransforms.clenshaw!(c, A, B, C, pts, phi0, zeros(N*M)), N, M)</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+  0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808
+ -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968
+  0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489
+ -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835
+  0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901
+ -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532
+  0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677
+ -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473
+  0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677
+ -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532
+  0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901
+ -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835
+  0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489
+ -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968
+  0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">scatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)
+surface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;sphere3.html&quot;))</code></pre><object type="text/html" data="../sphere3.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere3.html&quot;</code></pre><p>It only has one nonnegligible spherical harmonic coefficient. Can you spot it?</p><pre><code class="language-julia">V = PA*F
+U = threshold!(P\V, 400*eps())</code></pre><pre><code class="language-none">15×29 Matrix{Float64}:
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0
+ 0.658273  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0</code></pre><p>That nonnegligible coefficient should be</p><pre><code class="language-julia">ret = eval(&quot;√(2π/($(N-1)+1/2))&quot;)</code></pre><pre><code class="language-none">&quot;√(2π/(14+1/2))&quot;</code></pre><p>which is approximately</p><pre><code class="language-julia">eval(Meta.parse(ret))</code></pre><pre><code class="language-none">0.6582728344942353</code></pre><p>since the convention in this library is to orthonormalize.</p><pre><code class="language-julia">nrm2 = norm(U)</code></pre><pre><code class="language-none">0.6582728344942352</code></pre><p>Note that the integrals of both functions <span>$P_n(z\cdot y)$</span> and <span>$P_n(z\cdot x)$</span> and their <span>$L^2(\mathbb{S}^2)$</span> norms are the same because of rotational invariance. The integral of either is perhaps not interesting as it is mathematically zero, but the norms of either should be approximately the same.</p><pre><code class="language-julia">nrm1 ≈ nrm2</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../padua/">« Padua transform</a><a class="docs-footer-nextpage" href="../spinweighted/">Spin-weighted spherical harmonics »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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diff --git a/v0.15.15/generated/spinweighted/index.html b/v0.15.15/generated/spinweighted/index.html
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@@ -0,0 +1,56 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Spin-weighted spherical harmonics · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li class="is-active"><a class="tocitem" href>Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Spin-weighted spherical harmonics</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Spin-weighted spherical harmonics</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/spinweighted.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Spin-weighted-spherical-harmonics-1"><a class="docs-heading-anchor" href="#Spin-weighted-spherical-harmonics-1">Spin-weighted spherical harmonics</a><a class="docs-heading-anchor-permalink" href="#Spin-weighted-spherical-harmonics-1" title="Permalink"></a></h1><p>This example plays with analysis of:</p><div>\[f(r) = e^{{\rm i} k\cdot r},\]</div><p>for some <span>$k\in\mathbb{R}^3$</span> and where <span>$r\in\mathbb{S}^2$</span>, using spin-<span>$0$</span> spherical harmonics.</p><p>It applies ð, the spin-raising operator, both on the spin-<span>$0$</span> coefficients as well as the original function, followed by a spin-<span>$1$</span> analysis to compare coefficients.</p><p>For the storage pattern of the arrays, please consult the <a href="https://MikaelSlevinsky.github.io/FastTransforms">documentation</a>.</p><pre><code class="language-julia">using FastTransforms, LinearAlgebra</code></pre><p>The colatitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">N = 10
+θ = (0.5:N-0.5)/N</code></pre><pre><code class="language-none">0.05:0.1:0.95</code></pre><p>The longitudinal grid (mod <span>$\pi$</span>):</p><pre><code class="language-julia">M = 2*N-1
+φ = (0:M-1)*2/M</code></pre><pre><code class="language-none">0.0:0.10526315789473684:1.894736842105263</code></pre><p>Our choice of <span>$k$</span> and angular parametrization of <span>$r$</span>:</p><pre><code class="language-julia">k = [2/7, 3/7, 6/7]
+r = (θ,φ) -&gt; [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]</code></pre><pre><code class="language-none">#1 (generic function with 1 method)</code></pre><p>On the tensor product grid, our function samples are:</p><pre><code class="language-julia">F = [exp(im*(k⋅r(θ,φ))) for θ in θ, φ in φ]</code></pre><pre><code class="language-none">10×19 Matrix{ComplexF64}:
+ 0.628413+0.77788im   0.613246+0.789892im   0.603399+0.79744im    0.600106+0.79992im    0.603786+0.797146im   0.613972+0.789328im   0.629387+0.777092im   0.64815+0.761513im   0.668065+0.744103im   0.686931+0.726723im  0.702801+0.711386im    0.71416+0.699982im   0.720001+0.693973im    0.71983+0.694151im  0.713662+0.700491im   0.702017+0.71216im    0.685934+0.727664im  0.666955+0.745098im   0.647044+0.762452im
+ 0.626742+0.779227im  0.582025+0.813171im   0.552374+0.833596im   0.542362+0.840145im    0.55355+0.832816im   0.584193+0.811615im   0.629571+0.776943im   0.68294+0.730474im   0.736952+0.675945im   0.785185+0.619262im  0.823211+0.567736im   0.848825+0.528674im   0.861428+0.507879im   0.861065+0.508495im   0.84773+0.530428im   0.821392+0.570364im   0.782715+0.62238im   0.734019+0.679129im   0.679858+0.733344im
+ 0.690857+0.722991im  0.625071+0.780568im   0.580335+0.814378im   0.565059+0.82505im    0.582122+0.813101im   0.628309+0.777964im   0.694941+0.719066im  0.769832+0.638246im   0.840471+0.541857im   0.897514+0.440985im  0.936972+0.349406im   0.959893+0.280368im   0.969821+0.243819im   0.969549+0.244899im  0.958985+0.283457im   0.935221+0.354065im   0.894765+0.446538im  0.836798+0.547511im    0.76563+0.643282im
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+  0.99096-0.134156im  0.999703-0.0243628im  0.998928+0.0462861im  0.997566+0.0697274im  0.999053+0.0435207im  0.999562-0.0295972im  0.989978-0.141225im  0.960887-0.276941im   0.908431-0.418034im   0.837893-0.545834im  0.762849-0.646576im   0.700449-0.713703im   0.665602-0.746307im   0.666649-0.745372im  0.703339-0.710855im    0.76689-0.641779im   0.842129-0.539276im   0.91195-0.410301im   0.963143-0.26899im
+ 0.919472-0.393156im  0.950297-0.311346im   0.966254-0.257589im   0.970887-0.23954im    0.965686-0.259711im   0.948995-0.315292im    0.91723-0.398357im  0.867837-0.49685im    0.802371-0.596825im   0.727938-0.685643im  0.656033-0.754733im   0.599431-0.800426im   0.568692-0.82255im    0.569608-0.821916im  0.602006-0.798492im   0.659781-0.751458im   0.732172-0.68112im   0.806377-0.591401im   0.871077-0.491147im
+  0.80566-0.592379im  0.837633-0.546233im   0.856754-0.515725im   0.862863-0.505438im   0.856026-0.516933im   0.836173-0.548466im     0.8035-0.595305im  0.759389-0.650637im   0.707251-0.706962im   0.652712-0.757606im  0.602883-0.79783im    0.564968-0.825113im   0.544739-0.838606im   0.545338-0.838216im  0.566673-0.823943im   0.605429-0.795899im   0.655721-0.755004im  0.710305-0.703894im   0.762122-0.647434im
+ 0.695346-0.718675im   0.70912-0.705088im   0.717813-0.696236im   0.720677-0.693271im   0.717475-0.696585im   0.708471-0.70574im    0.694445-0.719545im  0.676692-0.736266im   0.656981-0.753907im   0.637428-0.77051im   0.620269-0.784389im   0.607563-0.794272im   0.600886-0.799335im   0.601083-0.799186im  0.608129-0.793839im   0.621132-0.783706im   0.638483-0.769636im  0.658105-0.752927im    0.67776-0.735284im</code></pre><p>We precompute a spin-<span>$0$</span> spherical harmonic–Fourier plan:</p><pre><code class="language-julia">P = plan_spinsph2fourier(F, 0)</code></pre><pre><code class="language-none">FastTransforms Spin-weighted spherical harmonic--Fourier plan for 10×19-element array of ComplexF64</code></pre><p>And an FFTW Fourier analysis plan on <span>$\mathbb{S}^2$</span>:</p><pre><code class="language-julia">PA = plan_spinsph_analysis(F, 0)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Fourier analysis on the sphere (spin-weighted) for 10×19-element array of ComplexF64</code></pre><p>Its spin-<span>$0$</span> spherical harmonic coefficients are:</p><pre><code class="language-julia">U⁰ = P\(PA*F)</code></pre><pre><code class="language-none">10×19 Matrix{ComplexF64}:
+      2.98294-8.51991e-17im     -0.560381+0.373587im        0.560381+0.373587im        0.0307268-0.0737442im       0.0307268+0.0737442im      0.00123905+0.0063329im     -0.00123905+0.0063329im    -0.000278656-0.000280997im  -0.000278656+0.000280997im    1.91763e-5+3.91877e-6im    -1.91763e-5+3.91877e-6im    -7.51512e-7+3.05775e-7im    -7.51512e-7-3.05775e-7im     1.62607e-8-2.39542e-8im    -1.62607e-8-2.39542e-8im   -7.57573e-12+9.06989e-10im   -7.6043e-12-9.06983e-10im  -1.32856e-11-2.14392e-11im   1.44574e-11-2.09394e-11im
+ -9.83939e-17+1.585im           -0.147488-0.221233im       -0.147488+0.221233im        0.0242802+0.0101168im      -0.0242802+0.0101168im       -0.001828+0.000357651im     -0.001828-0.000357651im    7.31346e-5-7.25251e-5im    -7.31346e-5-7.25251e-5im    -9.36425e-7+4.58234e-6im    -9.36425e-7-4.58234e-6im    -6.79393e-8-1.66977e-7im     6.79393e-8-1.66977e-7im     4.99533e-9+3.39094e-9im     4.99533e-9-3.39094e-9im   -1.78808e-10-1.49391e-12im   1.78807e-10-1.49874e-12im   3.97537e-12-2.47069e-12im   3.88749e-12+2.67669e-12im
+    -0.296042+1.9373e-16im      0.0419095-0.0279397im     -0.0419095-0.0279397im     -0.00179667+0.00431201im    -0.00179667-0.00431201im    -5.92556e-5-0.000302862im    5.92556e-5-0.000302862im    1.12623e-5+1.13569e-5im     1.12623e-5-1.13569e-5im    -6.70874e-7-1.37097e-7im     6.70874e-7-1.37097e-7im     2.31726e-8-9.42846e-9im     2.31726e-8+9.42846e-9im   -4.48157e-10+6.60198e-10im   4.48157e-10+6.60199e-10im   1.83282e-13-2.21049e-11im   1.86684e-13+2.21043e-11im   2.77137e-13+4.85399e-13im  -3.40625e-13+4.58308e-13im
+  7.69323e-17-0.0243812im      0.00315419+0.00473128im    0.00315419-0.00473128im   -0.000498246-0.000207603im   0.000498246-0.000207603im    3.42215e-5-6.6955e-6im      3.42215e-5+6.6955e-6im     -1.23971e-6+1.22938e-6im     1.23971e-6+1.22938e-6im     1.44141e-8-7.05344e-8im     1.44141e-8+7.05344e-8im    9.54963e-10+2.34704e-9im   -9.54963e-10+2.34704e-9im   -6.22737e-11-4.22728e-11im  -6.22738e-11+4.22728e-11im   2.09765e-12+1.71251e-14im  -2.09747e-12+1.79765e-14im  -5.56453e-13+3.38942e-13im  -5.39576e-13-3.78598e-13im
+ -0.000199834-6.42779e-17im  -0.000327232+0.000218154im  0.000327232+0.000218154im    1.67027e-5-4.00864e-5im     1.67027e-5+4.00864e-5im      5.5389e-7+2.83099e-6im     -5.5389e-7+2.83099e-6im    -1.01124e-7-1.01974e-7im    -1.01124e-7+1.01974e-7im     5.69484e-9+1.16377e-9im    -5.69484e-9+1.16377e-9im   -1.69612e-10+6.90117e-11im  -1.69612e-10-6.90117e-11im   2.98198e-12-4.39287e-12im    -2.982e-12-4.39288e-12im   -3.4901e-14+4.21981e-12im   -3.5709e-14-4.21967e-12im  -4.58998e-14-8.03356e-14im   5.63705e-14-7.58511e-14im
+ -6.51867e-17-0.000282488im    -7.0029e-6-1.05044e-5im    -7.0029e-6+1.05044e-5im     2.24809e-6+9.36704e-7im    -2.24809e-6+9.36704e-7im    -1.76539e-7+3.45402e-8im    -1.76539e-7-3.45402e-8im     6.55393e-9-6.49931e-9im    -6.55393e-9-6.49931e-9im    -7.1368e-11+3.49235e-10im   -7.1368e-11-3.49235e-10im  -4.99716e-12-1.22817e-11im   4.99717e-12-1.22817e-11im   1.69023e-11+1.14737e-11im   1.69023e-11-1.14737e-11im  -5.44912e-13-4.42073e-15im   5.44856e-13-4.70254e-15im   1.57991e-13-9.50528e-14im   1.52387e-13+1.08145e-13im
+   3.58969e-5-4.03624e-17im    -4.7402e-7+3.16014e-7im     4.7402e-7+3.16014e-7im    -3.23608e-8+7.76658e-8im    -3.23608e-8-7.76658e-8im     -1.6111e-9-8.2345e-9im       1.6111e-9-8.2345e-9im     2.28327e-10+2.30246e-10im   2.28327e-10-2.30246e-10im  -1.02557e-11-2.09578e-12im   1.02557e-11-2.09575e-12im   4.54949e-11-1.8511e-11im    4.54949e-11+1.85109e-11im  -5.65264e-13+8.32697e-13im   5.65261e-13+8.32682e-13im   9.40036e-15-1.14115e-12im   9.64888e-15+1.14112e-12im   8.75729e-15+1.53541e-14im  -1.07798e-14+1.45105e-14im
+  1.02759e-16+2.64492e-6im    -5.98533e-8-8.978e-8im     -5.98533e-8+8.978e-8im      -2.2753e-10-9.48042e-11im    2.2753e-10-9.48042e-11im   2.65455e-10-5.19369e-11im   2.65455e-10+5.19368e-11im  -1.37076e-11+1.35933e-11im   1.37076e-11+1.35933e-11im   3.35969e-11-1.64405e-10im   3.35969e-11+1.64405e-10im   1.96453e-12+4.82831e-12im  -1.96456e-12+4.8283e-12im   -8.01172e-12-5.43855e-12im  -8.01172e-12+5.43851e-12im    2.1536e-13+1.72771e-15im  -2.15343e-13+1.85925e-15im  -7.69585e-14+4.5967e-14im   -7.40005e-14-5.28702e-14im
+  -1.25204e-7-1.00025e-16im    6.65757e-9-4.43838e-9im   -6.65757e-9-4.43838e-9im   -1.43603e-11+3.44646e-11im  -1.43603e-11-3.44646e-11im   5.78451e-14+2.95763e-13im  -5.78679e-14+2.95759e-13im  -3.63314e-11-3.66368e-11im  -3.63314e-11+3.66367e-11im   7.38143e-13+1.5085e-13im   -7.38141e-13+1.50867e-13im  -7.24159e-12+2.94646e-12im   -7.2416e-12-2.94643e-12im   4.07078e-14-5.99547e-14im  -4.06954e-14-5.99559e-14im  -1.50544e-15+1.81789e-13im  -1.53538e-15-1.81804e-13im  -6.14456e-16-1.09039e-15im   7.91436e-16-1.0443e-15im
+ -1.37837e-16-3.0609e-9im     4.29751e-10+6.44627e-10im  4.29751e-10-6.44627e-10im  -5.01384e-12-2.08911e-12im   5.01382e-12-2.08911e-12im  -3.61552e-10+7.07385e-11im  -3.61552e-10-7.07385e-11im   2.83376e-12-2.81014e-12im  -2.83376e-12-2.81015e-12im  -4.57901e-11+2.24071e-10im  -4.57901e-11-2.24071e-10im  -4.06243e-13-9.98407e-13im   4.06234e-13-9.98416e-13im   1.09292e-11+7.419e-12im     1.09292e-11-7.41901e-12im  -4.45672e-14-3.63419e-16im    4.4548e-14-3.98703e-16im   1.05377e-13-6.28734e-14im   1.01301e-13+7.23958e-14im</code></pre><p>We can check its <span>$L^2(\mathbb{S}^2)$</span> norm against an exact result:</p><pre><code class="language-julia">norm(U⁰) ≈ sqrt(4π)</code></pre><pre><code class="language-none">true</code></pre><p>Spin can be incremented by applying ð, either on the spin-<span>$0$</span> coefficients:</p><pre><code class="language-julia">U¹c = zero(U⁰)
+for n in 1:N-1
+    U¹c[n, 1] = sqrt(n*(n+1))*U⁰[n+1, 1]
+end
+for m in 1:M÷2
+    for n in 0:N-1
+        U¹c[n+1, 2m] = -sqrt((n+m)*(n+m+1))*U⁰[n+1, 2m]
+        U¹c[n+1, 2m+1] = sqrt((n+m)*(n+m+1))*U⁰[n+1, 2m+1]
+    end
+end</code></pre><p>or on the original function through analysis with spin-<span>$1$</span> spherical harmonics:</p><pre><code class="language-julia">F = [-(k[1]*(im*cospi(θ)*cospi(φ) + sinpi(φ)) + k[2]*(im*cospi(θ)*sinpi(φ)-cospi(φ)) - im*k[3]*sinpi(θ))*exp(im*(k⋅r(θ,φ))) for θ in θ, φ in φ]</code></pre><pre><code class="language-none">10×19 Matrix{ComplexF64}:
+   0.384531+0.240303im     0.405167+0.0811656im   0.376168-0.08059im    0.296802-0.228644im      0.17173-0.345547im    0.0121942-0.415058im     -0.164084-0.425345im    -0.334877-0.37218im      -0.47719-0.260862im    -0.571781-0.105926im  -0.607006+0.0715576im   -0.58067+0.248234im      -0.499453+0.402825im     -0.376425+0.519276im   -0.227802+0.588046im  -0.0700889+0.605739im   0.0817378+0.573795im    0.214909+0.497059im   0.318781+0.382786im
+    0.16375+0.41829im      0.162116+0.268361im    0.128477+0.110061im   0.056034-0.0418675im  -0.0588234-0.167146im    -0.211042-0.242529im     -0.383203-0.247832im    -0.546769-0.173942im    -0.669506-0.0288607im   -0.726395+0.162453im  -0.708448+0.365492im   -0.624684+0.547246im      -0.496849+0.685091im     -0.350631+0.769743im   -0.208037+0.802572im  -0.0835191+0.79034im     0.016198+0.740573im   0.0899356+0.659195im    0.13893+0.55045im
+ 0.00394925+0.589002im   -0.0517508+0.441892im   -0.117739+0.283703im  -0.202276+0.132736im    -0.313608+0.0132761im   -0.450683-0.0475101im    -0.596088-0.0271995im   -0.717144+0.0808626im   -0.777618+0.259594im    -0.754769+0.470906im  -0.650847+0.67007im    -0.491452+0.823236im      -0.313141+0.917212im     -0.149502+0.957306im  -0.0230169+0.957535im   0.0563716+0.930505im   0.0891711+0.881918im    0.083394+0.810775im  0.0511118+0.713512im
+  -0.037706+0.764342im    -0.167663+0.63523im    -0.287398+0.487323im  -0.400578+0.346904im    -0.514827+0.244114im     -0.62967+0.207393im     -0.727882+0.254883im    -0.777945+0.383583im    -0.749353+0.563975im    -0.631836+0.748617im  -0.444017+0.892859im   -0.224888+0.974245im     -0.0160482+0.997806im      0.151723+0.986424im    0.261377+0.965157im    0.306018+0.948535im    0.286044+0.935214im    0.209798+0.910832im  0.0944472+0.857391im
+  0.0677134+0.90671im     -0.132933+0.832114im    -0.31272+0.722356im  -0.463011+0.610267im    -0.584223+0.531084im     -0.67363+0.512373im     -0.717075+0.564833im    -0.692616+0.674959im    -0.585463+0.805978im    -0.402896+0.912201im  -0.175697+0.960918im   0.0558086+0.947262im       0.258917+0.892857im      0.415705+0.832204im    0.518079+0.796763im    0.559103+0.802847im    0.530434+0.845158im    0.428907+0.898149im   0.265719+0.927327im
+   0.292353+0.944771im    0.0581069+0.961031im   -0.162367+0.923101im  -0.343726+0.861107im    -0.474077+0.809852im    -0.546787+0.794409im     -0.553921+0.82068im      -0.48849+0.87246im     -0.353637+0.917742im    -0.169005+0.924095im  0.0340849+0.875449im    0.226308+0.779766im       0.391603+0.66433im       0.527207+0.564551im    0.633493+0.513im       0.702424+0.529934im    0.714639+0.614543im    0.649544+0.740756im   0.502126+0.864782im
+   0.544556+0.82786im      0.335621+0.941682im     0.11692+0.992061im  -0.074329+0.994789im    -0.214433+0.975768im    -0.291963+0.955971im     -0.303796+0.942141im    -0.254076+0.925583im    -0.155653+0.88869im    -0.0290943+0.815954im    0.10377+0.703491im    0.228799+0.562131im       0.344287+0.414327im      0.457269+0.288908im    0.572819+0.215991im    0.682616+0.220188im    0.761104+0.310327im    0.774782+0.470071im   0.701202+0.658896im
+   0.711777+0.57455im      0.575876+0.753741im    0.402359+0.877629im   0.227778+0.943189im    0.0807159+0.961489im   -0.0227441+0.946886im     -0.078234+0.908848im   -0.0903981+0.849391im   -0.0697694+0.765587im   -0.0288206+0.65453im   0.0229208+0.517715im   0.0830404+0.363193im       0.157068+0.205921im      0.254332+0.067373im    0.379593-0.026087im    0.524118-0.0484074im   0.662039+0.0163403im    0.75688+0.163406im   0.777104+0.364037im
+   0.726602+0.264733im     0.673634+0.460754im    0.564658+0.62254im     0.42451+0.734172im     0.277783+0.792276im     0.142935+0.801596im     0.0303916+0.769731im   -0.0562551+0.703542im    -0.117442+0.608011im    -0.154422+0.487008im  -0.166521+0.34507im    -0.149734+0.189474im     -0.0974708+0.0321493im  -0.00385489-0.109276im    0.131046-0.212499im    0.296212-0.254862im    0.468111-0.220723im    0.615102-0.109082im   0.707182+0.0630756im
+   0.597178-0.0185423im    0.601301+0.161421im    0.546217+0.32944im    0.442188+0.46657im      0.304261+0.559965im     0.149097+0.603283im   -0.00741158+0.595734im    -0.151367+0.540622im    -0.271099+0.44408im     -0.356905+0.314404im  -0.400841+0.161998im   -0.397025-0.000359286im   -0.342634-0.157415im     -0.239438-0.292068im  -0.0953011-0.38711im    0.0751723-0.428079im    0.251638-0.406595im    0.410936-0.323077im    0.53139-0.187637im</code></pre><p>We change plans with spin-<span>$1$</span> now and reanalyze:</p><pre><code class="language-julia">P = plan_spinsph2fourier(F, 1)
+PA = plan_spinsph_analysis(F, 1)
+U¹s = P\(PA*F)</code></pre><pre><code class="language-none">10×19 Matrix{ComplexF64}:
+  1.03146e-17+2.24152im          0.792499-0.528332im        0.792499+0.528332im       -0.0752649+0.180636im       0.0752649+0.180636im     -0.00429218-0.0219378im     -0.00429218+0.0219378im      0.00124619+0.00125666im    -0.00124619+0.00125666im   -0.000105033-2.1464e-5im    -0.000105033+2.1464e-5im      4.87035e-6-1.98165e-6im    -4.87035e-6-1.98165e-6im    -1.21684e-7+1.79257e-7im    -1.21684e-7-1.79257e-7im     6.4556e-11-7.69602e-9im   -6.42651e-11-7.6961e-9im      1.3734e-10+1.99137e-10im   1.25853e-10-2.02909e-10im
+    -0.725151+1.27345e-16im      0.361271+0.541907im       -0.361271+0.541907im       -0.0841092-0.0350455im     -0.0841092+0.0350455im     0.00817504-0.00159947im    -0.00817504-0.00159947im   -0.000400574+0.000397236im  -0.000400574-0.000397236im    6.06873e-6-2.9697e-5im     -6.06873e-6-2.9697e-5im      5.08411e-7+1.24954e-6im     5.08411e-7-1.24954e-6im    -4.23861e-8-2.87724e-8im     4.23861e-8-2.87724e-8im     1.69612e-9+1.41282e-11im    1.69628e-9-1.41119e-11im  -4.07203e-11+2.96639e-11im   3.63017e-11+2.53159e-11im
+ -1.27506e-16-0.0844589im       -0.145179+0.096786im       -0.145179-0.096786im       0.00803495-0.0192839im    -0.00803495-0.0192839im    0.000324556+0.00165884im    0.000324556-0.00165884im    -7.29881e-5-7.36014e-5im     7.29881e-5-7.36014e-5im     5.02037e-6+1.02593e-6im     5.02037e-6-1.02593e-6im     -1.9664e-7+8.00072e-8im      1.9664e-7+8.00072e-8im     4.25378e-9-6.26388e-9im     4.25378e-9+6.26388e-9im    6.53269e-12+2.1811e-10im   -6.52146e-12+2.18144e-10im  -1.63776e-11+3.36599e-12im  -1.53622e-11-3.76795e-12im
+ -0.000893686-1.17031e-16im     -0.014106-0.0211589im       0.014106-0.0211589im      0.00272901+0.00113709im    0.00272901-0.00113709im   -0.00022178+4.33918e-5im     0.00022178+4.33918e-5im     9.27716e-6-9.19981e-6im     9.27716e-6+9.19981e-6im    -1.22275e-7+5.98394e-7im     1.22275e-7+5.98394e-7im    -9.06826e-9-2.22464e-8im    -9.06826e-9+2.22464e-8im    6.14926e-10+3.8178e-10im   -6.14926e-10+3.81779e-10im  -2.02946e-11+8.95683e-11im  -2.03114e-11-8.95764e-11im  -7.74569e-13-2.47296e-12im   9.78834e-13-2.19173e-12im
+ -1.95236e-18-0.00154725im     0.00179232-0.00119488im    0.00179232+0.00119488im   -0.000108246+0.00025979im   0.000108246+0.00025979im   -4.14499e-6-2.11852e-5im    -4.14499e-6+2.11852e-5im     8.58374e-7+8.65614e-7im    -8.58374e-7+8.65614e-7im    -5.40698e-8-1.11423e-8im    -5.40698e-8+1.11423e-8im     1.63049e-9-7.15813e-10im   -1.63049e-9-7.15813e-10im       2.6e-10+2.34806e-10im       2.6e-10-2.34805e-10im  -9.52905e-12-1.46897e-12im    9.5312e-12-1.47346e-12im   3.24098e-12-6.83906e-13im   3.02544e-12+8.1283e-13im
+  0.000232639-2.043e-17im      4.53837e-5+6.80755e-5im   -4.53837e-5+6.80755e-5im    -1.68233e-5-7.00961e-6im   -1.68233e-5+7.00961e-6im    1.49733e-6-2.92965e-7im    -1.49733e-6-2.92965e-7im    -6.18845e-8+6.17602e-8im    -6.18845e-8-6.17602e-8im    4.71847e-10-3.03855e-9im   -4.71847e-10-3.03855e-9im     1.02475e-9-3.12162e-10im    1.02475e-9+3.12161e-10im  -2.32851e-11+2.79721e-11im    2.3285e-11+2.79721e-11im    5.5136e-12-2.47804e-11im   5.51954e-12+2.47829e-11im   2.05767e-13+6.50664e-13im  -2.63471e-13+5.82309e-13im
+   2.6244e-17+1.97929e-5im     3.54721e-6-2.36505e-6im    3.54721e-6+2.36505e-6im     2.74198e-7-6.5817e-7im    -2.74198e-7-6.5817e-7im     1.49997e-8+7.82205e-8im     1.49997e-8-7.82205e-8im    -2.72196e-9-2.73494e-9im     2.72196e-9-2.73494e-9im    4.22222e-10-1.58584e-9im    4.22222e-10+1.58584e-9im     1.4028e-11+4.2318e-11im   -1.40281e-11+4.2318e-11im   -7.00664e-11-6.32065e-11im  -7.00664e-11+6.32064e-11im   1.81319e-12+2.78508e-13im   -1.8136e-12+2.79428e-13im  -8.89736e-13+1.90103e-13im  -8.28863e-13-2.30288e-13im
+   -1.0618e-6-5.64811e-17im    5.06265e-7+7.59331e-7im   -5.06265e-7+7.59331e-7im     2.28542e-9+1.27481e-9im    2.28542e-9-1.27481e-9im   -1.53825e-9+3.35011e-10im    1.53825e-9+3.35011e-10im   -2.24932e-9-2.42853e-9im    -2.24932e-9+2.42853e-9im    1.43487e-10+3.57671e-11im  -1.43487e-10+3.57671e-11im  -4.84249e-10+1.47683e-10im  -4.84249e-10-1.47683e-10im   9.17836e-12-1.10319e-11im  -9.17828e-12-1.10319e-11im  -2.61497e-12+1.18851e-11im  -2.61825e-12-1.18864e-11im  -8.21238e-14-2.58938e-13im   1.05896e-13-2.32283e-13im
+ -3.43863e-17-2.92736e-8im    -6.36569e-8+4.17996e-8im   -6.36569e-8-4.17996e-8im    6.18282e-10-1.39021e-9im  -6.18282e-10-1.39021e-9im  -4.16445e-10+7.77363e-11im  -4.16445e-10-7.77363e-11im    8.6631e-12-8.2083e-12im   -8.66306e-12-8.20835e-12im  -6.71953e-11+2.52391e-10im  -6.71953e-11-2.52391e-10im  -1.00987e-12-3.04635e-12im   1.00985e-12-3.0463e-12im    1.11584e-11+1.00647e-11im   1.11584e-11-1.00647e-11im  -1.30583e-13-2.0049e-14im     1.3063e-13-2.01245e-14im   1.41977e-13-3.03695e-14im   1.32244e-13+3.6862e-14im
+   -1.3507e-9+3.82397e-17im  -3.62349e-10-4.74615e-10im  3.62349e-10-4.74615e-10im    1.35757e-9-2.98609e-9im    1.35757e-9+2.98609e-9im  -2.68037e-12-1.17672e-11im   2.68035e-12-1.17672e-11im    3.06502e-9+3.30916e-9im     3.06502e-9-3.30916e-9im    -2.9668e-11-7.39518e-12im    2.9668e-11-7.39518e-12im   6.60325e-10-2.01412e-10im   6.60325e-10+2.01411e-10im  -1.89843e-12+2.28193e-12im   1.89842e-12+2.28192e-12im   3.56751e-12-1.62379e-11im   3.57202e-12+1.62398e-11im    1.6999e-14+5.3604e-14im   -2.19297e-14+4.80973e-14im</code></pre><p>Finally, we check <span>$L^2(\mathbb{S}^2)$</span> norms against another exact result:</p><pre><code class="language-julia">norm(U¹c) ≈ norm(U¹s) ≈ sqrt(8π/3*(k⋅k))</code></pre><pre><code class="language-none">true</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../sphere/">« Spherical harmonic addition theorem</a><a class="docs-footer-nextpage" href="../subspaceangles/">Subspace angles »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/generated/subspaceangles/index.html b/v0.15.15/generated/subspaceangles/index.html
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Subspace angles · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li class="is-active"><a class="tocitem" href>Subspace angles</a></li><li><a class="tocitem" href="../triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Subspace angles</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Subspace angles</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/subspaceangles.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Subspace-angles-1"><a class="docs-heading-anchor" href="#Subspace-angles-1">Subspace angles</a><a class="docs-heading-anchor-permalink" href="#Subspace-angles-1" title="Permalink"></a></h1><p>This example considers the angles between neighbouring Laguerre polynomials with a perturbed measure:</p><div>\[\cos\theta_n = \frac{\langle L_n, L_{n+k}\rangle}{\|L_n\|_2 \|L_{n+k}\|_2},\quad{\rm for}\quad 0\le n &lt; N-k,\]</div><p>where the inner product is defined by <span>$\langle f, g\rangle = \int_0^\infty f(x) g(x) x^\beta e^{-x}{\rm\,d}x$</span>.</p><p>We do so by connecting Laguerre polynomials to the normalized generalized Laguerre polynomials associated with the perturbed measure. It follows by the inner product of the connection coefficients that:</p><div>\[\cos\theta_n = \frac{(V^\top V)_{n, n+k}}{\sqrt{(V^\top V)_{n, n}(V^\top V)_{n+k, n+k}}}.\]</div><pre><code class="language-julia">using FastTransforms, LinearAlgebra</code></pre><p>The neighbouring index <code>k</code> and the maximum degree <code>N-1</code>:</p><pre><code class="language-julia">k, N = 1, 11</code></pre><pre><code class="language-none">(1, 11)</code></pre><p>The Laguerre connection parameters:</p><pre><code class="language-julia">α, β = 0.0, 0.125</code></pre><pre><code class="language-none">(0.0, 0.125)</code></pre><p>We precompute a Laguerre–Laguerre plan:</p><pre><code class="language-julia">P = plan_lag2lag(Float64, N, α, β; norm2=true)</code></pre><pre><code class="language-none">FastTransforms Laguerre--Laguerre plan for 11-element array of Float64</code></pre><p>We apply the plan to the identity, followed by the adjoint plan:</p><pre><code class="language-julia">VtV = parent(P*I)
+lmul!(P&#39;, VtV)</code></pre><pre><code class="language-none">11×11 Matrix{Float64}:
+  0.941743    -0.117718    -0.0515016  -0.0321885  -0.0231355  -0.01793    -0.0145681  -0.0122268  -0.0105074  -0.00919399  -0.00815966
+ -0.117718     1.07418     -0.125995   -0.0539157  -0.0333201  -0.0237861  -0.0183502  -0.0148608  -0.0124417  -0.0106716   -0.00932328
+ -0.0515016   -0.125995     1.14505    -0.131707   -0.0557687  -0.0342413  -0.024336   -0.0187146  -0.0151194  -0.0126345   -0.0108205
+ -0.0321885   -0.0539157   -0.131707    1.19444    -0.136106   -0.0572798  -0.0350206  -0.0248132  -0.0190369  -0.0153515   -0.0128093
+ -0.0231355   -0.0333201   -0.0557687  -0.136106    1.23272    -0.139703   -0.0585599  -0.0356975  -0.0252354  -0.0193261   -0.015562
+ -0.01793     -0.0237861   -0.0342413  -0.0572798  -0.139703    1.26415    -0.142756   -0.059673   -0.0362968  -0.0256145   -0.0195886
+ -0.0145681   -0.0183502   -0.024336   -0.0350206  -0.0585599  -0.142756    1.29092    -0.145414   -0.0606594  -0.0368352   -0.0259588
+ -0.0122268   -0.0148608   -0.0187146  -0.0248132  -0.0356975  -0.059673   -0.145414    1.31429    -0.147773   -0.0615464   -0.0373246
+ -0.0105074   -0.0124417   -0.0151194  -0.0190369  -0.0252354  -0.0362968  -0.0606594  -0.147773    1.33507    -0.149896    -0.062353
+ -0.00919399  -0.0106716   -0.0126345  -0.0153515  -0.0193261  -0.0256145  -0.0368352  -0.0615464  -0.149896    1.3538      -0.151829
+ -0.00815966  -0.00932328  -0.0108205  -0.0128093  -0.015562   -0.0195886  -0.0259588  -0.0373246  -0.062353   -0.151829     1.37089</code></pre><p>From this matrix, the angles are recovered from:</p><pre><code class="language-julia">θ = [acos(VtV[n, n+k]/sqrt(VtV[n, n]*VtV[n+k, n+k])) for n in 1:N-k]</code></pre><pre><code class="language-none">10-element Vector{Float64}:
+ 1.6881063520094897
+ 1.6846487354051982
+ 1.6836556387180577
+ 1.6831998143073255
+ 1.6829427202726823
+ 1.68277949501306
+ 1.682667534322365
+ 1.6825864250312665
+ 1.6825252245704025
+ 1.682477567030148</code></pre><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../spinweighted/">« Spin-weighted spherical harmonics</a><a class="docs-footer-nextpage" href="../triangle/">Calculus on the reference triangle »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Calculus on the reference triangle · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="../.."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../../assets/documenter.js"></script><script src="../../siteinfo.js"></script><script src="../../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../../"><img src="../../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="../../search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../padua/">Padua transform</a></li><li><a class="tocitem" href="../sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../subspaceangles/">Subspace angles</a></li><li class="is-active"><a class="tocitem" href>Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li><a class="is-disabled">Examples</a></li><li class="is-active"><a href>Calculus on the reference triangle</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Calculus on the reference triangle</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/triangle.jl" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="Calculus-on-the-reference-triangle-1"><a class="docs-heading-anchor" href="#Calculus-on-the-reference-triangle-1">Calculus on the reference triangle</a><a class="docs-heading-anchor-permalink" href="#Calculus-on-the-reference-triangle-1" title="Permalink"></a></h1><p>In this example, we sample a bivariate function:</p><div>\[f(x,y) = \frac{1}{1+x^2+y^2},\]</div><p>on the reference triangle with vertices <span>$(0,0)$</span>, <span>$(0,1)$</span>, and <span>$(1,0)$</span> and analyze it in a Proriol series. Then, we find Proriol series for each component of its gradient by term-by-term differentiation of our expansion, and we compare them with the true Proriol series by sampling an exact expression for the gradient.</p><p>We analyze <span>$f(x,y)$</span> on an <span>$N\times M$</span> mapped tensor product grid defined by:</p><div>\[\begin{aligned}
+x &amp; = (1+u)/2,\quad{\rm and}\quad y = (1-u)(1+v)/4,\quad {\rm where:}\\
+u_n &amp; = \cos\left[(n+\tfrac{1}{2})\pi/N\right],\quad{\rm for}\quad 0\le n &lt; N,\quad{\rm and}\\
+v_m &amp; = \cos\left[(m+\tfrac{1}{2})\pi/M\right],\quad{\rm for}\quad 0\le m &lt; M;
+\end{aligned}\]</div><p>we convert the function samples to mapped Chebyshev² coefficients using <code>plan_tri_analysis</code>; and finally, we transform the mapped Chebyshev² coefficients to Proriol coefficients using <code>plan_tri2cheb</code>.</p><p>For the storage pattern of the arrays, please consult the <a href="https://MikaelSlevinsky.github.io/FastTransforms">documentation</a>.</p><pre><code class="language-julia">using FastTransforms, LinearAlgebra, Plots
+const GENFIGS = joinpath(pkgdir(FastTransforms), &quot;docs/src/generated&quot;)
+!isdir(GENFIGS) &amp;&amp; mkdir(GENFIGS)
+plotlyjs()</code></pre><pre><code class="language-none">Plots.PlotlyJSBackend()</code></pre><p>Our function <span>$f$</span> and the Cartesian components of its gradient:</p><pre><code class="language-julia">f = (x,y) -&gt; 1/(1+x^2+y^2)
+fx = (x,y) -&gt; -2x/(1+x^2+y^2)^2
+fy = (x,y) -&gt; -2y/(1+x^2+y^2)^2</code></pre><pre><code class="language-none">#5 (generic function with 1 method)</code></pre><p>The polynomial degree:</p><pre><code class="language-julia">N = 15
+M = N</code></pre><pre><code class="language-none">15</code></pre><p>The parameters of the Proriol series:</p><pre><code class="language-julia">α, β, γ = 0, 0, 0</code></pre><pre><code class="language-none">(0, 0, 0)</code></pre><p>The <span>$u$</span> grid:</p><pre><code class="language-julia">u = [sinpi((N-2n-1)/(2N)) for n in 0:N-1]</code></pre><pre><code class="language-none">15-element Vector{Float64}:
+  0.9945218953682733
+  0.9510565162951536
+  0.8660254037844386
+  0.7431448254773942
+  0.5877852522924731
+  0.4067366430758002
+  0.20791169081775934
+  0.0
+ -0.20791169081775934
+ -0.4067366430758002
+ -0.5877852522924731
+ -0.7431448254773942
+ -0.8660254037844386
+ -0.9510565162951536
+ -0.9945218953682733</code></pre><p>And the <span>$v$</span> grid:</p><pre><code class="language-julia">v = [sinpi((M-2m-1)/(2M)) for m in 0:M-1]</code></pre><pre><code class="language-none">15-element Vector{Float64}:
+  0.9945218953682733
+  0.9510565162951536
+  0.8660254037844386
+  0.7431448254773942
+  0.5877852522924731
+  0.4067366430758002
+  0.20791169081775934
+  0.0
+ -0.20791169081775934
+ -0.4067366430758002
+ -0.5877852522924731
+ -0.7431448254773942
+ -0.8660254037844386
+ -0.9510565162951536
+ -0.9945218953682733</code></pre><p>Instead of using the <span>$u\times v$</span> grid, we use one with more accuracy near the origin. Defining <span>$x$</span> by:</p><pre><code class="language-julia">x = [sinpi((2N-2n-1)/(4N))^2 for n in 0:N-1]</code></pre><pre><code class="language-none">15-element Vector{Float64}:
+ 0.9972609476841365
+ 0.9755282581475768
+ 0.9330127018922194
+ 0.8715724127386971
+ 0.7938926261462365
+ 0.7033683215379002
+ 0.6039558454088797
+ 0.5000000000000001
+ 0.3960441545911204
+ 0.2966316784620999
+ 0.2061073738537634
+ 0.12842758726130288
+ 0.06698729810778066
+ 0.024471741852423214
+ 0.0027390523158633317</code></pre><p>And <span>$w$</span> by:</p><pre><code class="language-julia">w = [sinpi((2M-2m-1)/(4M))^2 for m in 0:M-1]</code></pre><pre><code class="language-none">15-element Vector{Float64}:
+ 0.9972609476841365
+ 0.9755282581475768
+ 0.9330127018922194
+ 0.8715724127386971
+ 0.7938926261462365
+ 0.7033683215379002
+ 0.6039558454088797
+ 0.5000000000000001
+ 0.3960441545911204
+ 0.2966316784620999
+ 0.2061073738537634
+ 0.12842758726130288
+ 0.06698729810778066
+ 0.024471741852423214
+ 0.0027390523158633317</code></pre><p>We see how the two grids are related:</p><pre><code class="language-julia">((1 .+ u)./2 ≈ x) * ((1 .- u).*(1 .+ v&#39;)/4 ≈ reverse(x).*w&#39;)</code></pre><pre><code class="language-none">true</code></pre><p>On the mapped tensor product grid, our function samples are:</p><pre><code class="language-julia">F = [f(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+ 0.50137   0.50137   0.50137   0.50137   0.50137   0.50137   0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371
+ 0.512229  0.512236  0.512249  0.512266  0.512286  0.512308  0.512328  0.512346  0.512361  0.512372  0.512379  0.512383  0.512385  0.512385  0.512386
+ 0.53334   0.533395  0.533499  0.53364   0.533806  0.533979  0.534145  0.534292  0.534412  0.5345    0.534558  0.534592  0.534607  0.534612  0.534613
+ 0.56305   0.563274  0.563699  0.564281  0.564961  0.565675  0.566362  0.56697   0.567464  0.56783   0.568072  0.568211  0.568275  0.568295  0.568299
+ 0.597903  0.598554  0.599792  0.601491  0.603486  0.60559   0.607622  0.609427  0.6109    0.611994  0.612719  0.613134  0.613325  0.613387  0.613397
+ 0.632017  0.633527  0.636406  0.640382  0.645085  0.650086  0.654955  0.659315  0.662898  0.665571  0.66735   0.66837   0.668842  0.668995  0.669018
+ 0.657568  0.660489  0.666088  0.673894  0.683237  0.693308  0.703247  0.712263  0.719753  0.725392  0.729168  0.731342  0.73235   0.732678  0.732728
+ 0.667275  0.672082  0.681371  0.694488  0.710446  0.727971  0.745606  0.761905  0.775667  0.786165  0.79326   0.79737   0.799283  0.799904  0.799999
+ 0.65806   0.664903  0.678251  0.69738   0.721111  0.74777   0.775252  0.801255  0.82368   0.841081  0.85299   0.859943  0.863194  0.864252  0.864414
+ 0.632907  0.641519  0.658477  0.683152  0.714388  0.750331  0.788365  0.825306  0.857936  0.883766  0.901708  0.912284  0.917254  0.918876  0.919123
+ 0.599054  0.608911  0.628482  0.657352  0.694582  0.738395  0.78593   0.833301  0.876165  0.910799  0.935231  0.94978   0.956655  0.958904  0.959246
+ 0.564342  0.574908  0.59603   0.627532  0.668777  0.718232  0.773048  0.82891   0.880558  0.923076  0.953504  0.971796  0.980486  0.983334  0.983768
+ 0.534691  0.545579  0.567447  0.600326  0.643856  0.69679   0.756419  0.818253  0.876403  0.924997  0.960184  0.981503  0.991676  0.995016  0.995526
+ 0.513598  0.524591  0.546739  0.58021   0.624846  0.679621  0.74199   0.80742   0.869666  0.922224  0.960591  0.983966  0.995154  0.998833  0.999394
+ 0.502741  0.513754  0.535975  0.569641  0.614694  0.670229  0.733797  0.800871  0.865052  0.919526  0.959458  0.983854  0.99555   0.999397  0.999985</code></pre><p>We superpose a surface plot of <span>$f$</span> on top of the grid:</p><pre><code class="language-julia">X = [x for x in x, w in w]
+Y = [x[N-n]*w[m+1] for n in 0:N-1, m in 0:M-1]
+scatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:blue)
+surface!(X, Y, F; legend=false, xlabel=&quot;x&quot;, ylabel=&quot;y&quot;, zlabel=&quot;f&quot;)
+savefig(joinpath(GENFIGS, &quot;proriol.html&quot;))</code></pre><object type="text/html" data="../proriol.html" style="width:100%;height:400px;"></object><pre><code class="language-none">&quot;/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/proriol.html&quot;</code></pre><p>We precompute a Proriol–Chebyshev² plan:</p><pre><code class="language-julia">P = plan_tri2cheb(F, α, β, γ)</code></pre><pre><code class="language-none">FastTransforms Proriol--Chebyshev² plan for 15×15-element array of Float64</code></pre><p>And an FFTW Chebyshev² plan on the triangle:</p><pre><code class="language-julia">PA = plan_tri_analysis(F)</code></pre><pre><code class="language-none">FastTransforms plan for FFTW Chebyshev analysis on the triangle for 15×15-element array of Float64</code></pre><p>Its Proriol-<span>$(α,β,γ)$</span> coefficients are:</p><pre><code class="language-julia">U = P\(PA*F)</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+  1.53694      -0.193325     -0.0251445     0.0109626    -0.000813095  -0.000299751   8.30397e-5   -1.59722e-6   -3.2141e-6     6.1667e-7     3.19775e-8   -3.21495e-8    4.17144e-9    6.97174e-10  -3.06613e-10
+ -0.111616      0.0391775    -0.00636098   -0.000168172   0.000311296  -5.50434e-5   -2.99195e-6    2.97964e-6   -4.20688e-7   -5.4534e-8     2.85785e-8   -2.74994e-9   -7.77992e-10   2.56775e-10  -1.20763e-11
+ -0.0620411     0.00717668    0.00153132   -0.000551474   4.1134e-5     1.40597e-5   -4.21186e-6    2.00844e-7    1.36869e-7   -3.34625e-8    3.38022e-10   1.36685e-9   -2.6459e-10   -1.30929e-11   1.45495e-11
+  0.0111316    -0.0036578     0.00043735    4.52913e-5   -2.72385e-5    3.78477e-6    3.57508e-7   -2.26663e-7    2.88459e-8    4.02905e-9   -1.98431e-9    2.01016e-10   4.97746e-11  -1.48758e-11  -2.03145e-12
+  0.00194132   -7.70184e-5   -0.000145948   3.68556e-5   -1.34273e-6   -1.26813e-6    3.06047e-7   -7.57685e-9   -1.11605e-8    2.45432e-9   -1.63544e-12  -1.03205e-10   9.87731e-12   5.4552e-12   -6.15786e-13
+ -0.000642637   0.000243768  -2.28339e-5   -5.91216e-6    2.28045e-6   -2.36988e-7   -4.55496e-8    1.90448e-8   -1.91046e-9   -4.16463e-10   1.54281e-10   1.00975e-11  -8.91873e-12  -7.74977e-13   5.33203e-13
+ -4.38389e-5   -1.71425e-5    1.23092e-5   -2.29813e-6   -6.48598e-8    1.17977e-7   -2.21226e-8   -4.58497e-10   1.02068e-9   -1.63471e-10  -4.64131e-11   6.91421e-12   3.5224e-12   -3.14287e-13  -2.28437e-13
+  2.79805e-5   -1.30453e-5    7.26152e-7    5.87656e-7   -1.71884e-7    1.12463e-8    5.13657e-9   -1.54461e-9    7.05239e-11   8.70592e-11   6.67155e-12  -5.87108e-12  -8.81458e-13   3.50646e-13   6.6012e-14
+  1.15026e-6    1.8828e-6    -8.87898e-7    1.24893e-7    1.74103e-8   -1.00961e-8    1.44036e-9    1.53829e-10  -9.59941e-11  -3.49153e-11   3.35896e-12   3.17799e-12  -1.72731e-14  -2.20896e-13  -4.40702e-15
+ -1.05261e-6    6.07061e-7    9.40225e-9   -4.93564e-8    1.14023e-8   -2.56371e-10  -4.79206e-10   1.50921e-11   6.48843e-11   1.18558e-11  -4.29768e-12  -1.50758e-12   2.19181e-13   1.20467e-13  -1.21247e-14
+ -1.0706e-7    -1.2895e-7     5.63778e-8   -5.46716e-9   -1.98245e-9    6.62772e-10   1.96009e-10  -4.05866e-11  -3.72009e-11  -3.44512e-12   3.09917e-12   6.84676e-13  -1.93699e-13  -6.20043e-14   1.20607e-14
+  4.44232e-8   -2.74042e-8   -3.41194e-9    3.7536e-9    -3.47875e-10  -3.34332e-10  -7.92618e-11   2.84843e-11   1.87606e-11   8.64622e-13  -1.73542e-12  -2.98547e-13   1.16631e-13   2.95637e-14  -7.54383e-15
+  1.13247e-8    6.98157e-9   -3.2324e-9    -1.06114e-10   1.55319e-10   1.35282e-10   2.8768e-11   -1.28905e-11  -7.59283e-12  -1.99177e-13   7.32667e-13   1.12735e-13  -5.05704e-14  -1.16743e-14   3.30983e-15
+ -2.57523e-9    1.14806e-9    1.12793e-10   2.51422e-11  -4.12541e-11  -3.49672e-11  -7.18293e-12   3.43673e-12   1.96276e-12   3.986e-14    -1.91745e-13  -2.85197e-14   1.33334e-14   2.99891e-15  -8.7656e-16
+ -7.03699e-10  -8.33285e-12  -8.53391e-12  -1.88826e-12   3.13558e-12   2.65053e-12   5.42528e-13  -2.61311e-13  -1.4878e-13   -2.93168e-15   1.45531e-14   2.15642e-15  -1.01318e-15  -2.26875e-16   6.66619e-17</code></pre><p>Similarly, our function&#39;s gradient samples are:</p><pre><code class="language-julia">Fx = [fx(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+ -0.501366    -0.501366    -0.501366    -0.501367   -0.501367   -0.501368   -0.501368    -0.501369    -0.501369    -0.501369    -0.501369    -0.501369    -0.501369    -0.50137    -0.50137
+ -0.511916    -0.511929    -0.511955    -0.51199    -0.51203    -0.512073   -0.512114    -0.51215     -0.512179    -0.512201    -0.512215    -0.512223    -0.512227    -0.512228   -0.512228
+ -0.530794    -0.530903    -0.53111     -0.531392   -0.531721   -0.532067   -0.532398    -0.532691    -0.532929    -0.533105    -0.533222    -0.533288    -0.533319    -0.533329   -0.53333
+ -0.552621    -0.553061    -0.553896    -0.555039   -0.556378   -0.557787   -0.559142    -0.560343    -0.56132     -0.562044    -0.562524    -0.562798    -0.562924    -0.562965   -0.562972
+ -0.567613    -0.568852    -0.571206    -0.574447   -0.578264   -0.582304   -0.586217    -0.589705    -0.59256     -0.594683    -0.596093    -0.5969      -0.597274    -0.597395   -0.597413
+ -0.561915    -0.564604    -0.569746    -0.576887   -0.585391   -0.594503   -0.603442    -0.611504    -0.618167    -0.623163    -0.626498    -0.628414    -0.629303    -0.629591   -0.629635
+ -0.522296    -0.526946    -0.535918    -0.548553   -0.563869   -0.580614   -0.59738     -0.612796    -0.625752    -0.635596    -0.64223     -0.646065    -0.647848    -0.648427   -0.648515
+ -0.445256    -0.451694    -0.464267    -0.482314   -0.504734   -0.529941   -0.555929    -0.580499    -0.60166     -0.618055    -0.629262    -0.635798    -0.638853    -0.639847   -0.639998
+ -0.343008    -0.350179    -0.364379    -0.385223   -0.411887   -0.442905   -0.476058    -0.508529    -0.537391    -0.560337    -0.576318    -0.585751    -0.590188    -0.591636   -0.591857
+ -0.237644    -0.244156    -0.257234    -0.276874   -0.302772   -0.334005   -0.368724    -0.404089    -0.436673    -0.463364    -0.482369    -0.49375     -0.499145    -0.500911   -0.501181
+ -0.14793     -0.152838    -0.162821    -0.178123   -0.198871   -0.22475    -0.254619    -0.286238    -0.316443    -0.341954    -0.360547    -0.371851    -0.377255    -0.37903    -0.379301
+ -0.0818036   -0.0848957   -0.0912482   -0.101149   -0.114882   -0.132501   -0.153497    -0.176483    -0.199161    -0.218858    -0.233525    -0.242571    -0.246928    -0.248365   -0.248585
+ -0.0383026   -0.0398784   -0.0431393   -0.0482832  -0.0555393  -0.0650468  -0.0766563   -0.0897011   -0.102903    -0.114631    -0.123518    -0.129064    -0.131754    -0.132643   -0.132779
+ -0.0129105   -0.013469    -0.0146303   -0.0164765  -0.0191091  -0.0226062  -0.0269458   -0.0319076   -0.0370169   -0.0416263   -0.0451619   -0.0473866   -0.0484703   -0.0488293  -0.0488842
+ -0.00138458  -0.00144591  -0.00157369  -0.0017776  -0.0020699  -0.0024608  -0.00294973  -0.00351363  -0.00409934  -0.00463189  -0.00504292  -0.00530263  -0.00542945  -0.0054715  -0.00547794</code></pre><p>and:</p><pre><code class="language-julia">Fy = [fy(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+ -0.00137327  -0.00134334  -0.0012848  -0.00120019  -0.00109322  -0.000968569  -0.000831675  -0.000688523  -0.000545372  -0.000408476  -0.00028382  -0.000176851  -9.22448e-5   -3.36988e-5   -3.77181e-6
+ -0.0128066   -0.0125278   -0.0119824  -0.0111941   -0.0101972   -0.00903524   -0.00775884   -0.0064238    -0.00508851   -0.00381138   -0.00264832  -0.00165022   -0.000860756  -0.000314451  -3.51956e-5
+ -0.0380049   -0.0371844   -0.0355776  -0.0332524   -0.0303075   -0.0268691    -0.0230859    -0.0191228    -0.0151537    -0.0113536    -0.00789053  -0.00491728   -0.00256498   -0.000937054  -0.000104882
+ -0.0812065   -0.0795001   -0.0761501  -0.0712824   -0.0650859   -0.0578104    -0.0497602    -0.0412837    -0.0327574    -0.0245665    -0.017084    -0.0106504    -0.00555645   -0.00203003   -0.000227217
+ -0.146958    -0.144069    -0.138361   -0.129983    -0.119184    -0.106332     -0.0919169    -0.0765485    -0.0609267    -0.0457968    -0.0318962   -0.0199018    -0.0103872    -0.00379541   -0.000424822
+ -0.236327    -0.232283    -0.224184   -0.212046    -0.195994    -0.176349     -0.153701     -0.128945     -0.103249     -0.0779568    -0.0544563   -0.0340361    -0.0177782    -0.00649768   -0.000727317
+ -0.341557    -0.337089    -0.327887   -0.313516    -0.293548    -0.267799     -0.236589     -0.200921     -0.162512     -0.123634     -0.0868006   -0.0544092    -0.028458     -0.0104055    -0.00116482
+ -0.444036    -0.44064     -0.433167   -0.420371    -0.400704    -0.372744     -0.335756     -0.290249     -0.238284     -0.183335     -0.129696    -0.0816541    -0.042795     -0.0156582    -0.00175299
+ -0.521645    -0.520944    -0.518445   -0.512009    -0.498657    -0.475067     -0.438456     -0.387746     -0.32456      -0.253471     -0.181141    -0.114718     -0.0602899    -0.0220791    -0.00247217
+ -0.561955    -0.56477     -0.56909    -0.572203    -0.569958    -0.557059     -0.528047     -0.479085     -0.410077     -0.325915     -0.235743    -0.15036      -0.0792838    -0.0290664    -0.00325507
+ -0.568241    -0.574301    -0.585148   -0.597987    -0.608136    -0.608908     -0.592332     -0.551271     -0.482733     -0.39071      -0.286235    -0.183948     -0.0973409    -0.0357278    -0.00400177
+ -0.553639    -0.562044    -0.577773   -0.598286    -0.618953    -0.632479     -0.629146     -0.598851     -0.535295     -0.440581     -0.326642    -0.211418     -0.112256     -0.0412478    -0.00462083
+ -0.532026    -0.541842    -0.560603   -0.586131    -0.614126    -0.637241     -0.644834     -0.624688     -0.567634     -0.473605     -0.354585    -0.230866     -0.122928     -0.0452109    -0.00506551
+ -0.513246    -0.523783    -0.544148   -0.572459    -0.604752    -0.633849     -0.648741     -0.635973     -0.584411     -0.492221     -0.371057    -0.242599     -0.129432     -0.0476343    -0.00533757
+ -0.502731    -0.513558    -0.534584   -0.564086    -0.5983      -0.630184     -0.648628     -0.639638     -0.591107     -0.500247     -0.378429    -0.247947     -0.132421     -0.0487506    -0.00546294</code></pre><p>For the partial derivative with respect to <span>$x$</span>, <a href="https://doi.org/10.1137/19M1245888">Olver et al.</a> derive simple expressions for the representation of this component using a Proriol-<span>$(α+1,β,γ+1)$</span> series.</p><pre><code class="language-julia">Gx = zeros(Float64, N, M)
+for m = 0:M-2
+    for n = 0:N-2
+        cf1 = m == 0 ? sqrt((n+1)*(n+2m+α+β+γ+3)/(2m+β+γ+2)*(m+γ+1)*8) : sqrt((n+1)*(n+2m+α+β+γ+3)/(2m+β+γ+1)*(m+β+γ+1)/(2m+β+γ+2)*(m+γ+1)*8)
+        cf2 = sqrt((n+α+1)*(m+1)/(2m+β+γ+2)*(m+β+1)/(2m+β+γ+3)*(n+2m+β+γ+3)*8)
+        Gx[n+1, m+1] = cf1*U[n+2, m+1] + cf2*U[n+1, m+2]
+    end
+end
+Px = plan_tri2cheb(Fx, α+1, β, γ+1)
+Ux = Px\(PA*Fx)</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+ -0.773299      0.0719368     0.0119032    -0.00401514    0.00019856    0.000113662  -2.54579e-5   -2.37734e-7    1.03154e-6   -1.60364e-7   -1.48715e-8    9.00448e-9   -8.97984e-10  -2.25712e-10   7.08345e-11
+ -0.223004      0.012725      0.00860848   -0.00187243   -6.32049e-5    8.83801e-5   -1.1938e-5    -1.70295e-6    7.84936e-7   -6.04351e-8   -2.29491e-8    6.45891e-9   -1.23274e-10  -2.55873e-10   5.02863e-11
+  0.11832      -0.0184961    -0.000231272   0.000708416  -0.000135183  -8.87531e-7    5.70658e-6   -1.08175e-6   -3.24208e-8    5.24395e-8   -8.50439e-9   -6.81366e-10   4.94759e-10  -5.56212e-11  -1.16264e-11
+ -0.00167066    0.00241796   -0.00105495    0.000134423   2.32113e-5   -1.10992e-5    1.1835e-6     2.55024e-7   -1.00326e-7    8.05316e-9    2.80938e-9   -8.7387e-10    3.23657e-11   3.71003e-11  -4.71069e-12
+ -0.00812992    0.00143193    9.5529e-5    -8.6497e-5     1.46322e-5    6.06568e-7   -7.52503e-7    1.2809e-7     6.41825e-9   -6.76798e-9    1.05309e-9    1.02809e-10  -6.38887e-11  -4.60391e-12   3.43243e-12
+  0.00134269   -0.000440563   9.61255e-5   -3.9763e-6    -4.07863e-6    1.16773e-6   -7.04875e-8   -3.76919e-8    1.09538e-8   -5.76688e-10  -3.72602e-10   6.21711e-11   2.34835e-11  -3.2882e-12   -1.02885e-12
+  0.000287063  -5.03055e-5   -1.79725e-5    8.218e-6     -1.05921e-6   -1.54886e-7    8.35392e-8   -1.11246e-8   -1.37121e-9    7.34787e-10   2.35493e-11  -4.77271e-11  -3.34076e-12   2.78949e-12   2.71204e-14
+ -0.000114154   3.91247e-5   -6.41411e-6   -4.57437e-7    4.91696e-7   -1.01409e-7    1.49415e-12   4.73486e-9   -8.87703e-10  -2.29361e-10   4.39281e-11   2.01683e-11  -2.11613e-12  -1.32213e-12   2.00985e-13
+  6.85033e-7   -1.42592e-6    2.06904e-6   -6.34246e-7    4.7282e-8     2.34694e-8   -7.6778e-9     5.5085e-10    4.78984e-10   2.6482e-11   -3.78611e-11  -5.10671e-12   2.54966e-12   4.06715e-13  -1.86401e-13
+  5.33318e-6   -2.34997e-6    2.9001e-7     9.45302e-8   -4.55097e-8    7.14241e-9    5.63984e-10  -6.44351e-10  -2.12017e-10   3.18388e-11   2.34425e-11  -6.60811e-13  -1.88678e-12  -1.33748e-14   1.29398e-13
+ -7.178e-7      3.37971e-7   -1.76689e-7    3.81304e-8   -1.11295e-9   -2.48346e-9    1.24297e-10   4.4888e-10    8.62743e-11  -3.44107e-11  -1.28198e-11   1.79781e-12   1.16066e-12  -8.54648e-14  -7.76709e-14
+ -1.15794e-7    9.93748e-8   -5.08059e-9   -9.45944e-9    2.65499e-9    1.0741e-9    -1.63514e-10  -2.32795e-10  -3.2556e-11    2.03989e-11   5.96492e-12  -1.21808e-12  -5.75477e-13   6.48277e-14   3.81309e-14
+  3.9894e-8    -2.50603e-8    1.18665e-8   -3.69658e-10  -9.43959e-10  -3.54061e-10   7.05516e-11   8.25944e-11   9.98239e-12  -7.57296e-12  -2.02892e-12   4.70119e-13   2.00989e-13  -2.57414e-14  -1.32683e-14
+ -2.62946e-9   -2.09989e-9   -2.15583e-10   7.49659e-11   1.79606e-10   6.58835e-11  -1.40885e-11  -1.57067e-11  -1.81381e-12   1.45833e-12   3.81132e-13  -9.14673e-14  -3.80526e-14   5.0449e-15    2.50893e-15
+ -2.54665e-10   1.01738e-11   9.71511e-12  -3.41148e-12  -8.12007e-12  -2.97149e-12   6.40143e-13   7.10069e-13   8.15917e-14  -6.60159e-14  -1.72076e-14   4.14493e-15   1.71957e-15  -2.28703e-16  -1.13413e-16</code></pre><p>For the partial derivative with respect to y, the analogous formulae result in a Proriol-<span>$(α,β+1,γ+1)$</span> series.</p><pre><code class="language-julia">Gy = zeros(Float64, N, M)
+for m = 0:M-2
+    for n = 0:N-2
+        Gy[n+1, m+1] = 4*sqrt((m+1)*(m+β+γ+2))*U[n+1, m+2]
+    end
+end
+Py = plan_tri2cheb(Fy, α, β+1, γ+1)
+Uy = Py\(PA*Fy)</code></pre><pre><code class="language-none">15×15 Matrix{Float64}:
+ -1.09361      -0.246364      0.151902     -0.0145451    -0.00656722    0.00215264   -4.78099e-5   -0.00010909    2.3401e-5     1.34141e-6   -1.47744e-6    2.0787e-7     3.67354e-8   -1.65807e-8    1.30376e-9
+  0.221621     -0.0623246    -0.00233026    0.00556863   -0.00120594   -7.75602e-5    8.91904e-5   -1.42786e-5   -2.06939e-6    1.19894e-6   -1.26335e-7   -3.89258e-8    1.42118e-8   -5.60413e-10  -5.94789e-10
+  0.0405975     0.0150038    -0.00764145    0.000735827   0.000308032  -0.000109184   6.01193e-6    4.6455e-6    -1.26982e-6    1.41852e-8    6.28061e-8   -1.31763e-8   -5.9232e-10    7.38193e-10  -7.35368e-11
+ -0.0206916     0.00428514    0.000627575  -0.000487257   8.29203e-5    9.26771e-6   -6.78478e-6    9.79044e-7    1.52891e-7   -8.32462e-8    9.23683e-9    2.37699e-9   -9.33549e-10  -2.54744e-11   5.13027e-11
+ -0.000435682  -0.00142999    0.000510686  -2.40196e-5   -2.77834e-5    7.93359e-6   -2.26768e-7   -3.78776e-7    9.31367e-8   -7.2912e-11   -4.72764e-9    9.19194e-10   1.83342e-10  -5.07975e-11  -9.73934e-12
+  0.00137896   -0.000223726  -8.19213e-5    4.07942e-5   -5.19191e-6   -1.18071e-6    5.70025e-7   -6.48815e-8   -1.5805e-8     6.74933e-9   -5.22325e-10  -3.74577e-10   2.04346e-11   2.31629e-11  -1.45178e-12
+ -9.69728e-5    0.000120605  -3.18437e-5   -1.1605e-6     2.58441e-6   -5.73589e-7   -1.36421e-8    3.47148e-8   -6.95597e-9   -3.86259e-10   4.86604e-10   7.26716e-11  -3.26991e-11  -5.56081e-12   2.18954e-12
+ -7.37954e-5    7.11448e-6    8.14267e-6   -3.07439e-6    2.46945e-7    1.33361e-7   -4.63869e-8    3.49405e-9    1.69907e-9   -3.52262e-10  -2.0628e-10    1.07045e-11   1.73416e-11  -1.88625e-13  -1.24581e-12
+  1.06509e-5   -8.69913e-6    1.73077e-6    3.10766e-7   -2.22347e-7    3.70118e-8    3.9365e-9    -2.94133e-9   -2.1645e-10    2.94085e-10   6.42746e-11  -2.03559e-11  -6.99252e-12   1.20561e-12   5.53973e-13
+  3.43376e-6    9.14735e-8   -6.84306e-7    2.05405e-7   -4.3435e-9    -1.35246e-8    2.85641e-9    1.15843e-9   -9.56842e-11  -1.59766e-10  -1.45705e-11   1.36984e-11   2.42347e-12  -9.13607e-13  -2.17217e-13
+ -7.29088e-7    5.54006e-7   -7.49665e-8   -3.61409e-8    1.78364e-8   -4.16571e-10  -1.36673e-9   -4.10814e-10   8.7904e-11    6.992e-11     1.76878e-12  -6.65703e-12  -7.49909e-13   4.67294e-13   7.67789e-14
+ -1.56131e-7   -3.60972e-8    5.21717e-8   -9.4804e-9    -1.42828e-9    2.71687e-10   4.84151e-10   1.24081e-10  -3.76632e-11  -2.38535e-11   1.85871e-13   2.38967e-12   2.02456e-13  -1.7174e-13   -2.30959e-14
+  4.09267e-8   -3.39594e-8   -3.06743e-9    7.64151e-10   3.1345e-10   -7.59843e-11  -1.14715e-10  -2.73663e-11   9.55255e-12   5.56757e-12  -1.22703e-13  -5.69904e-13  -4.1879e-14    4.1357e-14    5.08049e-15
+  8.57039e-9    6.52951e-9   -7.39973e-11  -9.29778e-11  -3.74097e-11   9.74901e-12   1.40429e-11   3.27131e-12  -1.19385e-12  -6.78321e-13   1.80885e-14   6.99172e-14   4.88938e-15  -5.08948e-15  -6.06714e-16
+ -2.86296e-9    1.21911e-13   2.03235e-12   2.54849e-12   1.02299e-12  -2.68873e-13  -3.8519e-13   -8.94733e-14   3.28267e-14   1.85955e-14  -5.06208e-16  -1.91829e-15  -1.33321e-16   1.39689e-16   1.65848e-17</code></pre><p>The <span>$2$</span>-norm relative error in differentiating the Proriol series for <span>$f(x,y)$</span> term-by-term and its sampled gradient is:</p><pre><code class="language-julia">hypot(norm(Ux-Gx), norm(Uy-Gy))/hypot(norm(Ux), norm(Uy))</code></pre><pre><code class="language-none">1.8769900875801852e-8</code></pre><p>This error can be improved upon by increasing <span>$N$</span> and <span>$M$</span>.</p><hr/><p><em>This page was generated using <a href="https://github.com/fredrikekre/Literate.jl">Literate.jl</a>.</em></p></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../subspaceangles/">« Subspace angles</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL="."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="assets/documenter.js"></script><script src="siteinfo.js"></script><script src="../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href><img src="assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action="search/"><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a><ul class="internal"><li><a class="tocitem" href="#Introduction-1"><span>Introduction</span></a></li><li><a class="tocitem" href="#Fast-orthogonal-polynomial-transforms-1"><span>Fast orthogonal polynomial transforms</span></a></li><li><a class="tocitem" href="#Nonuniform-fast-Fourier-transforms-1"><span>Nonuniform fast Fourier transforms</span></a></li><li><a class="tocitem" href="#Other-Exported-Methods-1"><span>Other Exported Methods</span></a></li><li><a class="tocitem" href="#Internal-Methods-1"><span>Internal Methods</span></a></li></ul></li><li><a class="tocitem" href="dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="generated/annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="generated/automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="generated/chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="generated/disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="generated/nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="generated/padua/">Padua transform</a></li><li><a class="tocitem" href="generated/sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="generated/spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="generated/subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="generated/triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Home</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Home</a></li></ul></nav><div class="docs-right"><a class="docs-edit-link" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/docs/src/index.md" title="Edit on GitHub"><span class="docs-icon fab"></span><span class="docs-label is-hidden-touch">Edit on GitHub</span></a><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article class="content" id="documenter-page"><h1 id="FastTransforms.jl-Documentation-1"><a class="docs-heading-anchor" href="#FastTransforms.jl-Documentation-1">FastTransforms.jl Documentation</a><a class="docs-heading-anchor-permalink" href="#FastTransforms.jl-Documentation-1" title="Permalink"></a></h1><h2 id="Introduction-1"><a class="docs-heading-anchor" href="#Introduction-1">Introduction</a><a class="docs-heading-anchor-permalink" href="#Introduction-1" title="Permalink"></a></h2><p><a href="https://github.com/JuliaApproximation/FastTransforms.jl"><code>FastTransforms.jl</code></a> allows the user to conveniently work with orthogonal polynomials with degrees well into the millions.</p><p>This package provides a Julia wrapper for the <a href="https://github.com/MikaelSlevinsky/FastTransforms">C library</a> of the same name. Additionally, all three types of nonuniform fast Fourier transforms available, as well as the Padua transform.</p><h2 id="Fast-orthogonal-polynomial-transforms-1"><a class="docs-heading-anchor" href="#Fast-orthogonal-polynomial-transforms-1">Fast orthogonal polynomial transforms</a><a class="docs-heading-anchor-permalink" href="#Fast-orthogonal-polynomial-transforms-1" title="Permalink"></a></h2><p>For this documentation, please see the documentation for <a href="https://github.com/MikaelSlevinsky/FastTransforms">FastTransforms</a>. Most transforms have separate forward and inverse plans. In some instances, however, the inverse is in the sense of least-squares, and therefore only the forward transform is planned.</p><h2 id="Nonuniform-fast-Fourier-transforms-1"><a class="docs-heading-anchor" href="#Nonuniform-fast-Fourier-transforms-1">Nonuniform fast Fourier transforms</a><a class="docs-heading-anchor-permalink" href="#Nonuniform-fast-Fourier-transforms-1" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.nufft1" href="#FastTransforms.nufft1"><code>FastTransforms.nufft1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Computes a nonuniform fast Fourier transform of type I:</p><div>\[f_j = \sum_{k=0}^{N-1} c_k e^{-2\pi{\rm i} \frac{j}{N} \omega_k},\quad{\rm for}\quad 0 \le j \le N-1.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/nufft.jl#L221-L227">source</a></section><section><div><p>Computes a 2D nonuniform fast Fourier transform of type I-I:</p><div>\[F_{i,j} = \sum_{k=0}^{M-1}\sum_{\ell=0}^{N-1} C_{k,\ell} e^{-2\pi{\rm i} (\frac{i}{M} \omega_k + \frac{j}{N} \pi_{\ell})},\quad{\rm for}\quad 0 \le i \le M-1,\quad 0 \le j \le N-1.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/nufft.jl#L305-L311">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.nufft2" href="#FastTransforms.nufft2"><code>FastTransforms.nufft2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Computes a nonuniform fast Fourier transform of type II:</p><div>\[f_j = \sum_{k=0}^{N-1} c_k e^{-2\pi{\rm i} x_j k},\quad{\rm for}\quad 0 \le j \le N-1.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/nufft.jl#L230-L236">source</a></section><section><div><p>Computes a 2D nonuniform fast Fourier transform of type II-II:</p><div>\[F_{i,j} = \sum_{k=0}^{M-1}\sum_{\ell=0}^{N-1} C_{k,\ell} e^{-2\pi{\rm i} (x_i k + y_j \ell)},\quad{\rm for}\quad 0 \le i \le M-1,\quad 0 \le j \le N-1.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/nufft.jl#L314-L320">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.nufft3" href="#FastTransforms.nufft3"><code>FastTransforms.nufft3</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Computes a nonuniform fast Fourier transform of type III:</p><div>\[f_j = \sum_{k=0}^{N-1} c_k e^{-2\pi{\rm i} x_j \omega_k},\quad{\rm for}\quad 0 \le j \le N-1.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/nufft.jl#L239-L245">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.inufft1" href="#FastTransforms.inufft1"><code>FastTransforms.inufft1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Computes an inverse nonuniform fast Fourier transform of type I.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/inufft.jl#L73-L75">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.inufft2" href="#FastTransforms.inufft2"><code>FastTransforms.inufft2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Computes an inverse nonuniform fast Fourier transform of type II.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/inufft.jl#L78-L80">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.paduatransform" href="#FastTransforms.paduatransform"><code>FastTransforms.paduatransform</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Padua Transform maps from interpolant values at the Padua points to the 2D Chebyshev coefficients.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/PaduaTransform.jl#L150-L152">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.ipaduatransform" href="#FastTransforms.ipaduatransform"><code>FastTransforms.ipaduatransform</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Inverse Padua Transform maps the 2D Chebyshev coefficients to the values of the interpolation polynomial at the Padua points.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/PaduaTransform.jl#L45-L47">source</a></section></article><h2 id="Other-Exported-Methods-1"><a class="docs-heading-anchor" href="#Other-Exported-Methods-1">Other Exported Methods</a><a class="docs-heading-anchor-permalink" href="#Other-Exported-Methods-1" title="Permalink"></a></h2><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.gaunt" href="#FastTransforms.gaunt"><code>FastTransforms.gaunt</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Calculates the Gaunt coefficients, defined by:</p><div>\[a(m,n,\mu,\nu,q) = \frac{2(n+\nu-2q)+1}{2} \frac{(n+\nu-2q-m-\mu)!}{(n+\nu-2q+m+\mu)!} \int_{-1}^{+1} P_n^m(x) P_\nu^\mu(x) P_{n+\nu-2q}^{m+\mu}(x) {\rm\,d}x.\]</div><p>or defined by:</p><div>\[P_n^m(x) P_\nu^\mu(x) = \sum_{q=0}^{q_{\rm max}} a(m,n,\mu,\nu,q) P_{n+\nu-2q}^{m+\mu}(x)\]</div><p>This is a Julia implementation of the stable recurrence described in:</p><p>Y.-l. Xu, Fast evaluation of Gaunt coefficients: recursive approach, <em>J. Comp. Appl. Math.</em>, <strong>85</strong>:53–65, 1997.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/gaunt.jl#L1-L16">source</a></section><section><div><p>Calculates the Gaunt coefficients in 64-bit floating-point arithmetic.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/gaunt.jl#L24-L26">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.paduapoints" href="#FastTransforms.paduapoints"><code>FastTransforms.paduapoints</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Returns coordinates of the <span>$(n+1)(n+2)/2$</span> Padua points.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/PaduaTransform.jl#L204-L206">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.sphevaluate" href="#FastTransforms.sphevaluate"><code>FastTransforms.sphevaluate</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Pointwise evaluation of real orthonormal spherical harmonic:</p><div>\[Y_\ell^m(\theta,\varphi) = (-1)^{|m|}\sqrt{(\ell+\frac{1}{2})\frac{(\ell-|m|)!}{(\ell+|m|)!}} P_\ell^{|m|}(\cos\theta) \sqrt{\frac{2-\delta_{m,0}}{2\pi}} \left\{\begin{array}{ccc} \cos m\varphi &amp; {\rm for} &amp; m \ge 0,\\ \sin(-m\varphi) &amp; {\rm for} &amp; m &lt; 0.\end{array}\right.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L407-L413">source</a></section></article><h2 id="Internal-Methods-1"><a class="docs-heading-anchor" href="#Internal-Methods-1">Internal Methods</a><a class="docs-heading-anchor-permalink" href="#Internal-Methods-1" title="Permalink"></a></h2><h3 id="Miscellaneous-Special-Functions-1"><a class="docs-heading-anchor" href="#Miscellaneous-Special-Functions-1">Miscellaneous Special Functions</a><a class="docs-heading-anchor-permalink" href="#Miscellaneous-Special-Functions-1" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.half" href="#FastTransforms.half"><code>FastTransforms.half</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute a typed 0.5.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L9-L11">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.two" href="#FastTransforms.two"><code>FastTransforms.two</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute a typed 2.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L17-L19">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.δ" href="#FastTransforms.δ"><code>FastTransforms.δ</code></a> — <span class="docstring-category">Function</span></header><section><div><p>The Kronecker <span>$\delta$</span> function:</p><div>\[\delta_{k,j} = \left\{\begin{array}{ccc} 1 &amp; {\rm for} &amp; k = j,\\ 0 &amp; {\rm for} &amp; k \ne j.\end{array}\right.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L23-L29">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.Λ" href="#FastTransforms.Λ"><code>FastTransforms.Λ</code></a> — <span class="docstring-category">Function</span></header><section><div><p>The Lambda function <span>$\Lambda(z) = \frac{\Gamma(z+\frac{1}{2})}{\Gamma(z+1)}$</span> for the ratio of gamma functions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L135-L137">source</a></section><section><div><p>For 64-bit floating-point arithmetic, the Lambda function uses the asymptotic series for <span>$\tau$</span> in Appendix B of</p><p>I. Bogaert and B. Michiels and J. Fostier, 𝒪(1) computation of Legendre polynomials and Gauss–Legendre nodes and weights for parallel computing, <em>SIAM J. Sci. Comput.</em>, <strong>34</strong>:C83–C101, 2012.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L140-L144">source</a></section><section><div><p>The Lambda function <span>$\Lambda(z,λ₁,λ₂) = \frac{\Gamma(z+\lambda_1)}{Γ(z+\lambda_2)}$</span> for the ratio of gamma functions.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L154-L156">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.lambertw" href="#FastTransforms.lambertw"><code>FastTransforms.lambertw</code></a> — <span class="docstring-category">Function</span></header><section><div><p>The principal branch of the Lambert-W function, defined by <span>$x = W_0(x) e^{W_0(x)}$</span>, computed using Halley&#39;s method for <span>$x \in [-e^{-1},\infty)$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L173-L175">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.pochhammer" href="#FastTransforms.pochhammer"><code>FastTransforms.pochhammer</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Pochhammer symbol <span>$(x)_n = \frac{\Gamma(x+n)}{\Gamma(x)}$</span> for the rising factorial.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L33-L35">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.stirlingseries" href="#FastTransforms.stirlingseries"><code>FastTransforms.stirlingseries</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Stirling&#39;s asymptotic series for <span>$\Gamma(z)$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L63-L65">source</a></section></article><h3 id="Modified-Chebyshev-Moment-Based-Quadrature-1"><a class="docs-heading-anchor" href="#Modified-Chebyshev-Moment-Based-Quadrature-1">Modified Chebyshev Moment-Based Quadrature</a><a class="docs-heading-anchor-permalink" href="#Modified-Chebyshev-Moment-Based-Quadrature-1" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.clenshawcurtisnodes" href="#FastTransforms.clenshawcurtisnodes"><code>FastTransforms.clenshawcurtisnodes</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute nodes of the Clenshaw—Curtis quadrature rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/clenshawcurtis.jl#L3-L5">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.clenshawcurtisweights" href="#FastTransforms.clenshawcurtisweights"><code>FastTransforms.clenshawcurtisweights</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute weights of the Clenshaw—Curtis quadrature rule with modified Chebyshev moments of the first kind <span>$\mu$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/clenshawcurtis.jl#L8-L10">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.fejernodes1" href="#FastTransforms.fejernodes1"><code>FastTransforms.fejernodes1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute nodes of Fejer&#39;s first quadrature rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/fejer.jl#L3-L5">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.fejerweights1" href="#FastTransforms.fejerweights1"><code>FastTransforms.fejerweights1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute weights of Fejer&#39;s first quadrature rule with modified Chebyshev moments of the first kind <span>$\mu$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/fejer.jl#L8-L10">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.fejernodes2" href="#FastTransforms.fejernodes2"><code>FastTransforms.fejernodes2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute nodes of Fejer&#39;s second quadrature rule.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/fejer.jl#L22-L24">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.fejerweights2" href="#FastTransforms.fejerweights2"><code>FastTransforms.fejerweights2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Compute weights of Fejer&#39;s second quadrature rule with modified Chebyshev moments of the second kind <span>$\mu$</span>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/fejer.jl#L27-L29">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevmoments1" href="#FastTransforms.chebyshevmoments1"><code>FastTransforms.chebyshevmoments1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the first kind:</p><div>\[    \int_{-1}^{+1} T_n(x) {\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L256-L262">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevjacobimoments1" href="#FastTransforms.chebyshevjacobimoments1"><code>FastTransforms.chebyshevjacobimoments1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the first kind with respect to the Jacobi weight:</p><div>\[    \int_{-1}^{+1} T_n(x) (1-x)^\alpha(1+x)^\beta{\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L271-L277">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevlogmoments1" href="#FastTransforms.chebyshevlogmoments1"><code>FastTransforms.chebyshevlogmoments1</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the first kind with respect to the logarithmic weight:</p><div>\[    \int_{-1}^{+1} T_n(x) \log\left(\frac{1-x}{2}\right){\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L290-L296">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevmoments2" href="#FastTransforms.chebyshevmoments2"><code>FastTransforms.chebyshevmoments2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the second kind:</p><div>\[    \int_{-1}^{+1} U_n(x) {\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L310-L316">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevjacobimoments2" href="#FastTransforms.chebyshevjacobimoments2"><code>FastTransforms.chebyshevjacobimoments2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the second kind with respect to the Jacobi weight:</p><div>\[    \int_{-1}^{+1} U_n(x) (1-x)^\alpha(1+x)^\beta{\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L325-L331">source</a></section></article><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.chebyshevlogmoments2" href="#FastTransforms.chebyshevlogmoments2"><code>FastTransforms.chebyshevlogmoments2</code></a> — <span class="docstring-category">Function</span></header><section><div><p>Modified Chebyshev moments of the second kind with respect to the logarithmic weight:</p><div>\[    \int_{-1}^{+1} U_n(x) \log\left(\frac{1-x}{2}\right){\rm\,d}x.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/specialfunctions.jl#L344-L350">source</a></section></article><h3 id="Elliptic-1"><a class="docs-heading-anchor" href="#Elliptic-1">Elliptic</a><a class="docs-heading-anchor-permalink" href="#Elliptic-1" title="Permalink"></a></h3><article class="docstring"><header><a class="docstring-binding" id="FastTransforms.Elliptic" href="#FastTransforms.Elliptic"><code>FastTransforms.Elliptic</code></a> — <span class="docstring-category">Module</span></header><section><div><p><code>FastTransforms</code> submodule for the computation of some elliptic integrals and functions.</p><p>Complete elliptic integrals of the first and second kinds:</p><div>\[K(k) = \int_0^{\frac{\pi}{2}} \frac{{\rm d}\theta}{\sqrt{1-k^2\sin^2\theta}},\quad{\rm and},\]</div><div>\[E(k) = \int_0^{\frac{\pi}{2}} \sqrt{1-k^2\sin^2\theta} {\rm\,d}\theta.\]</div><p>Jacobian elliptic functions:</p><div>\[x = \int_0^{\operatorname{sn}(x,k)} \frac{{\rm d}t}{\sqrt{(1-t^2)(1-k^2t^2)}},\]</div><div>\[x = \int_{\operatorname{cn}(x,k)}^1 \frac{{\rm d}t}{\sqrt{(1-t^2)[1-k^2(1-t^2)]}},\]</div><div>\[x = \int_{\operatorname{dn}(x,k)}^1 \frac{{\rm d}t}{\sqrt{(1-t^2)(t^2-1+k^2)}},\]</div><p>and the remaining nine are defined by:</p><div>\[\operatorname{pq}(x,k) = \frac{\operatorname{pr}(x,k)}{\operatorname{qr}(x,k)} = \frac{1}{\operatorname{qp}(x,k)}.\]</div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaApproximation/FastTransforms.jl/blob/e3d47a2d429b2c4425a520fb4bb4e3da4e3f10d4/src/elliptic.jl#L1-L26">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="dev/">Development »</a></nav></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v0.15.15/search/index.html b/v0.15.15/search/index.html
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+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Search · FastTransforms.jl</title><link href="https://fonts.googleapis.com/css?family=Lato|Roboto+Mono" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/5.11.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.11.1/katex.min.css" rel="stylesheet" type="text/css"/><script>documenterBaseURL=".."</script><script src="https://cdnjs.cloudflare.com/ajax/libs/require.js/2.3.6/require.min.js" data-main="../assets/documenter.js"></script><script src="../siteinfo.js"></script><script src="../../versions.js"></script><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-dark.css" data-theme-name="documenter-dark"/><link class="docs-theme-link" rel="stylesheet" type="text/css" href="../assets/themes/documenter-light.css" data-theme-name="documenter-light" data-theme-primary/><script src="../assets/themeswap.js"></script></head><body><div id="documenter"><nav class="docs-sidebar"><a class="docs-logo" href="../"><img src="../assets/logo.png" alt="FastTransforms.jl logo"/></a><div class="docs-package-name"><span class="docs-autofit">FastTransforms.jl</span></div><form class="docs-search" action><input class="docs-search-query" id="documenter-search-query" name="q" type="text" placeholder="Search docs"/></form><ul class="docs-menu"><li><a class="tocitem" href="../">Home</a></li><li><a class="tocitem" href="../dev/">Development</a></li><li><span class="tocitem">Examples</span><ul><li><a class="tocitem" href="../generated/annulus/">Integration on an annulus</a></li><li><a class="tocitem" href="../generated/automaticdifferentiation/">Automatic differentiation through spherical harmonic transforms</a></li><li><a class="tocitem" href="../generated/chebyshev/">Chebyshev transform</a></li><li><a class="tocitem" href="../generated/disk/">Holomorphic integration on the unit disk</a></li><li><a class="tocitem" href="../generated/nonlocaldiffusion/">Nonlocal diffusion on <span>$\mathbb{S}^2$</span></a></li><li><a class="tocitem" href="../generated/padua/">Padua transform</a></li><li><a class="tocitem" href="../generated/sphere/">Spherical harmonic addition theorem</a></li><li><a class="tocitem" href="../generated/spinweighted/">Spin-weighted spherical harmonics</a></li><li><a class="tocitem" href="../generated/subspaceangles/">Subspace angles</a></li><li><a class="tocitem" href="../generated/triangle/">Calculus on the reference triangle</a></li></ul></li></ul><div class="docs-version-selector field has-addons"><div class="control"><span class="docs-label button is-static is-size-7">Version</span></div><div class="docs-selector control is-expanded"><div class="select is-fullwidth is-size-7"><select id="documenter-version-selector"></select></div></div></div></nav><div class="docs-main"><header class="docs-navbar"><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Search</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Search</a></li></ul></nav><div class="docs-right"><a class="docs-settings-button fas fa-cog" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-sidebar-button fa fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a></div></header><article><p id="documenter-search-info">Loading search...</p><ul id="documenter-search-results"></ul></article></div><div class="modal" id="documenter-settings"><div class="modal-background"></div><div class="modal-card"><header class="modal-card-head"><p class="modal-card-title">Settings</p><button class="delete"></button></header><section class="modal-card-body"><p><label class="label">Theme</label><div class="select"><select id="documenter-themepicker"><option value="documenter-light">documenter-light</option><option value="documenter-dark">documenter-dark</option></select></div></p><hr/><p>This document was generated with <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> on <span class="colophon-date" title="Thursday 16 November 2023 15:03">Thursday 16 November 2023</span>. Using Julia version 1.9.4.</p></section><footer class="modal-card-foot"></footer></div></div></div></body><script src="../search_index.js"></script><script src="../assets/search.js"></script></html>
diff --git a/v0.15.15/search_index.js b/v0.15.15/search_index.js
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+var documenterSearchIndex = {"docs":
+[{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/spinweighted.jl\"","category":"page"},{"location":"generated/spinweighted/#Spin-weighted-spherical-harmonics-1","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"","category":"section"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"This example plays with analysis of:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"f(r) = e^rm i kcdot r","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"for some kinmathbbR^3 and where rinmathbbS^2, using spin-0 spherical harmonics.","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"It applies ð, the spin-raising operator, both on the spin-0 coefficients as well as the original function, followed by a spin-1 analysis to compare coefficients.","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"For the storage pattern of the arrays, please consult the documentation.","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"using FastTransforms, LinearAlgebra","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"The colatitudinal grid (mod pi):","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"N = 10\nθ = (0.5:N-0.5)/N","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"0.05:0.1:0.95","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"The longitudinal grid (mod pi):","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"M = 2*N-1\nφ = (0:M-1)*2/M","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"0.0:0.10526315789473684:1.894736842105263","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"Our choice of k and angular parametrization of r:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"k = [2/7, 3/7, 6/7]\nr = (θ,φ) -> [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"#1 (generic function with 1 method)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"On the tensor product grid, our function samples are:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"F = [exp(im*(k⋅r(θ,φ))) for θ in θ, φ in φ]","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"10×19 Matrix{ComplexF64}:\n 0.628413+0.77788im   0.613246+0.789892im   0.603399+0.79744im    0.600106+0.79992im    0.603786+0.797146im   0.613972+0.789328im   0.629387+0.777092im   0.64815+0.761513im   0.668065+0.744103im   0.686931+0.726723im  0.702801+0.711386im    0.71416+0.699982im   0.720001+0.693973im    0.71983+0.694151im  0.713662+0.700491im   0.702017+0.71216im    0.685934+0.727664im  0.666955+0.745098im   0.647044+0.762452im\n 0.626742+0.779227im  0.582025+0.813171im   0.552374+0.833596im   0.542362+0.840145im    0.55355+0.832816im   0.584193+0.811615im   0.629571+0.776943im   0.68294+0.730474im   0.736952+0.675945im   0.785185+0.619262im  0.823211+0.567736im   0.848825+0.528674im   0.861428+0.507879im   0.861065+0.508495im   0.84773+0.530428im   0.821392+0.570364im   0.782715+0.62238im   0.734019+0.679129im   0.679858+0.733344im\n 0.690857+0.722991im  0.625071+0.780568im   0.580335+0.814378im   0.565059+0.82505im    0.582122+0.813101im   0.628309+0.777964im   0.694941+0.719066im  0.769832+0.638246im   0.840471+0.541857im   0.897514+0.440985im  0.936972+0.349406im   0.959893+0.280368im   0.969821+0.243819im   0.969549+0.244899im  0.958985+0.283457im   0.935221+0.354065im   0.894765+0.446538im  0.836798+0.547511im    0.76563+0.643282im\n 0.799876+0.600166im  0.729022+0.68449im    0.678871+0.734257im   0.661444+0.749994im   0.680901+0.732375im   0.732596+0.680663im   0.804139+0.594441im  0.878702+0.477371im   0.940401+0.340068im    0.97989+0.199537im  0.997175+0.0751106im  0.999864-0.0165003im  0.997938-0.0641824im  0.998027-0.062782im  0.999923-0.0124432im  0.996684+0.0813636im  0.978303+0.207181im  0.937478+0.348046im   0.874727+0.484617im\n 0.914598+0.404364im  0.858511+0.512795im   0.815749+0.578405im   0.800419+0.599441im    0.81752+0.5759im     0.861473+0.507803im   0.917769+0.397116im  0.967817+0.251653im   0.996186+0.0872572im   0.99722-0.07452im   0.977203-0.212305im   0.950621-0.310353im    0.93288-0.360187im   0.933439-0.358735im  0.952008-0.306074im   0.978656-0.205506im   0.997827-0.065887im   0.99532+0.0966353im  0.965471+0.260509im\n 0.989052+0.147569im  0.963701+0.266985im   0.939852+0.341582im   0.930644+0.365927im   0.940896+0.338696im   0.965234+0.261387im   0.990188+0.13974im   0.999905-0.0137846im  0.983699-0.179822im    0.94183-0.33609im    0.88602-0.463647im   0.834409-0.551146im   0.804097-0.594498im   0.805021-0.593247im  0.836879-0.547388im   0.889222-0.457475im   0.944703-0.327927im  0.985349-0.170549im   0.999989-0.00462386im\n  0.99096-0.134156im  0.999703-0.0243628im  0.998928+0.0462861im  0.997566+0.0697274im  0.999053+0.0435207im  0.999562-0.0295972im  0.989978-0.141225im  0.960887-0.276941im   0.908431-0.418034im   0.837893-0.545834im  0.762849-0.646576im   0.700449-0.713703im   0.665602-0.746307im   0.666649-0.745372im  0.703339-0.710855im    0.76689-0.641779im   0.842129-0.539276im   0.91195-0.410301im   0.963143-0.26899im\n 0.919472-0.393156im  0.950297-0.311346im   0.966254-0.257589im   0.970887-0.23954im    0.965686-0.259711im   0.948995-0.315292im    0.91723-0.398357im  0.867837-0.49685im    0.802371-0.596825im   0.727938-0.685643im  0.656033-0.754733im   0.599431-0.800426im   0.568692-0.82255im    0.569608-0.821916im  0.602006-0.798492im   0.659781-0.751458im   0.732172-0.68112im   0.806377-0.591401im   0.871077-0.491147im\n  0.80566-0.592379im  0.837633-0.546233im   0.856754-0.515725im   0.862863-0.505438im   0.856026-0.516933im   0.836173-0.548466im     0.8035-0.595305im  0.759389-0.650637im   0.707251-0.706962im   0.652712-0.757606im  0.602883-0.79783im    0.564968-0.825113im   0.544739-0.838606im   0.545338-0.838216im  0.566673-0.823943im   0.605429-0.795899im   0.655721-0.755004im  0.710305-0.703894im   0.762122-0.647434im\n 0.695346-0.718675im   0.70912-0.705088im   0.717813-0.696236im   0.720677-0.693271im   0.717475-0.696585im   0.708471-0.70574im    0.694445-0.719545im  0.676692-0.736266im   0.656981-0.753907im   0.637428-0.77051im   0.620269-0.784389im   0.607563-0.794272im   0.600886-0.799335im   0.601083-0.799186im  0.608129-0.793839im   0.621132-0.783706im   0.638483-0.769636im  0.658105-0.752927im    0.67776-0.735284im","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"We precompute a spin-0 spherical harmonic–Fourier plan:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"P = plan_spinsph2fourier(F, 0)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"FastTransforms Spin-weighted spherical harmonic--Fourier plan for 10×19-element array of ComplexF64","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"And an FFTW Fourier analysis plan on mathbbS^2:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"PA = plan_spinsph_analysis(F, 0)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"FastTransforms plan for FFTW Fourier analysis on the sphere (spin-weighted) for 10×19-element array of ComplexF64","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"Its spin-0 spherical harmonic coefficients are:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"U⁰ = P\\(PA*F)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"10×19 Matrix{ComplexF64}:\n      2.98294-8.51991e-17im     -0.560381+0.373587im        0.560381+0.373587im        0.0307268-0.0737442im       0.0307268+0.0737442im      0.00123905+0.0063329im     -0.00123905+0.0063329im    -0.000278656-0.000280997im  -0.000278656+0.000280997im    1.91763e-5+3.91877e-6im    -1.91763e-5+3.91877e-6im    -7.51512e-7+3.05775e-7im    -7.51512e-7-3.05775e-7im     1.62607e-8-2.39542e-8im    -1.62607e-8-2.39542e-8im   -7.57573e-12+9.06989e-10im   -7.6043e-12-9.06983e-10im  -1.32856e-11-2.14392e-11im   1.44574e-11-2.09394e-11im\n -9.83939e-17+1.585im           -0.147488-0.221233im       -0.147488+0.221233im        0.0242802+0.0101168im      -0.0242802+0.0101168im       -0.001828+0.000357651im     -0.001828-0.000357651im    7.31346e-5-7.25251e-5im    -7.31346e-5-7.25251e-5im    -9.36425e-7+4.58234e-6im    -9.36425e-7-4.58234e-6im    -6.79393e-8-1.66977e-7im     6.79393e-8-1.66977e-7im     4.99533e-9+3.39094e-9im     4.99533e-9-3.39094e-9im   -1.78808e-10-1.49391e-12im   1.78807e-10-1.49874e-12im   3.97537e-12-2.47069e-12im   3.88749e-12+2.67669e-12im\n    -0.296042+1.9373e-16im      0.0419095-0.0279397im     -0.0419095-0.0279397im     -0.00179667+0.00431201im    -0.00179667-0.00431201im    -5.92556e-5-0.000302862im    5.92556e-5-0.000302862im    1.12623e-5+1.13569e-5im     1.12623e-5-1.13569e-5im    -6.70874e-7-1.37097e-7im     6.70874e-7-1.37097e-7im     2.31726e-8-9.42846e-9im     2.31726e-8+9.42846e-9im   -4.48157e-10+6.60198e-10im   4.48157e-10+6.60199e-10im   1.83282e-13-2.21049e-11im   1.86684e-13+2.21043e-11im   2.77137e-13+4.85399e-13im  -3.40625e-13+4.58308e-13im\n  7.69323e-17-0.0243812im      0.00315419+0.00473128im    0.00315419-0.00473128im   -0.000498246-0.000207603im   0.000498246-0.000207603im    3.42215e-5-6.6955e-6im      3.42215e-5+6.6955e-6im     -1.23971e-6+1.22938e-6im     1.23971e-6+1.22938e-6im     1.44141e-8-7.05344e-8im     1.44141e-8+7.05344e-8im    9.54963e-10+2.34704e-9im   -9.54963e-10+2.34704e-9im   -6.22737e-11-4.22728e-11im  -6.22738e-11+4.22728e-11im   2.09765e-12+1.71251e-14im  -2.09747e-12+1.79765e-14im  -5.56453e-13+3.38942e-13im  -5.39576e-13-3.78598e-13im\n -0.000199834-6.42779e-17im  -0.000327232+0.000218154im  0.000327232+0.000218154im    1.67027e-5-4.00864e-5im     1.67027e-5+4.00864e-5im      5.5389e-7+2.83099e-6im     -5.5389e-7+2.83099e-6im    -1.01124e-7-1.01974e-7im    -1.01124e-7+1.01974e-7im     5.69484e-9+1.16377e-9im    -5.69484e-9+1.16377e-9im   -1.69612e-10+6.90117e-11im  -1.69612e-10-6.90117e-11im   2.98198e-12-4.39287e-12im    -2.982e-12-4.39288e-12im   -3.4901e-14+4.21981e-12im   -3.5709e-14-4.21967e-12im  -4.58998e-14-8.03356e-14im   5.63705e-14-7.58511e-14im\n -6.51867e-17-0.000282488im    -7.0029e-6-1.05044e-5im    -7.0029e-6+1.05044e-5im     2.24809e-6+9.36704e-7im    -2.24809e-6+9.36704e-7im    -1.76539e-7+3.45402e-8im    -1.76539e-7-3.45402e-8im     6.55393e-9-6.49931e-9im    -6.55393e-9-6.49931e-9im    -7.1368e-11+3.49235e-10im   -7.1368e-11-3.49235e-10im  -4.99716e-12-1.22817e-11im   4.99717e-12-1.22817e-11im   1.69023e-11+1.14737e-11im   1.69023e-11-1.14737e-11im  -5.44912e-13-4.42073e-15im   5.44856e-13-4.70254e-15im   1.57991e-13-9.50528e-14im   1.52387e-13+1.08145e-13im\n   3.58969e-5-4.03624e-17im    -4.7402e-7+3.16014e-7im     4.7402e-7+3.16014e-7im    -3.23608e-8+7.76658e-8im    -3.23608e-8-7.76658e-8im     -1.6111e-9-8.2345e-9im       1.6111e-9-8.2345e-9im     2.28327e-10+2.30246e-10im   2.28327e-10-2.30246e-10im  -1.02557e-11-2.09578e-12im   1.02557e-11-2.09575e-12im   4.54949e-11-1.8511e-11im    4.54949e-11+1.85109e-11im  -5.65264e-13+8.32697e-13im   5.65261e-13+8.32682e-13im   9.40036e-15-1.14115e-12im   9.64888e-15+1.14112e-12im   8.75729e-15+1.53541e-14im  -1.07798e-14+1.45105e-14im\n  1.02759e-16+2.64492e-6im    -5.98533e-8-8.978e-8im     -5.98533e-8+8.978e-8im      -2.2753e-10-9.48042e-11im    2.2753e-10-9.48042e-11im   2.65455e-10-5.19369e-11im   2.65455e-10+5.19368e-11im  -1.37076e-11+1.35933e-11im   1.37076e-11+1.35933e-11im   3.35969e-11-1.64405e-10im   3.35969e-11+1.64405e-10im   1.96453e-12+4.82831e-12im  -1.96456e-12+4.8283e-12im   -8.01172e-12-5.43855e-12im  -8.01172e-12+5.43851e-12im    2.1536e-13+1.72771e-15im  -2.15343e-13+1.85925e-15im  -7.69585e-14+4.5967e-14im   -7.40005e-14-5.28702e-14im\n  -1.25204e-7-1.00025e-16im    6.65757e-9-4.43838e-9im   -6.65757e-9-4.43838e-9im   -1.43603e-11+3.44646e-11im  -1.43603e-11-3.44646e-11im   5.78451e-14+2.95763e-13im  -5.78679e-14+2.95759e-13im  -3.63314e-11-3.66368e-11im  -3.63314e-11+3.66367e-11im   7.38143e-13+1.5085e-13im   -7.38141e-13+1.50867e-13im  -7.24159e-12+2.94646e-12im   -7.2416e-12-2.94643e-12im   4.07078e-14-5.99547e-14im  -4.06954e-14-5.99559e-14im  -1.50544e-15+1.81789e-13im  -1.53538e-15-1.81804e-13im  -6.14456e-16-1.09039e-15im   7.91436e-16-1.0443e-15im\n -1.37837e-16-3.0609e-9im     4.29751e-10+6.44627e-10im  4.29751e-10-6.44627e-10im  -5.01384e-12-2.08911e-12im   5.01382e-12-2.08911e-12im  -3.61552e-10+7.07385e-11im  -3.61552e-10-7.07385e-11im   2.83376e-12-2.81014e-12im  -2.83376e-12-2.81015e-12im  -4.57901e-11+2.24071e-10im  -4.57901e-11-2.24071e-10im  -4.06243e-13-9.98407e-13im   4.06234e-13-9.98416e-13im   1.09292e-11+7.419e-12im     1.09292e-11-7.41901e-12im  -4.45672e-14-3.63419e-16im    4.4548e-14-3.98703e-16im   1.05377e-13-6.28734e-14im   1.01301e-13+7.23958e-14im","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"We can check its L^2(mathbbS^2) norm against an exact result:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"norm(U⁰) ≈ sqrt(4π)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"true","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"Spin can be incremented by applying ð, either on the spin-0 coefficients:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"U¹c = zero(U⁰)\nfor n in 1:N-1\n    U¹c[n, 1] = sqrt(n*(n+1))*U⁰[n+1, 1]\nend\nfor m in 1:M÷2\n    for n in 0:N-1\n        U¹c[n+1, 2m] = -sqrt((n+m)*(n+m+1))*U⁰[n+1, 2m]\n        U¹c[n+1, 2m+1] = sqrt((n+m)*(n+m+1))*U⁰[n+1, 2m+1]\n    end\nend","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"or on the original function through analysis with spin-1 spherical harmonics:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"F = [-(k[1]*(im*cospi(θ)*cospi(φ) + sinpi(φ)) + k[2]*(im*cospi(θ)*sinpi(φ)-cospi(φ)) - im*k[3]*sinpi(θ))*exp(im*(k⋅r(θ,φ))) for θ in θ, φ in φ]","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"10×19 Matrix{ComplexF64}:\n   0.384531+0.240303im     0.405167+0.0811656im   0.376168-0.08059im    0.296802-0.228644im      0.17173-0.345547im    0.0121942-0.415058im     -0.164084-0.425345im    -0.334877-0.37218im      -0.47719-0.260862im    -0.571781-0.105926im  -0.607006+0.0715576im   -0.58067+0.248234im      -0.499453+0.402825im     -0.376425+0.519276im   -0.227802+0.588046im  -0.0700889+0.605739im   0.0817378+0.573795im    0.214909+0.497059im   0.318781+0.382786im\n    0.16375+0.41829im      0.162116+0.268361im    0.128477+0.110061im   0.056034-0.0418675im  -0.0588234-0.167146im    -0.211042-0.242529im     -0.383203-0.247832im    -0.546769-0.173942im    -0.669506-0.0288607im   -0.726395+0.162453im  -0.708448+0.365492im   -0.624684+0.547246im      -0.496849+0.685091im     -0.350631+0.769743im   -0.208037+0.802572im  -0.0835191+0.79034im     0.016198+0.740573im   0.0899356+0.659195im    0.13893+0.55045im\n 0.00394925+0.589002im   -0.0517508+0.441892im   -0.117739+0.283703im  -0.202276+0.132736im    -0.313608+0.0132761im   -0.450683-0.0475101im    -0.596088-0.0271995im   -0.717144+0.0808626im   -0.777618+0.259594im    -0.754769+0.470906im  -0.650847+0.67007im    -0.491452+0.823236im      -0.313141+0.917212im     -0.149502+0.957306im  -0.0230169+0.957535im   0.0563716+0.930505im   0.0891711+0.881918im    0.083394+0.810775im  0.0511118+0.713512im\n  -0.037706+0.764342im    -0.167663+0.63523im    -0.287398+0.487323im  -0.400578+0.346904im    -0.514827+0.244114im     -0.62967+0.207393im     -0.727882+0.254883im    -0.777945+0.383583im    -0.749353+0.563975im    -0.631836+0.748617im  -0.444017+0.892859im   -0.224888+0.974245im     -0.0160482+0.997806im      0.151723+0.986424im    0.261377+0.965157im    0.306018+0.948535im    0.286044+0.935214im    0.209798+0.910832im  0.0944472+0.857391im\n  0.0677134+0.90671im     -0.132933+0.832114im    -0.31272+0.722356im  -0.463011+0.610267im    -0.584223+0.531084im     -0.67363+0.512373im     -0.717075+0.564833im    -0.692616+0.674959im    -0.585463+0.805978im    -0.402896+0.912201im  -0.175697+0.960918im   0.0558086+0.947262im       0.258917+0.892857im      0.415705+0.832204im    0.518079+0.796763im    0.559103+0.802847im    0.530434+0.845158im    0.428907+0.898149im   0.265719+0.927327im\n   0.292353+0.944771im    0.0581069+0.961031im   -0.162367+0.923101im  -0.343726+0.861107im    -0.474077+0.809852im    -0.546787+0.794409im     -0.553921+0.82068im      -0.48849+0.87246im     -0.353637+0.917742im    -0.169005+0.924095im  0.0340849+0.875449im    0.226308+0.779766im       0.391603+0.66433im       0.527207+0.564551im    0.633493+0.513im       0.702424+0.529934im    0.714639+0.614543im    0.649544+0.740756im   0.502126+0.864782im\n   0.544556+0.82786im      0.335621+0.941682im     0.11692+0.992061im  -0.074329+0.994789im    -0.214433+0.975768im    -0.291963+0.955971im     -0.303796+0.942141im    -0.254076+0.925583im    -0.155653+0.88869im    -0.0290943+0.815954im    0.10377+0.703491im    0.228799+0.562131im       0.344287+0.414327im      0.457269+0.288908im    0.572819+0.215991im    0.682616+0.220188im    0.761104+0.310327im    0.774782+0.470071im   0.701202+0.658896im\n   0.711777+0.57455im      0.575876+0.753741im    0.402359+0.877629im   0.227778+0.943189im    0.0807159+0.961489im   -0.0227441+0.946886im     -0.078234+0.908848im   -0.0903981+0.849391im   -0.0697694+0.765587im   -0.0288206+0.65453im   0.0229208+0.517715im   0.0830404+0.363193im       0.157068+0.205921im      0.254332+0.067373im    0.379593-0.026087im    0.524118-0.0484074im   0.662039+0.0163403im    0.75688+0.163406im   0.777104+0.364037im\n   0.726602+0.264733im     0.673634+0.460754im    0.564658+0.62254im     0.42451+0.734172im     0.277783+0.792276im     0.142935+0.801596im     0.0303916+0.769731im   -0.0562551+0.703542im    -0.117442+0.608011im    -0.154422+0.487008im  -0.166521+0.34507im    -0.149734+0.189474im     -0.0974708+0.0321493im  -0.00385489-0.109276im    0.131046-0.212499im    0.296212-0.254862im    0.468111-0.220723im    0.615102-0.109082im   0.707182+0.0630756im\n   0.597178-0.0185423im    0.601301+0.161421im    0.546217+0.32944im    0.442188+0.46657im      0.304261+0.559965im     0.149097+0.603283im   -0.00741158+0.595734im    -0.151367+0.540622im    -0.271099+0.44408im     -0.356905+0.314404im  -0.400841+0.161998im   -0.397025-0.000359286im   -0.342634-0.157415im     -0.239438-0.292068im  -0.0953011-0.38711im    0.0751723-0.428079im    0.251638-0.406595im    0.410936-0.323077im    0.53139-0.187637im","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"We change plans with spin-1 now and reanalyze:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"P = plan_spinsph2fourier(F, 1)\nPA = plan_spinsph_analysis(F, 1)\nU¹s = P\\(PA*F)","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"10×19 Matrix{ComplexF64}:\n  1.03146e-17+2.24152im          0.792499-0.528332im        0.792499+0.528332im       -0.0752649+0.180636im       0.0752649+0.180636im     -0.00429218-0.0219378im     -0.00429218+0.0219378im      0.00124619+0.00125666im    -0.00124619+0.00125666im   -0.000105033-2.1464e-5im    -0.000105033+2.1464e-5im      4.87035e-6-1.98165e-6im    -4.87035e-6-1.98165e-6im    -1.21684e-7+1.79257e-7im    -1.21684e-7-1.79257e-7im     6.4556e-11-7.69602e-9im   -6.42651e-11-7.6961e-9im      1.3734e-10+1.99137e-10im   1.25853e-10-2.02909e-10im\n    -0.725151+1.27345e-16im      0.361271+0.541907im       -0.361271+0.541907im       -0.0841092-0.0350455im     -0.0841092+0.0350455im     0.00817504-0.00159947im    -0.00817504-0.00159947im   -0.000400574+0.000397236im  -0.000400574-0.000397236im    6.06873e-6-2.9697e-5im     -6.06873e-6-2.9697e-5im      5.08411e-7+1.24954e-6im     5.08411e-7-1.24954e-6im    -4.23861e-8-2.87724e-8im     4.23861e-8-2.87724e-8im     1.69612e-9+1.41282e-11im    1.69628e-9-1.41119e-11im  -4.07203e-11+2.96639e-11im   3.63017e-11+2.53159e-11im\n -1.27506e-16-0.0844589im       -0.145179+0.096786im       -0.145179-0.096786im       0.00803495-0.0192839im    -0.00803495-0.0192839im    0.000324556+0.00165884im    0.000324556-0.00165884im    -7.29881e-5-7.36014e-5im     7.29881e-5-7.36014e-5im     5.02037e-6+1.02593e-6im     5.02037e-6-1.02593e-6im     -1.9664e-7+8.00072e-8im      1.9664e-7+8.00072e-8im     4.25378e-9-6.26388e-9im     4.25378e-9+6.26388e-9im    6.53269e-12+2.1811e-10im   -6.52146e-12+2.18144e-10im  -1.63776e-11+3.36599e-12im  -1.53622e-11-3.76795e-12im\n -0.000893686-1.17031e-16im     -0.014106-0.0211589im       0.014106-0.0211589im      0.00272901+0.00113709im    0.00272901-0.00113709im   -0.00022178+4.33918e-5im     0.00022178+4.33918e-5im     9.27716e-6-9.19981e-6im     9.27716e-6+9.19981e-6im    -1.22275e-7+5.98394e-7im     1.22275e-7+5.98394e-7im    -9.06826e-9-2.22464e-8im    -9.06826e-9+2.22464e-8im    6.14926e-10+3.8178e-10im   -6.14926e-10+3.81779e-10im  -2.02946e-11+8.95683e-11im  -2.03114e-11-8.95764e-11im  -7.74569e-13-2.47296e-12im   9.78834e-13-2.19173e-12im\n -1.95236e-18-0.00154725im     0.00179232-0.00119488im    0.00179232+0.00119488im   -0.000108246+0.00025979im   0.000108246+0.00025979im   -4.14499e-6-2.11852e-5im    -4.14499e-6+2.11852e-5im     8.58374e-7+8.65614e-7im    -8.58374e-7+8.65614e-7im    -5.40698e-8-1.11423e-8im    -5.40698e-8+1.11423e-8im     1.63049e-9-7.15813e-10im   -1.63049e-9-7.15813e-10im       2.6e-10+2.34806e-10im       2.6e-10-2.34805e-10im  -9.52905e-12-1.46897e-12im    9.5312e-12-1.47346e-12im   3.24098e-12-6.83906e-13im   3.02544e-12+8.1283e-13im\n  0.000232639-2.043e-17im      4.53837e-5+6.80755e-5im   -4.53837e-5+6.80755e-5im    -1.68233e-5-7.00961e-6im   -1.68233e-5+7.00961e-6im    1.49733e-6-2.92965e-7im    -1.49733e-6-2.92965e-7im    -6.18845e-8+6.17602e-8im    -6.18845e-8-6.17602e-8im    4.71847e-10-3.03855e-9im   -4.71847e-10-3.03855e-9im     1.02475e-9-3.12162e-10im    1.02475e-9+3.12161e-10im  -2.32851e-11+2.79721e-11im    2.3285e-11+2.79721e-11im    5.5136e-12-2.47804e-11im   5.51954e-12+2.47829e-11im   2.05767e-13+6.50664e-13im  -2.63471e-13+5.82309e-13im\n   2.6244e-17+1.97929e-5im     3.54721e-6-2.36505e-6im    3.54721e-6+2.36505e-6im     2.74198e-7-6.5817e-7im    -2.74198e-7-6.5817e-7im     1.49997e-8+7.82205e-8im     1.49997e-8-7.82205e-8im    -2.72196e-9-2.73494e-9im     2.72196e-9-2.73494e-9im    4.22222e-10-1.58584e-9im    4.22222e-10+1.58584e-9im     1.4028e-11+4.2318e-11im   -1.40281e-11+4.2318e-11im   -7.00664e-11-6.32065e-11im  -7.00664e-11+6.32064e-11im   1.81319e-12+2.78508e-13im   -1.8136e-12+2.79428e-13im  -8.89736e-13+1.90103e-13im  -8.28863e-13-2.30288e-13im\n   -1.0618e-6-5.64811e-17im    5.06265e-7+7.59331e-7im   -5.06265e-7+7.59331e-7im     2.28542e-9+1.27481e-9im    2.28542e-9-1.27481e-9im   -1.53825e-9+3.35011e-10im    1.53825e-9+3.35011e-10im   -2.24932e-9-2.42853e-9im    -2.24932e-9+2.42853e-9im    1.43487e-10+3.57671e-11im  -1.43487e-10+3.57671e-11im  -4.84249e-10+1.47683e-10im  -4.84249e-10-1.47683e-10im   9.17836e-12-1.10319e-11im  -9.17828e-12-1.10319e-11im  -2.61497e-12+1.18851e-11im  -2.61825e-12-1.18864e-11im  -8.21238e-14-2.58938e-13im   1.05896e-13-2.32283e-13im\n -3.43863e-17-2.92736e-8im    -6.36569e-8+4.17996e-8im   -6.36569e-8-4.17996e-8im    6.18282e-10-1.39021e-9im  -6.18282e-10-1.39021e-9im  -4.16445e-10+7.77363e-11im  -4.16445e-10-7.77363e-11im    8.6631e-12-8.2083e-12im   -8.66306e-12-8.20835e-12im  -6.71953e-11+2.52391e-10im  -6.71953e-11-2.52391e-10im  -1.00987e-12-3.04635e-12im   1.00985e-12-3.0463e-12im    1.11584e-11+1.00647e-11im   1.11584e-11-1.00647e-11im  -1.30583e-13-2.0049e-14im     1.3063e-13-2.01245e-14im   1.41977e-13-3.03695e-14im   1.32244e-13+3.6862e-14im\n   -1.3507e-9+3.82397e-17im  -3.62349e-10-4.74615e-10im  3.62349e-10-4.74615e-10im    1.35757e-9-2.98609e-9im    1.35757e-9+2.98609e-9im  -2.68037e-12-1.17672e-11im   2.68035e-12-1.17672e-11im    3.06502e-9+3.30916e-9im     3.06502e-9-3.30916e-9im    -2.9668e-11-7.39518e-12im    2.9668e-11-7.39518e-12im   6.60325e-10-2.01412e-10im   6.60325e-10+2.01411e-10im  -1.89843e-12+2.28193e-12im   1.89842e-12+2.28192e-12im   3.56751e-12-1.62379e-11im   3.57202e-12+1.62398e-11im    1.6999e-14+5.3604e-14im   -2.19297e-14+4.80973e-14im","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"Finally, we check L^2(mathbbS^2) norms against another exact result:","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"norm(U¹c) ≈ norm(U¹s) ≈ sqrt(8π/3*(k⋅k))","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"true","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"","category":"page"},{"location":"generated/spinweighted/#","page":"Spin-weighted spherical harmonics","title":"Spin-weighted spherical harmonics","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/annulus.jl\"","category":"page"},{"location":"generated/annulus/#Integration-on-an-annulus-1","page":"Integration on an annulus","title":"Integration on an annulus","text":"","category":"section"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"In this example, we explore integration of the function:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"  f(xy) = fracx^3x^2+y^2-frac14","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"over the annulus defined by (rtheta)  rho  r  1 0  theta  2pi with parameter rho = frac23. We will calculate the integral:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"  int_0^2piint_frac23^1 f(rcosthetarsintheta)^2rrmdrrmdtheta","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"by analyzing the function in an annulus polynomial series. We analyze the function on an Ntimes M tensor product grid defined by:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"beginaligned\nr_n  = sqrtcos^2left(n+tfrac12)pi2Nright + rho^2 sin^2left(n+tfrac12)pi2Nrightquadrm forquad 0le n  Nquadrm and\ntheta_m  = 2pi mMquadrm forquad 0le m  M\nendaligned","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"we convert the function samples to Chebyshev×Fourier coefficients using plan_annulus_analysis; and finally, we transform the Chebyshev×Fourier coefficients to annulus polynomial coefficients using plan_ann2cxf.","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"For the storage pattern of the arrays, please consult the documentation.","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"using FastTransforms, LinearAlgebra, Plots\nconst GENFIGS = joinpath(pkgdir(FastTransforms), \"docs/src/generated\")\n!isdir(GENFIGS) && mkdir(GENFIGS)\nplotlyjs()","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"Plots.PlotlyJSBackend()","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"Our function f on the annulus:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"f = (x,y) -> x^3/(x^2+y^2-1/4)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"#1 (generic function with 1 method)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"The annulus polynomial degree:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"N = 8\nM = 4N-3","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"29","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"The annulus inner radius:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"ρ = 2/3","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"0.6666666666666666","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"The radial grid:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"r = [begin t = (N-n-0.5)/(2N); ct = sinpi(t); st = cospi(t); sqrt(ct^2+ρ^2*st^2) end for n in 0:N-1]","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"8-element Vector{Float64}:\n 0.9973277184004194\n 0.9763124517373388\n 0.9362410410518701\n 0.8811435628419545\n 0.8173313074308551\n 0.7535895152498838\n 0.7008983100472356\n 0.6706577864713554","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"The angular grid (mod pi):","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"θ = (0:M-1)*2/M","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"0.0:0.06896551724137931:1.9310344827586206","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"On the mapped tensor product grid, our function samples are:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"F = [f(r*cospi(θ), r*sinpi(θ)) for r in r, θ in θ]","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"8×29 Matrix{Float64}:\n 1.33215  1.24089  0.995869  0.672118  0.361447  0.136908  0.0255072  0.000211389  -0.00564085  -0.0675532  -0.235438  -0.509748  -0.838068  -1.13371  -1.30886  -1.30886  -1.13371  -0.838068  -0.509748  -0.235438  -0.0675532  -0.00564085  0.000211389  0.0255072  0.136908  0.361447  0.672118  0.995869  1.24089\n 1.32342  1.23275  0.989337  0.66771   0.359076  0.13601   0.0253399  0.000210003  -0.00560385  -0.0671101  -0.233894  -0.506405  -0.832572  -1.12628  -1.30028  -1.30028  -1.12628  -0.832572  -0.506405  -0.233894  -0.0671101  -0.00560385  0.000210003  0.0253399  0.13601   0.359076  0.66771   0.989337  1.23275\n 1.30981  1.22008  0.979168  0.660847  0.355385  0.134612  0.0250795  0.000207844  -0.00554625  -0.0664203  -0.23149   -0.5012    -0.824014  -1.1147   -1.28691  -1.28691  -1.1147   -0.824014  -0.5012    -0.23149   -0.0664203  -0.00554625  0.000207844  0.0250795  0.134612  0.355385  0.660847  0.979168  1.22008\n 1.29961  1.21057  0.97154   0.655698  0.352617  0.133563  0.0248841  0.000206225  -0.00550305  -0.0659028  -0.229687  -0.497295  -0.817594  -1.10601  -1.27689  -1.27689  -1.10601  -0.817594  -0.497295  -0.229687  -0.0659028  -0.00550305  0.000206225  0.0248841  0.133563  0.352617  0.655698  0.97154   1.21057\n 1.30613  1.21665  0.976415  0.658989  0.354386  0.134233  0.025009   0.00020726   -0.00553066  -0.0662336  -0.230839  -0.499791  -0.821697  -1.11156  -1.28329  -1.28329  -1.11156  -0.821697  -0.499791  -0.230839  -0.0662336  -0.00553066  0.00020726   0.025009   0.134233  0.354386  0.658989  0.976415  1.21665\n 1.34623  1.25399  1.00639   0.679218  0.365265  0.138354  0.0257767  0.000213622  -0.00570044  -0.0682668  -0.237925  -0.515133  -0.846922  -1.14569  -1.32269  -1.32269  -1.14569  -0.846922  -0.515133  -0.237925  -0.0682668  -0.00570044  0.000213622  0.0257767  0.138354  0.365265  0.679218  1.00639   1.25399\n 1.42719  1.32941  1.06692   0.720069  0.387234  0.146675  0.027327   0.00022647   -0.00604329  -0.0723726  -0.252235  -0.546115  -0.897858  -1.21459  -1.40224  -1.40224  -1.21459  -0.897858  -0.546115  -0.252235  -0.0723726  -0.00604329  0.00022647   0.027327   0.146675  0.387234  0.720069  1.06692   1.32941\n 1.5099   1.40645  1.12874   0.761795  0.409673  0.155175  0.0289105  0.000239594  -0.00639348  -0.0765664  -0.266852  -0.577762  -0.949887  -1.28498  -1.4835   -1.4835   -1.28498  -0.949887  -0.577762  -0.266852  -0.0765664  -0.00639348  0.000239594  0.0289105  0.155175  0.409673  0.761795  1.12874   1.40645","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"X = [r*cospi(θ) for r in r, θ in θ]\nY = [r*sinpi(θ) for r in r, θ in θ]\nscatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:red)\nsurface!(X, Y, F; legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"annulus.html\"))","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"<object type=\"text/html\" data=\"../annulus.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/annulus.html\"","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"We precompute an Annulus–Chebyshev×Fourier plan:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"α, β, γ = 0, 0, 0\nP = plan_ann2cxf(F, α, β, γ, ρ)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"FastTransforms Annulus--Chebyshev×Fourier plan for 8×29-element array of Float64","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"And an FFTW Chebyshev×Fourier analysis plan on the annulus:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"PA = plan_annulus_analysis(F, ρ)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"FastTransforms plan for FFTW Chebyshev×Fourier analysis on the annulus for 8×29-element array of Float64","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"Its annulus coefficients are:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"U = P\\(PA*F)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"8×29 Matrix{Float64}:\n -2.45849e-17   2.92896e-17   0.926725      2.04896e-17  -7.722e-18     6.1888e-17    0.29418      -1.81602e-17   2.67464e-17   1.20498e-17  -6.62939e-18   1.11857e-17  -1.67703e-17  -6.13512e-19  -3.42122e-17   6.23458e-17   1.8968e-17    3.12444e-17   4.92041e-18   3.83711e-17   7.86308e-17  -1.08653e-17   5.78808e-17  -1.56088e-17  -3.34631e-17  -8.2245e-18    3.76837e-17  -3.30615e-17  -4.36512e-17\n -9.36993e-18  -2.254e-18    -0.124037     -5.91733e-18   3.70137e-17  -1.89099e-17  -0.0976704     1.024e-18    -2.32787e-17  -9.77876e-18   2.00575e-17  -1.04302e-17   7.97476e-19  -5.50321e-18   4.69595e-17  -4.01755e-17  -1.55142e-18  -2.52689e-17   1.02515e-18  -2.67731e-17  -6.90711e-17   5.4336e-18   -5.62647e-17   1.0013e-17    1.53665e-17   7.96412e-18  -4.27121e-17   2.50418e-17   4.09539e-17\n -2.1258e-17    1.12715e-18   0.042116      9.94105e-19  -1.44328e-17   9.15449e-18   0.0336531     3.6262e-19    1.41794e-17   7.39131e-18  -9.39246e-18   6.73552e-18   7.9017e-18    1.31493e-18  -1.74808e-17   2.30498e-17  -4.92523e-18   1.03454e-17  -1.03774e-17   1.67754e-17   1.97933e-17  -8.57e-18      3.57962e-17  -1.14124e-17  -3.35749e-17  -5.45601e-18   2.98569e-17  -2.14064e-17  -3.95395e-17\n -5.78545e-18   4.00391e-18  -0.0139459     3.14722e-18  -1.97145e-18   5.82968e-18  -0.011224      6.26797e-18   2.25101e-17   6.88701e-18  -1.706e-18     7.40166e-18   3.44473e-18   9.55486e-18   5.33772e-18   2.9721e-18   -8.00488e-18   3.40533e-18   4.2453e-18    2.2961e-19   -1.44173e-17   7.73146e-18  -2.06172e-17   5.91455e-18   1.1306e-17    3.25478e-18  -1.21454e-17   8.18752e-18   4.67076e-18\n -2.40148e-17   7.71573e-19   0.00458845   -2.03822e-18   1.86344e-17   3.19547e-18   0.00369818   -1.86152e-18  -1.04804e-17   8.11326e-19   1.0092e-17   -1.77139e-18  -1.80973e-18  -6.8012e-18    1.80129e-18  -4.24712e-18   6.46529e-18  -7.2048e-18    7.11746e-18  -4.72462e-18   1.73345e-17  -5.27319e-18   1.40121e-17  -1.67467e-18  -4.79598e-19   8.00009e-19   6.60738e-18  -3.34661e-18  -2.0813e-18\n  2.61466e-17   1.71852e-19  -0.00150441    7.97602e-19  -9.38596e-18  -3.21855e-18  -0.00121128   -4.47164e-19  -8.79109e-18  -4.83245e-18   2.65743e-18  -5.47568e-18  -5.50836e-19  -2.9175e-18    7.42411e-18  -5.70705e-18  -3.31104e-18  -3.85137e-19   2.72442e-18  -5.31797e-19  -2.48579e-18   3.59849e-18   7.3637e-19    3.4972e-18    6.6109e-18    1.53405e-18   6.20867e-18   4.33464e-18   7.06298e-18\n  6.05256e-17  -4.20047e-18   0.000517281  -2.62968e-18   1.29799e-17  -9.06153e-18   0.000424358  -4.57265e-18   3.91183e-18  -6.80939e-18  -9.8607e-18   -2.399e-18     2.87152e-18   6.6648e-19   -2.13866e-17   1.69496e-20   4.87425e-18   5.37575e-18  -1.38669e-17   3.57204e-19  -5.42692e-18   2.48838e-18  -1.15939e-17   4.39475e-19   3.73151e-18  -1.63971e-18   2.61275e-18   1.39577e-18   8.50526e-18\n -1.16089e-17   6.39707e-19  -0.000162126   3.55753e-18   7.44168e-18   4.28763e-18  -5.40419e-5    5.16629e-18   7.08965e-18   5.4486e-18    6.55323e-18   4.64571e-18   2.63303e-18   6.04678e-19   6.15346e-19  -2.13942e-18  -1.32656e-17  -3.57457e-18   1.16079e-17  -5.67995e-18  -1.01101e-17  -4.98049e-18   1.02985e-17  -2.89642e-18  -1.8487e-17   -2.30036e-18   2.95997e-18  -1.26575e-18  -1.033e-17","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"The annulus coefficients are useful for integration. The integral of f(xy)^2 over the annulus is approximately the square of the 2-norm of the coefficients:","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"norm(U)^2, 5π/8*(1675/4536+9*log(3)/32-3*log(7)/32)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"(0.9735516844404255, 0.973547572736036)","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"","category":"page"},{"location":"generated/annulus/#","page":"Integration on an annulus","title":"Integration on an annulus","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/subspaceangles.jl\"","category":"page"},{"location":"generated/subspaceangles/#Subspace-angles-1","page":"Subspace angles","title":"Subspace angles","text":"","category":"section"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"This example considers the angles between neighbouring Laguerre polynomials with a perturbed measure:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"costheta_n = fraclangle L_n L_n+krangleL_n_2 L_n+k_2quadrm forquad 0le n  N-k","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"where the inner product is defined by langle f grangle = int_0^infty f(x) g(x) x^beta e^-xrmdx.","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"We do so by connecting Laguerre polynomials to the normalized generalized Laguerre polynomials associated with the perturbed measure. It follows by the inner product of the connection coefficients that:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"costheta_n = frac(V^top V)_n n+ksqrt(V^top V)_n n(V^top V)_n+k n+k","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"using FastTransforms, LinearAlgebra","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"The neighbouring index k and the maximum degree N-1:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"k, N = 1, 11","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"(1, 11)","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"The Laguerre connection parameters:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"α, β = 0.0, 0.125","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"(0.0, 0.125)","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"We precompute a Laguerre–Laguerre plan:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"P = plan_lag2lag(Float64, N, α, β; norm2=true)","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"FastTransforms Laguerre--Laguerre plan for 11-element array of Float64","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"We apply the plan to the identity, followed by the adjoint plan:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"VtV = parent(P*I)\nlmul!(P', VtV)","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"11×11 Matrix{Float64}:\n  0.941743    -0.117718    -0.0515016  -0.0321885  -0.0231355  -0.01793    -0.0145681  -0.0122268  -0.0105074  -0.00919399  -0.00815966\n -0.117718     1.07418     -0.125995   -0.0539157  -0.0333201  -0.0237861  -0.0183502  -0.0148608  -0.0124417  -0.0106716   -0.00932328\n -0.0515016   -0.125995     1.14505    -0.131707   -0.0557687  -0.0342413  -0.024336   -0.0187146  -0.0151194  -0.0126345   -0.0108205\n -0.0321885   -0.0539157   -0.131707    1.19444    -0.136106   -0.0572798  -0.0350206  -0.0248132  -0.0190369  -0.0153515   -0.0128093\n -0.0231355   -0.0333201   -0.0557687  -0.136106    1.23272    -0.139703   -0.0585599  -0.0356975  -0.0252354  -0.0193261   -0.015562\n -0.01793     -0.0237861   -0.0342413  -0.0572798  -0.139703    1.26415    -0.142756   -0.059673   -0.0362968  -0.0256145   -0.0195886\n -0.0145681   -0.0183502   -0.024336   -0.0350206  -0.0585599  -0.142756    1.29092    -0.145414   -0.0606594  -0.0368352   -0.0259588\n -0.0122268   -0.0148608   -0.0187146  -0.0248132  -0.0356975  -0.059673   -0.145414    1.31429    -0.147773   -0.0615464   -0.0373246\n -0.0105074   -0.0124417   -0.0151194  -0.0190369  -0.0252354  -0.0362968  -0.0606594  -0.147773    1.33507    -0.149896    -0.062353\n -0.00919399  -0.0106716   -0.0126345  -0.0153515  -0.0193261  -0.0256145  -0.0368352  -0.0615464  -0.149896    1.3538      -0.151829\n -0.00815966  -0.00932328  -0.0108205  -0.0128093  -0.015562   -0.0195886  -0.0259588  -0.0373246  -0.062353   -0.151829     1.37089","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"From this matrix, the angles are recovered from:","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"θ = [acos(VtV[n, n+k]/sqrt(VtV[n, n]*VtV[n+k, n+k])) for n in 1:N-k]","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"10-element Vector{Float64}:\n 1.6881063520094897\n 1.6846487354051982\n 1.6836556387180577\n 1.6831998143073255\n 1.6829427202726823\n 1.68277949501306\n 1.682667534322365\n 1.6825864250312665\n 1.6825252245704025\n 1.682477567030148","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"","category":"page"},{"location":"generated/subspaceangles/#","page":"Subspace angles","title":"Subspace angles","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/chebyshev.jl\"","category":"page"},{"location":"generated/chebyshev/#Chebyshev-transform-1","page":"Chebyshev transform","title":"Chebyshev transform","text":"","category":"section"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"This demonstrates the Chebyshev transform and inverse transform, explaining precisely the normalization and points","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"using FastTransforms\nn = 20","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"20","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"First kind points to first kind polynomials","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"p_1 = chebyshevpoints(Float64, n, Val(1))\nf = exp.(p_1)\nf̌ = chebyshevtransform(f, Val(1))\nf̃ = x -> [cos(k*acos(x)) for k=0:n-1]' * f̌\nf̃(0.1) ≈ exp(0.1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"First kind polynomials to first kind points","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"ichebyshevtransform(f̌, Val(1)) ≈ exp.(p_1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"Second kind points to first kind polynomials","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"p_2 = chebyshevpoints(Float64, n, Val(2))\nf = exp.(p_2)\nf̌ = chebyshevtransform(f, Val(2))\nf̃ = x -> [cos(k*acos(x)) for k=0:n-1]' * f̌\nf̃(0.1) ≈ exp(0.1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"First kind polynomials to second kind points","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"ichebyshevtransform(f̌, Val(2)) ≈ exp.(p_2)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"First kind points to second kind polynomials","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"p_1 = chebyshevpoints(Float64, n, Val(1))\nf = exp.(p_1)\nf̌ = chebyshevutransform(f, Val(1))\nf̃ = x -> [sin((k+1)*acos(x))/sin(acos(x)) for k=0:n-1]' * f̌\nf̃(0.1) ≈ exp(0.1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"Second kind polynomials to first kind points","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"ichebyshevutransform(f̌, Val(1)) ≈ exp.(p_1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"Second kind points to second kind polynomials","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"p_2 = chebyshevpoints(Float64, n, Val(2))[2:n-1]\nf = exp.(p_2)\nf̌ = chebyshevutransform(f, Val(2))\nf̃ = x -> [sin((k+1)*acos(x))/sin(acos(x)) for k=0:n-3]' * f̌\nf̃(0.1) ≈ exp(0.1)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"Second kind polynomials to second kind points","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"ichebyshevutransform(f̌, Val(2)) ≈ exp.(p_2)","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"true","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"","category":"page"},{"location":"generated/chebyshev/#","page":"Chebyshev transform","title":"Chebyshev transform","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/triangle.jl\"","category":"page"},{"location":"generated/triangle/#Calculus-on-the-reference-triangle-1","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"","category":"section"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"In this example, we sample a bivariate function:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"f(xy) = frac11+x^2+y^2","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"on the reference triangle with vertices (00), (01), and (10) and analyze it in a Proriol series. Then, we find Proriol series for each component of its gradient by term-by-term differentiation of our expansion, and we compare them with the true Proriol series by sampling an exact expression for the gradient.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"We analyze f(xy) on an Ntimes M mapped tensor product grid defined by:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"beginaligned\nx  = (1+u)2quadrm andquad y = (1-u)(1+v)4quad rm where\nu_n  = cosleft(n+tfrac12)piNrightquadrm forquad 0le n  Nquadrm and\nv_m  = cosleft(m+tfrac12)piMrightquadrm forquad 0le m  M\nendaligned","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"we convert the function samples to mapped Chebyshev² coefficients using plan_tri_analysis; and finally, we transform the mapped Chebyshev² coefficients to Proriol coefficients using plan_tri2cheb.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"For the storage pattern of the arrays, please consult the documentation.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"using FastTransforms, LinearAlgebra, Plots\nconst GENFIGS = joinpath(pkgdir(FastTransforms), \"docs/src/generated\")\n!isdir(GENFIGS) && mkdir(GENFIGS)\nplotlyjs()","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Plots.PlotlyJSBackend()","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Our function f and the Cartesian components of its gradient:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"f = (x,y) -> 1/(1+x^2+y^2)\nfx = (x,y) -> -2x/(1+x^2+y^2)^2\nfy = (x,y) -> -2y/(1+x^2+y^2)^2","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"#5 (generic function with 1 method)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"The polynomial degree:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"N = 15\nM = N","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"The parameters of the Proriol series:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"α, β, γ = 0, 0, 0","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"(0, 0, 0)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"The u grid:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"u = [sinpi((N-2n-1)/(2N)) for n in 0:N-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15-element Vector{Float64}:\n  0.9945218953682733\n  0.9510565162951536\n  0.8660254037844386\n  0.7431448254773942\n  0.5877852522924731\n  0.4067366430758002\n  0.20791169081775934\n  0.0\n -0.20791169081775934\n -0.4067366430758002\n -0.5877852522924731\n -0.7431448254773942\n -0.8660254037844386\n -0.9510565162951536\n -0.9945218953682733","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"And the v grid:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"v = [sinpi((M-2m-1)/(2M)) for m in 0:M-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15-element Vector{Float64}:\n  0.9945218953682733\n  0.9510565162951536\n  0.8660254037844386\n  0.7431448254773942\n  0.5877852522924731\n  0.4067366430758002\n  0.20791169081775934\n  0.0\n -0.20791169081775934\n -0.4067366430758002\n -0.5877852522924731\n -0.7431448254773942\n -0.8660254037844386\n -0.9510565162951536\n -0.9945218953682733","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Instead of using the utimes v grid, we use one with more accuracy near the origin. Defining x by:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"x = [sinpi((2N-2n-1)/(4N))^2 for n in 0:N-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15-element Vector{Float64}:\n 0.9972609476841365\n 0.9755282581475768\n 0.9330127018922194\n 0.8715724127386971\n 0.7938926261462365\n 0.7033683215379002\n 0.6039558454088797\n 0.5000000000000001\n 0.3960441545911204\n 0.2966316784620999\n 0.2061073738537634\n 0.12842758726130288\n 0.06698729810778066\n 0.024471741852423214\n 0.0027390523158633317","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"And w by:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"w = [sinpi((2M-2m-1)/(4M))^2 for m in 0:M-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15-element Vector{Float64}:\n 0.9972609476841365\n 0.9755282581475768\n 0.9330127018922194\n 0.8715724127386971\n 0.7938926261462365\n 0.7033683215379002\n 0.6039558454088797\n 0.5000000000000001\n 0.3960441545911204\n 0.2966316784620999\n 0.2061073738537634\n 0.12842758726130288\n 0.06698729810778066\n 0.024471741852423214\n 0.0027390523158633317","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"We see how the two grids are related:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"((1 .+ u)./2 ≈ x) * ((1 .- u).*(1 .+ v')/4 ≈ reverse(x).*w')","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"true","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"On the mapped tensor product grid, our function samples are:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"F = [f(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n 0.50137   0.50137   0.50137   0.50137   0.50137   0.50137   0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371  0.501371\n 0.512229  0.512236  0.512249  0.512266  0.512286  0.512308  0.512328  0.512346  0.512361  0.512372  0.512379  0.512383  0.512385  0.512385  0.512386\n 0.53334   0.533395  0.533499  0.53364   0.533806  0.533979  0.534145  0.534292  0.534412  0.5345    0.534558  0.534592  0.534607  0.534612  0.534613\n 0.56305   0.563274  0.563699  0.564281  0.564961  0.565675  0.566362  0.56697   0.567464  0.56783   0.568072  0.568211  0.568275  0.568295  0.568299\n 0.597903  0.598554  0.599792  0.601491  0.603486  0.60559   0.607622  0.609427  0.6109    0.611994  0.612719  0.613134  0.613325  0.613387  0.613397\n 0.632017  0.633527  0.636406  0.640382  0.645085  0.650086  0.654955  0.659315  0.662898  0.665571  0.66735   0.66837   0.668842  0.668995  0.669018\n 0.657568  0.660489  0.666088  0.673894  0.683237  0.693308  0.703247  0.712263  0.719753  0.725392  0.729168  0.731342  0.73235   0.732678  0.732728\n 0.667275  0.672082  0.681371  0.694488  0.710446  0.727971  0.745606  0.761905  0.775667  0.786165  0.79326   0.79737   0.799283  0.799904  0.799999\n 0.65806   0.664903  0.678251  0.69738   0.721111  0.74777   0.775252  0.801255  0.82368   0.841081  0.85299   0.859943  0.863194  0.864252  0.864414\n 0.632907  0.641519  0.658477  0.683152  0.714388  0.750331  0.788365  0.825306  0.857936  0.883766  0.901708  0.912284  0.917254  0.918876  0.919123\n 0.599054  0.608911  0.628482  0.657352  0.694582  0.738395  0.78593   0.833301  0.876165  0.910799  0.935231  0.94978   0.956655  0.958904  0.959246\n 0.564342  0.574908  0.59603   0.627532  0.668777  0.718232  0.773048  0.82891   0.880558  0.923076  0.953504  0.971796  0.980486  0.983334  0.983768\n 0.534691  0.545579  0.567447  0.600326  0.643856  0.69679   0.756419  0.818253  0.876403  0.924997  0.960184  0.981503  0.991676  0.995016  0.995526\n 0.513598  0.524591  0.546739  0.58021   0.624846  0.679621  0.74199   0.80742   0.869666  0.922224  0.960591  0.983966  0.995154  0.998833  0.999394\n 0.502741  0.513754  0.535975  0.569641  0.614694  0.670229  0.733797  0.800871  0.865052  0.919526  0.959458  0.983854  0.99555   0.999397  0.999985","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"X = [x for x in x, w in w]\nY = [x[N-n]*w[m+1] for n in 0:N-1, m in 0:M-1]\nscatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:blue)\nsurface!(X, Y, F; legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"proriol.html\"))","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"<object type=\"text/html\" data=\"../proriol.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/proriol.html\"","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"We precompute a Proriol–Chebyshev² plan:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"P = plan_tri2cheb(F, α, β, γ)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"FastTransforms Proriol--Chebyshev² plan for 15×15-element array of Float64","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"And an FFTW Chebyshev² plan on the triangle:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"PA = plan_tri_analysis(F)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"FastTransforms plan for FFTW Chebyshev analysis on the triangle for 15×15-element array of Float64","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Its Proriol-(αβγ) coefficients are:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"U = P\\(PA*F)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n  1.53694      -0.193325     -0.0251445     0.0109626    -0.000813095  -0.000299751   8.30397e-5   -1.59722e-6   -3.2141e-6     6.1667e-7     3.19775e-8   -3.21495e-8    4.17144e-9    6.97174e-10  -3.06613e-10\n -0.111616      0.0391775    -0.00636098   -0.000168172   0.000311296  -5.50434e-5   -2.99195e-6    2.97964e-6   -4.20688e-7   -5.4534e-8     2.85785e-8   -2.74994e-9   -7.77992e-10   2.56775e-10  -1.20763e-11\n -0.0620411     0.00717668    0.00153132   -0.000551474   4.1134e-5     1.40597e-5   -4.21186e-6    2.00844e-7    1.36869e-7   -3.34625e-8    3.38022e-10   1.36685e-9   -2.6459e-10   -1.30929e-11   1.45495e-11\n  0.0111316    -0.0036578     0.00043735    4.52913e-5   -2.72385e-5    3.78477e-6    3.57508e-7   -2.26663e-7    2.88459e-8    4.02905e-9   -1.98431e-9    2.01016e-10   4.97746e-11  -1.48758e-11  -2.03145e-12\n  0.00194132   -7.70184e-5   -0.000145948   3.68556e-5   -1.34273e-6   -1.26813e-6    3.06047e-7   -7.57685e-9   -1.11605e-8    2.45432e-9   -1.63544e-12  -1.03205e-10   9.87731e-12   5.4552e-12   -6.15786e-13\n -0.000642637   0.000243768  -2.28339e-5   -5.91216e-6    2.28045e-6   -2.36988e-7   -4.55496e-8    1.90448e-8   -1.91046e-9   -4.16463e-10   1.54281e-10   1.00975e-11  -8.91873e-12  -7.74977e-13   5.33203e-13\n -4.38389e-5   -1.71425e-5    1.23092e-5   -2.29813e-6   -6.48598e-8    1.17977e-7   -2.21226e-8   -4.58497e-10   1.02068e-9   -1.63471e-10  -4.64131e-11   6.91421e-12   3.5224e-12   -3.14287e-13  -2.28437e-13\n  2.79805e-5   -1.30453e-5    7.26152e-7    5.87656e-7   -1.71884e-7    1.12463e-8    5.13657e-9   -1.54461e-9    7.05239e-11   8.70592e-11   6.67155e-12  -5.87108e-12  -8.81458e-13   3.50646e-13   6.6012e-14\n  1.15026e-6    1.8828e-6    -8.87898e-7    1.24893e-7    1.74103e-8   -1.00961e-8    1.44036e-9    1.53829e-10  -9.59941e-11  -3.49153e-11   3.35896e-12   3.17799e-12  -1.72731e-14  -2.20896e-13  -4.40702e-15\n -1.05261e-6    6.07061e-7    9.40225e-9   -4.93564e-8    1.14023e-8   -2.56371e-10  -4.79206e-10   1.50921e-11   6.48843e-11   1.18558e-11  -4.29768e-12  -1.50758e-12   2.19181e-13   1.20467e-13  -1.21247e-14\n -1.0706e-7    -1.2895e-7     5.63778e-8   -5.46716e-9   -1.98245e-9    6.62772e-10   1.96009e-10  -4.05866e-11  -3.72009e-11  -3.44512e-12   3.09917e-12   6.84676e-13  -1.93699e-13  -6.20043e-14   1.20607e-14\n  4.44232e-8   -2.74042e-8   -3.41194e-9    3.7536e-9    -3.47875e-10  -3.34332e-10  -7.92618e-11   2.84843e-11   1.87606e-11   8.64622e-13  -1.73542e-12  -2.98547e-13   1.16631e-13   2.95637e-14  -7.54383e-15\n  1.13247e-8    6.98157e-9   -3.2324e-9    -1.06114e-10   1.55319e-10   1.35282e-10   2.8768e-11   -1.28905e-11  -7.59283e-12  -1.99177e-13   7.32667e-13   1.12735e-13  -5.05704e-14  -1.16743e-14   3.30983e-15\n -2.57523e-9    1.14806e-9    1.12793e-10   2.51422e-11  -4.12541e-11  -3.49672e-11  -7.18293e-12   3.43673e-12   1.96276e-12   3.986e-14    -1.91745e-13  -2.85197e-14   1.33334e-14   2.99891e-15  -8.7656e-16\n -7.03699e-10  -8.33285e-12  -8.53391e-12  -1.88826e-12   3.13558e-12   2.65053e-12   5.42528e-13  -2.61311e-13  -1.4878e-13   -2.93168e-15   1.45531e-14   2.15642e-15  -1.01318e-15  -2.26875e-16   6.66619e-17","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Similarly, our function's gradient samples are:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Fx = [fx(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n -0.501366    -0.501366    -0.501366    -0.501367   -0.501367   -0.501368   -0.501368    -0.501369    -0.501369    -0.501369    -0.501369    -0.501369    -0.501369    -0.50137    -0.50137\n -0.511916    -0.511929    -0.511955    -0.51199    -0.51203    -0.512073   -0.512114    -0.51215     -0.512179    -0.512201    -0.512215    -0.512223    -0.512227    -0.512228   -0.512228\n -0.530794    -0.530903    -0.53111     -0.531392   -0.531721   -0.532067   -0.532398    -0.532691    -0.532929    -0.533105    -0.533222    -0.533288    -0.533319    -0.533329   -0.53333\n -0.552621    -0.553061    -0.553896    -0.555039   -0.556378   -0.557787   -0.559142    -0.560343    -0.56132     -0.562044    -0.562524    -0.562798    -0.562924    -0.562965   -0.562972\n -0.567613    -0.568852    -0.571206    -0.574447   -0.578264   -0.582304   -0.586217    -0.589705    -0.59256     -0.594683    -0.596093    -0.5969      -0.597274    -0.597395   -0.597413\n -0.561915    -0.564604    -0.569746    -0.576887   -0.585391   -0.594503   -0.603442    -0.611504    -0.618167    -0.623163    -0.626498    -0.628414    -0.629303    -0.629591   -0.629635\n -0.522296    -0.526946    -0.535918    -0.548553   -0.563869   -0.580614   -0.59738     -0.612796    -0.625752    -0.635596    -0.64223     -0.646065    -0.647848    -0.648427   -0.648515\n -0.445256    -0.451694    -0.464267    -0.482314   -0.504734   -0.529941   -0.555929    -0.580499    -0.60166     -0.618055    -0.629262    -0.635798    -0.638853    -0.639847   -0.639998\n -0.343008    -0.350179    -0.364379    -0.385223   -0.411887   -0.442905   -0.476058    -0.508529    -0.537391    -0.560337    -0.576318    -0.585751    -0.590188    -0.591636   -0.591857\n -0.237644    -0.244156    -0.257234    -0.276874   -0.302772   -0.334005   -0.368724    -0.404089    -0.436673    -0.463364    -0.482369    -0.49375     -0.499145    -0.500911   -0.501181\n -0.14793     -0.152838    -0.162821    -0.178123   -0.198871   -0.22475    -0.254619    -0.286238    -0.316443    -0.341954    -0.360547    -0.371851    -0.377255    -0.37903    -0.379301\n -0.0818036   -0.0848957   -0.0912482   -0.101149   -0.114882   -0.132501   -0.153497    -0.176483    -0.199161    -0.218858    -0.233525    -0.242571    -0.246928    -0.248365   -0.248585\n -0.0383026   -0.0398784   -0.0431393   -0.0482832  -0.0555393  -0.0650468  -0.0766563   -0.0897011   -0.102903    -0.114631    -0.123518    -0.129064    -0.131754    -0.132643   -0.132779\n -0.0129105   -0.013469    -0.0146303   -0.0164765  -0.0191091  -0.0226062  -0.0269458   -0.0319076   -0.0370169   -0.0416263   -0.0451619   -0.0473866   -0.0484703   -0.0488293  -0.0488842\n -0.00138458  -0.00144591  -0.00157369  -0.0017776  -0.0020699  -0.0024608  -0.00294973  -0.00351363  -0.00409934  -0.00463189  -0.00504292  -0.00530263  -0.00542945  -0.0054715  -0.00547794","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"and:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Fy = [fy(x[n+1], x[N-n]*w[m+1]) for n in 0:N-1, m in 0:M-1]","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n -0.00137327  -0.00134334  -0.0012848  -0.00120019  -0.00109322  -0.000968569  -0.000831675  -0.000688523  -0.000545372  -0.000408476  -0.00028382  -0.000176851  -9.22448e-5   -3.36988e-5   -3.77181e-6\n -0.0128066   -0.0125278   -0.0119824  -0.0111941   -0.0101972   -0.00903524   -0.00775884   -0.0064238    -0.00508851   -0.00381138   -0.00264832  -0.00165022   -0.000860756  -0.000314451  -3.51956e-5\n -0.0380049   -0.0371844   -0.0355776  -0.0332524   -0.0303075   -0.0268691    -0.0230859    -0.0191228    -0.0151537    -0.0113536    -0.00789053  -0.00491728   -0.00256498   -0.000937054  -0.000104882\n -0.0812065   -0.0795001   -0.0761501  -0.0712824   -0.0650859   -0.0578104    -0.0497602    -0.0412837    -0.0327574    -0.0245665    -0.017084    -0.0106504    -0.00555645   -0.00203003   -0.000227217\n -0.146958    -0.144069    -0.138361   -0.129983    -0.119184    -0.106332     -0.0919169    -0.0765485    -0.0609267    -0.0457968    -0.0318962   -0.0199018    -0.0103872    -0.00379541   -0.000424822\n -0.236327    -0.232283    -0.224184   -0.212046    -0.195994    -0.176349     -0.153701     -0.128945     -0.103249     -0.0779568    -0.0544563   -0.0340361    -0.0177782    -0.00649768   -0.000727317\n -0.341557    -0.337089    -0.327887   -0.313516    -0.293548    -0.267799     -0.236589     -0.200921     -0.162512     -0.123634     -0.0868006   -0.0544092    -0.028458     -0.0104055    -0.00116482\n -0.444036    -0.44064     -0.433167   -0.420371    -0.400704    -0.372744     -0.335756     -0.290249     -0.238284     -0.183335     -0.129696    -0.0816541    -0.042795     -0.0156582    -0.00175299\n -0.521645    -0.520944    -0.518445   -0.512009    -0.498657    -0.475067     -0.438456     -0.387746     -0.32456      -0.253471     -0.181141    -0.114718     -0.0602899    -0.0220791    -0.00247217\n -0.561955    -0.56477     -0.56909    -0.572203    -0.569958    -0.557059     -0.528047     -0.479085     -0.410077     -0.325915     -0.235743    -0.15036      -0.0792838    -0.0290664    -0.00325507\n -0.568241    -0.574301    -0.585148   -0.597987    -0.608136    -0.608908     -0.592332     -0.551271     -0.482733     -0.39071      -0.286235    -0.183948     -0.0973409    -0.0357278    -0.00400177\n -0.553639    -0.562044    -0.577773   -0.598286    -0.618953    -0.632479     -0.629146     -0.598851     -0.535295     -0.440581     -0.326642    -0.211418     -0.112256     -0.0412478    -0.00462083\n -0.532026    -0.541842    -0.560603   -0.586131    -0.614126    -0.637241     -0.644834     -0.624688     -0.567634     -0.473605     -0.354585    -0.230866     -0.122928     -0.0452109    -0.00506551\n -0.513246    -0.523783    -0.544148   -0.572459    -0.604752    -0.633849     -0.648741     -0.635973     -0.584411     -0.492221     -0.371057    -0.242599     -0.129432     -0.0476343    -0.00533757\n -0.502731    -0.513558    -0.534584   -0.564086    -0.5983      -0.630184     -0.648628     -0.639638     -0.591107     -0.500247     -0.378429    -0.247947     -0.132421     -0.0487506    -0.00546294","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"For the partial derivative with respect to x, Olver et al. derive simple expressions for the representation of this component using a Proriol-(α+1βγ+1) series.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Gx = zeros(Float64, N, M)\nfor m = 0:M-2\n    for n = 0:N-2\n        cf1 = m == 0 ? sqrt((n+1)*(n+2m+α+β+γ+3)/(2m+β+γ+2)*(m+γ+1)*8) : sqrt((n+1)*(n+2m+α+β+γ+3)/(2m+β+γ+1)*(m+β+γ+1)/(2m+β+γ+2)*(m+γ+1)*8)\n        cf2 = sqrt((n+α+1)*(m+1)/(2m+β+γ+2)*(m+β+1)/(2m+β+γ+3)*(n+2m+β+γ+3)*8)\n        Gx[n+1, m+1] = cf1*U[n+2, m+1] + cf2*U[n+1, m+2]\n    end\nend\nPx = plan_tri2cheb(Fx, α+1, β, γ+1)\nUx = Px\\(PA*Fx)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n -0.773299      0.0719368     0.0119032    -0.00401514    0.00019856    0.000113662  -2.54579e-5   -2.37734e-7    1.03154e-6   -1.60364e-7   -1.48715e-8    9.00448e-9   -8.97984e-10  -2.25712e-10   7.08345e-11\n -0.223004      0.012725      0.00860848   -0.00187243   -6.32049e-5    8.83801e-5   -1.1938e-5    -1.70295e-6    7.84936e-7   -6.04351e-8   -2.29491e-8    6.45891e-9   -1.23274e-10  -2.55873e-10   5.02863e-11\n  0.11832      -0.0184961    -0.000231272   0.000708416  -0.000135183  -8.87531e-7    5.70658e-6   -1.08175e-6   -3.24208e-8    5.24395e-8   -8.50439e-9   -6.81366e-10   4.94759e-10  -5.56212e-11  -1.16264e-11\n -0.00167066    0.00241796   -0.00105495    0.000134423   2.32113e-5   -1.10992e-5    1.1835e-6     2.55024e-7   -1.00326e-7    8.05316e-9    2.80938e-9   -8.7387e-10    3.23657e-11   3.71003e-11  -4.71069e-12\n -0.00812992    0.00143193    9.5529e-5    -8.6497e-5     1.46322e-5    6.06568e-7   -7.52503e-7    1.2809e-7     6.41825e-9   -6.76798e-9    1.05309e-9    1.02809e-10  -6.38887e-11  -4.60391e-12   3.43243e-12\n  0.00134269   -0.000440563   9.61255e-5   -3.9763e-6    -4.07863e-6    1.16773e-6   -7.04875e-8   -3.76919e-8    1.09538e-8   -5.76688e-10  -3.72602e-10   6.21711e-11   2.34835e-11  -3.2882e-12   -1.02885e-12\n  0.000287063  -5.03055e-5   -1.79725e-5    8.218e-6     -1.05921e-6   -1.54886e-7    8.35392e-8   -1.11246e-8   -1.37121e-9    7.34787e-10   2.35493e-11  -4.77271e-11  -3.34076e-12   2.78949e-12   2.71204e-14\n -0.000114154   3.91247e-5   -6.41411e-6   -4.57437e-7    4.91696e-7   -1.01409e-7    1.49415e-12   4.73486e-9   -8.87703e-10  -2.29361e-10   4.39281e-11   2.01683e-11  -2.11613e-12  -1.32213e-12   2.00985e-13\n  6.85033e-7   -1.42592e-6    2.06904e-6   -6.34246e-7    4.7282e-8     2.34694e-8   -7.6778e-9     5.5085e-10    4.78984e-10   2.6482e-11   -3.78611e-11  -5.10671e-12   2.54966e-12   4.06715e-13  -1.86401e-13\n  5.33318e-6   -2.34997e-6    2.9001e-7     9.45302e-8   -4.55097e-8    7.14241e-9    5.63984e-10  -6.44351e-10  -2.12017e-10   3.18388e-11   2.34425e-11  -6.60811e-13  -1.88678e-12  -1.33748e-14   1.29398e-13\n -7.178e-7      3.37971e-7   -1.76689e-7    3.81304e-8   -1.11295e-9   -2.48346e-9    1.24297e-10   4.4888e-10    8.62743e-11  -3.44107e-11  -1.28198e-11   1.79781e-12   1.16066e-12  -8.54648e-14  -7.76709e-14\n -1.15794e-7    9.93748e-8   -5.08059e-9   -9.45944e-9    2.65499e-9    1.0741e-9    -1.63514e-10  -2.32795e-10  -3.2556e-11    2.03989e-11   5.96492e-12  -1.21808e-12  -5.75477e-13   6.48277e-14   3.81309e-14\n  3.9894e-8    -2.50603e-8    1.18665e-8   -3.69658e-10  -9.43959e-10  -3.54061e-10   7.05516e-11   8.25944e-11   9.98239e-12  -7.57296e-12  -2.02892e-12   4.70119e-13   2.00989e-13  -2.57414e-14  -1.32683e-14\n -2.62946e-9   -2.09989e-9   -2.15583e-10   7.49659e-11   1.79606e-10   6.58835e-11  -1.40885e-11  -1.57067e-11  -1.81381e-12   1.45833e-12   3.81132e-13  -9.14673e-14  -3.80526e-14   5.0449e-15    2.50893e-15\n -2.54665e-10   1.01738e-11   9.71511e-12  -3.41148e-12  -8.12007e-12  -2.97149e-12   6.40143e-13   7.10069e-13   8.15917e-14  -6.60159e-14  -1.72076e-14   4.14493e-15   1.71957e-15  -2.28703e-16  -1.13413e-16","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"For the partial derivative with respect to y, the analogous formulae result in a Proriol-(αβ+1γ+1) series.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"Gy = zeros(Float64, N, M)\nfor m = 0:M-2\n    for n = 0:N-2\n        Gy[n+1, m+1] = 4*sqrt((m+1)*(m+β+γ+2))*U[n+1, m+2]\n    end\nend\nPy = plan_tri2cheb(Fy, α, β+1, γ+1)\nUy = Py\\(PA*Fy)","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"15×15 Matrix{Float64}:\n -1.09361      -0.246364      0.151902     -0.0145451    -0.00656722    0.00215264   -4.78099e-5   -0.00010909    2.3401e-5     1.34141e-6   -1.47744e-6    2.0787e-7     3.67354e-8   -1.65807e-8    1.30376e-9\n  0.221621     -0.0623246    -0.00233026    0.00556863   -0.00120594   -7.75602e-5    8.91904e-5   -1.42786e-5   -2.06939e-6    1.19894e-6   -1.26335e-7   -3.89258e-8    1.42118e-8   -5.60413e-10  -5.94789e-10\n  0.0405975     0.0150038    -0.00764145    0.000735827   0.000308032  -0.000109184   6.01193e-6    4.6455e-6    -1.26982e-6    1.41852e-8    6.28061e-8   -1.31763e-8   -5.9232e-10    7.38193e-10  -7.35368e-11\n -0.0206916     0.00428514    0.000627575  -0.000487257   8.29203e-5    9.26771e-6   -6.78478e-6    9.79044e-7    1.52891e-7   -8.32462e-8    9.23683e-9    2.37699e-9   -9.33549e-10  -2.54744e-11   5.13027e-11\n -0.000435682  -0.00142999    0.000510686  -2.40196e-5   -2.77834e-5    7.93359e-6   -2.26768e-7   -3.78776e-7    9.31367e-8   -7.2912e-11   -4.72764e-9    9.19194e-10   1.83342e-10  -5.07975e-11  -9.73934e-12\n  0.00137896   -0.000223726  -8.19213e-5    4.07942e-5   -5.19191e-6   -1.18071e-6    5.70025e-7   -6.48815e-8   -1.5805e-8     6.74933e-9   -5.22325e-10  -3.74577e-10   2.04346e-11   2.31629e-11  -1.45178e-12\n -9.69728e-5    0.000120605  -3.18437e-5   -1.1605e-6     2.58441e-6   -5.73589e-7   -1.36421e-8    3.47148e-8   -6.95597e-9   -3.86259e-10   4.86604e-10   7.26716e-11  -3.26991e-11  -5.56081e-12   2.18954e-12\n -7.37954e-5    7.11448e-6    8.14267e-6   -3.07439e-6    2.46945e-7    1.33361e-7   -4.63869e-8    3.49405e-9    1.69907e-9   -3.52262e-10  -2.0628e-10    1.07045e-11   1.73416e-11  -1.88625e-13  -1.24581e-12\n  1.06509e-5   -8.69913e-6    1.73077e-6    3.10766e-7   -2.22347e-7    3.70118e-8    3.9365e-9    -2.94133e-9   -2.1645e-10    2.94085e-10   6.42746e-11  -2.03559e-11  -6.99252e-12   1.20561e-12   5.53973e-13\n  3.43376e-6    9.14735e-8   -6.84306e-7    2.05405e-7   -4.3435e-9    -1.35246e-8    2.85641e-9    1.15843e-9   -9.56842e-11  -1.59766e-10  -1.45705e-11   1.36984e-11   2.42347e-12  -9.13607e-13  -2.17217e-13\n -7.29088e-7    5.54006e-7   -7.49665e-8   -3.61409e-8    1.78364e-8   -4.16571e-10  -1.36673e-9   -4.10814e-10   8.7904e-11    6.992e-11     1.76878e-12  -6.65703e-12  -7.49909e-13   4.67294e-13   7.67789e-14\n -1.56131e-7   -3.60972e-8    5.21717e-8   -9.4804e-9    -1.42828e-9    2.71687e-10   4.84151e-10   1.24081e-10  -3.76632e-11  -2.38535e-11   1.85871e-13   2.38967e-12   2.02456e-13  -1.7174e-13   -2.30959e-14\n  4.09267e-8   -3.39594e-8   -3.06743e-9    7.64151e-10   3.1345e-10   -7.59843e-11  -1.14715e-10  -2.73663e-11   9.55255e-12   5.56757e-12  -1.22703e-13  -5.69904e-13  -4.1879e-14    4.1357e-14    5.08049e-15\n  8.57039e-9    6.52951e-9   -7.39973e-11  -9.29778e-11  -3.74097e-11   9.74901e-12   1.40429e-11   3.27131e-12  -1.19385e-12  -6.78321e-13   1.80885e-14   6.99172e-14   4.88938e-15  -5.08948e-15  -6.06714e-16\n -2.86296e-9    1.21911e-13   2.03235e-12   2.54849e-12   1.02299e-12  -2.68873e-13  -3.8519e-13   -8.94733e-14   3.28267e-14   1.85955e-14  -5.06208e-16  -1.91829e-15  -1.33321e-16   1.39689e-16   1.65848e-17","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"The 2-norm relative error in differentiating the Proriol series for f(xy) term-by-term and its sampled gradient is:","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"hypot(norm(Ux-Gx), norm(Uy-Gy))/hypot(norm(Ux), norm(Uy))","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"1.8769900875801852e-8","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"This error can be improved upon by increasing N and M.","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"","category":"page"},{"location":"generated/triangle/#","page":"Calculus on the reference triangle","title":"Calculus on the reference triangle","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/nonlocaldiffusion.jl\"","category":"page"},{"location":"generated/nonlocaldiffusion/#Nonlocal-diffusion-on-\\mathbb{S}2-1","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"","category":"section"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"This example calculates the spectrum of the nonlocal diffusion operator:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"mathcalL_delta u = int_mathbbS^2 rho_delta(mathbfx-mathbfy)leftu(mathbfx) - u(mathbfy)right mathrmdOmega(mathbfy)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"defined in Eq. (2) of","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"R. M. Slevinsky, H. Montanelli, and Q. Du, A spectral method for nonlocal diffusion operators on the sphere, J. Comp. Phys., 372:893–911, 2018.","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"In the above, 0delta2, -1alpha1, and the kernel:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"rho_delta(mathbfx-mathbfy) = frac4(1+alpha)pi delta^2+2alpha fracchi_0delta(mathbfx-mathbfy)mathbfx-mathbfy^2-2alpha","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"where chi_I(cdot) is the indicator function on the set I.","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"This nonlocal operator is diagonalized by spherical harmonics:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"mathcalL_delta Y_ell^m(mathbfx) = lambda_ell(alpha delta) Y_ell^m(mathbfx)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"and its eigenfunctions are given by the generalized Funk–Hecke formula:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"lambda_ell(alpha delta) = frac(1+alpha) 2^2+alphadelta^2+2alphaint_1-delta^22^1 leftP_ell(t)-1right (1-t)^alpha-1 mathrmd t","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"In the paper, the authors use Clenshaw–Curtis quadrature and asymptotic evaluation of Legendre polynomials to achieve mathcalO(n^2log n) complexity for the evaluation of the first n eigenvalues. With a change of basis, this complexity can be reduced to mathcalO(nlog n).","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"First, we represent:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"P_n(t) - 1 = sum_j=0^n-1 leftP_j+1(t) - P_j(t)right = -sum_j=0^n-1 (1-t) P_j^(10)(t)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"Then, we represent P_j^(10)(t) with Jacobi polynomials P_i^(alpha0)(t) and we integrate using DLMF 18.9.16:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"int_x^1 P_i^(alpha0)(t)(1-t)^alphamathrmdt = left beginarraycc frac(1-x)^alpha+1alpha+1  mathrmfori=0 frac12i(1-x)^alpha+1(1+x)P_i-1^(alpha+11)(x)  mathrmfori0endarrayright","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"The code below implements this algorithm, making use of the Jacobi–Jacobi transform plan_jac2jac. For numerical stability, the conversion from Jacobi polynomials P_j^(10)(t) to P_i^(alpha0)(t) is divided into conversion from P_j^(10)(t) to P_k^(00)(t), before conversion from P_k^(00)(t) to P_i^(alpha0)(t).","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"using FastTransforms, LinearAlgebra\n\nfunction oprec!(n::Integer, v::AbstractVector, alpha::Real, delta2::Real)\n    if n > 0\n        v[1] = 1\n    end\n    if n > 1\n        v[2] = (4*alpha+8-(alpha+4)*delta2)/4\n    end\n    for i = 1:n-2\n        v[i+2] = (((2*i+alpha+2)*(2*i+alpha+4)+alpha*(alpha+2))/(2*(i+1)*(2*i+alpha+2))*(2*i+alpha+3)/(i+alpha+3) - delta2/4*(2*i+alpha+3)/(i+1)*(2*i+alpha+4)/(i+alpha+3))*v[i+1] - (i+alpha+1)/(i+alpha+3)*(2*i+alpha+4)/(2*i+alpha+2)*v[i]\n    end\n    return v\nend\n\nfunction evaluate_lambda(n::Integer, alpha::T, delta::T) where T\n    delta2 = delta*delta\n    scl = (1+alpha)*(2-delta2/2)\n\n    lambda = Vector{T}(undef, n)\n\n    if n > 0\n        lambda[1] = 0\n    end\n    if n > 1\n        lambda[2] = -2\n    end\n\n    oprec!(n-2, view(lambda, 3:n), alpha, delta2)\n\n    for i = 2:n-1\n        lambda[i+1] *= -scl/(i-1)\n    end\n\n    p = plan_jac2jac(T, n-1, zero(T), zero(T), alpha, zero(T))\n\n    lmul!(p', view(lambda, 2:n))\n\n    for i = 2:n-1\n        lambda[i+1] = ((2i-1)*lambda[i+1] + (i-1)*lambda[i])/i\n    end\n\n    for i = 2:n-1\n        lambda[i+1] += lambda[i]\n    end\n\n    return lambda\nend","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"evaluate_lambda (generic function with 1 method)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"The spectrum in Float64:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"lambda = evaluate_lambda(10, -0.5, 1.0)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"10-element Vector{Float64}:\n   0.0\n  -2.0\n  -5.5\n  -9.75\n -14.09375\n -18.203125\n -22.08984375\n -25.935546875\n -29.8870849609375\n -33.95416259765625","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"The spectrum in BigFloat:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"lambdabf = evaluate_lambda(10, parse(BigFloat, \"-0.5\"), parse(BigFloat, \"1.0\"))","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"10-element Vector{BigFloat}:\n   0.0\n  -2.0\n  -5.5\n  -9.75\n -14.09375\n -18.203125\n -22.08984375\n -25.935546875\n -29.8870849609375\n -33.95416259765625","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"The infty-norm relative error:","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"norm(lambda-lambdabf, Inf)/norm(lambda, Inf)","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"0.0","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"","category":"page"},{"location":"generated/nonlocaldiffusion/#","page":"Nonlocal diffusion on mathbbS^2","title":"Nonlocal diffusion on mathbbS^2","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/disk.jl\"","category":"page"},{"location":"generated/disk/#Holomorphic-integration-on-the-unit-disk-1","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"","category":"section"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"In this example, we explore integration of a harmonic function:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"  f(xy) = fracx^2-y^2+1(x^2-y^2+1)^2+(2xy+1)^2","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"over the unit disk. In this case, we know from complex analysis that the integral of a holomorphic function is equal to pi times f(00). We analyze the function on an Ntimes M tensor product grid defined by:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"beginaligned\nr_n  = cosleft(n+tfrac12)pi2Nrightquadrm forquad 0le n  Nquadrm and\ntheta_m  = 2pi mMquadrm forquad 0le m  M\nendaligned","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"we convert the function samples to Chebyshev×Fourier coefficients using plan_disk_analysis; and finally, we transform the Chebyshev×Fourier coefficients to Zernike polynomial coefficients using plan_disk2cxf.","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"For the storage pattern of the arrays, please consult the documentation.","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"using FastTransforms, LinearAlgebra, Plots\nconst GENFIGS = joinpath(pkgdir(FastTransforms), \"docs/src/generated\")\n!isdir(GENFIGS) && mkdir(GENFIGS)\nplotlyjs()","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Plots.PlotlyJSBackend()","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Our function f on the disk:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"f = (x,y) -> (x^2-y^2+1)/((x^2-y^2+1)^2+(2x*y+1)^2)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"#1 (generic function with 1 method)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The Zernike polynomial degree:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"N = 15\nM = 4N-3","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"57","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The radial grid:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"r = [sinpi((N-n-0.5)/(2N)) for n in 0:N-1]","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"15-element Vector{Float64}:\n 0.9986295347545738\n 0.9876883405951378\n 0.9659258262890683\n 0.9335804264972017\n 0.8910065241883678\n 0.838670567945424\n 0.7771459614569709\n 0.7071067811865476\n 0.6293203910498375\n 0.5446390350150271\n 0.45399049973954675\n 0.35836794954530027\n 0.25881904510252074\n 0.15643446504023087\n 0.052335956242943835","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The angular grid (mod pi):","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"θ = (0:M-1)*2/M","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"0.0:0.03508771929824561:1.9649122807017543","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"On the mapped tensor product grid, our function samples are:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"F = [f(r*cospi(θ), r*sinpi(θ)) for r in r, θ in θ]","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"15×57 Matrix{Float64}:\n 0.400329  0.36696   0.336645  0.308443  0.281619  0.25557   0.22977   0.203733  0.176996  0.149111  0.119689  0.0885456  0.0561428  0.0249494  0.00382185  0.0233794  0.192001  0.82415   1.84146   1.85719   1.41721   1.08969   0.879424  0.739148  0.639757  0.565314  0.506844  0.459027  0.418538  0.383193  0.351486  0.32233   0.294899  0.268532  0.24267   0.216811  0.190481  0.163223  0.134611  0.104328  0.0724218  0.0400826  0.0120549  0.00476215  0.075801  0.422295  1.37342   1.98551   1.63411   1.23553   0.973247  0.802761  0.685557  0.600091  0.534475  0.481845  0.438023\n 0.402946  0.369531  0.339215  0.31106   0.284337  0.258454  0.232899  0.207211  0.180965  0.153777  0.125364  0.0957188  0.0656309  0.0381784  0.0233592   0.0535023  0.23469   0.838287  1.74173   1.78814   1.39763   1.08662   0.881061  0.742049  0.642889  0.56837   0.509752  0.461793  0.421195  0.385781  0.35405   0.324917  0.297559  0.271324  0.245665  0.220098  0.194183  0.16751   0.139734  0.110675  0.0806214  0.0512076  0.0280171  0.0289628   0.112787  0.46247   1.32844   1.88443   1.59532   1.22668   0.973254  0.805245  0.688639  0.603204  0.53746   0.48468   0.44073\n 0.408107  0.374635  0.344345  0.316308  0.289809  0.264275  0.239228  0.214259  0.189018  0.16325   0.136874  0.110236   0.0847405  0.0645701  0.0616188   0.110283   0.308499  0.852043  1.57431   1.65952   1.35481   1.07725   0.882418  0.74674   0.648492  0.574076  0.515313  0.467166  0.426411  0.390904  0.359157  0.330094  0.302904  0.276953  0.251718  0.226757  0.201691  0.176211  0.150131  0.123537  0.0971828  0.0735249  0.059617   0.0756242   0.180187  0.525812  1.24639   1.70902   1.5172    1.20513   0.970751  0.808756  0.693948  0.608911  0.543108  0.490146  0.446017\n 0.415648  0.382189  0.352011  0.324209  0.298096  0.273134  0.248897  0.225051  0.201367  0.177773  0.154485  0.132336   0.113545   0.103633   0.116351    0.186253   0.393918  0.849832  1.38148   1.49082   1.28527   1.05638   0.879972  0.751049  0.655222  0.581588  0.52299   0.474802  0.433974  0.398441  0.366752  0.33786   0.310977  0.2855    0.260948  0.236942  0.213198  0.189555  0.166059  0.143176  0.122289   0.106906   0.105724   0.140558    0.26534   0.588182  1.1413    1.4992    1.40336   1.16548   0.961348  0.810521  0.699782  0.616152  0.550745  0.497814  0.453615\n 0.425289  0.392035  0.362148  0.334773  0.309271  0.285158  0.262081  0.239809  0.218269  0.197619  0.178435  0.162105   0.151689   0.153844   0.183081    0.270225   0.470832  0.826183  1.19548   1.30726   1.19053   1.01926   0.869418  0.751971  0.661094  0.589601  0.531924  0.48414   0.443527  0.408177  0.376729  0.348191  0.321822  0.297066  0.273507  0.250853  0.228945  0.20781   0.187783  0.169776  0.15586    0.150546   0.163666   0.216532    0.352149  0.631169  1.0287    1.29056   1.26502   1.10458   0.940232  0.806897  0.703689  0.623316  0.559314  0.506989  0.463072\n 0.436597  0.403911  0.374626  0.347975  0.323392  0.300472  0.278957  0.258746  0.239942  0.222959  0.208736  0.199165   0.19792    0.212076   0.254963    0.349717   0.526163  0.785631  1.03278   1.13127   1.07899   0.964458  0.847102  0.746235  0.663661  0.596384  0.540917  0.494365  0.454527  0.419771  0.388896  0.361011  0.335454  0.311744  0.289549  0.268688  0.249152  0.23118   0.215414  0.203195  0.197165   0.20243    0.228745   0.293986    0.426183  0.648643  0.920719  1.10477   1.11859   1.02459   0.904279  0.794291  0.702811  0.628337  0.567372  0.51668   0.47372\n 0.448951  0.417414  0.389209  0.363706  0.340449  0.319139  0.299632  0.28197   0.266434  0.253672  0.244908  0.242329   0.249735   0.273549   0.32399     0.414856   0.556748  0.73654   0.898135  0.976631  0.96284   0.895308  0.811683  0.731268  0.660475  0.599969  0.54849   0.504405  0.466222  0.432719  0.402938  0.376152  0.351819  0.329563  0.309162  0.29056   0.273906  0.259647  0.248682  0.242655  0.244458   0.259053   0.294635   0.36347     0.47935   0.644419  0.824368  0.950029  0.979333  0.933025  0.853895  0.770471  0.694553  0.628995  0.573203  0.525623  0.484659\n 0.461538  0.431966  0.405508  0.381723  0.360304  0.341079  0.324035  0.309345  0.297441  0.289121  0.285721  0.289387   0.303423   0.332641   0.383252    0.461146   0.566675  0.686278  0.79016   0.848441  0.853234  0.818825  0.765072  0.706268  0.649804  0.598546  0.553073  0.513009  0.477665  0.446331  0.418379  0.393304  0.370732  0.350422  0.332279  0.316375  0.303005  0.292765  0.286694  0.286496  0.294846   0.315771   0.354858   0.418544    0.510882  0.626287  0.742362  0.826153  0.856971  0.839629  0.793294  0.735701  0.677489  0.623454  0.575098  0.532405  0.494793\n 0.473406  0.446815  0.422943  0.401579  0.382592  0.365953  0.35177   0.340321  0.332115  0.327962  0.329086  0.337225   0.354715   0.384367   0.428886    0.489368   0.562769  0.639621  0.705232  0.746138  0.75726   0.742897  0.711918  0.672777  0.631361  0.591026  0.553364  0.51894   0.487799  0.459755  0.434554  0.411958  0.391793  0.373976  0.358542  0.345678  0.33577   0.329466  0.327769  0.332147  0.344633   0.367837   0.404636   0.457191    0.524883  0.601613  0.674803  0.729338  0.755332  0.752747  0.728907  0.692933  0.652092  0.610928  0.571808  0.535736  0.502968\n 0.483592  0.461074  0.44072   0.422552  0.406616  0.393018  0.381958  0.373761  0.368913  0.368096  0.372211  0.382374   0.399829   0.425704   0.460521    0.503436   0.551426  0.599039  0.639428  0.66664   0.677821  0.673802  0.657934  0.634338  0.606657  0.577562  0.548776  0.521299  0.49565   0.472064  0.450625  0.431361  0.4143    0.399515  0.387153  0.377475  0.370881  0.36795   0.369472  0.37646   0.390112   0.411659   0.442005   0.481097    0.527085  0.575698  0.62056   0.654949  0.674261  0.67754   0.667091  0.646854  0.620817  0.592158  0.563054  0.534833  0.508227\n 0.491347  0.47384   0.457857  0.443596  0.43124   0.420991  0.413088  0.407835  0.405607  0.406854  0.41208   0.421791   0.436393   0.456016   0.480289    0.508089   0.537411  0.565495  0.589313  0.606297  0.614986  0.615273  0.608182  0.595383  0.578689  0.55973   0.539808  0.519875  0.500596  0.482417  0.465645  0.450499  0.437168  0.425839  0.416729  0.410109  0.406316  0.405766  0.408937  0.416345  0.428463   0.445585   0.467622   0.493853    0.522719  0.551798  0.578117  0.598782  0.611716  0.616137  0.612554  0.602381  0.587414  0.569403  0.549822  0.529795  0.510121\n 0.496372  0.484362  0.473263  0.463344  0.454844  0.447987  0.442992  0.440085  0.43949   0.441422  0.446059  0.453506   0.463734   0.476516   0.491364    0.507491   0.523832  0.539138  0.552155  0.561824  0.567461  0.568845  0.566188  0.560036  0.551118  0.54022   0.528088  0.515374  0.502621  0.490272  0.478681  0.468141  0.458903  0.451197  0.445243  0.441264  0.439485  0.440128  0.443394  0.44943   0.458281   0.469829   0.483724   0.499329    0.51571   0.531695  0.546006  0.557461  0.565171  0.568681  0.567994  0.563506  0.555873  0.545868  0.534265  0.521767  0.508973\n 0.498951  0.492196  0.485875  0.480211  0.475399  0.471612  0.469002  0.467693  0.467782  0.469331  0.472348  0.476782   0.482503   0.489293   0.496841    0.504746   0.512549  0.519761  0.525915  0.530618  0.533588  0.534687  0.533917  0.531408  0.527389  0.522155  0.516029  0.509344  0.502414  0.495534  0.488967  0.482948  0.477687  0.473367  0.470152  0.468178  0.467558  0.468372  0.470657  0.474394  0.479493   0.485782   0.492995   0.500776    0.508691  0.516259  0.522997  0.528468  0.532332  0.534375  0.53453   0.532867  0.52957   0.524904  0.519183  0.512736  0.505891\n 0.499854  0.497256  0.494799  0.492592  0.490727  0.489288  0.488339  0.487926  0.488075  0.488789  0.490046  0.491797   0.493969   0.496462   0.499157    0.501918   0.5046    0.507061  0.509167  0.510805  0.511889  0.512367  0.512222  0.51147   0.510163  0.508376  0.506206  0.503765  0.501171  0.498544  0.496003  0.493658  0.491611  0.48995   0.488749  0.488063  0.48793   0.488363  0.489352  0.490864  0.492836   0.495182   0.497793   0.500538    0.503278  0.505867  0.508166  0.51005   0.51142   0.512206  0.512372  0.511919  0.510882  0.509324  0.507332  0.505012  0.502479\n 0.499998  0.4997    0.499416  0.49916   0.498945  0.498781  0.498675  0.498633  0.498657  0.498746  0.498895  0.499098   0.499346   0.499625   0.499922    0.500224   0.500515  0.500781  0.50101   0.501189  0.50131   0.501367  0.501358  0.501283  0.501146  0.500953  0.500715  0.500442  0.500148  0.499848  0.499555  0.499284  0.499047  0.498856  0.49872   0.498646  0.498637  0.498693  0.498813  0.498991  0.499217   0.499482   0.499772   0.500074    0.500372  0.500652  0.500901  0.501106  0.501257  0.501347  0.501371  0.501328  0.501222  0.501056  0.500839  0.500582  0.500297","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"X = [r*cospi(θ) for r in r, θ in θ]\nY = [r*sinpi(θ) for r in r, θ in θ]\nscatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:red)\nsurface!(X, Y, F; legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"zernike.html\"))","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"<object type=\"text/html\" data=\"../zernike.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/zernike.html\"","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"We precompute a (generalized) Zernike–Chebyshev×Fourier plan:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"α, β = 0, 0\nP = plan_disk2cxf(F, α, β)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"FastTransforms Zernike--Chebyshev×Fourier plan for 15×57-element array of Float64","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"And an FFTW Chebyshev×Fourier analysis plan on the disk:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"PA = plan_disk_analysis(F)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"FastTransforms plan for FFTW Chebyshev×Fourier analysis on the disk for 15×57-element array of Float64","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Its Zernike coefficients are:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"U = P\\(PA*F)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"15×57 Matrix{Float64}:\n  0.886227     3.60709e-6  -1.8336e-6   -0.361801     3.60559e-11  -1.17688e-6   6.36308e-6   0.140125     -0.140125     -6.35177e-6   -7.70959e-6  1.89039e-10  0.118427     1.54098e-5  7.4099e-7    -0.0522214    -0.0522214    -1.71856e-5  1.64002e-5   0.0472361    -5.20197e-10  4.08953e-7   -3.63399e-5  -0.0217254    0.0217254    3.88099e-5   3.92308e-5  -1.24018e-9   -0.0202253    -8.31939e-5  -2.14893e-7   0.00949917    0.00949917   8.82306e-5   -8.80125e-5   -0.00898531   2.80468e-9   -1.10226e-7   0.000185657   0.00427337   -0.00427337   -0.000194603  -0.000194714  6.17793e-9   0.00408335   0.000406568  5.5777e-8    -0.00195832   -0.0019583    -0.000423167  0.000423111  0.00188439   -1.33894e-8   2.79926e-8   -0.000878195  -0.00090912   0.000909147\n  3.08825e-17  4.60728e-6  -2.33805e-6  -4.33e-11     4.33e-11     -1.22625e-6   6.53675e-6   2.91135e-17  -1.46429e-10  -5.65109e-6   -6.90982e-6  1.84987e-10  1.84987e-10  1.21904e-5  6.29629e-7   -4.19031e-10  -7.40235e-18  -1.21069e-5  1.14861e-5   4.50193e-10  -4.50193e-10  3.03358e-7   -2.25713e-5   1.03258e-17  9.39347e-10  2.10848e-5   2.13797e-5  -9.62216e-10  -9.62216e-10  -3.90991e-5  -1.42777e-7   1.94644e-9    2.80911e-17  3.51181e-5   -3.49801e-5   -1.94972e-9   1.94972e-9   -6.65696e-8   6.06806e-5    1.30586e-17  -3.87473e-9   -4.9981e-5    -5.00452e-5   3.82278e-9   3.82278e-9   7.63297e-5   3.09339e-8   -7.49277e-9    1.61027e-18  -5.04164e-5   5.03866e-5   7.2952e-9    -7.2952e-9    1.38574e-8   -4.45519e-5    2.60005e-17  1.36316e-8\n  3.54191e-17  4.76065e-6  -2.40899e-6  -4.59639e-11  4.59638e-11  -1.12866e-6   5.89804e-6   6.18124e-18  -1.43511e-10  -4.51295e-6   -5.57325e-6  1.70088e-10  1.70088e-10  8.73447e-6  4.92668e-7   -3.63967e-10  -2.11966e-17  -7.74165e-6  7.28634e-6   3.70513e-10  -3.70513e-10  2.09854e-7   -1.26794e-5  -9.92069e-18  7.33255e-10  1.02945e-5   1.04878e-5  -7.12279e-10  -7.12279e-10  -1.63841e-5  -8.90173e-8   1.36506e-9   -1.87551e-17  1.23112e-5   -1.22292e-5   -1.29344e-9   1.29344e-9   -3.78749e-8   1.71213e-5   -9.44761e-18  -2.42653e-9   -1.07347e-5   -1.07697e-5   2.25423e-9   2.25423e-9   1.13275e-5   1.62097e-8   -4.14789e-9    7.15519e-18  -4.10621e-6   4.09201e-6   3.57033e-9   -3.57033e-9   7.2136e-9    -3.89728e-6    8.38482e-18  7.03625e-9\n  3.7535e-19   4.3306e-6   -2.18254e-6  -4.50915e-11  4.50915e-11  -9.41975e-7   4.79767e-6   2.32655e-17  -1.3221e-10   -3.27045e-6   -4.09126e-6  1.48194e-10  1.48194e-10  5.69834e-6  3.57019e-7   -3.00851e-10   4.15138e-18  -4.50516e-6  4.19432e-6   2.90868e-10  -2.90868e-10  1.35612e-7   -6.44339e-6   6.75322e-18  5.46652e-10  4.50749e-6   4.62617e-6  -5.03847e-10  -5.03847e-10  -6.09951e-6  -5.21037e-8   9.1491e-10    2.51335e-18  3.77955e-6   -3.73364e-6   -8.19854e-10  8.19854e-10  -2.03036e-8   4.12363e-6    2.10797e-17  -1.45125e-9   -1.88522e-6   -1.90324e-6   1.26862e-9   1.26862e-9   1.23872e-6   7.40728e-9   -2.01666e-9    5.16575e-18  -6.4875e-7    6.41095e-7   1.96336e-9   -1.96336e-9   3.94603e-9   -4.95856e-7    9.84193e-18  3.81545e-9\n -1.18289e-17  3.55971e-6  -1.7846e-6   -4.1593e-11   4.1593e-11   -7.20914e-7   3.55774e-6  -5.44669e-18  -1.15465e-10  -2.16169e-6   -2.74892e-6  1.22948e-10  1.22948e-10  3.3937e-6   2.40326e-7   -2.37394e-10   8.29477e-18  -2.38904e-6  2.19119e-6   2.18301e-10  -2.18301e-10  8.19355e-8   -2.95988e-6  -1.46774e-18  3.89943e-10  1.76401e-6   1.8323e-6   -3.41184e-10  -3.41184e-10  -2.0084e-6   -2.86395e-8   5.87175e-10  -3.7024e-18   1.01021e-6   -9.86038e-7   -4.97705e-10  4.97705e-10  -1.02636e-8   8.36501e-7   -1.91606e-17  -8.31421e-10  -2.51578e-7   -2.59455e-7   6.11155e-10  6.11155e-10  2.81636e-7   4.14107e-9   -1.17835e-9    6.44999e-18  -1.31206e-7   1.26866e-7   1.1332e-9    -1.1332e-9    2.26757e-9   -8.50354e-8    4.13504e-18  2.17398e-9\n  2.9532e-17   2.67365e-6  -1.33163e-6  -3.63778e-11  3.63778e-11  -5.08751e-7   2.4183e-6   -1.47781e-17  -9.60672e-11  -1.3062e-6    -1.69561e-6  9.74399e-11  9.74399e-11  1.84711e-6  1.50509e-7   -1.79257e-10   8.4605e-19   -1.15523e-6  1.03773e-6   1.56975e-10  -1.56975e-10  4.63055e-8   -1.22747e-6  -7.64459e-19  2.66772e-10  6.14181e-7   6.51026e-7  -2.21796e-10  -2.21796e-10  -5.82251e-7  -1.47961e-8   3.62177e-10   4.04991e-18  2.3447e-7    -2.22474e-7   -2.90765e-10  2.90765e-10  -4.27394e-9   1.32135e-7    1.10407e-18  -3.9572e-10   -7.37753e-8   -7.83499e-8   3.78556e-10  3.78556e-10  7.69466e-8   2.43764e-9   -7.22143e-10  -2.20019e-18  -3.3267e-8    3.06793e-8   6.86748e-10  -6.86748e-10  1.36854e-9   -1.89956e-8    5.29828e-18  1.30213e-9\n  4.8454e-18   1.84493e-6  -9.11632e-7  -3.03234e-11  3.03234e-11  -3.31998e-7   1.51086e-6   9.13653e-18  -7.63919e-11  -7.22019e-7   -9.61716e-7  7.39635e-11  7.39635e-11  9.19025e-7  8.7759e-8    -1.29855e-10  -1.00058e-17  -5.0973e-7   4.44593e-7   1.08464e-10  -1.08464e-10  2.44943e-8   -4.5896e-7   -7.25056e-18  1.75682e-10  1.89131e-7   2.07797e-7  -1.3908e-10   -1.3908e-10   -1.48285e-7  -7.20906e-9   2.15876e-10  -9.44039e-18  4.31232e-8   -3.83843e-8   -1.35983e-10  1.35983e-10  -2.58242e-9   4.86298e-8   -3.52213e-18  -2.58784e-10  -2.49419e-8   -2.77411e-8   2.45364e-10  2.45364e-10  2.49291e-8   1.50968e-9   -4.63692e-10   6.50763e-18  -1.04761e-8   8.85511e-9   4.36633e-10  -4.36633e-10  8.66632e-10  -5.46345e-9    2.04425e-18  8.19335e-10\n -2.37746e-17  1.17276e-6  -5.74087e-7  -2.41606e-11  2.41606e-11  -2.00616e-7   8.68671e-7  -1.72499e-18  -5.82253e-11  -3.64941e-7   -5.01985e-7  5.39205e-11  5.39205e-11  4.17975e-7  4.76625e-8   -9.05511e-11  -4.9981e-18   -2.05562e-7  1.71822e-7   7.23176e-11  -7.23176e-11  1.21586e-8   -1.5476e-7    2.16322e-18  1.11916e-10  5.11842e-8   6.01101e-8  -8.43279e-11  -8.43279e-11  -2.90142e-8  -2.68449e-9   9.8079e-11   -4.79653e-18  1.93294e-8   -1.63497e-8   -9.30964e-11  9.30964e-11  -1.64272e-9   2.0359e-8    -2.13593e-18  -1.75944e-10  -9.61519e-9   -1.14155e-8   1.65598e-10  1.65598e-10  9.47999e-9   9.81067e-10  -3.10521e-10  -2.38645e-18  -4.06062e-9   2.99682e-9   2.90001e-10  -2.90001e-10  5.7406e-10   -2.00747e-9   -3.59072e-18  5.39466e-10\n  8.95539e-18  6.87558e-7  -3.32907e-7  -1.84685e-11  1.84685e-11  -1.12306e-7   4.59773e-7  -2.97799e-18  -4.265e-11    -1.68481e-7   -2.41286e-7  3.78985e-11  3.78985e-11  1.73828e-7  2.4139e-8    -6.10346e-11  -1.33435e-18  -7.61356e-8  5.9745e-8    4.66938e-11  -4.66938e-11  5.69883e-9   -4.73542e-8  -2.61397e-18  6.84382e-11  1.00798e-8   1.31808e-8  -3.64534e-11  -3.64534e-11  -1.46721e-8  -1.7526e-9    6.92775e-11  -5.64422e-18  9.70857e-9   -7.74328e-9   -6.54378e-11  6.54378e-11  -1.09391e-9   9.61505e-9    2.81389e-19  -1.23027e-10  -4.18802e-9   -5.39773e-9   1.15147e-10  1.15147e-10  4.18575e-9   6.64834e-10  -2.1464e-10    7.04116e-18  -1.89907e-9   1.17239e-9   1.99193e-10  -1.99193e-10  3.95103e-10  -9.19881e-10   1.86274e-18  3.68061e-10\n  2.15782e-17  3.71865e-7  -1.77783e-7  -1.35612e-11  1.35612e-11  -5.82608e-8   2.24022e-7   3.72333e-18  -3.01692e-11  -7.09608e-8   -1.06944e-7  2.57607e-11  2.57607e-11  6.63405e-8  1.14574e-8   -3.98083e-11   1.83302e-17  -2.62265e-8  1.87191e-8   2.83655e-11  -2.83655e-11  1.81554e-9   -1.02616e-8   1.27257e-18  2.72302e-11  5.57557e-9   7.66477e-9  -2.60181e-11  -2.60181e-11  -8.14921e-9  -1.19076e-9   4.92954e-11   1.47536e-17  5.39512e-9   -4.04931e-9   -4.64096e-11  4.64096e-11  -7.54615e-10  5.0669e-9     1.0689e-17   -8.69428e-11  -2.04308e-9   -2.88332e-9   8.10649e-11  8.10649e-11  2.11288e-9   4.64752e-10  -1.50494e-10   5.16894e-18  -1.03471e-9   5.23655e-10  1.39056e-10  -1.39056e-10  2.79431e-10  -5.01563e-10   5.97653e-18  2.55748e-10\n -1.47947e-17  1.85546e-7  -8.74169e-8  -9.64281e-12  9.6428e-12   -2.80375e-8   1.00537e-7  -7.35134e-19  -2.06073e-11  -2.73295e-8   -4.39821e-8  1.69233e-11  1.69233e-11  2.34206e-8  5.10163e-9   -2.35204e-11   6.51352e-18  -5.91169e-9  3.77929e-9   9.88461e-12  -9.88462e-12  1.24842e-9   -6.38622e-9   4.02236e-18  1.91141e-11  3.32832e-9   4.77417e-9  -1.82332e-11  -1.82332e-11  -4.89671e-9  -8.28984e-10  3.44828e-11   7.48581e-18  3.25458e-9   -2.31249e-9   -3.24e-11     3.24e-11     -5.30949e-10  2.93011e-9   -6.11335e-18  -6.05679e-11  -1.10379e-9   -1.6978e-9    5.63435e-11  5.63436e-11  1.1914e-9    3.3001e-10   -1.04342e-10  -2.57553e-18  -6.27959e-10  2.63577e-10  9.6157e-11   -9.6157e-11   2.00002e-10  -3.071e-10     7.37827e-18  1.76348e-10\n -3.12442e-17  8.54426e-8  -3.95787e-8  -6.58743e-12  6.58744e-12  -1.26163e-8   4.18408e-8  -1.80052e-17  -1.3631e-11   -9.62687e-9   -1.67874e-8  9.48623e-12  9.48623e-12  4.72571e-9  1.23574e-9   -6.65263e-12  -3.83785e-18  -3.91558e-9  2.44388e-9   6.57828e-12  -6.57828e-12  8.65402e-10  -4.14906e-9   2.72883e-18  1.2711e-11   2.09945e-9   3.10576e-9  -1.21149e-11  -1.21149e-11  -3.10737e-9  -5.79121e-10  2.28905e-11   6.23804e-18  2.07394e-9   -1.41354e-9   -2.1486e-11   2.1486e-11   -3.73369e-10  1.81245e-9   -1.03001e-17  -4.01214e-11  -6.48005e-10  -1.06694e-9   3.72789e-11  3.72789e-11  7.26798e-10  2.33379e-10  -6.89482e-11   4.73336e-18  -4.05112e-10  1.46777e-10  6.34527e-11  -6.34527e-11  1.42127e-10  -1.99851e-10   7.62512e-18  1.16198e-10\n  1.33271e-17  3.66259e-8  -1.66324e-8  -4.39971e-12  4.39972e-12  -5.20978e-9   1.59586e-8  -1.01503e-17  -7.0843e-12   -1.58674e-9   -2.96274e-9  1.91297e-12  1.91297e-12  3.12298e-9  8.33281e-10  -3.95183e-12  -6.31239e-18  -2.58884e-9  1.5939e-9    3.90661e-12  -3.90663e-12  5.8643e-10   -2.71374e-9   3.31823e-18  7.54633e-12  1.34984e-9   2.03322e-9  -7.18992e-12  -7.18992e-12  -2.00561e-9  -3.94051e-10  1.35798e-11  -3.88588e-18  1.34233e-9   -8.92165e-10  -1.27412e-11  1.27412e-11  -2.54934e-10  1.15296e-9   -7.65968e-18  -2.37812e-11  -3.99094e-10  -6.85581e-10  2.20855e-11  2.20855e-11  4.59097e-10  1.5982e-10   -4.0826e-11   -2.81128e-18  -2.64588e-10  8.74454e-11  3.75507e-11  -3.75507e-11  9.75761e-11  -1.31247e-10  -3.71219e-18  6.87229e-11\n -1.29499e-17  1.42637e-8  -6.34424e-9  -2.10396e-12  2.10396e-12  -6.84193e-10  1.98342e-9   2.18678e-18  -7.77242e-13  -9.64872e-10  -1.8079e-9   8.82102e-13  8.82104e-13  1.90051e-9  5.11075e-10  -1.82214e-12   9.26204e-18  -1.57577e-9  9.64939e-10  1.80117e-12  -1.80117e-12  3.60351e-10  -1.64478e-9   5.54127e-18  3.47897e-12  8.12528e-10  1.2328e-9   -3.31434e-12  -3.31434e-12  -1.2092e-9   -2.42517e-10  6.2592e-12   -3.29227e-18  8.10242e-10  -5.33001e-10  -5.872e-12    5.872e-12    -1.57104e-10  6.91093e-10  -6.13378e-18  -1.09586e-11  -2.3601e-10   -4.12661e-10  1.01758e-11  1.01758e-11  2.74436e-10  9.85995e-11  -1.88077e-11  -5.45761e-18  -1.60322e-10  5.09818e-11  1.7296e-11   -1.7296e-11   6.02559e-11  -7.9705e-11    4.13813e-19  3.16487e-11\n -2.57377e-17  3.5367e-9   -1.55057e-9  -5.05721e-14  5.05682e-14  -1.24617e-9   3.61129e-9  -3.1012e-18   -1.49119e-13  -1.75608e-9   -3.29176e-9  1.69228e-13  1.6923e-13   3.45928e-9  9.31108e-10  -3.49575e-13  -1.75255e-18  -2.86824e-9  1.75527e-9   3.45548e-13  -3.4555e-13   6.56655e-10  -2.99235e-9  -1.63745e-18  6.67424e-13  1.47702e-9   2.24293e-9  -6.35833e-13  -6.35832e-13  -2.1985e-9   -4.42011e-10  1.20077e-12   2.0917e-18   1.47335e-9   -9.68009e-10  -1.12648e-12  1.12649e-12  -2.86382e-10  1.25563e-9    2.55539e-19  -2.10227e-12  -4.28097e-10  -7.50132e-10  1.95208e-12  1.95208e-12  4.98453e-10  1.79759e-10  -3.60793e-12   1.51272e-18  -2.91666e-10  9.23134e-11  3.31791e-12  -3.31791e-12  1.09866e-10  -1.45042e-10  -9.98777e-19  6.07111e-12","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The Zernike coefficients are useful for integration. The integral of f(xy) over the disk should be pi2 by harmonicity. The coefficient of Z_00 multiplied by √π is:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"U[1, 1]*sqrt(π)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"1.5707963267948968","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Using an orthonormal basis, the integral of f(xy)^2 over the disk is approximately the square of the 2-norm of the coefficients:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"(0.9789599193439185, 0.9789599179781414)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"But there's more! Next, we repeat the experiment using the Dunkl-Xu orthonormal polynomials supported on the rectangularized disk.","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"N = 2N\nM = N","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"30","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"We analyze the function on an Ntimes M mapped tensor product xy-grid defined by:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"beginaligned\nx_n  = cosleft(frac2n+12Npiright) = sinleft(fracN-2n-12Npiright)quad rm for quad 0 le n  Nquadrm and\nz_m  = cosleft(frac2m+12Mpiright) = sinleft(fracM-2m-12Mpiright)quad rm for quad 0 le m  M\ny_nm  = sqrt1-x_n^2z_m\nendaligned","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Slightly more accuracy can be expected by using an auxiliary array:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"  w_n = sinleft(frac2n+12Npiright)quad rm for quad 0 le n  N","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"so that y_nm = w_nz_m.","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The x grid","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"w = [sinpi((n+0.5)/N) for n in 0:N-1]\nx = [sinpi((N-2n-1)/(2N)) for n in 0:N-1]","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"30-element Vector{Float64}:\n  0.9986295347545738\n  0.9876883405951378\n  0.9659258262890683\n  0.9335804264972017\n  0.8910065241883678\n  0.838670567945424\n  0.7771459614569709\n  0.7071067811865476\n  0.6293203910498375\n  0.5446390350150271\n  0.45399049973954675\n  0.35836794954530027\n  0.25881904510252074\n  0.15643446504023087\n  0.052335956242943835\n -0.052335956242943835\n -0.15643446504023087\n -0.25881904510252074\n -0.35836794954530027\n -0.45399049973954675\n -0.5446390350150271\n -0.6293203910498375\n -0.7071067811865476\n -0.7771459614569709\n -0.838670567945424\n -0.8910065241883678\n -0.9335804264972017\n -0.9659258262890683\n -0.9876883405951378\n -0.9986295347545738","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The z grid","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"z = [sinpi((M-2m-1)/(2M)) for m in 0:M-1]","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"30-element Vector{Float64}:\n  0.9986295347545738\n  0.9876883405951378\n  0.9659258262890683\n  0.9335804264972017\n  0.8910065241883678\n  0.838670567945424\n  0.7771459614569709\n  0.7071067811865476\n  0.6293203910498375\n  0.5446390350150271\n  0.45399049973954675\n  0.35836794954530027\n  0.25881904510252074\n  0.15643446504023087\n  0.052335956242943835\n -0.052335956242943835\n -0.15643446504023087\n -0.25881904510252074\n -0.35836794954530027\n -0.45399049973954675\n -0.5446390350150271\n -0.6293203910498375\n -0.7071067811865476\n -0.7771459614569709\n -0.838670567945424\n -0.8910065241883678\n -0.9335804264972017\n -0.9659258262890683\n -0.9876883405951378\n -0.9986295347545738","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"On the mapped tensor product grid, our function samples are:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"F = [f(x[n], w[n]*z) for n in 1:N, z in z]","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"30×30 Matrix{Float64}:\n 0.383725    0.383905   0.384264   0.384798  0.3855    0.386365  0.387383  0.388542  0.389832  0.391237  0.392744  0.394337  0.395997  0.397708  0.399451  0.401207  0.402957  0.404681  0.406361  0.407977  0.409512  0.410949  0.41227   0.413462  0.41451   0.415403  0.41613   0.416683   0.417055   0.417242\n 0.353509    0.354039   0.355094   0.356664  0.358732  0.36128   0.364281  0.367707  0.371524  0.375695  0.380177  0.384927  0.389897  0.395036  0.400292  0.405609  0.41093   0.416197  0.421352  0.426336  0.431089  0.435556  0.439683  0.443417  0.446713  0.449527  0.451824  0.453573   0.454752   0.455346\n 0.325652    0.32653    0.328275   0.330873  0.334296  0.338513  0.343483  0.349158  0.355488  0.362412  0.36987   0.377792  0.386108  0.394741  0.40361   0.412629  0.421708  0.43075   0.439655  0.44832   0.456637  0.464501  0.471805  0.478449  0.484336  0.489382  0.493512  0.496665   0.498793   0.499866\n 0.29943     0.300665   0.303122   0.306774  0.311585  0.317506  0.324478  0.332436  0.341308  0.351018  0.361484  0.372625  0.384354  0.396582  0.409213  0.422145  0.435264  0.448446  0.461551  0.474426  0.486904  0.498809  0.50996   0.520175  0.529284  0.537127  0.54357   0.548501   0.551834   0.553515\n 0.274261    0.275876   0.279088   0.283858  0.290132  0.297838  0.306895  0.317212  0.328692  0.341239  0.354758  0.36916   0.384358  0.400269  0.416811  0.43389   0.451401  0.469213  0.487163  0.505054  0.522647  0.539669  0.555819  0.570781  0.584246  0.595923  0.605564  0.612965   0.617979   0.620509\n 0.249651    0.251685   0.255724   0.261714  0.269574  0.279203  0.290482  0.303282  0.31747   0.332923  0.349529  0.367198  0.385862  0.405474  0.426001  0.44741   0.469656  0.492656  0.516277  0.540305  0.564443  0.588294  0.611378  0.633149  0.653036  0.670489  0.685018  0.696234   0.703855   0.707707\n 0.225163    0.227669   0.232643   0.240006  0.249642  0.261402  0.275112  0.290582  0.307622  0.326061  0.345762  0.366637  0.388654  0.411835  0.43625   0.461998  0.489179  0.517862  0.548041  0.579594  0.612236  0.645481  0.678629  0.710777  0.740882  0.76785   0.790662  0.808467   0.820649   0.826828\n 0.200384    0.203443   0.209507   0.218467  0.230156  0.244357  0.260808  0.279223  0.299317  0.32084   0.343606  0.367524  0.392611  0.418996  0.446912  0.47667   0.508629  0.543152  0.580544  0.620979  0.664413  0.710473  0.758363  0.806792  0.853985  0.897808  0.936015  0.966541   0.987766   0.99863\n 0.174918    0.178645   0.186025   0.196908  0.211057  0.228154  0.247802  0.269562  0.292995  0.317717  0.343461  0.370116  0.397762  0.426667  0.457278  0.490195  0.526141  0.565917  0.610353  0.660232  0.716173  0.778452  0.846763  0.919914  0.995547  1.07001   1.13854   1.19588    1.23718    1.25878\n 0.148385    0.152947   0.161975   0.175262  0.192474  0.213137  0.23665   0.262328  0.289486  0.317533  0.346071  0.374964  0.404363  0.43471   0.4667    0.501255  0.539494  0.582713  0.632375  0.690092  0.75756   0.836429  0.928002  1.03272   1.1493    1.27371   1.39809   1.51064    1.59716    1.64443\n 0.120453    0.126104   0.137278   0.153696  0.174875  0.200102  0.228448  0.258839  0.290208  0.321663  0.352638  0.382979  0.41296   0.443231  0.47475   0.508726  0.546578  0.589942  0.640699  0.701019  0.773401  0.860651  0.965732  1.0913    1.23871   1.40612   1.58568   1.76048    1.90408    1.98636\n 0.0909577   0.098092   0.112194   0.132868  0.159398  0.19068   0.225238  0.261383  0.297474  0.332223  0.364913  0.395469  0.424393  0.452621  0.481372  0.512033  0.546102  0.585165  0.630904  0.685083  0.749484  0.825684  0.914588  1.01552   1.12484   1.23449   1.33202   1.40445    1.44601    1.46226\n 0.0602361   0.0695018  0.0877988  0.114536  0.148582  0.188133  0.230785  0.273857  0.314915  0.352268  0.385224  0.414044  0.439685  0.46349   0.486923  0.511411  0.53824   0.568495  0.60296   0.641919  0.684785  0.729453  0.77136   0.802572  0.811931  0.788253  0.727788  0.642222   0.558465   0.506932\n 0.0300951   0.0426105  0.0672646  0.103059  0.148022  0.199015  0.251986  0.302743  0.347947  0.385818  0.416228  0.440285  0.45973   0.476426  0.492035  0.507855  0.524738  0.542996  0.562232  0.581051  0.596627  0.604238  0.597148  0.56764   0.510053  0.425442  0.32469   0.226238   0.149204   0.107374\n 0.00673069  0.0245336  0.0593763  0.109244  0.17025   0.236535  0.301213  0.358181  0.403763  0.437224  0.460093  0.47501   0.484736  0.491598  0.497272  0.502743  0.508304  0.513517  0.517087  0.516699  0.508899  0.489293  0.453432  0.398651  0.326385  0.243411  0.160485  0.0888546  0.0371183  0.010234\n 0.010234    0.0371183  0.0888546  0.160485  0.243411  0.326385  0.398651  0.453432  0.489293  0.508899  0.516699  0.517087  0.513517  0.508304  0.502743  0.497272  0.491598  0.484736  0.47501   0.460093  0.437224  0.403763  0.358181  0.301213  0.236535  0.17025   0.109244  0.0593763  0.0245336  0.00673069\n 0.107374    0.149204   0.226238   0.32469   0.425442  0.510053  0.56764   0.597148  0.604238  0.596627  0.581051  0.562232  0.542996  0.524738  0.507855  0.492035  0.476426  0.45973   0.440285  0.416228  0.385818  0.347947  0.302743  0.251986  0.199015  0.148022  0.103059  0.0672646  0.0426105  0.0300951\n 0.506932    0.558465   0.642222   0.727788  0.788253  0.811931  0.802572  0.77136   0.729453  0.684785  0.641919  0.60296   0.568495  0.53824   0.511411  0.486923  0.46349   0.439685  0.414044  0.385224  0.352268  0.314915  0.273857  0.230785  0.188133  0.148582  0.114536  0.0877988  0.0695018  0.0602361\n 1.46226     1.44601    1.40445    1.33202   1.23449   1.12484   1.01552   0.914588  0.825684  0.749484  0.685083  0.630904  0.585165  0.546102  0.512033  0.481372  0.452621  0.424393  0.395469  0.364913  0.332223  0.297474  0.261383  0.225238  0.19068   0.159398  0.132868  0.112194   0.098092   0.0909577\n 1.98636     1.90408    1.76048    1.58568   1.40612   1.23871   1.0913    0.965732  0.860651  0.773401  0.701019  0.640699  0.589942  0.546578  0.508726  0.47475   0.443231  0.41296   0.382979  0.352638  0.321663  0.290208  0.258839  0.228448  0.200102  0.174875  0.153696  0.137278   0.126104   0.120453\n 1.64443     1.59716    1.51064    1.39809   1.27371   1.1493    1.03272   0.928002  0.836429  0.75756   0.690092  0.632375  0.582713  0.539494  0.501255  0.4667    0.43471   0.404363  0.374964  0.346071  0.317533  0.289486  0.262328  0.23665   0.213137  0.192474  0.175262  0.161975   0.152947   0.148385\n 1.25878     1.23718    1.19588    1.13854   1.07001   0.995547  0.919914  0.846763  0.778452  0.716173  0.660232  0.610353  0.565917  0.526141  0.490195  0.457278  0.426667  0.397762  0.370116  0.343461  0.317717  0.292995  0.269562  0.247802  0.228154  0.211057  0.196908  0.186025   0.178645   0.174918\n 0.99863     0.987766   0.966541   0.936015  0.897808  0.853985  0.806792  0.758363  0.710473  0.664413  0.620979  0.580544  0.543152  0.508629  0.47667   0.446912  0.418996  0.392611  0.367524  0.343606  0.32084   0.299317  0.279223  0.260808  0.244357  0.230156  0.218467  0.209507   0.203443   0.200384\n 0.826828    0.820649   0.808467   0.790662  0.76785   0.740882  0.710777  0.678629  0.645481  0.612236  0.579594  0.548041  0.517862  0.489179  0.461998  0.43625   0.411835  0.388654  0.366637  0.345762  0.326061  0.307622  0.290582  0.275112  0.261402  0.249642  0.240006  0.232643   0.227669   0.225163\n 0.707707    0.703855   0.696234   0.685018  0.670489  0.653036  0.633149  0.611378  0.588294  0.564443  0.540305  0.516277  0.492656  0.469656  0.44741   0.426001  0.405474  0.385862  0.367198  0.349529  0.332923  0.31747   0.303282  0.290482  0.279203  0.269574  0.261714  0.255724   0.251685   0.249651\n 0.620509    0.617979   0.612965   0.605564  0.595923  0.584246  0.570781  0.555819  0.539669  0.522647  0.505054  0.487163  0.469213  0.451401  0.43389   0.416811  0.400269  0.384358  0.36916   0.354758  0.341239  0.328692  0.317212  0.306895  0.297838  0.290132  0.283858  0.279088   0.275876   0.274261\n 0.553515    0.551834   0.548501   0.54357   0.537127  0.529284  0.520175  0.50996   0.498809  0.486904  0.474426  0.461551  0.448446  0.435264  0.422145  0.409213  0.396582  0.384354  0.372625  0.361484  0.351018  0.341308  0.332436  0.324478  0.317506  0.311585  0.306774  0.303122   0.300665   0.29943\n 0.499866    0.498793   0.496665   0.493512  0.489382  0.484336  0.478449  0.471805  0.464501  0.456637  0.44832   0.439655  0.43075   0.421708  0.412629  0.40361   0.394741  0.386108  0.377792  0.36987   0.362412  0.355488  0.349158  0.343483  0.338513  0.334296  0.330873  0.328275   0.32653    0.325652\n 0.455346    0.454752   0.453573   0.451824  0.449527  0.446713  0.443417  0.439683  0.435556  0.431089  0.426336  0.421352  0.416197  0.41093   0.405609  0.400292  0.395036  0.389897  0.384927  0.380177  0.375695  0.371524  0.367707  0.364281  0.36128   0.358732  0.356664  0.355094   0.354039   0.353509\n 0.417242    0.417055   0.416683   0.41613   0.415403  0.41451   0.413462  0.41227   0.410949  0.409512  0.407977  0.406361  0.404681  0.402957  0.401207  0.399451  0.397708  0.395997  0.394337  0.392744  0.391237  0.389832  0.388542  0.387383  0.386365  0.3855    0.384798  0.384264   0.383905   0.383725","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"X = [x for x in x, z in z]\nY = [w*z for w in w, z in z]\nscatter3d(vec(X), vec(Y), vec(0F); markersize=0.75, markercolor=:green)\nsurface!(X, Y, F; legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"dunklxu.html\"))","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"<object type=\"text/html\" data=\"../dunklxu.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/dunklxu.html\"","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"We precompute a Dunkl-Xu–Chebyshev plan:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"P = plan_rectdisk2cheb(F, β)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"FastTransforms Dunkl-Xu--Chebyshev² plan for 30×30-element array of Float64","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"And an FFTW Chebyshev² analysis plan on the rectangularized disk:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"PA = plan_rectdisk_analysis(F)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"FastTransforms plan for FFTW Chebyshev analysis on the rectangularized disk for 30×30-element array of Float64","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Its Dunkl-Xu coefficients are:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"U = P\\(PA*F)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"30×30 Matrix{Float64}:\n  0.886226      2.91482e-18  -6.09829e-7    7.46859e-18  -0.0236857    -1.03089e-18  -0.00550977    1.55635e-18  -0.000650943   5.16951e-19   2.15779e-9   -3.61345e-20   1.86065e-5    1.15602e-18   4.38992e-6    4.86495e-19   4.19398e-7   -2.36331e-18  -1.00953e-7    2.61786e-18  -8.14396e-8    1.00901e-18  -3.94076e-8   -5.05452e-19  -1.67897e-8   -9.68766e-19  -6.33162e-9   -2.79749e-18  -2.11252e-9    8.20668e-19\n -1.82504e-18  -0.361799     -4.06548e-18  -0.062663     -1.26332e-18   2.72128e-6   -1.4716e-19    0.00252359   -1.53351e-18   0.000679258  -5.06658e-18   9.1001e-5     6.2766e-18    1.03955e-6   -6.44725e-19  -2.31664e-6    4.06045e-18  -3.11859e-7   -1.29757e-18   1.77496e-7   -4.52069e-18   1.44389e-7    4.00752e-18   6.82707e-8   -7.73146e-18   2.5634e-8     3.6454e-18    7.91583e-9   -4.99128e-19   1.6359e-9\n -5.19659e-7    1.77123e-18   0.105921     -4.37394e-18   0.0404829     3.53441e-19   0.00663284   -7.04472e-19  -5.56102e-6   -1.76702e-19  -0.000301082   9.63513e-21  -8.77391e-5   -2.28415e-19  -1.39615e-5   -6.02861e-20  -1.31088e-6    1.21769e-19  -2.80392e-7    5.33368e-20  -2.38006e-7    9.26254e-20  -1.39444e-7   -8.23221e-20  -5.76521e-8   -2.26363e-19  -1.77475e-8   -8.51099e-19  -3.52357e-9    2.71521e-19\n -1.32446e-18   0.125331      5.16222e-18   1.52509e-6    1.52224e-18  -0.013651      4.59065e-19  -0.00478429    1.7437e-18   -0.000775222   5.39444e-18   4.86933e-6   -6.32553e-18   4.00219e-5    6.1449e-19    1.28528e-5   -3.66863e-18   2.68143e-6    1.10971e-18   5.35246e-7    3.65472e-18   1.5728e-7    -3.05701e-18   5.72745e-8    5.55166e-18   1.62262e-8   -2.45695e-18   4.075e-10     3.06319e-19  -1.20696e-9\n -0.0886209     5.87339e-18  -0.0913638     3.09208e-18  -0.0231032    -7.65237e-19   2.55845e-6   -3.00844e-20   0.00173316    8.97087e-22   0.000591205   3.74945e-21   9.51801e-5   -2.71771e-19  -9.67049e-7   -1.57546e-19  -5.17388e-6    9.69671e-19  -1.60228e-6   -1.2848e-18   -2.52759e-7   -5.71811e-19   9.35469e-9    3.22564e-19   2.66735e-8    6.83271e-19   1.62648e-8    1.93725e-18   7.6679e-9    -5.72686e-19\n -2.97095e-19  -2.79797e-6   -7.50681e-18   0.0328526    -2.04986e-18   0.0160342     4.40714e-19   0.00332497   -1.61538e-18  -8.62281e-6   -4.81324e-18  -0.000228689   5.24108e-18  -7.87989e-5   -4.77978e-19  -1.43006e-5    2.61738e-18  -1.11779e-6   -7.23908e-19   2.57992e-8   -2.15228e-18  -9.03781e-8    1.59592e-18  -8.97012e-8   -2.50435e-18  -4.18139e-8    9.49482e-19  -1.37244e-8   -1.26486e-19  -2.86072e-9\n  0.0632999     3.41915e-18   0.0392743     2.04798e-19   3.65838e-6   -1.28777e-18  -0.00566089   -8.19676e-20  -0.00237159    2.32247e-19  -0.0004495    -2.03756e-20   7.81213e-6    5.90042e-19   3.39614e-5    2.90117e-19   1.24485e-5   -1.55416e-18   2.90796e-6    1.87269e-18   5.68462e-7    7.70684e-19   1.34604e-7   -4.06242e-19   3.66282e-8   -7.1747e-19    6.0499e-9    -2.08524e-18  -9.48683e-10   6.16421e-19\n  3.09716e-18  -0.0381303     6.85278e-18  -0.0305859     1.24178e-18  -0.00858298    1.57978e-18   4.65679e-6    1.48577e-18   0.000859316   3.66318e-18   0.000335164  -3.67668e-18   6.02308e-5    2.74714e-19  -1.60502e-6   -1.31714e-18  -4.61957e-6    2.8105e-19   -1.57519e-6    5.32057e-19  -2.83912e-7   -1.10903e-19   6.48665e-9   -9.75956e-20   2.64839e-8    4.45112e-20   1.29647e-8   -5.92566e-21   3.53416e-9\n -0.0246173     1.28294e-18  -7.2626e-6    -5.42555e-19   0.0116417    -1.5197e-18    0.00624266   -1.5262e-18    0.00144602   -1.20352e-19  -1.39151e-5    7.19328e-21  -0.000132715  -7.90881e-19  -5.15476e-5   -3.3778e-19   -1.08626e-5    1.76166e-18  -1.14678e-6   -1.99294e-18  -1.60201e-8   -7.73951e-19  -6.95967e-8    3.34098e-19  -5.06628e-8    6.43971e-19  -1.89806e-8    1.87268e-18  -4.88118e-9   -5.53209e-19\n  2.98082e-18   0.0318389    -6.74309e-18   0.0141265    -2.2857e-18    5.77928e-6    1.85861e-18  -0.00227906   -7.38706e-19  -0.00104803   -2.16033e-18  -0.000212855   1.40664e-18   1.03295e-5   -1.06259e-19   2.34123e-5   -4.7078e-20    9.30847e-6    1.52155e-19   2.35417e-6    9.37069e-19   3.9768e-7    -8.25039e-19   5.08658e-8    1.53656e-18  -3.96513e-9   -7.02953e-19  -6.27377e-9    9.37749e-20  -2.22939e-9\n  4.3203e-6    -1.01216e-18  -0.0150888     3.64998e-18  -0.0112343    -2.60809e-18  -0.00328812   -3.25601e-19   1.04744e-5    6.53008e-19   0.00039214   -6.12143e-20   0.000165953   7.88511e-19   3.20022e-5    3.78167e-19  -1.20827e-6   -1.64546e-18  -2.94655e-6    1.7585e-18   -7.04511e-7    5.42632e-19  -5.6071e-8    -2.74245e-19   3.46324e-8   -5.26347e-19   2.06785e-8   -1.52684e-18   7.17059e-9    4.53041e-19\n  2.97978e-18  -0.013664      6.79816e-18  -1.51866e-5    2.56186e-19   0.00436874    2.27725e-18   0.00244523    8.55161e-19   0.000590637   5.06774e-19  -2.14758e-5   -9.87345e-20  -7.38896e-5   -2.0589e-19   -3.13213e-5    1.16495e-18  -7.72648e-6   -4.88283e-19  -1.29269e-6   -1.50713e-18  -2.78823e-7    1.30362e-18  -5.90858e-8   -2.41505e-18  -1.01665e-8    1.09315e-18  -5.87834e-11  -1.44524e-19   6.08272e-10\n  0.00851225   -3.44209e-18   0.0134873    -4.45863e-18   0.00537692   -8.6344e-19    6.02617e-6   -2.59858e-18  -0.000910525   1.20144e-19  -0.000437065  -4.63497e-20  -8.7068e-5    -8.54955e-19   1.1278e-5    -2.24346e-19   1.49731e-5    1.34347e-18   4.52269e-6   -1.05164e-18   1.07064e-6   -4.12598e-19   1.46243e-7    1.8322e-19   -1.38814e-8    3.81734e-19  -1.70166e-8    1.17383e-18  -7.00317e-9   -3.2114e-19\n -4.81915e-19   1.53467e-5   -3.48518e-18  -0.00600077   -1.54362e-18  -0.00428943    1.3639e-18   -0.00126564    6.40514e-19   2.25421e-5    1.15139e-18   0.000179497  -3.15573e-18   8.01025e-5    1.19841e-19   1.7027e-5    -2.29661e-18   1.57076e-6    6.35428e-19   2.06968e-7    1.82846e-18   6.4408e-8    -1.42283e-18   3.71494e-8    2.72152e-18   1.54347e-8   -1.30644e-18   4.19595e-9    1.83024e-19   6.39706e-10\n -0.00737561    4.33251e-19  -0.00609917    5.13286e-18  -2.74248e-5   -1.08183e-18   0.00166484   -1.58033e-19   0.000938074   9.62032e-19   0.000214292  -1.42549e-19  -2.95524e-5    4.47723e-19  -4.43089e-5    3.81922e-19  -1.48998e-5   -5.38424e-19  -4.66705e-6    8.07988e-19  -1.1166e-6     2.92867e-19  -1.75326e-7   -2.39274e-19   6.20197e-11  -3.48375e-19   1.22805e-8   -7.91504e-19   5.74874e-9    3.3781e-19\n -1.50034e-18   0.00528716    2.7886e-18    0.00556329   -4.46317e-19   0.00208938   -2.35225e-19  -5.2783e-7     1.28332e-19  -0.000359085  -2.52064e-18  -0.000171677   2.32232e-18  -2.96656e-5   -7.48237e-19   2.10201e-6    1.13125e-18   2.03799e-6   -1.16185e-19   7.36548e-7   -1.66045e-18   1.34796e-7    2.01546e-18  -8.41342e-9   -3.41003e-18  -1.56944e-8    1.27476e-18  -6.34761e-9   -1.27924e-19  -1.40381e-9\n  0.00325817   -2.45633e-19   3.77292e-5   -6.14046e-18  -0.00236387    1.66876e-18  -0.0016225    -1.50793e-18  -0.000450124   3.28208e-19   4.2479e-5    -1.59362e-19   9.29879e-5   -6.17023e-19   3.37099e-5    5.05904e-19   1.28552e-5    9.75982e-19   3.9506e-6    -2.67608e-19   9.51441e-7   -1.69696e-19   1.58677e-7   -2.67634e-19   5.78941e-9   -8.37328e-20  -8.22477e-9    7.13035e-19  -4.24338e-9    2.06127e-19\n -1.92472e-18  -0.00475403   -5.91543e-19  -0.00260261    2.78168e-19  -4.17061e-5   -1.84423e-18   0.000603349   1.75828e-18   0.000321014   3.76947e-18   4.91036e-5   -6.29248e-18  -1.33075e-5   -6.34022e-19  -9.95643e-6   -3.43015e-18  -4.40482e-6    1.36517e-18  -1.35103e-6    2.23042e-18  -2.69324e-7   -4.75928e-19  -1.41967e-8    1.79959e-18   1.40866e-8   -1.45174e-18   7.16251e-9    3.37102e-19   1.77508e-9\n -2.1087e-5     4.50168e-18   0.00246819    5.59021e-18   0.00221801    9.29436e-19   0.000774953   1.30231e-18  -2.27028e-5    6.11546e-19  -0.000146058  -2.55988e-19  -5.59485e-5   -4.2841e-19   -2.5516e-5     1.26531e-18  -9.52201e-6    5.35149e-19  -2.90084e-6    4.21316e-19  -7.0138e-7     2.6213e-19   -1.20528e-7   -4.14798e-19  -6.49799e-9   -3.96214e-19   5.20338e-9   -3.60057e-19   2.87275e-9    6.14152e-19\n  4.47127e-21   0.00217575   -2.94804e-18   7.86173e-5   -5.74207e-19  -0.000845473  -3.00544e-18  -0.000526267  -6.48906e-19  -9.24417e-5   -3.83389e-18   2.85383e-5    8.31841e-19   2.55329e-5   -1.4905e-18    1.39518e-5   -4.26975e-19   5.53959e-6   -1.18541e-19   1.63754e-6   -1.05016e-18   3.34514e-7    2.56192e-18   2.71988e-8   -3.29911e-18  -1.21682e-8    9.01268e-19  -7.17118e-9    1.50771e-19  -1.87466e-9\n -0.00127442    2.89389e-19  -0.00226313   -4.46728e-18  -0.00105975    1.64027e-18  -4.70324e-5    7.69626e-19   0.000173699  -1.45736e-19   6.84882e-5   -3.31713e-19   3.73772e-5   -1.13667e-20   1.67333e-5    8.04904e-19   6.1804e-6     5.06204e-19   1.87498e-6   -1.61079e-19   4.54341e-7    3.94803e-19   7.92679e-8    1.21931e-20   4.9557e-9    -3.19611e-20  -3.08203e-9   -1.34464e-19  -1.77447e-9    2.78404e-19\n  1.91167e-18  -7.54358e-5    3.5257e-18    0.000953128   2.00801e-18   0.00073895   -2.05146e-18   0.000186348   1.79056e-18  -3.08415e-5    2.42912e-18  -4.20801e-5    2.90394e-19  -2.97992e-5    3.9062e-20   -1.49958e-5   -7.82959e-19  -5.73922e-6   -1.84621e-18  -1.67382e-6    1.1383e-18   -3.45419e-7   -1.14846e-18  -3.19319e-8    3.34489e-18   1.04223e-8   -1.00359e-18   6.70585e-9    2.9619e-19    1.79997e-9\n  0.00115733    1.26766e-18   0.00108248    4.04541e-18   0.000140675  -2.95318e-19  -0.00015525    2.01371e-18  -6.00244e-5   -6.23205e-19  -3.94963e-5   -2.51751e-19  -2.12639e-5    5.94277e-19  -9.44009e-6   -1.69513e-20  -3.47007e-6   -8.14934e-19  -1.05071e-6   -6.08742e-19  -2.54885e-7    5.11695e-19  -4.47918e-8    8.87238e-19  -2.98189e-9    8.42475e-19   1.6509e-9    -1.1719e-18    9.71987e-10  -6.89756e-19\n  1.43485e-18  -0.000757848  -5.39556e-18  -0.000843449  -8.62549e-19  -0.000328982   2.58778e-19   8.77607e-7   -2.05965e-19   4.13033e-5   -9.57155e-19   4.36922e-5    3.10512e-18   2.88832e-5   -1.32965e-19   1.41096e-5    1.04901e-18   5.3233e-6    -1.31593e-18   1.5442e-6    -6.91619e-19   3.20051e-7    9.90121e-19   3.10541e-8   -3.54625e-19  -8.83962e-9    3.59484e-19  -5.9456e-9    -6.76568e-19  -1.61537e-9\n -0.000553886  -2.83344e-18  -0.000187639  -1.79892e-18   0.000102621  -1.99574e-18   3.50362e-5   -6.73422e-19   2.80559e-5   -9.65978e-19   1.831e-5      2.44116e-19   9.80506e-6    8.6229e-19    4.33835e-6   -1.76767e-19   1.59166e-6    3.81142e-19   4.81568e-7    1.3699e-18    1.16874e-7   -1.00262e-19   2.05996e-8   -1.24595e-18   1.40536e-9   -1.66699e-19  -7.42251e-10   8.35404e-19  -4.4125e-10    1.03896e-19\n  3.66637e-19   0.00067785    7.99019e-18   0.000443404   1.40538e-18   5.25409e-5    8.65411e-19  -8.79182e-6   -2.94255e-19  -3.88737e-5    5.6295e-19   -3.84611e-5   -2.42411e-18  -2.48679e-5   -5.79018e-20  -1.20249e-5   -7.04044e-19  -4.51391e-6    7.82627e-19  -1.30691e-6    1.08722e-18  -2.71299e-7    6.3856e-19   -2.67727e-8    2.94439e-19   7.24306e-9   -7.0046e-19    4.95787e-9   -9.33544e-19   1.35319e-9\n  0.000104898  -1.05592e-18  -4.97719e-5   -5.85949e-19  -1.14056e-5    6.6917e-19   -1.12136e-5    4.34839e-19  -8.949e-6      4.06004e-19  -5.82665e-6   -2.37517e-19  -3.11536e-6   -5.88588e-19  -1.37708e-6    5.28526e-19  -5.04943e-7   -1.6762e-19   -1.52739e-7   -3.44619e-19  -3.7074e-8    -1.92945e-19  -6.54014e-9    1.13273e-19  -4.49338e-10   6.89746e-19   2.34081e-10  -4.65733e-19   1.39557e-10  -5.44661e-19\n -3.10808e-18  -0.000389793  -3.14687e-18  -8.04943e-5   -2.87651e-19  -3.68665e-5   -2.39537e-18   8.03845e-6   -3.64421e-19   2.97453e-5   -6.17914e-19   2.89916e-5    1.07312e-18   1.86472e-5    4.40338e-19   8.99472e-6    1.66864e-18   3.37228e-6   -1.12296e-18   9.75922e-7   -2.07688e-19   2.02668e-7    4.25707e-21   2.00821e-8    1.41624e-19  -5.36499e-9    1.09196e-19  -3.68864e-9   -1.60289e-19  -1.00792e-9\n  1.54054e-5    1.3469e-18    1.00144e-6    1.82904e-19   1.23964e-6   -8.86981e-20   1.21824e-6    5.88101e-20   9.71898e-7   -1.0139e-19    6.32656e-7   -8.23915e-20   3.38215e-7    1.52369e-19   1.49487e-7   -1.10294e-19   5.48103e-8   -2.0251e-19    1.65791e-8    6.6719e-20    4.02426e-9    1.20342e-19   7.09969e-10  -6.40354e-20   4.88112e-11  -5.32019e-20  -2.53943e-11   1.22809e-19  -1.51441e-11   7.69628e-20\n -1.53496e-18   0.000145153   1.15554e-19   0.000143445  -5.81062e-20   6.55677e-5    2.32816e-19  -1.45469e-5    2.72345e-19  -5.3233e-5     4.51728e-20  -5.18305e-5   -3.6008e-21   -3.33247e-5   -1.62663e-19  -1.60719e-5   -4.71441e-19  -6.0251e-6     7.67245e-20  -1.74358e-6    3.53714e-20  -3.62096e-7    2.92342e-20  -3.58901e-8   -1.45255e-19   9.57958e-9   -1.47136e-20   6.5884e-9     3.52877e-19   1.80042e-9","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"The Dunkl-Xu coefficients are useful for integration. The integral of f(xy) over the disk should be pi2 by harmonicity. The coefficient of P_00 multiplied by √π is:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"U[1, 1]*sqrt(π)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"1.5707955409153043","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"Using an orthonormal basis, the integral of f(xy)^2 over the disk is approximately the square of the 2-norm of the coefficients:","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"norm(U)^2, π/(2*sqrt(2))*log1p(sqrt(2))","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"(0.978937045726087, 0.9789599179781414)","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"","category":"page"},{"location":"generated/disk/#","page":"Holomorphic integration on the unit disk","title":"Holomorphic integration on the unit disk","text":"This page was generated using Literate.jl.","category":"page"},{"location":"dev/#Development-Documentation-1","page":"Development","title":"Development Documentation","text":"","category":"section"},{"location":"dev/#","page":"Development","title":"Development","text":"The core of FastTransforms.jl is developed in parallel with the C library of the same name. Julia and C interoperability is enhanced by the BinaryBuilder infrastructure, which provides the user a safe and seamless experience using a package in a different language.","category":"page"},{"location":"dev/#Why-two-packages?-1","page":"Development","title":"Why two packages?","text":"","category":"section"},{"location":"dev/#","page":"Development","title":"Development","text":"Orthogonal polynomial transforms are performance-sensitive imperative tasks. Yet, many of Julia's rich and evolving language features are simply unnecessary for defining these computational routines. Moreover, rapid language changes in Julia (as compared to C) have been more than a perturbation to this repository in the past.","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"The C library generates assembly for vectorized operations such as single instruction multiple data (SIMD) that is more efficient than that generated by a compiler without human intervention. It also uses OpenMP to introduce shared memory parallelism for large tasks. Finally, calling into precompiled binaries reduces the Julia package's pre-compilation and dependencies, improving the user experience. Some of these capabilities also exist in Julia, but with C there is frankly more control over performance.","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"C libraries are easier to call from any other language, partly explaining why the Python package manager Spack already supports the C library through third-party efforts.","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"In Julia, a parametric composite type with unrestricted type parameters is just about as big as Any. Such a type allows the Julia API to far exceed the C API in its ability to unify all of the orthogonal polynomial transforms and present them as linear operators. The mutable struct FTPlan{T, N, K}, together with AdjointFTPlan and TransposeFTPlan, are the core Julia types in this repository. Whereas T is understood to represent element type of the plan and N represents the number of leading dimensions of the array on which it operates, K is a mere enumeration which serves to distinguish the orthogonal polynomials at play. For example, FTPlan{Float64, 1, LEG2CHEB} represents the necessary pre-computations to convert 64-bit Legendre series to Chebyshev series (of the first kind). N == 1 because Chebyshev and Legendre series are naturally represented with vectors of coefficients. However, this particular plan may operate not only on vectors but also on matrices, column-by-column.","category":"page"},{"location":"dev/#The-developer's-right-to-build-from-source-1","page":"Development","title":"The developer's right to build from source","text":"","category":"section"},{"location":"dev/#","page":"Development","title":"Development","text":"Precompiled binaries are important for users, but development in C may be greatly accelerated by coupling it with a dynamic language such as Julia. For this reason, the repository preserves the developer's right to build the C library from source by setting an environment variable to trigger the build script:","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"julia> ENV[\"FT_BUILD_FROM_SOURCE\"] = \"true\"\n\"true\"\n\n(@v1.5) pkg> build FastTransforms\n   Building FFTW ──────────→ `~/.julia/packages/FFTW/ayqyZ/deps/build.log`\n   Building TimeZones ─────→ `~/.julia/packages/TimeZones/K98G0/deps/build.log`\n   Building FastTransforms → `~/.julia/dev/FastTransforms/deps/build.log`\n\njulia> using FastTransforms\n[ Info: Precompiling FastTransforms [057dd010-8810-581a-b7be-e3fc3b93f78c]\n","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"This lets the developer experiment with new features through ccalling into bleeding edge source code. Customizing the build script further allows the developer to track a different branch or even a fork.","category":"page"},{"location":"dev/#From-release-to-release-to-release-1","page":"Development","title":"From release to release to release","text":"","category":"section"},{"location":"dev/#","page":"Development","title":"Development","text":"To get from a C library release to a Julia package release, the developer needs to update Yggdrasil's build_tarballs.jl script for the new version and its 256-bit SHA. On macOS, the SHA can be found by:","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"shell> curl https://codeload.github.com/MikaelSlevinsky/FastTransforms/tar.gz/v0.6.2 --output FastTransforms.tar.gz\n  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n                                 Dload  Upload   Total   Spent    Left  Speed\n100  168k    0  168k    0     0   429k      0 --:--:-- --:--:-- --:--:--  429k\n\nshell> shasum -a 256 FastTransforms.tar.gz\nfd00befcb0c20ba962a8744a7b9139355071ee95be70420de005b7c0f6e023aa  FastTransforms.tar.gz\n\nshell> rm -f FastTransforms.tar.gz\n","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"Using SHA.jl, the SHA can also be found by:","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"shell> curl https://codeload.github.com/MikaelSlevinsky/FastTransforms/tar.gz/v0.6.2 --output FastTransforms.tar.gz\n  % Total    % Received % Xferd  Average Speed   Time    Time     Time  Current\n                                 Dload  Upload   Total   Spent    Left  Speed\n100  168k    0  168k    0     0   442k      0 --:--:-- --:--:-- --:--:--  443k\n\njulia> using SHA\n\njulia> open(\"FastTransforms.tar.gz\") do f\n           bytes2hex(sha256(f))\n       end\n\"fd00befcb0c20ba962a8744a7b9139355071ee95be70420de005b7c0f6e023aa\"\n\nshell> rm -f FastTransforms.tar.gz\n","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"Then we wait for the friendly folks at JuliaPackaging to merge the pull request to Yggdrasil, triggering a new release of the FastTransforms_jll.jl meta package that stores all precompiled binaries. With this release, we update the FastTransforms.jl Project.toml to point to the latest release and register the new version.","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"Since development of Yggdrasil is quite rapid, a fork may easily become stale. Git permits the developer to forcibly make a master branch on a fork even with upstream master:","category":"page"},{"location":"dev/#","page":"Development","title":"Development","text":"git fetch upstream\ngit checkout master\ngit reset --hard upstream/master\ngit push origin master --force","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/sphere.jl\"","category":"page"},{"location":"generated/sphere/#Spherical-harmonic-addition-theorem-1","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"","category":"section"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"This example confirms numerically that","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"f(z) = fracP_n(zcdot y) - P_n(xcdot y)zcdot y - xcdot y","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"is actually a degree-(n-1) polynomial on mathbbS^2, where P_n is the degree-n Legendre polynomial, and xyz in mathbbS^2. To verify, we sample the function on a Ntimes M equiangular grid defined by:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"beginaligned\ntheta_n  = (n+tfrac12)piNquadrm forquad 0le n  Nquadrm and\nvarphi_m  = 2pi mMquadrm forquad 0le m  M\nendaligned","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"we convert the function samples to Fourier coefficients using plan_sph_analysis; and finally, we transform the Fourier coefficients to spherical harmonic coefficients using plan_sph2fourier.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"In the basis of spherical harmonics, it is plain to see the addition theorem in action, since P_n(xcdot y) should only consist of exact-degree-n harmonics.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"For the storage pattern of the arrays, please consult the documentation.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"function threshold!(A::AbstractArray, ϵ)\n    for i in eachindex(A)\n        if abs(A[i]) < ϵ A[i] = 0 end\n    end\n    A\nend\n\nusing FastTransforms, LinearAlgebra, Plots\nconst GENFIGS = joinpath(pkgdir(FastTransforms), \"docs/src/generated\")\n!isdir(GENFIGS) && mkdir(GENFIGS)\nplotlyjs()","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Plots.PlotlyJSBackend()","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"The colatitudinal grid (mod pi):","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"N = 15\nθ = (0.5:N-0.5)/N","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"0.03333333333333333:0.06666666666666667:0.9666666666666667","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"The longitudinal grid (mod pi):","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"M = 2*N-1\nφ = (0:M-1)*2/M","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"0.0:0.06896551724137931:1.9310344827586206","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Arbitrarily, we place x at the North pole:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"x = [0,0,1]","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"3-element Vector{Int64}:\n 0\n 0\n 1","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Another vector is completely free:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"y = normalize([.123,.456,.789])","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"3-element Vector{Float64}:\n 0.13375998748853216\n 0.4958906853233388\n 0.8580213831581455","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Thus z in mathbbS^2 is our variable vector, parameterized in spherical coordinates:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"z = (θ,φ) -> [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"#1 (generic function with 1 method)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"On the tensor product grid, the Legendre polynomial P_n(zcdot y) is:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"A = [(2k+1)/(k+1) for k in 0:N-1]\nB = zeros(N)\nC = [k/(k+1) for k in 0:N]\nc = zeros(N); c[N] = 1\npts = vec([z(θ, φ)⋅y for θ in θ, φ in φ])\nphi0 = ones(N*M)\nF = reshape(FastTransforms.clenshaw!(c, A, B, C, pts, phi0, zeros(N*M)), N, M)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n  0.264259    0.299171     0.304985    0.288068    0.261038    0.237692     0.228241    0.236528     0.259192    0.286391     0.304437    0.300462     0.26755      0.207601     0.130208    0.0483744   -0.0262845   -0.0865116   -0.129804   -0.156955   -0.169985    -0.170403    -0.158265    -0.132139   -0.0899937  -0.0308858   0.0429655   0.124641    0.202756\n  0.212068    0.303332     0.129215   -0.186607   -0.387155   -0.383993    -0.338172   -0.379747    -0.392602   -0.206438     0.109443    0.299961     0.225231    -0.0101802   -0.207053   -0.258628    -0.187516    -0.070652     0.0323131   0.0988479   0.12977      0.130741     0.102005     0.0380582  -0.0627707  -0.180155   -0.256899   -0.215501   -0.0267606\n -0.115553    0.236712     0.221776   -0.251073   -0.32857     0.421619     0.986223    0.482429    -0.299585   -0.280602     0.198511    0.253762    -0.0930651   -0.258938    -0.0793421   0.160653     0.233501     0.154045     0.0336174  -0.0560314  -0.0990238   -0.100375    -0.0604041    0.0261339   0.145985    0.231751    0.1719     -0.0610864  -0.255787\n -0.18454    -0.186901     0.216999    0.207436   -0.278408   -0.36511     -0.189358   -0.35156     -0.304334    0.180746     0.238643   -0.165767    -0.202157     0.128252     0.217098   -0.00943667  -0.200512    -0.194373    -0.0821865   0.0208264   0.0732008    0.0748654    0.0260895   -0.074028   -0.188494   -0.206184   -0.027257    0.20837     0.147067\n  0.233218   -0.0443128   -0.25662     0.0443223   0.302577    0.209245     0.107407    0.198264     0.305263    0.0716125   -0.25045    -0.0709297    0.228915     0.0560634   -0.209167   -0.109098     0.135993     0.209367     0.121014    0.0107106  -0.049922    -0.0518826    0.00472316   0.112882    0.206906    0.148044   -0.0921222  -0.214775    0.0327421\n -0.14959     0.176398     0.159536   -0.157586   -0.253853   -0.135785    -0.0630475  -0.127292    -0.249419   -0.174706     0.141057    0.191837    -0.130845    -0.171771     0.128955    0.181407    -0.058914    -0.206946    -0.154207   -0.0410986   0.0276329    0.029906    -0.034464    -0.146673   -0.208687   -0.0754426   0.17029     0.145612   -0.156134\n  0.03232    -0.216991    -0.0542418   0.201432    0.206916    0.0892457    0.0316764   0.0822717    0.200041    0.210302    -0.0334057  -0.219505     0.00906962   0.211107    -0.0222883  -0.209099    -0.0231776    0.189332     0.183999    0.0724419  -0.00503206  -0.00766855   0.065182     0.177672    0.19593    -0.0044746  -0.206821   -0.0443208   0.20777\n  0.0772106   0.200813    -0.0345837  -0.214416   -0.166372   -0.0543381   -0.0063074  -0.0483886   -0.158601   -0.217382    -0.0533452   0.193042     0.0976693   -0.187906    -0.085199    0.193101     0.105896    -0.154519    -0.211246   -0.107108   -0.019323    -0.0162213   -0.09921     -0.206977   -0.166608    0.0879047   0.201099   -0.0639311  -0.196895\n -0.161616   -0.14919      0.105731    0.2116      0.130202    0.0251362   -0.0160611   0.0199531    0.122174    0.210305     0.12046    -0.134582    -0.17451      0.114917     0.174042   -0.130385    -0.182374     0.0957622    0.234753    0.148573    0.0475436    0.0437788    0.140028     0.233975    0.113813   -0.1691     -0.148371    0.159712    0.133414\n  0.208908    0.0728989   -0.161008   -0.198486   -0.0961065   0.00135321   0.037119    0.00590617  -0.0881639  -0.194067    -0.170766    0.0549875    0.211431    -0.00338118  -0.21986     0.016122     0.234375     0.00021735  -0.247537   -0.203094   -0.0836434   -0.0787903   -0.19406     -0.253043   -0.023216    0.231655    0.0407554  -0.218225   -0.0261102\n -0.203495    0.0220031    0.200371    0.176174    0.0619327  -0.0270702   -0.058089   -0.0310551    0.0543296   0.169516     0.204695    0.0395021   -0.194934    -0.128043     0.183785    0.141369    -0.211961    -0.150004     0.2205      0.283345    0.137864     0.130789     0.275142     0.23809    -0.126501   -0.226893    0.11958     0.198142   -0.109095\n  0.12233    -0.127714    -0.219526   -0.142772   -0.0253159   0.0536809    0.080125    0.0571016   -0.0183211  -0.134724    -0.218347   -0.140698     0.10537      0.230635    -0.0169741  -0.260275     0.00868827   0.306062    -0.0323035  -0.400665   -0.252906    -0.23893     -0.40434     -0.0688019   0.303902    0.0393269  -0.259455   -0.0416906   0.225524\n  0.0533261   0.221676     0.20588     0.0928744  -0.0169863  -0.083121    -0.10464    -0.0859165   -0.0229991   0.0845139    0.199903    0.226054     0.0700661   -0.185075    -0.235303    0.0671548    0.306034     0.0030983   -0.399433   -0.020757    0.815719     0.855083     0.0350084   -0.404293   -0.0323252   0.304047    0.0929697  -0.224541   -0.198835\n -0.251975   -0.233798    -0.13019    -0.0152352   0.0703864   0.11835      0.133806    0.120358     0.0748091  -0.00825682  -0.122061   -0.22853     -0.255028    -0.136944     0.097903    0.288106     0.247787    -0.0273998   -0.313828   -0.4047     -0.353264    -0.349855    -0.403561    -0.327222   -0.0497156   0.234981    0.294129    0.11465    -0.123547\n  0.0890404   0.00957584  -0.0584588  -0.110278   -0.145276   -0.165114    -0.171728   -0.165964    -0.14708    -0.113177    -0.062519    0.00451035   0.0834519    0.16497      0.23634     0.285407     0.305513     0.298672     0.274919    0.248139    0.230823     0.230209     0.246547     0.273036    0.297446    0.305825    0.287718    0.240496    0.170292","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"X = [sinpi(θ)*cospi(φ) for θ in θ, φ in φ]\nY = [sinpi(θ)*sinpi(φ) for θ in θ, φ in φ]\nZ = [cospi(θ) for θ in θ, φ in φ]\nscatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)\nsurface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"sphere1.html\"))","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"<object type=\"text/html\" data=\"../sphere1.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere1.html\"","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"We show the cut in the surface to help illustrate the definition of the grid. In particular, we do not sample the poles.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"We precompute a spherical harmonic–Fourier plan:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"P = plan_sph2fourier(F)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"FastTransforms Spherical harmonic--Fourier plan for 15×29-element array of Float64","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"And an FFTW Fourier analysis plan on mathbbS^2:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"PA = plan_sph_analysis(F)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"FastTransforms plan for FFTW Fourier analysis on the sphere for 15×29-element array of Float64","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Its spherical harmonic coefficients demonstrate that it is exact-degree-n:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"V = PA*F\nU = threshold!(P\\V, 400*eps())","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0         -1.66397e-5  2.73274e-5\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0         -0.000271538  -7.91038e-5   0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         3.29805e-5  -0.00164832   0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.00703526  -0.00174747  0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0122275  0.0220184  0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0        -0.0503776  0.0488881  0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0       -0.134224  -0.0799001   0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0729185  -0.259962   0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.337609  0.00337719  0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0610941  0.235853  0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.0       0.0       0.0289877  -0.0164793  0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0         0.0        0.0       0.190197  0.192109  0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.0       0.0        -0.0788841  0.135585  0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.0       0.188313  0.0507949   0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0\n 0.142187  0.0       0.0         0.0        0.0       0.0       0.0       0.0         0.0        0.0        0.0       0.0       0.0         0.0         0.0        0.0        0.0         0.0        0.0        0.0        0.0        0.0          0.0         0.0          0.0          0.0           0.0          0.0         0.0","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"The L^2(mathbbS^2) norm of the function is:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"nrm1 = norm(U)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"0.6582728344942355","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Similarly, on the tensor product grid, our function samples are:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Pnxy = FastTransforms.clenshaw!(c, A, B, C, [x⋅y], [1.0], [0.0])[1]\nF = [(F[n, m] - Pnxy)/(z(θ[n], φ[m])⋅y - x⋅y) for n in 1:N, m in 1:M]","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n  5.19948      4.13834      2.99067      1.90658      1.02691     0.455272    0.249877    0.429314    0.977414    1.83893      2.91328     4.06148      5.13287      6.0026       6.60156      6.92544     7.02254     6.96965     6.84793     6.72603     6.65164      6.64905     6.71906     6.83899     6.96269     7.02276     6.93845     6.63197     6.05227\n  5.95491      2.78879     -1.44975     -4.81316     -5.93907    -5.32122    -4.74802    -5.26014    -5.93537    -4.96628     -1.72861     2.51536      5.80241      7.01649      6.35996      4.76275     3.10172     1.83264     1.03553     0.610092    0.43191      0.426508    0.591355    0.996377    1.76414     3.00054     4.64424     6.26964     7.0226\n  6.89687      5.65236      0.11585     -5.28724     -4.64181     1.51819     5.42995     1.95544    -4.33608    -5.4796      -0.331651    5.39124      6.95616      4.78949      1.90996      0.265776   -0.0679633   0.206459    0.546026    0.760489    0.851318     0.854026    0.770114    0.565133    0.231314   -0.0604333   0.208258    1.74968     4.58324\n  3.06027      6.5357       5.89997     -0.165743    -5.46592    -5.06636    -3.28816    -4.90175    -5.62054    -0.644121     5.6253      6.677        3.31846      0.440384    -0.00401181   0.652985    1.01303     0.876591    0.580633    0.35795     0.254199     0.250991    0.347269    0.561893    0.857659    1.01648     0.69514     0.0273999   0.337402\n -0.070137     1.60923      5.43093      6.93528      3.91137    -0.131309   -1.75656    -0.336142    3.61343     6.85843      5.66343     1.83509     -0.053904     0.487406     1.01741      0.644213    0.136921    0.0101545   0.134135    0.275013    0.346961     0.349218    0.282296    0.144972    0.0138328   0.115298    0.603776    1.01615     0.548272\n  0.945078     0.135483     0.27158      2.71505      5.55048     6.82449     7.00499     6.85725     5.69314     2.92844      0.369819    0.0844295    0.912316     0.807551     0.149683     0.0509116   0.357273    0.499174    0.407141    0.269902    0.193177     0.1907      0.262329    0.397299    0.498435    0.37596     0.0666419   0.119637    0.764012\n  0.3347       0.96741      0.756526     0.0516758    0.0403323   0.667862    1.0399      0.710559    0.0718486   0.0205398    0.70939     0.987443     0.382027     0.0075432    0.314675     0.493074    0.249535    0.0255986   0.0288774   0.124344    0.187529     0.189637    0.130366    0.0344678   0.0191719   0.228563    0.486554    0.340488    0.0125441\n  0.19163      0.0244645    0.474228     0.953439     0.971777    0.756739    0.645454    0.743468    0.95977     0.969839     0.515354    0.0373859    0.165042     0.488731     0.32132      0.0219213   0.0963195   0.301654    0.329627    0.240493    0.171995     0.169627    0.234193    0.325354    0.310183    0.111448    0.0141702   0.296273    0.495085\n  0.41699      0.454012     0.154439     0.00689009   0.147415    0.349199    0.434542    0.359728    0.162073    0.00898106   0.134876    0.43942      0.434649     0.100528     0.0376636    0.284172    0.302882    0.085971   -0.0128005   0.0446154   0.109712     0.112106    0.0501911  -0.0122374   0.0727995   0.291434    0.297253    0.0501979   0.0815347\n  0.00653828   0.144506     0.416175     0.496049     0.398793    0.286378    0.242449    0.28086     0.390091    0.493228     0.429442    0.163601     0.00423886   0.186207     0.340647     0.145106   -0.0125214   0.139641    0.288402    0.253913    0.179097     0.176118    0.248108    0.291182    0.154331   -0.0106262   0.126633    0.337571    0.204303\n  0.334489     0.165749     0.014265     0.0385386    0.156172    0.253936    0.289478    0.258454    0.164306    0.0451436    0.010362    0.151498     0.32921      0.257363     0.0225829    0.0493168   0.268651    0.220231   -0.0026208  -0.0383697   0.0440181    0.047986   -0.0336588  -0.0128432   0.205569    0.277144    0.0634765   0.012466    0.242082\n  0.0666146    0.257095     0.341563     0.293211     0.203674    0.139862    0.117949    0.137043    0.198126    0.287354     0.341672    0.267702     0.0789497   -0.00992474   0.150427     0.293905    0.12293    -0.051658    0.138809    0.33873     0.255252     0.247571    0.340446    0.15898    -0.0503184   0.104503    0.292551    0.165851   -0.00643622\n  0.106032    -0.00382806   0.00704658   0.088086     0.17021     0.221457    0.238521    0.223661    0.174806    0.0942214    0.0112304  -0.00679647   0.0953468    0.252997     0.275056     0.0878466  -0.0516354   0.119191    0.338121    0.128404   -0.323093    -0.344224    0.0980961   0.340427    0.138821   -0.0504052   0.0724608   0.267888    0.261055\n  0.286625     0.280994     0.220196     0.149338     0.0951419   0.0642734   0.0542416   0.0629728   0.0923113   0.144964     0.215269    0.278062     0.288893     0.21207      0.0695276   -0.0416382  -0.0180382   0.136094    0.292814    0.340282    0.310784     0.308881    0.339519    0.300016    0.148439   -0.0107592  -0.0450601   0.0595874   0.203734\n  0.0747987    0.122395     0.163672     0.195512     0.217272    0.229726    0.233902    0.230262    0.2184      0.197306     0.166153    0.125451     0.0781262    0.0298766   -0.0118277   -0.0400996  -0.0514099  -0.0472393  -0.0335309  -0.0182388  -0.00839924  -0.0080514  -0.0173325  -0.0324517  -0.0465243  -0.0515701  -0.0414172  -0.0142377   0.0267486","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"scatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)\nsurface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"sphere2.html\"))","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"<object type=\"text/html\" data=\"../sphere2.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere2.html\"","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Its spherical harmonic coefficients demonstrate that it is degree-(n-1):","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"V = PA*F\nU = threshold!(P\\V, 400*eps())","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n  2.07907     0.87453     0.235893    0.069594   -0.119618    0.0581001   0.0586842   0.0859934  -0.0488866  -0.015775   -0.060899   -0.0291623  -0.000291717  -0.00253358   0.00903247   0.000694039   0.000413142  -0.00117608  0.0011413   0.000780662  0.00140576  0.000942806  -0.000234181  8.63587e-6  -0.00043161  -0.000121732  -3.54626e-5  0.0  0.0\n  1.51317     0.44642     0.120416   -0.169934    0.292081    0.328839    0.332145    0.288911   -0.164244   -0.0423205  -0.163378   -0.0586349  -0.000586539  -0.00145765   0.00519666  -0.00998075   -0.00594126   -0.00862106  0.00836616  0.00369554   0.00665466  0.00342882   -0.000851678  2.16057e-5  -0.00107982   0.0           0.0         0.0  0.0\n  0.36606    -0.627659   -0.169303   -0.592046    1.0176      0.703541    0.710614    0.503834   -0.286426   -0.056082   -0.216504   -0.0224552  -0.000224625   0.0140577   -0.0501173   -0.0493515    -0.0293776    -0.0276576   0.0268398   0.00914327   0.0164645   0.00585456   -0.0014542    0.0          0.0          0.0           0.0         0.0  0.0\n -0.225238   -1.3923     -0.375555   -0.884141    1.51965     0.893241    0.902221    0.498016   -0.283118   -0.0162747  -0.0628284   0.165928    0.00165982    0.0536982   -0.191439    -0.123087     -0.0732701    -0.0534663   0.0518855   0.0122482    0.0220556   0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.0279478  -1.24976    -0.337105   -0.80053     1.37594     0.669715    0.676448    0.113165   -0.0643333   0.096013    0.370657    0.512707    0.00512874    0.109365    -0.389897    -0.195697     -0.116493     -0.0592355   0.0574841   0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.642706   -0.460978   -0.124343   -0.408306    0.701792    0.115506    0.116667   -0.53107     0.30191     0.2422      0.935011    0.866631    0.00866913    0.145962    -0.520371    -0.183527     -0.109249      0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.924445    0.171516    0.0462641  -0.0394459   0.0677993  -0.395183   -0.399156   -1.05835     0.601662    0.335991    1.29709     0.970497    0.00970813    0.116526    -0.415426     0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.619857    0.0934262   0.0252005   0.0128822  -0.0221418  -0.505099   -0.510177   -1.1197      0.636541    0.30573     1.18027     0.65018     0.00650392    0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.0816312  -0.512221   -0.138165   -0.239451    0.411566   -0.194804   -0.196763   -0.706203    0.401471    0.16128     0.622619    0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n -0.15003    -0.975789   -0.263206   -0.507765    0.872741    0.197111    0.199092   -0.186337    0.105931    0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.105958   -0.834521   -0.225101   -0.515565    0.886148    0.287159    0.290046    0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.530802   -0.266039   -0.0717606  -0.261012    0.448626    0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.668154    0.140073    0.0377829   0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.390394    0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0\n  0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0         0.0           0.0          0.0          0.0           0.0           0.0         0.0         0.0          0.0         0.0           0.0          0.0          0.0          0.0           0.0         0.0  0.0","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Finally, the Legendre polynomial P_n(zcdot x) is aligned with the grid:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"pts = vec([z(θ, φ)⋅x for θ in θ, φ in φ])\nF = reshape(FastTransforms.clenshaw!(c, A, B, C, pts, phi0, zeros(N*M)), N, M)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n  0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808\n -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968\n  0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489\n -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835\n  0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901\n -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532\n  0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677\n -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473  -0.209473\n  0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677   0.210677\n -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532  -0.214532\n  0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901   0.221901\n -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835  -0.234835\n  0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489   0.258489\n -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968   -0.30968\n  0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808   0.501808","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"We superpose a surface plot of f on top of the grid:","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"scatter3d(vec(X), vec(Y), vec(Z); markersize=1.25, markercolor=:violetred)\nsurface!(X, Y, Z; surfacecolor=F, legend=false, xlabel=\"x\", ylabel=\"y\", zlabel=\"f\")\nsavefig(joinpath(GENFIGS, \"sphere3.html\"))","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"<object type=\"text/html\" data=\"../sphere3.html\" style=\"width:100%;height:400px;\"></object>","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"\"/home/runner/work/FastTransforms.jl/FastTransforms.jl/docs/src/generated/sphere3.html\"","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"It only has one nonnegligible spherical harmonic coefficient. Can you spot it?","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"V = PA*F\nU = threshold!(P\\V, 400*eps())","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"15×29 Matrix{Float64}:\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.0       0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0\n 0.658273  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"That nonnegligible coefficient should be","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"ret = eval(\"√(2π/($(N-1)+1/2))\")","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"\"√(2π/(14+1/2))\"","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"which is approximately","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"eval(Meta.parse(ret))","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"0.6582728344942353","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"since the convention in this library is to orthonormalize.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"nrm2 = norm(U)","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"0.6582728344942352","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"Note that the integrals of both functions P_n(zcdot y) and P_n(zcdot x) and their L^2(mathbbS^2) norms are the same because of rotational invariance. The integral of either is perhaps not interesting as it is mathematically zero, but the norms of either should be approximately the same.","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"nrm1 ≈ nrm2","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"true","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"","category":"page"},{"location":"generated/sphere/#","page":"Spherical harmonic addition theorem","title":"Spherical harmonic addition theorem","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/automaticdifferentiation.jl\"","category":"page"},{"location":"generated/automaticdifferentiation/#Automatic-differentiation-through-spherical-harmonic-transforms-1","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"","category":"section"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"This example finds a positive value of lambda in:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"f(r) = sinlambda (kcdot r)","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"for some krinmathbbS^2 such that int_mathbbS^2 f^2 rmdOmega = 1. We do this by using derivative information through:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"dfracpartial fpartial lambda = (kcdot r) coslambda (kcdot r)","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"using FastTransforms, LinearAlgebra","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"The colatitudinal grid (mod pi):","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"N = 15\nθ = (0.5:N-0.5)/N","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"0.03333333333333333:0.06666666666666667:0.9666666666666667","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"The longitudinal grid (mod pi):","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"M = 2*N-1\nφ = (0:M-1)*2/M","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"0.0:0.06896551724137931:1.9310344827586206","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"We precompute a spherical harmonic–Fourier plan:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"P = plan_sph2fourier(Float64, N)","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"FastTransforms Spherical harmonic--Fourier plan for 15×29-element array of Float64","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"And an FFTW Fourier analysis plan on mathbbS^2:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"PA = plan_sph_analysis(Float64, N, M)","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"FastTransforms plan for FFTW Fourier analysis on the sphere for 15×29-element array of Float64","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"Our choice of k and angular parametrization of r:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"k = [2/7, 3/7, 6/7]\nr = (θ,φ) -> [sinpi(θ)*cospi(φ), sinpi(θ)*sinpi(φ), cospi(θ)]","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"#1 (generic function with 1 method)","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"Our initial guess for lambda:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"λ = 1.0","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"1.0","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"Then we run Newton iteration and grab an espresso:","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"for _ in 1:7\n    F = [sin(λ*(k⋅r(θ,φ))) for θ in θ, φ in φ]\n    Fλ = [(k⋅r(θ,φ))*cos(λ*(k⋅r(θ,φ))) for θ in θ, φ in φ]\n    U = P\\(PA*F)\n    Uλ = P\\(PA*Fλ)\n    global λ = λ - (norm(U)^2-1)/(2*sum(U.*Uλ))\n    println(\"λ: $(rpad(λ, 18)) and the 2-norm: $(rpad(norm(U), 18))\")\nend","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"λ: 0.5565017029393282 and the 2-norm: 1.8510924318185522\nλ: 0.5031571262839711 and the 2-norm: 1.1041845914870363\nλ: 0.5010418434316174 and the 2-norm: 1.0040147091934821\nλ: 0.5010383094266805 and the 2-norm: 1.0000066984258869\nλ: 0.5010383094167955 and the 2-norm: 1.0000000000187361\nλ: 0.5010383094167954 and the 2-norm: 1.0000000000000002\nλ: 0.5010383094167955 and the 2-norm: 0.9999999999999999\n","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"","category":"page"},{"location":"generated/automaticdifferentiation/#","page":"Automatic differentiation through spherical harmonic transforms","title":"Automatic differentiation through spherical harmonic transforms","text":"This page was generated using Literate.jl.","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"EditURL = \"https://github.com/JuliaApproximation/FastTransforms.jl/blob/master/examples/padua.jl\"","category":"page"},{"location":"generated/padua/#Padua-transform-1","page":"Padua transform","title":"Padua transform","text":"","category":"section"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"This demonstrates the Padua transform and inverse transform, explaining precisely the normalization and points","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"using FastTransforms","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"We define the Padua points and extract Cartesian components:","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"N = 15\npts = paduapoints(N)\nx = pts[:,1]\ny = pts[:,2];\nnothing #hide","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"We take the Padua transform of the function:","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"f = (x,y) -> exp(x + cos(y))\nf̌ = paduatransform(f.(x , y));\nnothing #hide","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"and use the coefficients to create an approximation to the function f:","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"f̃ = (x,y) -> begin\n    j = 1\n    ret = 0.0\n    for n in 0:N, k in 0:n\n        ret += f̌[j]*cos((n-k)*acos(x)) * cos(k*acos(y))\n        j += 1\n    end\n    ret\nend","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"#3 (generic function with 1 method)","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"At a particular point, is the function well-approximated?","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"f̃(0.1,0.2) ≈ f(0.1,0.2)","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"true","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"Does the inverse transform bring us back to the grid?","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"ipaduatransform(f̌) ≈ f̃.(x,y)","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"true","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"","category":"page"},{"location":"generated/padua/#","page":"Padua transform","title":"Padua transform","text":"This page was generated using Literate.jl.","category":"page"},{"location":"#FastTransforms.jl-Documentation-1","page":"Home","title":"FastTransforms.jl Documentation","text":"","category":"section"},{"location":"#Introduction-1","page":"Home","title":"Introduction","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.jl allows the user to conveniently work with orthogonal polynomials with degrees well into the millions.","category":"page"},{"location":"#","page":"Home","title":"Home","text":"This package provides a Julia wrapper for the C library of the same name. Additionally, all three types of nonuniform fast Fourier transforms available, as well as the Padua transform.","category":"page"},{"location":"#Fast-orthogonal-polynomial-transforms-1","page":"Home","title":"Fast orthogonal polynomial transforms","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"For this documentation, please see the documentation for FastTransforms. Most transforms have separate forward and inverse plans. In some instances, however, the inverse is in the sense of least-squares, and therefore only the forward transform is planned.","category":"page"},{"location":"#Nonuniform-fast-Fourier-transforms-1","page":"Home","title":"Nonuniform fast Fourier transforms","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"nufft1","category":"page"},{"location":"#FastTransforms.nufft1","page":"Home","title":"FastTransforms.nufft1","text":"Computes a nonuniform fast Fourier transform of type I:\n\nf_j = sum_k=0^N-1 c_k e^-2pirm i fracjN omega_kquadrm forquad 0 le j le N-1\n\n\n\n\n\nComputes a 2D nonuniform fast Fourier transform of type I-I:\n\nF_ij = sum_k=0^M-1sum_ell=0^N-1 C_kell e^-2pirm i (fraciM omega_k + fracjN pi_ell)quadrm forquad 0 le i le M-1quad 0 le j le N-1\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"nufft2","category":"page"},{"location":"#FastTransforms.nufft2","page":"Home","title":"FastTransforms.nufft2","text":"Computes a nonuniform fast Fourier transform of type II:\n\nf_j = sum_k=0^N-1 c_k e^-2pirm i x_j kquadrm forquad 0 le j le N-1\n\n\n\n\n\nComputes a 2D nonuniform fast Fourier transform of type II-II:\n\nF_ij = sum_k=0^M-1sum_ell=0^N-1 C_kell e^-2pirm i (x_i k + y_j ell)quadrm forquad 0 le i le M-1quad 0 le j le N-1\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"nufft3","category":"page"},{"location":"#FastTransforms.nufft3","page":"Home","title":"FastTransforms.nufft3","text":"Computes a nonuniform fast Fourier transform of type III:\n\nf_j = sum_k=0^N-1 c_k e^-2pirm i x_j omega_kquadrm forquad 0 le j le N-1\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"inufft1","category":"page"},{"location":"#FastTransforms.inufft1","page":"Home","title":"FastTransforms.inufft1","text":"Computes an inverse nonuniform fast Fourier transform of type I.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"inufft2","category":"page"},{"location":"#FastTransforms.inufft2","page":"Home","title":"FastTransforms.inufft2","text":"Computes an inverse nonuniform fast Fourier transform of type II.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"paduatransform","category":"page"},{"location":"#FastTransforms.paduatransform","page":"Home","title":"FastTransforms.paduatransform","text":"Padua Transform maps from interpolant values at the Padua points to the 2D Chebyshev coefficients.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"ipaduatransform","category":"page"},{"location":"#FastTransforms.ipaduatransform","page":"Home","title":"FastTransforms.ipaduatransform","text":"Inverse Padua Transform maps the 2D Chebyshev coefficients to the values of the interpolation polynomial at the Padua points.\n\n\n\n\n\n","category":"function"},{"location":"#Other-Exported-Methods-1","page":"Home","title":"Other Exported Methods","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"gaunt","category":"page"},{"location":"#FastTransforms.gaunt","page":"Home","title":"FastTransforms.gaunt","text":"Calculates the Gaunt coefficients, defined by:\n\na(mnmunuq) = frac2(n+nu-2q)+12 frac(n+nu-2q-m-mu)(n+nu-2q+m+mu) int_-1^+1 P_n^m(x) P_nu^mu(x) P_n+nu-2q^m+mu(x) rmdx\n\nor defined by:\n\nP_n^m(x) P_nu^mu(x) = sum_q=0^q_rm max a(mnmunuq) P_n+nu-2q^m+mu(x)\n\nThis is a Julia implementation of the stable recurrence described in:\n\nY.-l. Xu, Fast evaluation of Gaunt coefficients: recursive approach, J. Comp. Appl. Math., 85:53–65, 1997.\n\n\n\n\n\nCalculates the Gaunt coefficients in 64-bit floating-point arithmetic.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"paduapoints","category":"page"},{"location":"#FastTransforms.paduapoints","page":"Home","title":"FastTransforms.paduapoints","text":"Returns coordinates of the (n+1)(n+2)2 Padua points.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"sphevaluate","category":"page"},{"location":"#FastTransforms.sphevaluate","page":"Home","title":"FastTransforms.sphevaluate","text":"Pointwise evaluation of real orthonormal spherical harmonic:\n\nY_ell^m(thetavarphi) = (-1)^msqrt(ell+frac12)frac(ell-m)(ell+m) P_ell^m(costheta) sqrtfrac2-delta_m02pi leftbeginarrayccc cos mvarphi  rm for  m ge 0 sin(-mvarphi)  rm for  m  0endarrayright\n\n\n\n\n\n","category":"function"},{"location":"#Internal-Methods-1","page":"Home","title":"Internal Methods","text":"","category":"section"},{"location":"#Miscellaneous-Special-Functions-1","page":"Home","title":"Miscellaneous Special Functions","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.half","category":"page"},{"location":"#FastTransforms.half","page":"Home","title":"FastTransforms.half","text":"Compute a typed 0.5.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.two","category":"page"},{"location":"#FastTransforms.two","page":"Home","title":"FastTransforms.two","text":"Compute a typed 2.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.δ","category":"page"},{"location":"#FastTransforms.δ","page":"Home","title":"FastTransforms.δ","text":"The Kronecker delta function:\n\ndelta_kj = leftbeginarrayccc 1  rm for  k = j 0  rm for  k ne jendarrayright\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.Λ","category":"page"},{"location":"#FastTransforms.Λ","page":"Home","title":"FastTransforms.Λ","text":"The Lambda function Lambda(z) = fracGamma(z+frac12)Gamma(z+1) for the ratio of gamma functions.\n\n\n\n\n\nFor 64-bit floating-point arithmetic, the Lambda function uses the asymptotic series for tau in Appendix B of\n\nI. Bogaert and B. Michiels and J. Fostier, 𝒪(1) computation of Legendre polynomials and Gauss–Legendre nodes and weights for parallel computing, SIAM J. Sci. Comput., 34:C83–C101, 2012.\n\n\n\n\n\nThe Lambda function Lambda(zλ₁λ₂) = fracGamma(z+lambda_1)Γ(z+lambda_2) for the ratio of gamma functions.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.lambertw","category":"page"},{"location":"#FastTransforms.lambertw","page":"Home","title":"FastTransforms.lambertw","text":"The principal branch of the Lambert-W function, defined by x = W_0(x) e^W_0(x), computed using Halley's method for x in -e^-1infty).\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.pochhammer","category":"page"},{"location":"#FastTransforms.pochhammer","page":"Home","title":"FastTransforms.pochhammer","text":"Pochhammer symbol (x)_n = fracGamma(x+n)Gamma(x) for the rising factorial.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.stirlingseries","category":"page"},{"location":"#FastTransforms.stirlingseries","page":"Home","title":"FastTransforms.stirlingseries","text":"Stirling's asymptotic series for Gamma(z).\n\n\n\n\n\n","category":"function"},{"location":"#Modified-Chebyshev-Moment-Based-Quadrature-1","page":"Home","title":"Modified Chebyshev Moment-Based Quadrature","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.clenshawcurtisnodes","category":"page"},{"location":"#FastTransforms.clenshawcurtisnodes","page":"Home","title":"FastTransforms.clenshawcurtisnodes","text":"Compute nodes of the Clenshaw—Curtis quadrature rule.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.clenshawcurtisweights","category":"page"},{"location":"#FastTransforms.clenshawcurtisweights","page":"Home","title":"FastTransforms.clenshawcurtisweights","text":"Compute weights of the Clenshaw—Curtis quadrature rule with modified Chebyshev moments of the first kind mu.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.fejernodes1","category":"page"},{"location":"#FastTransforms.fejernodes1","page":"Home","title":"FastTransforms.fejernodes1","text":"Compute nodes of Fejer's first quadrature rule.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.fejerweights1","category":"page"},{"location":"#FastTransforms.fejerweights1","page":"Home","title":"FastTransforms.fejerweights1","text":"Compute weights of Fejer's first quadrature rule with modified Chebyshev moments of the first kind mu.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.fejernodes2","category":"page"},{"location":"#FastTransforms.fejernodes2","page":"Home","title":"FastTransforms.fejernodes2","text":"Compute nodes of Fejer's second quadrature rule.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.fejerweights2","category":"page"},{"location":"#FastTransforms.fejerweights2","page":"Home","title":"FastTransforms.fejerweights2","text":"Compute weights of Fejer's second quadrature rule with modified Chebyshev moments of the second kind mu.\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevmoments1","category":"page"},{"location":"#FastTransforms.chebyshevmoments1","page":"Home","title":"FastTransforms.chebyshevmoments1","text":"Modified Chebyshev moments of the first kind:\n\n    int_-1^+1 T_n(x) rmdx\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevjacobimoments1","category":"page"},{"location":"#FastTransforms.chebyshevjacobimoments1","page":"Home","title":"FastTransforms.chebyshevjacobimoments1","text":"Modified Chebyshev moments of the first kind with respect to the Jacobi weight:\n\n    int_-1^+1 T_n(x) (1-x)^alpha(1+x)^betarmdx\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevlogmoments1","category":"page"},{"location":"#FastTransforms.chebyshevlogmoments1","page":"Home","title":"FastTransforms.chebyshevlogmoments1","text":"Modified Chebyshev moments of the first kind with respect to the logarithmic weight:\n\n    int_-1^+1 T_n(x) logleft(frac1-x2right)rmdx\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevmoments2","category":"page"},{"location":"#FastTransforms.chebyshevmoments2","page":"Home","title":"FastTransforms.chebyshevmoments2","text":"Modified Chebyshev moments of the second kind:\n\n    int_-1^+1 U_n(x) rmdx\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevjacobimoments2","category":"page"},{"location":"#FastTransforms.chebyshevjacobimoments2","page":"Home","title":"FastTransforms.chebyshevjacobimoments2","text":"Modified Chebyshev moments of the second kind with respect to the Jacobi weight:\n\n    int_-1^+1 U_n(x) (1-x)^alpha(1+x)^betarmdx\n\n\n\n\n\n","category":"function"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.chebyshevlogmoments2","category":"page"},{"location":"#FastTransforms.chebyshevlogmoments2","page":"Home","title":"FastTransforms.chebyshevlogmoments2","text":"Modified Chebyshev moments of the second kind with respect to the logarithmic weight:\n\n    int_-1^+1 U_n(x) logleft(frac1-x2right)rmdx\n\n\n\n\n\n","category":"function"},{"location":"#Elliptic-1","page":"Home","title":"Elliptic","text":"","category":"section"},{"location":"#","page":"Home","title":"Home","text":"FastTransforms.Elliptic","category":"page"},{"location":"#FastTransforms.Elliptic","page":"Home","title":"FastTransforms.Elliptic","text":"FastTransforms submodule for the computation of some elliptic integrals and functions.\n\nComplete elliptic integrals of the first and second kinds:\n\nK(k) = int_0^fracpi2 fracrm dthetasqrt1-k^2sin^2thetaquadrm and\n\nE(k) = int_0^fracpi2 sqrt1-k^2sin^2theta rmdtheta\n\nJacobian elliptic functions:\n\nx = int_0^operatornamesn(xk) fracrm dtsqrt(1-t^2)(1-k^2t^2)\n\nx = int_operatornamecn(xk)^1 fracrm dtsqrt(1-t^2)1-k^2(1-t^2)\n\nx = int_operatornamedn(xk)^1 fracrm dtsqrt(1-t^2)(t^2-1+k^2)\n\nand the remaining nine are defined by:\n\noperatornamepq(xk) = fracoperatornamepr(xk)operatornameqr(xk) = frac1operatornameqp(xk)\n\n\n\n\n\n","category":"module"}]
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