From e3989d8d06a8be20fabcb2ec1b1135c84b917d22 Mon Sep 17 00:00:00 2001
From: "Documenter.jl" <documenter@juliadocs.github.io>
Date: Thu, 16 May 2024 17:37:27 +0000
Subject: [PATCH] build based on c4092a1

---
 stable                                    |    2 +-
 v1                                        |    2 +-
 v1.9                                      |    2 +-
 v1.9.4/.documenter-siteinfo.json          |    1 +
 v1.9.4/assets/documenter.js               | 1050 +++++++++++++++++++++
 v1.9.4/assets/themes/documenter-dark.css  |    7 +
 v1.9.4/assets/themes/documenter-light.css |    9 +
 v1.9.4/assets/themeswap.js                |   84 ++
 v1.9.4/assets/warner.js                   |   52 +
 v1.9.4/index.html                         |    2 +
 v1.9.4/objects.inv                        |  Bin 0 -> 2422 bytes
 v1.9.4/pages/api/index.html               |  219 +++++
 v1.9.4/pages/quickstart/index.html        |   89 ++
 v1.9.4/search_index.js                    |    3 +
 v1.9.4/siteinfo.js                        |    1 +
 versions.js                               |    2 +-
 16 files changed, 1521 insertions(+), 4 deletions(-)
 create mode 100644 v1.9.4/.documenter-siteinfo.json
 create mode 100644 v1.9.4/assets/documenter.js
 create mode 100644 v1.9.4/assets/themes/documenter-dark.css
 create mode 100644 v1.9.4/assets/themes/documenter-light.css
 create mode 100644 v1.9.4/assets/themeswap.js
 create mode 100644 v1.9.4/assets/warner.js
 create mode 100644 v1.9.4/index.html
 create mode 100644 v1.9.4/objects.inv
 create mode 100644 v1.9.4/pages/api/index.html
 create mode 100644 v1.9.4/pages/quickstart/index.html
 create mode 100644 v1.9.4/search_index.js
 create mode 100644 v1.9.4/siteinfo.js

diff --git a/stable b/stable
index 5a910d1d..7651c372 120000
--- a/stable
+++ b/stable
@@ -1 +1 @@
-v1.9.3
\ No newline at end of file
+v1.9.4
\ No newline at end of file
diff --git a/v1 b/v1
index 5a910d1d..7651c372 120000
--- a/v1
+++ b/v1
@@ -1 +1 @@
-v1.9.3
\ No newline at end of file
+v1.9.4
\ No newline at end of file
diff --git a/v1.9 b/v1.9
index 5a910d1d..7651c372 120000
--- a/v1.9
+++ b/v1.9
@@ -1 +1 @@
-v1.9.3
\ No newline at end of file
+v1.9.4
\ No newline at end of file
diff --git a/v1.9.4/.documenter-siteinfo.json b/v1.9.4/.documenter-siteinfo.json
new file mode 100644
index 00000000..650ae7cc
--- /dev/null
+++ b/v1.9.4/.documenter-siteinfo.json
@@ -0,0 +1 @@
+{"documenter":{"julia_version":"1.6.7","generation_timestamp":"2024-05-16T17:37:22","documenter_version":"1.4.1"}}
\ No newline at end of file
diff --git a/v1.9.4/assets/documenter.js b/v1.9.4/assets/documenter.js
new file mode 100644
index 00000000..c6562b55
--- /dev/null
+++ b/v1.9.4/assets/documenter.js
@@ -0,0 +1,1050 @@
+// Generated by Documenter.jl
+requirejs.config({
+  paths: {
+    'highlight-julia': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/julia.min',
+    'headroom': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/headroom.min',
+    'jqueryui': 'https://cdnjs.cloudflare.com/ajax/libs/jqueryui/1.13.2/jquery-ui.min',
+    'katex-auto-render': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/contrib/auto-render.min',
+    'jquery': 'https://cdnjs.cloudflare.com/ajax/libs/jquery/3.7.0/jquery.min',
+    'headroom-jquery': 'https://cdnjs.cloudflare.com/ajax/libs/headroom/0.12.0/jQuery.headroom.min',
+    'katex': 'https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/katex.min',
+    'highlight': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min',
+    'highlight-julia-repl': 'https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/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($) {
+$(document).ready(function() {
+    hljs.highlightAll();
+})
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+let timer = 0;
+var isExpanded = true;
+
+$(document).on("click", ".docstring header", function () {
+  let articleToggleTitle = "Expand docstring";
+
+  debounce(() => {
+    if ($(this).siblings("section").is(":visible")) {
+      $(this)
+        .find(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-down")
+        .addClass("fa-chevron-right");
+    } else {
+      $(this)
+        .find(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-right")
+        .addClass("fa-chevron-down");
+
+      articleToggleTitle = "Collapse docstring";
+    }
+
+    $(this)
+      .find(".docstring-article-toggle-button")
+      .prop("title", articleToggleTitle);
+    $(this).siblings("section").slideToggle();
+  });
+});
+
+$(document).on("click", ".docs-article-toggle-button", function (event) {
+  let articleToggleTitle = "Expand docstring";
+  let navArticleToggleTitle = "Expand all docstrings";
+  let animationSpeed = event.noToggleAnimation ? 0 : 400;
+
+  debounce(() => {
+    if (isExpanded) {
+      $(this).removeClass("fa-chevron-up").addClass("fa-chevron-down");
+      $(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-down")
+        .addClass("fa-chevron-right");
+
+      isExpanded = false;
+
+      $(".docstring section").slideUp(animationSpeed);
+    } else {
+      $(this).removeClass("fa-chevron-down").addClass("fa-chevron-up");
+      $(".docstring-article-toggle-button")
+        .removeClass("fa-chevron-right")
+        .addClass("fa-chevron-down");
+
+      isExpanded = true;
+      articleToggleTitle = "Collapse docstring";
+      navArticleToggleTitle = "Collapse all docstrings";
+
+      $(".docstring section").slideDown(animationSpeed);
+    }
+
+    $(this).prop("title", navArticleToggleTitle);
+    $(".docstring-article-toggle-button").prop("title", articleToggleTitle);
+  });
+});
+
+function debounce(callback, timeout = 300) {
+  if (Date.now() - timer > timeout) {
+    callback();
+  }
+
+  clearTimeout(timer);
+
+  timer = Date.now();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require([], function() {
+function addCopyButtonCallbacks() {
+  for (const el of document.getElementsByTagName("pre")) {
+    const button = document.createElement("button");
+    button.classList.add("copy-button", "fa-solid", "fa-copy");
+    button.setAttribute("aria-label", "Copy this code block");
+    button.setAttribute("title", "Copy");
+
+    el.appendChild(button);
+
+    const success = function () {
+      button.classList.add("success", "fa-check");
+      button.classList.remove("fa-copy");
+    };
+
+    const failure = function () {
+      button.classList.add("error", "fa-xmark");
+      button.classList.remove("fa-copy");
+    };
+
+    button.addEventListener("click", function () {
+      copyToClipboard(el.innerText).then(success, failure);
+
+      setTimeout(function () {
+        button.classList.add("fa-copy");
+        button.classList.remove("success", "fa-check", "fa-xmark");
+      }, 5000);
+    });
+  }
+}
+
+function copyToClipboard(text) {
+  // clipboard API is only available in secure contexts
+  if (window.navigator && window.navigator.clipboard) {
+    return window.navigator.clipboard.writeText(text);
+  } else {
+    return new Promise(function (resolve, reject) {
+      try {
+        const el = document.createElement("textarea");
+        el.textContent = text;
+        el.style.position = "fixed";
+        el.style.opacity = 0;
+        document.body.appendChild(el);
+        el.select();
+        document.execCommand("copy");
+
+        resolve();
+      } catch (err) {
+        reject(err);
+      } finally {
+        document.body.removeChild(el);
+      }
+    });
+  }
+}
+
+if (document.readyState === "loading") {
+  document.addEventListener("DOMContentLoaded", addCopyButtonCallbacks);
+} else {
+  addCopyButtonCallbacks();
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+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 () {
+  $("#documenter .docs-navbar").headroom({
+    tolerance: { up: 10, down: 10 },
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+  let meta = $("div[data-docstringscollapsed]").data();
+
+  if (meta?.docstringscollapsed) {
+    $("#documenter-article-toggle-button").trigger({
+      type: "click",
+      noToggleAnimation: true,
+    });
+  }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+/*
+To get an in-depth about the thought process you can refer: https://hetarth02.hashnode.dev/series/gsoc
+
+PSEUDOCODE:
+
+Searching happens automatically as the user types or adjusts the selected filters.
+To preserve responsiveness, as much as possible of the slow parts of the search are done
+in a web worker. Searching and result generation are done in the worker, and filtering and
+DOM updates are done in the main thread. The filters are in the main thread as they should
+be very quick to apply. This lets filters be changed without re-searching with minisearch
+(which is possible even if filtering is on the worker thread) and also lets filters be
+changed _while_ the worker is searching and without message passing (neither of which are
+possible if filtering is on the worker thread)
+
+SEARCH WORKER:
+
+Import minisearch
+
+Build index
+
+On message from main thread
+  run search
+  find the first 200 unique results from each category, and compute their divs for display
+    note that this is necessary and sufficient information for the main thread to find the
+    first 200 unique results from any given filter set
+  post results to main thread
+
+MAIN:
+
+Launch worker
+
+Declare nonconstant globals (worker_is_running,  last_search_text, unfiltered_results)
+
+On text update
+  if worker is not running, launch_search()
+
+launch_search
+  set worker_is_running to true, set last_search_text to the search text
+  post the search query to worker
+
+on message from worker
+  if last_search_text is not the same as the text in the search field,
+    the latest search result is not reflective of the latest search query, so update again
+    launch_search()
+  otherwise
+    set worker_is_running to false
+
+  regardless, display the new search results to the user
+  save the unfiltered_results as a global
+  update_search()
+
+on filter click
+  adjust the filter selection
+  update_search()
+
+update_search
+  apply search filters by looping through the unfiltered_results and finding the first 200
+    unique results that match the filters
+
+  Update the DOM
+*/
+
+/////// SEARCH WORKER ///////
+
+function worker_function(documenterSearchIndex, documenterBaseURL, filters) {
+  importScripts(
+    "https://cdn.jsdelivr.net/npm/minisearch@6.1.0/dist/umd/index.min.js"
+  );
+
+  let data = documenterSearchIndex.map((x, key) => {
+    x["id"] = key; // minisearch requires a unique for each object
+    return x;
+  });
+
+  // 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
+  const stopWords = new Set([
+    "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",
+  ]);
+
+  let index = new MiniSearch({
+    fields: ["title", "text"], // fields to index for full-text search
+    storeFields: ["location", "title", "text", "category", "page"], // fields to return with results
+    processTerm: (term) => {
+      let word = stopWords.has(term) ? null : term;
+      if (word) {
+        // custom trimmer that doesn't strip @ and !, which are used in julia macro and function names
+        word = word
+          .replace(/^[^a-zA-Z0-9@!]+/, "")
+          .replace(/[^a-zA-Z0-9@!]+$/, "");
+
+        word = word.toLowerCase();
+      }
+
+      return word ?? null;
+    },
+    // add . as a separator, because otherwise "title": "Documenter.Anchors.add!", would not
+    // find anything if searching for "add!", only for the entire qualification
+    tokenize: (string) => string.split(/[\s\-\.]+/),
+    // options which will be applied during the search
+    searchOptions: {
+      prefix: true,
+      boost: { title: 100 },
+      fuzzy: 2,
+    },
+  });
+
+  index.addAll(data);
+
+  /**
+   *  Used to map characters to HTML entities.
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  const htmlEscapes = {
+    "&": "&amp;",
+    "<": "&lt;",
+    ">": "&gt;",
+    '"': "&quot;",
+    "'": "&#39;",
+  };
+
+  /**
+   * Used to match HTML entities and HTML characters.
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  const reUnescapedHtml = /[&<>"']/g;
+  const reHasUnescapedHtml = RegExp(reUnescapedHtml.source);
+
+  /**
+   * Escape function from lodash
+   * Refer: https://github.com/lodash/lodash/blob/main/src/escape.ts
+   */
+  function escape(string) {
+    return string && reHasUnescapedHtml.test(string)
+      ? string.replace(reUnescapedHtml, (chr) => htmlEscapes[chr])
+      : string || "";
+  }
+
+  /**
+   * Make the result component given a minisearch result data object and the value
+   * of the search input as queryString. To view the result object structure, refer:
+   * https://lucaong.github.io/minisearch/modules/_minisearch_.html#searchresult
+   *
+   * @param {object} result
+   * @param {string} querystring
+   * @returns string
+   */
+  function make_search_result(result, querystring) {
+    let search_divider = `<div class="search-divider w-100"></div>`;
+    let display_link =
+      result.location.slice(Math.max(0), Math.min(50, result.location.length)) +
+      (result.location.length > 30 ? "..." : ""); // To cut-off the link because it messes with the overflow of the whole div
+
+    if (result.page !== "") {
+      display_link += ` (${result.page})`;
+    }
+
+    let textindex = new RegExp(`${querystring}`, "i").exec(result.text);
+    let text =
+      textindex !== null
+        ? result.text.slice(
+            Math.max(textindex.index - 100, 0),
+            Math.min(
+              textindex.index + querystring.length + 100,
+              result.text.length
+            )
+          )
+        : ""; // cut-off text before and after from the match
+
+    text = text.length ? escape(text) : "";
+
+    let display_result = text.length
+      ? "..." +
+        text.replace(
+          new RegExp(`${escape(querystring)}`, "i"), // For first occurrence
+          '<span class="search-result-highlight py-1">$&</span>'
+        ) +
+        "..."
+      : ""; // highlights the match
+
+    let in_code = false;
+    if (!["page", "section"].includes(result.category.toLowerCase())) {
+      in_code = true;
+    }
+
+    // We encode the full url to escape some special characters which can lead to broken links
+    let result_div = `
+        <a href="${encodeURI(
+          documenterBaseURL + "/" + result.location
+        )}" class="search-result-link w-100 is-flex is-flex-direction-column gap-2 px-4 py-2">
+          <div class="w-100 is-flex is-flex-wrap-wrap is-justify-content-space-between is-align-items-flex-start">
+            <div class="search-result-title has-text-weight-bold ${
+              in_code ? "search-result-code-title" : ""
+            }">${escape(result.title)}</div>
+            <div class="property-search-result-badge">${result.category}</div>
+          </div>
+          <p>
+            ${display_result}
+          </p>
+          <div
+            class="has-text-left"
+            style="font-size: smaller;"
+            title="${result.location}"
+          >
+            <i class="fas fa-link"></i> ${display_link}
+          </div>
+        </a>
+        ${search_divider}
+      `;
+
+    return result_div;
+  }
+
+  self.onmessage = function (e) {
+    let query = e.data;
+    let results = index.search(query, {
+      filter: (result) => {
+        // Only return relevant results
+        return result.score >= 1;
+      },
+    });
+
+    // Pre-filter to deduplicate and limit to 200 per category to the extent
+    // possible without knowing what the filters are.
+    let filtered_results = [];
+    let counts = {};
+    for (let filter of filters) {
+      counts[filter] = 0;
+    }
+    let present = {};
+
+    for (let result of results) {
+      cat = result.category;
+      cnt = counts[cat];
+      if (cnt < 200) {
+        id = cat + "---" + result.location;
+        if (present[id]) {
+          continue;
+        }
+        present[id] = true;
+        filtered_results.push({
+          location: result.location,
+          category: cat,
+          div: make_search_result(result, query),
+        });
+      }
+    }
+
+    postMessage(filtered_results);
+  };
+}
+
+// `worker = Threads.@spawn worker_function(documenterSearchIndex)`, but in JavaScript!
+const filters = [
+  ...new Set(documenterSearchIndex["docs"].map((x) => x.category)),
+];
+const worker_str =
+  "(" +
+  worker_function.toString() +
+  ")(" +
+  JSON.stringify(documenterSearchIndex["docs"]) +
+  "," +
+  JSON.stringify(documenterBaseURL) +
+  "," +
+  JSON.stringify(filters) +
+  ")";
+const worker_blob = new Blob([worker_str], { type: "text/javascript" });
+const worker = new Worker(URL.createObjectURL(worker_blob));
+
+/////// SEARCH MAIN ///////
+
+// Whether the worker is currently handling a search. This is a boolean
+// as the worker only ever handles 1 or 0 searches at a time.
+var worker_is_running = false;
+
+// The last search text that was sent to the worker. This is used to determine
+// if the worker should be launched again when it reports back results.
+var last_search_text = "";
+
+// The results of the last search. This, in combination with the state of the filters
+// in the DOM, is used compute the results to display on calls to update_search.
+var unfiltered_results = [];
+
+// Which filter is currently selected
+var selected_filter = "";
+
+$(document).on("input", ".documenter-search-input", function (event) {
+  if (!worker_is_running) {
+    launch_search();
+  }
+});
+
+function launch_search() {
+  worker_is_running = true;
+  last_search_text = $(".documenter-search-input").val();
+  worker.postMessage(last_search_text);
+}
+
+worker.onmessage = function (e) {
+  if (last_search_text !== $(".documenter-search-input").val()) {
+    launch_search();
+  } else {
+    worker_is_running = false;
+  }
+
+  unfiltered_results = e.data;
+  update_search();
+};
+
+$(document).on("click", ".search-filter", function () {
+  if ($(this).hasClass("search-filter-selected")) {
+    selected_filter = "";
+  } else {
+    selected_filter = $(this).text().toLowerCase();
+  }
+
+  // This updates search results and toggles classes for UI:
+  update_search();
+});
+
+/**
+ * Make/Update the search component
+ */
+function update_search() {
+  let querystring = $(".documenter-search-input").val();
+
+  if (querystring.trim()) {
+    if (selected_filter == "") {
+      results = unfiltered_results;
+    } else {
+      results = unfiltered_results.filter((result) => {
+        return selected_filter == result.category.toLowerCase();
+      });
+    }
+
+    let search_result_container = ``;
+    let modal_filters = make_modal_body_filters();
+    let search_divider = `<div class="search-divider w-100"></div>`;
+
+    if (results.length) {
+      let links = [];
+      let count = 0;
+      let search_results = "";
+
+      for (var i = 0, n = results.length; i < n && count < 200; ++i) {
+        let result = results[i];
+        if (result.location && !links.includes(result.location)) {
+          search_results += result.div;
+          count++;
+          links.push(result.location);
+        }
+      }
+
+      if (count == 1) {
+        count_str = "1 result";
+      } else if (count == 200) {
+        count_str = "200+ results";
+      } else {
+        count_str = count + " results";
+      }
+      let result_count = `<div class="is-size-6">${count_str}</div>`;
+
+      search_result_container = `
+            <div class="is-flex is-flex-direction-column gap-2 is-align-items-flex-start">
+                ${modal_filters}
+                ${search_divider}
+                ${result_count}
+                <div class="is-clipped w-100 is-flex is-flex-direction-column gap-2 is-align-items-flex-start has-text-justified mt-1">
+                  ${search_results}
+                </div>
+            </div>
+        `;
+    } else {
+      search_result_container = `
+           <div class="is-flex is-flex-direction-column gap-2 is-align-items-flex-start">
+               ${modal_filters}
+               ${search_divider}
+               <div class="is-size-6">0 result(s)</div>
+            </div>
+            <div class="has-text-centered my-5 py-5">No result found!</div>
+       `;
+    }
+
+    if ($(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").removeClass("is-justify-content-center");
+    }
+
+    $(".search-modal-card-body").html(search_result_container);
+  } else {
+    if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").addClass("is-justify-content-center");
+    }
+
+    $(".search-modal-card-body").html(`
+      <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+    `);
+  }
+}
+
+/**
+ * Make the modal filter html
+ *
+ * @returns string
+ */
+function make_modal_body_filters() {
+  let str = filters
+    .map((val) => {
+      if (selected_filter == val.toLowerCase()) {
+        return `<a href="javascript:;" class="search-filter search-filter-selected"><span>${val}</span></a>`;
+      } else {
+        return `<a href="javascript:;" class="search-filter"><span>${val}</span></a>`;
+      }
+    })
+    .join("");
+
+  return `
+        <div class="is-flex gap-2 is-flex-wrap-wrap is-justify-content-flex-start is-align-items-center search-filters">
+            <span class="is-size-6">Filters:</span>
+            ${str}
+        </div>`;
+}
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// 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
+  $(document).keyup(function (e) {
+    if (e.keyCode == 27) settings.removeClass("is-active");
+  });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+$(document).ready(function () {
+  let search_modal_header = `
+    <header class="modal-card-head gap-2 is-align-items-center is-justify-content-space-between w-100 px-3">
+      <div class="field mb-0 w-100">
+        <p class="control has-icons-right">
+          <input class="input documenter-search-input" type="text" placeholder="Search" />
+          <span class="icon is-small is-right has-text-primary-dark">
+            <i class="fas fa-magnifying-glass"></i>
+          </span>
+        </p>
+      </div>
+      <div class="icon is-size-4 is-clickable close-search-modal">
+        <i class="fas fa-times"></i>
+      </div>
+    </header>
+  `;
+
+  let initial_search_body = `
+    <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+  `;
+
+  let search_modal_footer = `
+    <footer class="modal-card-foot">
+      <span>
+        <kbd class="search-modal-key-hints">Ctrl</kbd> +
+        <kbd class="search-modal-key-hints">/</kbd> to search
+      </span>
+      <span class="ml-3"> <kbd class="search-modal-key-hints">esc</kbd> to close </span>
+    </footer>
+  `;
+
+  $(document.body).append(
+    `
+      <div class="modal" id="search-modal">
+        <div class="modal-background"></div>
+        <div class="modal-card search-min-width-50 search-min-height-100 is-justify-content-center">
+          ${search_modal_header}
+          <section class="modal-card-body is-flex is-flex-direction-column is-justify-content-center gap-4 search-modal-card-body">
+            ${initial_search_body}
+          </section>
+          ${search_modal_footer}
+        </div>
+      </div>
+    `
+  );
+
+  document.querySelector(".docs-search-query").addEventListener("click", () => {
+    openModal();
+  });
+
+  document
+    .querySelector(".close-search-modal")
+    .addEventListener("click", () => {
+      closeModal();
+    });
+
+  $(document).on("click", ".search-result-link", function () {
+    closeModal();
+  });
+
+  document.addEventListener("keydown", (event) => {
+    if ((event.ctrlKey || event.metaKey) && event.key === "/") {
+      openModal();
+    } else if (event.key === "Escape") {
+      closeModal();
+    }
+
+    return false;
+  });
+
+  // Functions to open and close a modal
+  function openModal() {
+    let searchModal = document.querySelector("#search-modal");
+
+    searchModal.classList.add("is-active");
+    document.querySelector(".documenter-search-input").focus();
+  }
+
+  function closeModal() {
+    let searchModal = document.querySelector("#search-modal");
+    let initial_search_body = `
+      <div class="has-text-centered my-5 py-5">Type something to get started!</div>
+    `;
+
+    searchModal.classList.remove("is-active");
+    document.querySelector(".documenter-search-input").blur();
+
+    if (!$(".search-modal-card-body").hasClass("is-justify-content-center")) {
+      $(".search-modal-card-body").addClass("is-justify-content-center");
+    }
+
+    $(".documenter-search-input").val("");
+    $(".search-modal-card-body").html(initial_search_body);
+  }
+
+  document
+    .querySelector("#search-modal .modal-background")
+    .addEventListener("click", () => {
+      closeModal();
+    });
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// 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 = $("#documenter .docs-menu .is-active").get(0);
+  if (typeof active !== "undefined") {
+    sidebar.scrollTop = active.offsetTop - sidebar.offsetTop - 15;
+  }
+});
+
+})
+////////////////////////////////////////////////////////////////////////////////
+require(['jquery'], function($) {
+
+// Theme picker setup
+$(document).ready(function () {
+  // onchange callback
+  $("#documenter-themepicker").change(function themepick_callback(ev) {
+    var themename = $("#documenter-themepicker option:selected").attr("value");
+    if (themename === "auto") {
+      // set_theme(window.matchMedia('(prefers-color-scheme: dark)').matches ? 'dark' : 'light');
+      window.localStorage.removeItem("documenter-theme");
+    } else {
+      // set_theme(themename);
+      window.localStorage.setItem("documenter-theme", themename);
+    }
+    // We re-use the global function from themeswap.js to actually do the swapping.
+    set_theme_from_local_storage();
+  });
+
+  // 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 () {
+  // If the version selector is disabled with DOCUMENTER_VERSION_SELECTOR_DISABLED in the
+  // siteinfo.js file, we just return immediately and not display the version selector.
+  if (
+    typeof DOCUMENTER_VERSION_SELECTOR_DISABLED === "boolean" &&
+    DOCUMENTER_VERSION_SELECTOR_DISABLED
+  ) {
+    return;
+  }
+
+  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/v1.9.4/assets/themes/documenter-dark.css b/v1.9.4/assets/themes/documenter-dark.css
new file mode 100644
index 00000000..1d717015
--- /dev/null
+++ b/v1.9.4/assets/themes/documenter-dark.css
@@ -0,0 +1,7 @@
+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 .file-cta,html.theme--documenter-dark .file-name,html.theme--documenter-dark .select select,html.theme--documenter-dark .textarea,html.theme--documenter-dark .input,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark .button{-moz-appearance:none;-webkit-appearance:none;align-items:center;border:1px solid transparent;border-radius:.4em;box-shadow:none;display:inline-flex;font-size:1rem;height:2.5em;justify-content:flex-start;line-height:1.5;padding-bottom:calc(0.5em - 1px);padding-left:calc(0.75em - 1px);padding-right:calc(0.75em - 1px);padding-top:calc(0.5em - 1px);position:relative;vertical-align:top}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 .file-cta:focus,html.theme--documenter-dark .file-name:focus,html.theme--documenter-dark .select select:focus,html.theme--documenter-dark .textarea:focus,html.theme--documenter-dark .input:focus,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:focus,html.theme--documenter-dark .button:focus,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 .is-focused.file-cta,html.theme--documenter-dark .is-focused.file-name,html.theme--documenter-dark .select select.is-focused,html.theme--documenter-dark .is-focused.textarea,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.button,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 .file-cta:active,html.theme--documenter-dark .file-name:active,html.theme--documenter-dark .select select:active,html.theme--documenter-dark .textarea:active,html.theme--documenter-dark .input:active,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input:active,html.theme--documenter-dark .button:active,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,html.theme--documenter-dark .is-active.file-cta,html.theme--documenter-dark .is-active.file-name,html.theme--documenter-dark .select select.is-active,html.theme--documenter-dark .is-active.textarea,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.button{outline:none}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],html.theme--documenter-dark .file-cta[disabled],html.theme--documenter-dark .file-name[disabled],html.theme--documenter-dark .select select[disabled],html.theme--documenter-dark .textarea[disabled],html.theme--documenter-dark .input[disabled],html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input[disabled],html.theme--documenter-dark .button[disabled],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,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 .select select,fieldset[disabled] html.theme--documenter-dark .textarea,fieldset[disabled] html.theme--documenter-dark .input,fieldset[disabled] html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input,html.theme--documenter-dark fieldset[disabled] .select select,html.theme--documenter-dark .select fieldset[disabled] select,html.theme--documenter-dark fieldset[disabled] .textarea,html.theme--documenter-dark fieldset[disabled] .input,html.theme--documenter-dark fieldset[disabled] #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 .button,html.theme--documenter-dark fieldset[disabled] .button{cursor:not-allowed}html.theme--documenter-dark .tabs,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 .breadcrumb,html.theme--documenter-dark .file,html.theme--documenter-dark .button,.is-unselectable{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none}html.theme--documenter-dark .navbar-link:not(.is-arrowless)::after,html.theme--documenter-dark .select:not(.is-multiple):not(.is-loading)::after{border:3px solid rgba(0,0,0,0);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 .admonition:not(:last-child),html.theme--documenter-dark .tabs:not(:last-child),html.theme--documenter-dark .pagination:not(:last-child),html.theme--documenter-dark .message:not(:last-child),html.theme--documenter-dark .level:not(:last-child),html.theme--documenter-dark .breadcrumb:not(:last-child),html.theme--documenter-dark .block:not(:last-child),html.theme--documenter-dark .title:not(:last-child),html.theme--documenter-dark .subtitle:not(:last-child),html.theme--documenter-dark .table-container:not(:last-child),html.theme--documenter-dark .table:not(:last-child),html.theme--documenter-dark .progress:not(:last-child),html.theme--documenter-dark .notification:not(:last-child),html.theme--documenter-dark .content:not(:last-child),html.theme--documenter-dark .box:not(:last-child){margin-bottom:1.5rem}html.theme--documenter-dark .modal-close,html.theme--documenter-dark .delete{-webkit-touch-callout:none;-webkit-user-select:none;-moz-user-select:none;-ms-user-select:none;user-select:none;-moz-appearance:none;-webkit-appearance:none;background-color:rgba(10,10,10,0.2);border:none;border-radius:9999px;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 .modal-close::before,html.theme--documenter-dark .delete::before,html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{background-color:#fff;content:"";display:block;left:50%;position:absolute;top:50%;transform:translateX(-50%) translateY(-50%) rotate(45deg);transform-origin:center center}html.theme--documenter-dark .modal-close::before,html.theme--documenter-dark .delete::before{height:2px;width:50%}html.theme--documenter-dark .modal-close::after,html.theme--documenter-dark .delete::after{height:50%;width:2px}html.theme--documenter-dark .modal-close:hover,html.theme--documenter-dark .delete:hover,html.theme--documenter-dark .modal-close:focus,html.theme--documenter-dark .delete:focus{background-color:rgba(10,10,10,0.3)}html.theme--documenter-dark .modal-close:active,html.theme--documenter-dark .delete:active{background-color:rgba(10,10,10,0.4)}html.theme--documenter-dark .is-small.modal-close,html.theme--documenter-dark #documenter .docs-sidebar 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+  Maintainer: @ericwbailey
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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 #fff #fff !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 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.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-danger.is-light{background-color:#fdeeec;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:hover,html.theme--documenter-dark .button.is-danger.is-light.is-hovered{background-color:#fce3e0;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-danger.is-light:active,html.theme--documenter-dark .button.is-danger.is-light.is-active{background-color:#fcd8d5;border-color:transparent;color:#ec311d}html.theme--documenter-dark .button.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button{font-size:.75rem}html.theme--documenter-dark .button.is-small:not(.is-rounded),html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.button:not(.is-rounded){border-radius:3px}html.theme--documenter-dark .button.is-normal{font-size:1rem}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:#5e6d6f;box-shadow:none;opacity:.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 * 0.5));top:calc(50% - (1em * 0.5));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:9999px;padding-left:calc(1em + 0.25em);padding-right:calc(1em + 0.25em)}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:.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){font-size:.75rem}html.theme--documenter-dark .buttons.are-small .button:not(.is-normal):not(.is-medium):not(.is-large):not(.is-rounded){border-radius:3px}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}@media screen and (max-width: 768px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.5625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1rem}}@media screen and (min-width: 769px) and (max-width: 1055px){html.theme--documenter-dark .button.is-responsive.is-small,html.theme--documenter-dark #documenter .docs-sidebar form.docs-search>input.is-responsive{font-size:.65625rem}html.theme--documenter-dark .button.is-responsive,html.theme--documenter-dark .button.is-responsive.is-normal{font-size:.75rem}html.theme--documenter-dark .button.is-responsive.is-medium{font-size:1rem}html.theme--documenter-dark .button.is-responsive.is-large{font-size:1.25rem}}html.theme--documenter-dark .container{flex-grow:1;margin:0 auto;position:relative;width:auto}html.theme--documenter-dark .container.is-fluid{max-width:none !important;padding-left:32px;padding-right:32px;width:100%}@media screen and (min-width: 1056px){html.theme--documenter-dark .container{max-width:992px}}@media screen and (max-width: 1215px){html.theme--documenter-dark .container.is-widescreen:not(.is-max-desktop){max-width:1152px}}@media screen and (max-width: 1407px){html.theme--documenter-dark .container.is-fullhd:not(.is-max-desktop):not(.is-max-widescreen){max-width:1344px}}@media screen and (min-width: 1216px){html.theme--documenter-dark .container:not(.is-max-desktop){max-width:1152px}}@media screen and (min-width: 1408px){html.theme--documenter-dark .container:not(.is-max-desktop):not(.is-max-widescreen){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.is-lower-alpha:not([type]){list-style-type:lower-alpha}html.theme--documenter-dark .content ol.is-lower-roman:not([type]){list-style-type:lower-roman}html.theme--documenter-dark .content ol.is-upper-alpha:not([type]){list-style-type:upper-alpha}html.theme--documenter-dark .content ol.is-upper-roman:not([type]){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;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:inherit}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:.75rem}html.theme--documenter-dark .content.is-normal{font-size:1rem}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 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#documenter .docs-sidebar .docs-logo>img img.is-rounded{border-radius:9999px}html.theme--documenter-dark .image.is-fullwidth,html.theme--documenter-dark #documenter .docs-sidebar .docs-logo>img.is-fullwidth{width:100%}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 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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 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diff --git a/v1.9.4/assets/themes/documenter-light.css b/v1.9.4/assets/themes/documenter-light.css
new file mode 100644
index 00000000..07f9d088
--- /dev/null
+++ b/v1.9.4/assets/themes/documenter-light.css
@@ -0,0 +1,9 @@
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.katex-mathml{top:0;right:0}.katex-display,mjx-container,.MathJax_Display{margin:0.5em 0 !important}html{-moz-osx-font-smoothing:auto;-webkit-font-smoothing:auto}li.no-marker{list-style:none}#documenter .docs-main>article{overflow-wrap:break-word}#documenter .docs-main>article .math-container{overflow-x:auto;overflow-y:hidden}@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}#documenter .docs-main>header,#documenter .docs-main>nav{max-width:100%;width:100%;margin:0}}#documenter .docs-main header.docs-navbar{background-color:#fff;border-bottom:1px solid #dbdbdb;z-index:2;min-height:4rem;margin-bottom:1rem;display:flex}#documenter .docs-main header.docs-navbar .breadcrumb{flex-grow:1;overflow-x:hidden}#documenter .docs-main 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.docs-footer .docs-footer-nextpage,#documenter .docs-main .docs-footer .docs-footer-prevpage{flex-grow:1}#documenter .docs-main .docs-footer .docs-footer-nextpage{text-align:right}#documenter .docs-main .docs-footer .flexbox-break{flex-basis:100%;height:0}#documenter .docs-main .docs-footer .footer-message{font-size:0.8em;margin:0.5em auto 0 auto;text-align:center}#documenter .docs-sidebar{display:flex;flex-direction:column;color:#0a0a0a;background-color:#f5f5f5;border-right:1px solid #dbdbdb;padding:0;flex:0 0 18rem;z-index:5;font-size:1rem;position:fixed;left:-18rem;width:18rem;height:100%;transition:left 0.3s}#documenter .docs-sidebar.visible{left:0;box-shadow:.4rem 0rem .8rem #bbb}@media screen and (min-width: 1056px){#documenter .docs-sidebar.visible{box-shadow:none}}@media screen and (min-width: 1056px){#documenter .docs-sidebar{left:0;top:0}}#documenter .docs-sidebar .docs-logo{margin-top:1rem;padding:0 1rem}#documenter .docs-sidebar 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.tocitem::before{content:"⚬";margin-right:0.4em}#documenter .docs-sidebar form.docs-search{margin:auto;margin-top:0.5rem;margin-bottom:0.5rem}#documenter .docs-sidebar form.docs-search>input{width:14.4rem}#documenter .docs-sidebar #documenter-search-query{color:#707070;width:14.4rem;box-shadow:inset 0 1px 2px rgba(10,10,10,0.1)}@media screen and (min-width: 1056px){#documenter .docs-sidebar ul.docs-menu{overflow-y:auto;-webkit-overflow-scroll:touch}#documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar{width:.3rem;background:none}#documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb{border-radius:5px 0px 0px 5px;background:#e0e0e0}#documenter .docs-sidebar ul.docs-menu::-webkit-scrollbar-thumb:hover{background:#ccc}}@media screen and (max-width: 1055px){#documenter .docs-sidebar{overflow-y:auto;-webkit-overflow-scroll:touch}#documenter .docs-sidebar::-webkit-scrollbar{width:.3rem;background:none}#documenter .docs-sidebar::-webkit-scrollbar-thumb{border-radius:5px 0px 0px 5px;background:#e0e0e0}#documenter .docs-sidebar::-webkit-scrollbar-thumb:hover{background:#ccc}}kbd.search-modal-key-hints{border-radius:0.25rem;border:1px solid rgba(0,0,0,0.6);box-shadow:0 2px 0 1px rgba(0,0,0,0.6);cursor:default;font-size:0.9rem;line-height:1.5;min-width:0.75rem;text-align:center;padding:0.1rem 0.3rem;position:relative;top:-1px}.search-min-width-50{min-width:50%}.search-min-height-100{min-height:100%}.search-modal-card-body{max-height:calc(100vh - 15rem)}.search-result-link{border-radius:0.7em;transition:all 300ms}.search-result-link:hover,.search-result-link:focus{background-color:rgba(0,128,128,0.1)}.search-result-link .property-search-result-badge,.search-result-link .search-filter{transition:all 300ms}.property-search-result-badge,.search-filter{padding:0.15em 0.5em;font-size:0.8em;font-style:italic;text-transform:none !important;line-height:1.5;color:#f5f5f5;background-color:rgba(51,65,85,0.501961);border-radius:0.6rem}.search-result-link:hover .property-search-result-badge,.search-result-link:hover .search-filter,.search-result-link:focus .property-search-result-badge,.search-result-link:focus .search-filter{color:#f1f5f9;background-color:#333}.search-filter{color:#333;background-color:#f5f5f5;transition:all 300ms}.search-filter:hover,.search-filter:focus{color:#333}.search-filter-selected{color:#f5f5f5;background-color:rgba(139,0,139,0.5)}.search-filter-selected:hover,.search-filter-selected:focus{color:#f5f5f5}.search-result-highlight{background-color:#ffdd57;color:black}.search-divider{border-bottom:1px solid #dbdbdb}.search-result-title{width:85%;color:#333}.search-result-code-title{font-size:0.875rem;font-family:"JuliaMono","SFMono-Regular","Menlo","Consolas","Liberation Mono","DejaVu Sans Mono",monospace}#search-modal .modal-card-body::-webkit-scrollbar,#search-modal .filter-tabs::-webkit-scrollbar{height:10px;width:10px;background-color:transparent}#search-modal .modal-card-body::-webkit-scrollbar-thumb,#search-modal .filter-tabs::-webkit-scrollbar-thumb{background-color:gray;border-radius:1rem}#search-modal .modal-card-body::-webkit-scrollbar-track,#search-modal .filter-tabs::-webkit-scrollbar-track{-webkit-box-shadow:inset 0 0 6px rgba(0,0,0,0.6);background-color:transparent}.w-100{width:100%}.gap-2{gap:0.5rem}.gap-4{gap:1rem}.gap-8{gap:2rem}.ansi span.sgr1{font-weight:bolder}.ansi span.sgr2{font-weight:lighter}.ansi span.sgr3{font-style:italic}.ansi span.sgr4{text-decoration:underline}.ansi span.sgr7{color:#fff;background-color:#222}.ansi span.sgr8{color:transparent}.ansi span.sgr8 span{color:transparent}.ansi span.sgr9{text-decoration:line-through}.ansi span.sgr30{color:#242424}.ansi span.sgr31{color:#a7201f}.ansi span.sgr32{color:#066f00}.ansi span.sgr33{color:#856b00}.ansi span.sgr34{color:#2149b0}.ansi span.sgr35{color:#7d4498}.ansi span.sgr36{color:#007989}.ansi span.sgr37{color:gray}.ansi span.sgr40{background-color:#242424}.ansi span.sgr41{background-color:#a7201f}.ansi span.sgr42{background-color:#066f00}.ansi span.sgr43{background-color:#856b00}.ansi span.sgr44{background-color:#2149b0}.ansi span.sgr45{background-color:#7d4498}.ansi span.sgr46{background-color:#007989}.ansi span.sgr47{background-color:gray}.ansi span.sgr90{color:#616161}.ansi span.sgr91{color:#cb3c33}.ansi span.sgr92{color:#0e8300}.ansi span.sgr93{color:#a98800}.ansi span.sgr94{color:#3c5dcd}.ansi span.sgr95{color:#9256af}.ansi span.sgr96{color:#008fa3}.ansi span.sgr97{color:#f5f5f5}.ansi span.sgr100{background-color:#616161}.ansi span.sgr101{background-color:#cb3c33}.ansi span.sgr102{background-color:#0e8300}.ansi span.sgr103{background-color:#a98800}.ansi span.sgr104{background-color:#3c5dcd}.ansi span.sgr105{background-color:#9256af}.ansi span.sgr106{background-color:#008fa3}.ansi span.sgr107{background-color:#f5f5f5}code.language-julia-repl>span.hljs-meta{color:#066f00;font-weight:bolder}/*!
+  Theme: Default
+  Description: Original highlight.js style
+  Author: (c) Ivan Sagalaev <maniac@softwaremaniacs.org>
+  Maintainer: @highlightjs/core-team
+  Website: https://highlightjs.org/
+  License: see project LICENSE
+  Touched: 2021
+*/pre code.hljs{display:block;overflow-x:auto;padding:1em}code.hljs{padding:3px 5px}.hljs{background:#F3F3F3;color:#444}.hljs-comment{color:#697070}.hljs-tag,.hljs-punctuation{color:#444a}.hljs-tag .hljs-name,.hljs-tag .hljs-attr{color:#444}.hljs-keyword,.hljs-attribute,.hljs-selector-tag,.hljs-meta .hljs-keyword,.hljs-doctag,.hljs-name{font-weight:bold}.hljs-type,.hljs-string,.hljs-number,.hljs-selector-id,.hljs-selector-class,.hljs-quote,.hljs-template-tag,.hljs-deletion{color:#880000}.hljs-title,.hljs-section{color:#880000;font-weight:bold}.hljs-regexp,.hljs-symbol,.hljs-variable,.hljs-template-variable,.hljs-link,.hljs-selector-attr,.hljs-operator,.hljs-selector-pseudo{color:#ab5656}.hljs-literal{color:#695}.hljs-built_in,.hljs-bullet,.hljs-code,.hljs-addition{color:#397300}.hljs-meta{color:#1f7199}.hljs-meta .hljs-string{color:#38a}.hljs-emphasis{font-style:italic}.hljs-strong{font-weight:bold}.gap-4{gap:1rem}
diff --git a/v1.9.4/assets/themeswap.js b/v1.9.4/assets/themeswap.js
new file mode 100644
index 00000000..9f5eebe6
--- /dev/null
+++ b/v1.9.4/assets/themeswap.js
@@ -0,0 +1,84 @@
+// Small function to quickly swap out themes. Gets put into the <head> tag..
+function set_theme_from_local_storage() {
+  // Initialize the theme to null, which means default
+  var theme = null;
+  // If the browser supports the localstorage and is not disabled then try to get the
+  // documenter theme
+  if (window.localStorage != null) {
+    // Get the user-picked theme from localStorage. May be `null`, which means the default
+    // theme.
+    theme = window.localStorage.getItem("documenter-theme");
+  }
+  // Check if the users preference is for dark color scheme
+  var darkPreference =
+    window.matchMedia("(prefers-color-scheme: dark)").matches === true;
+  // 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 = [];
+  var primaryLightTheme = null;
+  var primaryDarkTheme = null;
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    // The <link> tag of each style sheet is expected to have a data-theme-name attribute
+    // 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
+    if (themename === null) continue;
+    // To distinguish the default (primary) theme, it needs to have the data-theme-primary
+    // attribute set.
+    if (ss.ownerNode.getAttribute("data-theme-primary") !== null) {
+      primaryLightTheme = themename;
+    }
+    // Check if the theme is primary dark theme so that we could store its name in darkTheme
+    if (ss.ownerNode.getAttribute("data-theme-primary-dark") !== null) {
+      primaryDarkTheme = themename;
+    }
+    // If we find a matching theme (and it's not the default), we'll set active to non-null
+    if (themename === theme) active = i;
+    // Store the style sheets of inactive themes so that we could disable them
+    if (themename !== theme) disabled.push(ss);
+  }
+  var activeTheme = null;
+  if (active !== null) {
+    // If we did find an active theme, we'll (1) add the theme--$(theme) class to <html>
+    document.getElementsByTagName("html")[0].className = "theme--" + theme;
+    activeTheme = theme;
+  } else {
+    // If we did _not_ find an active theme, then we need to fall back to the primary theme
+    // which can either be dark or light, depending on the user's OS preference.
+    var activeTheme = darkPreference ? primaryDarkTheme : primaryLightTheme;
+    // In case it somehow happens that the relevant primary theme was not found in the
+    // preceding loop, we abort without doing anything.
+    if (activeTheme === null) {
+      console.error("Unable to determine primary theme.");
+      return;
+    }
+    // When switching to the primary light theme, then we must not have a class name
+    // for the <html> tag. That's only for non-primary or the primary dark theme.
+    if (darkPreference) {
+      document.getElementsByTagName("html")[0].className =
+        "theme--" + activeTheme;
+    } else {
+      document.getElementsByTagName("html")[0].className = "";
+    }
+  }
+  for (var i = 0; i < document.styleSheets.length; i++) {
+    var ss = document.styleSheets[i];
+    // The <link> tag of each style sheet is expected to have a data-theme-name attribute
+    // 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
+    if (themename === null) continue;
+    // we'll disable all the stylesheets, except for the active one
+    ss.disabled = !(themename == activeTheme);
+  }
+}
+set_theme_from_local_storage();
diff --git a/v1.9.4/assets/warner.js b/v1.9.4/assets/warner.js
new file mode 100644
index 00000000..3f6f5d00
--- /dev/null
+++ b/v1.9.4/assets/warner.js
@@ -0,0 +1,52 @@
+function maybeAddWarning() {
+  // DOCUMENTER_NEWEST is defined in versions.js, DOCUMENTER_CURRENT_VERSION and DOCUMENTER_STABLE
+  // in siteinfo.js.
+  // If either of these are undefined something went horribly wrong, so we abort.
+  if (
+    window.DOCUMENTER_NEWEST === undefined ||
+    window.DOCUMENTER_CURRENT_VERSION === undefined ||
+    window.DOCUMENTER_STABLE === undefined
+  ) {
+    return;
+  }
+
+  // Current version is not a version number, so we can't tell if it's the newest version. Abort.
+  if (!/v(\d+\.)*\d+/.test(window.DOCUMENTER_CURRENT_VERSION)) {
+    return;
+  }
+
+  // Current version is newest version, so no need to add a warning.
+  if (window.DOCUMENTER_NEWEST === window.DOCUMENTER_CURRENT_VERSION) {
+    return;
+  }
+
+  // Add a noindex meta tag (unless one exists) so that search engines don't index this version of the docs.
+  if (document.body.querySelector('meta[name="robots"]') === null) {
+    const meta = document.createElement("meta");
+    meta.name = "robots";
+    meta.content = "noindex";
+
+    document.getElementsByTagName("head")[0].appendChild(meta);
+  }
+
+  const div = document.createElement("div");
+  div.classList.add("outdated-warning-overlay");
+  const closer = document.createElement("button");
+  closer.classList.add("outdated-warning-closer", "delete");
+  closer.addEventListener("click", function () {
+    document.body.removeChild(div);
+  });
+  const href = window.documenterBaseURL + "/../" + window.DOCUMENTER_STABLE;
+  div.innerHTML =
+    'This documentation is not for the latest stable release, but for either the development version or an older release.<br><a href="' +
+    href +
+    '">Click here to go to the documentation for the latest stable release.</a>';
+  div.appendChild(closer);
+  document.body.appendChild(div);
+}
+
+if (document.readyState === "loading") {
+  document.addEventListener("DOMContentLoaded", maybeAddWarning);
+} else {
+  maybeAddWarning();
+}
diff --git a/v1.9.4/index.html b/v1.9.4/index.html
new file mode 100644
index 00000000..d31eef25
--- /dev/null
+++ b/v1.9.4/index.html
@@ -0,0 +1,2 @@
+<!DOCTYPE html>
+<html lang="en"><head><meta charset="UTF-8"/><meta name="viewport" content="width=device-width, initial-scale=1.0"/><title>Home · StaticArrays.jl</title><meta name="title" content="Home · StaticArrays.jl"/><meta property="og:title" content="Home · StaticArrays.jl"/><meta property="twitter:title" content="Home · StaticArrays.jl"/><meta name="description" content="Documentation for StaticArrays.jl."/><meta property="og:description" content="Documentation for StaticArrays.jl."/><meta property="twitter:description" content="Documentation for StaticArrays.jl."/><meta property="og:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/"/><meta property="twitter:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/"/><link rel="canonical" href="https://JuliaArrays.github.io/StaticArrays.jl/stable/"/><script data-outdated-warner src="assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="search_index.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" data-theme-primary-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><link href="assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href>StaticArrays.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li class="is-active"><a class="tocitem" href>Home</a></li><li><a class="tocitem" href="pages/api/">API</a></li><li><a class="tocitem" href="pages/quickstart/">Quick Start</a></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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><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-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/master/docs/src/index.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Static-Arrays"><a class="docs-heading-anchor" href="#Static-Arrays">Static Arrays</a><a id="Static-Arrays-1"></a><a class="docs-heading-anchor-permalink" href="#Static-Arrays" title="Permalink"></a></h1><p><em>Statically sized arrays for Julia</em></p><p><strong>StaticArrays</strong> provides a framework for implementing statically sized arrays in Julia, using the abstract type <code>StaticArray{Size,T,N} &lt;: AbstractArray{T,N}</code>. Subtypes of <a href="pages/api/#StaticArraysCore.StaticArray"><code>StaticArray</code></a> will provide fast implementations of common array and linear algebra operations. Note that here &quot;statically sized&quot; means that the size can be determined from the <em>type</em>, and &quot;static&quot; does <strong>not</strong> necessarily imply <code>immutable</code>.</p><p>The package also provides some concrete static array types: <a href="pages/api/#SVector"><code>SVector</code></a>, <a href="pages/api/#SMatrix"><code>SMatrix</code></a> and <a href="pages/api/#SArray"><code>SArray</code></a>, which may be used as-is (or else embedded in your own type). Mutable versions <a href="pages/api/#StaticArraysCore.MVector"><code>MVector</code></a>, <a href="pages/api/#StaticArraysCore.MMatrix"><code>MMatrix</code></a> and <a href="pages/api/#StaticArraysCore.MArray"><code>MArray</code></a> are also exported, as well as <a href="pages/api/#StaticArraysCore.SizedArray"><code>SizedArray</code></a> for annotating standard <code>Array</code>s with static size information. Further, the abstract <a href="pages/api/#FieldVector"><code>FieldVector</code></a> can be used to make fast static vectors out of any uniform Julia &quot;struct&quot;.</p></article><nav class="docs-footer"><a class="docs-footer-nextpage" href="pages/api/">API »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><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> version 1.4.1 on <span class="colophon-date" title="Thursday 16 May 2024 17:37">Thursday 16 May 2024</span>. 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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>API · StaticArrays.jl</title><meta name="title" content="API · StaticArrays.jl"/><meta property="og:title" content="API · StaticArrays.jl"/><meta property="twitter:title" content="API · StaticArrays.jl"/><meta name="description" content="Documentation for StaticArrays.jl."/><meta property="og:description" content="Documentation for StaticArrays.jl."/><meta property="twitter:description" content="Documentation for StaticArrays.jl."/><meta property="og:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/api/"/><meta property="twitter:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/api/"/><link rel="canonical" href="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/api/"/><script data-outdated-warner src="../../assets/warner.js"></script><link 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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" data-theme-primary-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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">StaticArrays.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li class="is-active"><a class="tocitem" href>API</a><ul class="internal"><li><a class="tocitem" href="#Guide"><span>Guide</span></a></li><li><a class="tocitem" href="#Docstrings"><span>Docstrings</span></a></li></ul></li><li><a class="tocitem" href="../quickstart/">Quick Start</a></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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>API</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>API</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/master/docs/src/pages/api.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="API"><a class="docs-heading-anchor" href="#API">API</a><a id="API-1"></a><a class="docs-heading-anchor-permalink" href="#API" title="Permalink"></a></h1><h2 id="Guide"><a class="docs-heading-anchor" href="#Guide">Guide</a><a id="Guide-1"></a><a class="docs-heading-anchor-permalink" href="#Guide" title="Permalink"></a></h2><h3 id="SVector"><a class="docs-heading-anchor" href="#SVector"><code>SVector</code></a><a id="SVector-1"></a><a class="docs-heading-anchor-permalink" href="#SVector" title="Permalink"></a></h3><p>The simplest static array is the type <code>SVector{N,T}</code>, which provides an immutable vector of fixed length <code>N</code> and type <code>T</code>.</p><p><code>SVector</code> defines a series of convenience constructors, so you can just type e.g. <code>SVector(1,2,3)</code>. Alternatively there is an intelligent <code>@SVector</code> macro where you can use native Julia array literals syntax, comprehensions, and the <code>zeros()</code>, <code>ones()</code>, <code>fill()</code>, <code>rand()</code> and <code>randn()</code> functions, such as <code>@SVector [1,2,3]</code>, <code>@SVector Float64[1,2,3]</code>, <code>@SVector [f(i) for i = 1:10]</code>, <code>@SVector zeros(3)</code>, <code>@SVector randn(Float32, 4)</code>, etc (Note: the range of a comprehension is evaluated at global scope by the macro, and must be made of combinations of literal values, functions, or global variables, but is not limited to just simple ranges. Extending this to (hopefully statically known by type-inference) local-scope variables is hoped for the future. The <code>zeros()</code>, <code>ones()</code>, <code>fill()</code>, <code>rand()</code>, <code>randn()</code>, and <code>randexp()</code> functions do not have this limitation.)</p><h3 id="SMatrix"><a class="docs-heading-anchor" href="#SMatrix"><code>SMatrix</code></a><a id="SMatrix-1"></a><a class="docs-heading-anchor-permalink" href="#SMatrix" title="Permalink"></a></h3><p>Statically sized <code>N×M</code> matrices are provided by <code>SMatrix{N,M,T,L}</code>.</p><p>Here <code>L</code> is the <code>length</code> of the matrix, such that <code>N × M = L</code>. However, convenience constructors are provided, so that <code>L</code>, <code>T</code> and even <code>M</code> are unnecessary. At minimum, you can type <code>SMatrix{2}(1,2,3,4)</code> to create a 2×2 matrix (the total number of elements must divide evenly into <code>N</code>). A convenience macro <code>@SMatrix [1 2; 3 4]</code> is provided (which also accepts comprehensions and the <code>zeros()</code>, <code>ones()</code>, <code>fill()</code>, <code>rand()</code>, <code>randn()</code>, and <code>randexp()</code> functions).</p><h3 id="SArray"><a class="docs-heading-anchor" href="#SArray"><code>SArray</code></a><a id="SArray-1"></a><a class="docs-heading-anchor-permalink" href="#SArray" title="Permalink"></a></h3><p>A container with arbitrarily many dimensions is defined as <code>struct SArray{Size,T,N,L} &lt;: StaticArray{Size,T,N}</code>, where <code>Size = Tuple{S1, S2, ...}</code> is a tuple of <code>Int</code>s. You can easily construct one with the <code>@SArray</code> macro, supporting all the features of <code>@SVector</code> and <code>@SMatrix</code> (but with arbitrary dimension).</p><p>The main reason <code>SVector</code> and <code>SMatrix</code> are defined is to make it easier to define the types without the extra tuple characters (compare <code>SVector{3}</code> to <code>SArray{Tuple{3}}</code>).</p><h3 id="Scalar"><a class="docs-heading-anchor" href="#Scalar"><code>Scalar</code></a><a id="Scalar-1"></a><a class="docs-heading-anchor-permalink" href="#Scalar" title="Permalink"></a></h3><p>Sometimes you want to broadcast an operation, but not over one of your inputs. A classic example is attempting to displace a collection of vectors by the same vector. We can now do this with the <code>Scalar</code> type:</p><pre><code class="language-julia hljs">[[1,2,3], [4,5,6]] .+ Scalar([1,0,-1]) # [[2,2,2], [5,5,5]]</code></pre><p><code>Scalar</code> is simply an implementation of an immutable, 0-dimensional <code>StaticArray</code>.</p><h3 id="The-Size-trait"><a class="docs-heading-anchor" href="#The-Size-trait">The <code>Size</code> trait</a><a id="The-Size-trait-1"></a><a class="docs-heading-anchor-permalink" href="#The-Size-trait" title="Permalink"></a></h3><p>The size of a statically sized array is a static parameter associated with the type of the array. The <code>Size</code> trait is provided as an abstract representation of the dimensions of a static array. An array <code>sa::SA</code> of size <code>(dims...)</code> is associated with <code>Size{(dims...)}()</code>. The following are equivalent constructors:</p><pre><code class="language-julia hljs">Size{(dims...,)}()
+Size(dims...)
+Size(sa::StaticArray)
+Size(SA) # SA &lt;: StaticArray</code></pre><p>This is extremely useful for (a) performing dispatch depending on the size of an array, and (b) passing array dimensions that the compiler can reason about.</p><p>An example of size-based dispatch for the determinant of a matrix would be:</p><pre><code class="language-julia hljs">det(x::StaticMatrix) = _det(Size(x), x)
+_det(::Size{(1,1)}, x::StaticMatrix) = x[1,1]
+_det(::Size{(2,2)}, x::StaticMatrix) = x[1,1]*x[2,2] - x[1,2]*x[2,1]
+# and other definitions as necessary</code></pre><p>Examples of using <code>Size</code> as a compile-time constant include</p><pre><code class="language-julia hljs">reshape(svector, Size(2,2))  # Convert SVector{4} to SMatrix{2,2}
+SizedMatrix{3,3}(rand(3,3))  # Construct a random 3×3 SizedArray (see below)</code></pre><h3 id="Indexing"><a class="docs-heading-anchor" href="#Indexing">Indexing</a><a id="Indexing-1"></a><a class="docs-heading-anchor-permalink" href="#Indexing" title="Permalink"></a></h3><p>Statically sized indexing can be realized by indexing each dimension by a scalar, a <code>StaticVector</code> or <code>:</code>. Indexing in this way will result a statically sized array (even if the input was dynamically sized, in the case of <code>StaticVector</code> indices) of the closest type (as defined by <code>similar_type</code>).</p><p>Conversely, indexing a statically sized array with a dynamically sized index (such as a <code>Vector{Integer}</code> or <code>UnitRange{Integer}</code>) will result in a standard (dynamically sized) <code>Array</code>.</p><h3 id="similar_type()"><a class="docs-heading-anchor" href="#similar_type()"><code>similar_type()</code></a><a id="similar_type()-1"></a><a class="docs-heading-anchor-permalink" href="#similar_type()" title="Permalink"></a></h3><p>Since immutable arrays need to be constructed &quot;all-at-once&quot;, we need a way of obtaining an appropriate constructor if the element type or dimensions of the output array differs from the input. To this end, <code>similar_type</code> is introduced, behaving just like <code>similar</code>, except that it returns a type. Relevant methods are:</p><pre><code class="language-julia hljs">similar_type(::Type{A}) where {A &lt;: StaticArray} # defaults to A
+similar_type(::Type{A}, ::Type{ElType}) where {A &lt;: StaticArray, ElType} # Change element type
+similar_type(::Type{A}, size::Size) where {A &lt;: AbstractArray} # Change size
+similar_type(::Type{A}, ::Type{ElType}, size::Size) where {A &lt;: AbstractArray, ElType} # Change both</code></pre><p>These setting will affect everything, from indexing, to matrix multiplication and <code>broadcast</code>. Users wanting introduce a new array type should <em>only</em> overload the last method in the above.</p><p>Use of <code>similar</code> will fall back to a mutable container, such as a <code>MVector</code> (see below), and it requires use of the <code>Size</code> trait if you wish to set a new static size (or else a dynamically sized <code>Array</code> will be generated when specifying the size as plain integers).</p><h3 id="Collecting-directly-into-static-arrays"><a class="docs-heading-anchor" href="#Collecting-directly-into-static-arrays">Collecting directly into static arrays</a><a id="Collecting-directly-into-static-arrays-1"></a><a class="docs-heading-anchor-permalink" href="#Collecting-directly-into-static-arrays" title="Permalink"></a></h3><p>You can collect <a href="https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-iteration">iterators</a> into static arrays directly with <a href="#StaticArrays.sacollect"><code>StaticArrays.sacollect</code></a>. The size needs to be specified, but the element type is optional.</p><h3 id="Mutable-arrays:-MVector,-MMatrix-and-MArray"><a class="docs-heading-anchor" href="#Mutable-arrays:-MVector,-MMatrix-and-MArray">Mutable arrays: <code>MVector</code>, <code>MMatrix</code> and <code>MArray</code></a><a id="Mutable-arrays:-MVector,-MMatrix-and-MArray-1"></a><a class="docs-heading-anchor-permalink" href="#Mutable-arrays:-MVector,-MMatrix-and-MArray" title="Permalink"></a></h3><p>These statically sized arrays are identical to the above, but are defined as <code>mutable struct</code>s, instead of immutable <code>struct</code>s. Because they are mutable, they allow <code>setindex!</code> to be defined (achieved through pointer manipulation, into a tuple).</p><p>As a consequence of Julia&#39;s internal implementation, these mutable containers live on the heap, not the stack. Their memory must be allocated and tracked by the garbage collector. Nevertheless, there is opportunity for speed improvements relative to <code>Base.Array</code> because (a) there may be one less pointer indirection, (b) their (typically small) static size allows for additional loop unrolling and inlining, and consequentially (c) their mutating methods like <code>map!</code> are extremely fast. Benchmarking shows that operations such as addition and matrix multiplication are faster for <code>MMatrix</code> than <code>Matrix</code>, at least for sizes up to 14 × 14, though keep in mind that optimal speed will be obtained by using mutating functions (like <code>map!</code> or <code>A_mul_B!</code>) where possible, rather than reallocating new memory.</p><p>Mutable static arrays also happen to be very useful containers that can be constructed on the heap (with the ability to use <code>setindex!</code>, etc), and later copied as e.g. an immutable <code>SVector</code> to the stack for use, or into e.g. an <code>Array{SVector}</code> for storage.</p><p>Convenience macros <code>@MVector</code>, <code>@MMatrix</code> and <code>@MArray</code> are provided.</p><h3 id="SizedArray:-a-decorate-size-wrapper-for-Array"><a class="docs-heading-anchor" href="#SizedArray:-a-decorate-size-wrapper-for-Array"><code>SizedArray</code>: a decorate size wrapper for <code>Array</code></a><a id="SizedArray:-a-decorate-size-wrapper-for-Array-1"></a><a class="docs-heading-anchor-permalink" href="#SizedArray:-a-decorate-size-wrapper-for-Array" title="Permalink"></a></h3><p>Another convenient mutable type is the <code>SizedArray</code>, which is just a wrapper-type about a standard Julia <code>Array</code> which declares its known size. For example, if we knew that <code>a</code> was a 2×2 <code>Matrix</code>, then we can type <code>sa = SizedArray{Tuple{2,2}}(a)</code> to construct a new object which knows the type (the size will be verified automatically). For one and two dimensions, a more convenient syntax for obtaining a <code>SizedArray</code> is by using the <code>SizedMatrix</code> and <code>SizedVector</code> aliases, e.g. <code>sa = SizedMatrix{2,2}(a)</code>.</p><p>Then, methods on <code>sa</code> will use the specialized code provided by the <em>StaticArrays</em> package, which in many cases will be much, much faster. For example, calling <code>eigen(sa)</code> will be significantly faster than <code>eigen(a)</code> since it will perform a specialized 2×2 matrix diagonalization rather than a general algorithm provided by Julia and <em>LAPACK</em>.</p><p>In some cases it will make more sense to use a <code>SizedArray</code>, and in other cases an <code>MArray</code> might be preferable.</p><h3 id="FieldVector"><a class="docs-heading-anchor" href="#FieldVector"><code>FieldVector</code></a><a id="FieldVector-1"></a><a class="docs-heading-anchor-permalink" href="#FieldVector" title="Permalink"></a></h3><p>Sometimes it is useful to give your own struct types the properties of a vector. <em>StaticArrays</em> can take care of this for you by allowing you to inherit from <code>FieldVector{N, T}</code>. For example, consider:</p><pre><code class="language-julia hljs">struct Point3D &lt;: FieldVector{3, Float64}
+    x::Float64
+    y::Float64
+    z::Float64
+end</code></pre><p>With this type, users can easily access fields to <code>p = Point3D(x,y,z)</code> using <code>p.x</code>, <code>p.y</code> or <code>p.z</code>, or alternatively via <code>p[1]</code>, <code>p[2]</code>, or <code>p[3]</code>. You may even permute the coordinates with <code>p[SVector(3,2,1)]</code>). Furthermore, <code>Point3D</code> is a complete <code>AbstractVector</code> implementation where you can add, subtract or scale vectors, multiply them by matrices, etc.</p><p><em>Note</em>: the three components of an ordinary <code>v::SVector{3}</code> can also be accessed as <code>v.x</code>, <code>v.y</code>, and <code>v.z</code>, so there is no need for a <code>FieldVector</code> to use this convention.</p><p>It is also worth noting that <code>FieldVector</code>s may be mutable or immutable, and that <code>setindex!</code> is defined for use on mutable types. For immutable containers, you may want to define a method for <code>similar_type</code> so that operations leave the type constant (otherwise they may fall back to <code>SVector</code>). For mutable containers, you may want to define a default constructor (no inputs) and an appropriate method for <code>similar</code>,</p><h3 id="Implementing-your-own-types"><a class="docs-heading-anchor" href="#Implementing-your-own-types">Implementing your own types</a><a id="Implementing-your-own-types-1"></a><a class="docs-heading-anchor-permalink" href="#Implementing-your-own-types" title="Permalink"></a></h3><p>You can easily create your own <code>StaticArray</code> type, by defining linear <code>getindex</code> (and optionally <code>setindex!</code> for mutable types –- see <code>setindex!(::MArray, val, i)</code> in <em>MArray.jl</em> for an example of how to achieve this through pointer manipulation). Your type should define a constructor that takes a tuple of the data (and mutable containers may want to define a default constructor).</p><p>Other useful functions to overload may be <code>similar_type</code> (and <code>similar</code> for mutable containers).</p><h3 id="Conversions-from-Array"><a class="docs-heading-anchor" href="#Conversions-from-Array">Conversions from <code>Array</code></a><a id="Conversions-from-Array-1"></a><a class="docs-heading-anchor-permalink" href="#Conversions-from-Array" title="Permalink"></a></h3><p>In order to convert from a dynamically sized <code>AbstractArray</code> to one of the statically sized array types, you must specify the size explicitly.  For example,</p><pre><code class="language-julia hljs">v = [1,2]
+
+m = [1 2;
+     3 4]
+
+# ... a lot of intervening code
+
+sv = SVector{2}(v)
+sm = SMatrix{2,2}(m)
+sa = SArray{Tuple{2,2}}(m)
+
+sized_v = SizedVector{2}(v)
+sized_m = SizedMatrix{2,2}(m)</code></pre><p>We have avoided adding <code>SVector(v::AbstractVector)</code> as a valid constructor to help users avoid the type instability (and potential performance disaster, if used without care) of this innocuous looking expression.</p><h3 id="Arrays-of-static-arrays"><a class="docs-heading-anchor" href="#Arrays-of-static-arrays">Arrays of static arrays</a><a id="Arrays-of-static-arrays-1"></a><a class="docs-heading-anchor-permalink" href="#Arrays-of-static-arrays" title="Permalink"></a></h3><p>Storing a large number of static arrays is convenient as an array of static arrays. For example, a collection of positions (3D coordinates –- <code>SVector{3,Float64}</code>) could be represented as a <code>Vector{SVector{3,Float64}}</code>.</p><p>Another common way of storing the same data is as a 3×<code>N</code> <code>Matrix{Float64}</code>. Rather conveniently, such types have <em>exactly</em> the same binary layout in memory, and therefore we can use <code>reinterpret</code> to convert between the two formats</p><pre><code class="language-julia hljs">function svectors(x::Matrix{T}, ::Val{N}) where {T,N}
+    size(x,1) == N || error(&quot;sizes mismatch&quot;)
+    isbitstype(T) || error(&quot;use for bitstypes only&quot;)
+    reinterpret(SVector{N,T}, vec(x))
+end</code></pre><p>Such a conversion does not copy the data, rather it refers to the <em>same</em> memory. Arguably, a <code>Vector</code> of <code>SVector</code>s is often preferable to a <code>Matrix</code> because it provides a better abstraction of the objects contained in the array and it allows the fast <em>StaticArrays</em> methods to act on elements.</p><p>However, the resulting object is a Base.ReinterpretArray, not an Array, which carries some runtime penalty on every single access. If you can afford the memory for a copy and can live with the non-shared mutation semantics, then it is better to pull a copy by e.g.</p><pre><code class="language-julia hljs">function svectorscopy(x::Matrix{T}, ::Val{N}) where {T,N}
+    size(x,1) == N || error(&quot;sizes mismatch&quot;)
+    isbitstype(T) || error(&quot;use for bitstypes only&quot;)
+    copy(reinterpret(SVector{N,T}, vec(x)))
+end</code></pre><p>For example:</p><pre><code class="nohighlight hljs">julia&gt; M=reshape(collect(1:6), (2,3))
+2×3 Array{Int64,2}:
+ 1  3  5
+ 2  4  6
+
+julia&gt; svectors(M, Val{2}())
+3-element reinterpret(SArray{Tuple{2},Int64,1,2}, ::Array{Int64,1}):
+ [1, 2]
+ [3, 4]
+ [5, 6]
+
+julia&gt; svectorscopy(M, Val{2}())
+3-element Array{SArray{Tuple{2},Int64,1,2},1}:
+ [1, 2]
+ [3, 4]
+ [5, 6]</code></pre><h3 id="Working-with-mutable-and-immutable-arrays"><a class="docs-heading-anchor" href="#Working-with-mutable-and-immutable-arrays">Working with mutable and immutable arrays</a><a id="Working-with-mutable-and-immutable-arrays-1"></a><a class="docs-heading-anchor-permalink" href="#Working-with-mutable-and-immutable-arrays" title="Permalink"></a></h3><p>Generally, it is performant to rebind an <em>immutable</em> array, such as</p><pre><code class="language-julia hljs">function average_position(positions::Vector{SVector{3,Float64}})
+    x = zeros(SVector{3,Float64})
+    for pos ∈ positions
+        x = x + pos
+    end
+    return x / length(positions)
+end</code></pre><p>so long as the <code>Type</code> of the rebound variable (<code>x</code>, above) does not change.</p><p>On the other hand, the above code for mutable containers like <code>Array</code>, <code>MArray</code> or <code>SizedArray</code> is <em>not</em> very efficient. Mutable containers must be <em>allocated</em> and later <em>garbage collected</em>, and for small, fixed-size arrays this can be a leading contribution to the cost. In the above code, a new array will be instantiated and allocated on each iteration of the loop. In order to avoid unnecessary allocations, it is best to allocate an array only once and apply mutating functions to it:</p><pre><code class="language-julia hljs">function average_position(positions::Vector{SVector{3,Float64}})
+    x = zeros(MVector{3,Float64})
+    for pos ∈ positions
+        x .+= pos
+    end
+    x ./= length(positions)
+    return x
+end</code></pre><p>The functions <code>setindex</code>, <code>push</code>, <code>pop</code>, <code>pushfirst</code>, <code>popfirst</code>, <code>insert</code> and <code>deleteat</code> are provided for performing certain specific operations on static arrays, in analogy with the standard functions <code>setindex!</code>, <code>push!</code>, <code>pop!</code>, etc. (Note that if the size of the static array changes, the type of the output will differ from the input.)</p><p>When building static arrays iteratively, it is usually efficient to build up an <code>MArray</code> first and then convert. The allocation will be elided by recent Julia compilers, resulting in very efficient code:</p><pre><code class="language-julia hljs">function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}
+    v = zero(MVector{N,T})
+    v[I] = one(T)
+    SVector(v)
+end</code></pre><h3 id="SIMD-optimizations"><a class="docs-heading-anchor" href="#SIMD-optimizations">SIMD optimizations</a><a id="SIMD-optimizations-1"></a><a class="docs-heading-anchor-permalink" href="#SIMD-optimizations" title="Permalink"></a></h3><p>It seems Julia and LLVM are smart enough to use processor vectorization extensions like SSE and AVX - however they are currently partially disabled by default. Run Julia with <code>julia -O</code> or <code>julia -O3</code> to enable these optimizations, and many of your (immutable) <code>StaticArray</code> methods <em>should</em> become significantly faster!</p><h2 id="Docstrings"><a class="docs-heading-anchor" href="#Docstrings">Docstrings</a><a id="Docstrings-1"></a><a class="docs-heading-anchor-permalink" href="#Docstrings" title="Permalink"></a></h2><ul><li><a href="#StaticArrays.Args"><code>StaticArrays.Args</code></a></li><li><a href="#StaticArrays.SA"><code>StaticArrays.SA</code></a></li><li><a href="#StaticArrays.SHermitianCompact"><code>StaticArrays.SHermitianCompact</code></a></li><li><a href="#StaticArrays.SOneTo"><code>StaticArrays.SOneTo</code></a></li><li><a href="#StaticArrays.Scalar"><code>StaticArrays.Scalar</code></a></li><li><a href="#StaticArrays.StaticMatMulLike"><code>StaticArrays.StaticMatMulLike</code></a></li><li><a href="#StaticArrays.TSize"><code>StaticArrays.TSize</code></a></li><li><a href="#StaticArrays._InitialValue"><code>StaticArrays._InitialValue</code></a></li><li><a href="#StaticArraysCore.Dynamic"><code>StaticArraysCore.Dynamic</code></a></li><li><a href="#StaticArraysCore.FieldArray"><code>StaticArraysCore.FieldArray</code></a></li><li><a href="#StaticArraysCore.FieldMatrix"><code>StaticArraysCore.FieldMatrix</code></a></li><li><a href="#StaticArraysCore.FieldVector"><code>StaticArraysCore.FieldVector</code></a></li><li><a href="#StaticArraysCore.MArray"><code>StaticArraysCore.MArray</code></a></li><li><a href="#StaticArraysCore.MMatrix"><code>StaticArraysCore.MMatrix</code></a></li><li><a href="#StaticArraysCore.MVector"><code>StaticArraysCore.MVector</code></a></li><li><a href="#StaticArraysCore.SArray"><code>StaticArraysCore.SArray</code></a></li><li><a href="#StaticArraysCore.SMatrix"><code>StaticArraysCore.SMatrix</code></a></li><li><a href="#StaticArraysCore.SVector"><code>StaticArraysCore.SVector</code></a></li><li><a href="#StaticArraysCore.Size"><code>StaticArraysCore.Size</code></a></li><li><a href="#StaticArraysCore.SizedArray"><code>StaticArraysCore.SizedArray</code></a></li><li><a href="#StaticArraysCore.StaticArray"><code>StaticArraysCore.StaticArray</code></a></li><li><a href="#Base.setindex-Tuple{StaticArray, Any, Int64}"><code>Base.setindex</code></a></li><li><a href="#Base.similar-Tuple{SA} where SA&lt;:StaticArray"><code>Base.similar</code></a></li><li><a href="#LinearAlgebra.qr-Tuple{StaticArray{Tuple{N, M}, T, 2} where {N, M, T}}"><code>LinearAlgebra.qr</code></a></li><li><a href="#StaticArrays._construct_similar-Union{Tuple{ET}, Tuple{L}, Tuple{Any, Size, Tuple{ET, Vararg{ET, L}}}} where {L, ET}"><code>StaticArrays._construct_similar</code></a></li><li><a href="#StaticArrays._lind-Union{Tuple{tA}, Tuple{sa}, Tuple{Symbol, Type{StaticArrays.TSize{sa, tA}}, Int64, Int64}} where {sa, tA}"><code>StaticArrays._lind</code></a></li><li><a href="#StaticArrays._muladd_expr-Tuple{Array{Expr, N} where N, Array{Expr, N} where N, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:StaticArrays.AlphaBeta}"><code>StaticArrays._muladd_expr</code></a></li><li><a href="#StaticArrays._size-Tuple{Any}"><code>StaticArrays._size</code></a></li><li><a href="#StaticArrays.arithmetic_closure-Union{Tuple{Type{T}}, Tuple{T}} where T"><code>StaticArrays.arithmetic_closure</code></a></li><li><a href="#StaticArrays.check_dims-Union{Tuple{sc}, Tuple{sb}, Tuple{sa}, Tuple{Size{sc}, Size{sa}, Size{sb}}} where {sa, sb, sc}"><code>StaticArrays.check_dims</code></a></li><li><a href="#StaticArrays.construct_type-Union{Tuple{SA}, Tuple{Type{SA}, Any}} where SA&lt;:StaticArray"><code>StaticArrays.construct_type</code></a></li><li><a href="#StaticArrays.deleteat-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.deleteat</code></a></li><li><a href="#StaticArrays.dimmatch"><code>StaticArrays.dimmatch</code></a></li><li><a href="#StaticArrays.gen_by_access-Tuple{Any, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:(StaticArray{Tuple{N, M}, T, 2} where {N, M, T}), Type}"><code>StaticArrays.gen_by_access</code></a></li><li><a href="#StaticArrays.gen_by_access"><code>StaticArrays.gen_by_access</code></a></li><li><a href="#StaticArrays.insert-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any, Any}"><code>StaticArrays.insert</code></a></li><li><a href="#StaticArrays.mul_result_structure-Tuple{Any, Any}"><code>StaticArrays.mul_result_structure</code></a></li><li><a href="#StaticArrays.multiplied_dimension-Tuple{Type{var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T), Type{var&quot;#s22&quot;} where var&quot;#s22&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T)}"><code>StaticArrays.multiplied_dimension</code></a></li><li><a href="#StaticArrays.pop-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}"><code>StaticArrays.pop</code></a></li><li><a href="#StaticArrays.popfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}"><code>StaticArrays.popfirst</code></a></li><li><a href="#StaticArrays.push-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.push</code></a></li><li><a href="#StaticArrays.pushfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.pushfirst</code></a></li><li><a href="#StaticArrays.sacollect"><code>StaticArrays.sacollect</code></a></li><li><a href="#StaticArrays.same_size-Tuple"><code>StaticArrays.same_size</code></a></li><li><a href="#StaticArrays.sizematch-Union{Tuple{S2}, Tuple{S1}, Tuple{Size{S1}, Size{S2}}} where {S1, S2}"><code>StaticArrays.sizematch</code></a></li><li><a href="#StaticArrays.sizematch-Union{Tuple{S}, Tuple{Size{S}, StaticArray}} where S"><code>StaticArrays.sizematch</code></a></li><li><a href="#StaticArrays.uplo_access-NTuple{5, Any}"><code>StaticArrays.uplo_access</code></a></li><li><a href="#StaticArraysCore.similar_type"><code>StaticArraysCore.similar_type</code></a></li><li><a href="#StaticArraysCore.size_to_tuple-Union{Tuple{Type{T}}, Tuple{T}} where T&lt;:Tuple"><code>StaticArraysCore.size_to_tuple</code></a></li><li><a href="#StaticArrays.@MArray-Tuple{Any}"><code>StaticArrays.@MArray</code></a></li><li><a href="#StaticArrays.@MMatrix-Tuple{Any}"><code>StaticArrays.@MMatrix</code></a></li><li><a href="#StaticArrays.@MVector-Tuple{Any}"><code>StaticArrays.@MVector</code></a></li><li><a href="#StaticArrays.@SArray-Tuple{Any}"><code>StaticArrays.@SArray</code></a></li><li><a href="#StaticArrays.@SMatrix-Tuple{Any}"><code>StaticArrays.@SMatrix</code></a></li><li><a href="#StaticArrays.@SVector-Tuple{Any}"><code>StaticArrays.@SVector</code></a></li></ul><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.StaticMatMulLike" href="#StaticArrays.StaticMatMulLike"><code>StaticArrays.StaticMatMulLike</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">StaticMatMulLike</code></pre><p>Static wrappers used for multiplication dispatch.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L16-L20">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.Args" href="#StaticArrays.Args"><code>StaticArrays.Args</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">Args</code></pre><p>A help wrapper to distinguish <code>SA(x...)</code> and <code>SA((x...,))</code></p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/convert.jl#L1-L5">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.SA" href="#StaticArrays.SA"><code>StaticArrays.SA</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SA[ elements ]
+SA{T}[ elements ]</code></pre><p>Create <code>SArray</code> literals using array construction syntax. The element type is inferred by promoting <code>elements</code> to a common type or set to <code>T</code> when <code>T</code> is provided explicitly.</p><p><strong>Examples:</strong></p><ul><li><code>SA[1.0, 2.0]</code> creates a length-2 <code>SVector</code> of <code>Float64</code> elements.</li><li><code>SA[1 2; 3 4]</code> creates a 2×2 SMatrix of <code>Int</code>s.</li><li><code>SA[1 2]</code> creates a 1×2 SMatrix of <code>Int</code>s.</li><li><code>SA{Float32}[1, 2]</code> creates a length-2 <code>SVector</code> of <code>Float32</code> elements.</li></ul><p>A couple of helpful type aliases are also provided:</p><ul><li><code>SA_F64[1, 2]</code> creates a length-2 <code>SVector</code> of <code>Float64</code> elements</li><li><code>SA_F32[1, 2]</code> creates a length-2 <code>SVector</code> of <code>Float32</code> elements</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/initializers.jl#L1-L20">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.SHermitianCompact" href="#StaticArrays.SHermitianCompact"><code>StaticArrays.SHermitianCompact</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SHermitianCompact{N, T, L} &lt;: StaticMatrix{N, N, T}</code></pre><p>A <a href="#StaticArraysCore.StaticArray"><code>StaticArray</code></a> subtype that represents a Hermitian matrix. Unlike <code>LinearAlgebra.Hermitian</code>, <code>SHermitianCompact</code> stores only the lower triangle of the matrix (as an <code>SVector</code>). The lower triangle is stored in column-major order. For example, for an <code>SHermitianCompact{3}</code>, the indices of the stored elements can be visualized as follows:</p><pre><code class="nohighlight hljs">┌ 1 ⋅ ⋅ ┐
+| 2 4 ⋅ |
+└ 3 5 6 ┘</code></pre><p>Type parameters:</p><ul><li><code>N</code>: matrix dimension;</li><li><code>T</code>: element type for lower triangle;</li><li><code>L</code>: length of the <code>SVector</code> storing the lower triangular elements.</li></ul><p>Note that <code>L</code> is always the <code>N</code>th <a href="https://en.wikipedia.org/wiki/Triangular_number">triangular number</a>.</p><p>An <code>SHermitianCompact</code> may be constructed either:</p><ul><li>from an <code>AbstractVector</code> containing the lower triangular elements; or</li><li>from a <code>Tuple</code> containing both upper and lower triangular elements in column major order; or</li><li>from another <code>StaticMatrix</code>.</li></ul><p>For the latter two cases, only the lower triangular elements are used; the upper triangular elements are ignored.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SHermitianCompact.jl#L1-L31">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.SOneTo" href="#StaticArrays.SOneTo"><code>StaticArrays.SOneTo</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SOneTo(n)</code></pre><p>Return a statically-sized <code>AbstractUnitRange</code> starting at <code>1</code>, functioning as the <code>axes</code> of a <code>StaticArray</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SOneTo.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.Scalar" href="#StaticArrays.Scalar"><code>StaticArrays.Scalar</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">Scalar{T}(x::T)</code></pre><p>Construct a statically-sized 0-dimensional array that contains a single element, <code>x</code>. This type is particularly useful for influencing broadcasting operations.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/Scalar.jl#L1-L6">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.TSize" href="#StaticArrays.TSize"><code>StaticArrays.TSize</code></a> — <span class="docstring-category">Type</span></header><section><div><p>Size that stores whether a Matrix is a Transpose Useful when selecting multiplication methods, and avoiding allocations when dealing with the <code>Transpose</code> type by passing around the original matrix. Should pair with <code>parent</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L178-L183">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays._InitialValue" href="#StaticArrays._InitialValue"><code>StaticArrays._InitialValue</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">_InitialValue</code></pre><p>A singleton type for representing &quot;universal&quot; initial value (identity element).</p><p>The idea is that, given <code>op</code> for <code>mapfoldl</code>, virtually, we define an &quot;extended&quot; version of it by</p><pre><code class="nohighlight hljs">op′(::_InitialValue, x) = x
+op′(acc, x) = op(acc, x)</code></pre><p>This is just a conceptually useful model to have in mind and we don&#39;t actually define <code>op′</code> here  (yet?).  But see <code>Base.BottomRF</code> for how it might work in action.</p><p>(It is related to that you can always turn a semigroup without an identity into a monoid by &quot;adjoining&quot; an element that acts as the identity.)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/mapreduce.jl#L1-L18">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Base.setindex-Tuple{StaticArray, Any, Int64}" href="#Base.setindex-Tuple{StaticArray, Any, Int64}"><code>Base.setindex</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">setindex(vec::StaticArray, x, index::Int)</code></pre><p>Return a new array with the item at <code>index</code> replaced by <code>x</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; setindex(@SVector[1,2,3], 4, 2)
+3-element SVector{3, Int64} with indices SOneTo(3):
+ 1
+ 4
+ 3
+
+julia&gt; setindex(@SMatrix[2 4; 6 8], 1, 2)
+2×2 SMatrix{2, 2, Int64, 4} with indices SOneTo(2)×SOneTo(2):
+ 2  4
+ 1  8</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L166-L184">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="Base.similar-Tuple{SA} where SA&lt;:StaticArray" href="#Base.similar-Tuple{SA} where SA&lt;:StaticArray"><code>Base.similar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">similar(static_array)
+similar(static_array, T)
+similar(array, ::Size)
+similar(array, T, ::Size)</code></pre><p>Constructs and returns a mutable but statically-sized array (i.e. a <code>StaticArray</code>). If the input <code>array</code> is not a <code>StaticArray</code>, then the <code>Size</code> is required to determine the output size (or else a dynamically sized array will be returned).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/abstractarray.jl#L106-L115">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="LinearAlgebra.qr-Tuple{StaticArray{Tuple{N, M}, T, 2} where {N, M, T}}" href="#LinearAlgebra.qr-Tuple{StaticArray{Tuple{N, M}, T, 2} where {N, M, T}}"><code>LinearAlgebra.qr</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">qr(A::StaticMatrix,
+   pivot::Union{Val{true}, Val{false}, LinearAlgebra.PivotingStrategy} = Val(false))</code></pre><p>Compute the QR factorization of <code>A</code>. The factors can be obtained by iteration:</p><pre><code class="language-julia hljs">julia&gt; A = @SMatrix rand(3,4);
+
+julia&gt; Q, R = qr(A);
+
+julia&gt; Q * R ≈ A
+true</code></pre><p>or by using <code>getfield</code>:</p><pre><code class="language-julia hljs">julia&gt; F = qr(A);
+
+julia&gt; F.Q * F.R ≈ A
+true</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/qr.jl#L35-L58">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays._construct_similar-Union{Tuple{ET}, Tuple{L}, Tuple{Any, Size, Tuple{ET, Vararg{ET, L}}}} where {L, ET}" href="#StaticArrays._construct_similar-Union{Tuple{ET}, Tuple{L}, Tuple{Any, Size, Tuple{ET, Vararg{ET, L}}}} where {L, ET}"><code>StaticArrays._construct_similar</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">_construct_similar(a, ::Size, elements::NTuple)</code></pre><p>Construct a static array of similar type to <code>a</code> with the given <code>elements</code>.</p><p>When <code>a</code> is an instance or a concrete type the element type <code>eltype(a)</code> is used. However, when <code>a</code> is a <code>UnionAll</code> type such as <code>SMatrix{2,2}</code>, the promoted type of <code>elements</code> is used instead.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/abstractarray.jl#L90-L98">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays._lind-Union{Tuple{tA}, Tuple{sa}, Tuple{Symbol, Type{StaticArrays.TSize{sa, tA}}, Int64, Int64}} where {sa, tA}" href="#StaticArrays._lind-Union{Tuple{tA}, Tuple{sa}, Tuple{Symbol, Type{StaticArrays.TSize{sa, tA}}, Int64, Int64}} where {sa, tA}"><code>StaticArrays._lind</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Obtain an expression for the linear index of var[k,j], taking transposes into account</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L381">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays._muladd_expr-Tuple{Array{Expr, N} where N, Array{Expr, N} where N, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:StaticArrays.AlphaBeta}" href="#StaticArrays._muladd_expr-Tuple{Array{Expr, N} where N, Array{Expr, N} where N, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:StaticArrays.AlphaBeta}"><code>StaticArrays._muladd_expr</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Combine left and right sides of an assignment expression, short-cutting         lhs = α * rhs + β * lhs,     element-wise. If α = 1, the multiplication by α is removed. If β = 0, the second rhs term is removed.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L359-L364">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays._size-Tuple{Any}" href="#StaticArrays._size-Tuple{Any}"><code>StaticArrays._size</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Return either the statically known Size() or runtime size()</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/traits.jl#L91-L93">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.arithmetic_closure-Union{Tuple{Type{T}}, Tuple{T}} where T" href="#StaticArrays.arithmetic_closure-Union{Tuple{Type{T}}, Tuple{T}} where T"><code>StaticArrays.arithmetic_closure</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">arithmetic_closure(T)</code></pre><p>Return the type which values of type <code>T</code> will promote to under a combination of the arithmetic operations <code>+, -, *</code> and <code>/</code>.</p><pre><code class="language-julia-repl hljs">julia&gt; import StaticArrays.arithmetic_closure
+
+julia&gt; arithmetic_closure(Bool)
+Float64
+
+julia&gt; arithmetic_closure(Int32)
+Float64
+
+julia&gt; arithmetic_closure(BigFloat)
+BigFloat
+
+julia&gt; arithmetic_closure(BigInt)
+BigFloat</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/arraymath.jl#L182-L202">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.check_dims-Union{Tuple{sc}, Tuple{sb}, Tuple{sa}, Tuple{Size{sc}, Size{sa}, Size{sb}}} where {sa, sb, sc}" href="#StaticArrays.check_dims-Union{Tuple{sc}, Tuple{sb}, Tuple{sa}, Tuple{Size{sc}, Size{sa}, Size{sb}}} where {sa, sb, sc}"><code>StaticArrays.check_dims</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Validate the dimensions of a matrix multiplication, including matrix-vector products</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L252">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.construct_type-Union{Tuple{SA}, Tuple{Type{SA}, Any}} where SA&lt;:StaticArray" href="#StaticArrays.construct_type-Union{Tuple{SA}, Tuple{Type{SA}, Any}} where SA&lt;:StaticArray"><code>StaticArrays.construct_type</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">SA′ = construct_type(::Type{SA}, x) where {SA&lt;:StaticArray}</code></pre><p>Pick a proper constructor <code>SA′</code> based on <code>x</code> if <code>SA(x)</code>/<code>SA(x...)</code> has no specific definition. The default returned <code>SA′</code> is <code>SA</code> itself for user defined <code>StaticArray</code>s. This differs from  <code>similar_type()</code> in that <code>SA′</code> should always be a subtype of <code>SA</code>.</p><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>To distinguish <code>SA(x...)</code> and <code>SA(x::Tuple)</code>, the former calls  <code>construct_type(SA, StaticArrays.Args(x))</code> instead of <code>construct_type(SA, x)</code>.</p></div></div><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Please make sure <code>SA&#39;(x)</code> has a specific definition if the default behavior is overloaded.  Otherwise construction might fall into infinite recursion.</p></div></div><hr/><p>The adaption rules for official <code>StaticArray</code>s could be summarized as:</p><p><strong><code>SA &lt;: FieldArray</code>: <code>eltype</code> adaptable</strong></p><p><code>FieldArray</code>s are always static-sized. We only derive <code>SA′</code>&#39;s <code>eltype</code> using type promotion if needed.</p><p><strong><code>SA &lt;: Union{SArray, MArray, SHermitianCompact, SizedArray}</code>: <code>size</code>/<code>eltype</code> adaptable</strong></p><ul><li>SA(x::Tuple)</li></ul><p>If <code>SA</code> is fully static-sized, then we first try to fill <code>SA</code> with <code>x</code>&#39;s elements.  If failed and <code>length(SA) == 1</code>, then we try to fill <code>SA</code> with <code>x</code> itself.</p><p>If <code>SA</code> is not fully static-sized, then we always try to fill <code>SA</code> with <code>x</code>&#39;s elements,  and the constructor&#39;s <code>Size</code> is derived based on:</p><ol><li>If <code>SA &lt;: StaticVector</code>, then we use <code>length(x)</code> as the output <code>Length</code> </li><li>If <code>SA &lt;: StaticMatrix{M}</code>, then we use <code>(M, N)</code> (<code>N = length(x) ÷ M</code>) as the output <code>Size</code></li><li>If <code>SA &lt;: StaticMatrix{M,M} where M</code>, then we use <code>(N, N)</code> (<code>N = sqrt(length(x)</code>) as the output <code>Size</code>.</li></ol><ul><li>SA(x...)</li></ul><p>Similar to <code>Tuple</code>, but we never fill <code>SA</code> with <code>x</code> itself.</p><ul><li>SA(x::StaticArray)</li></ul><p>We treat <code>x</code> as <code>Tuple</code> whenever possible. If failed, then try to inherit <code>x</code>&#39;s <code>Size</code>.</p><ul><li>SA(x::AbstractArray)</li></ul><p><code>x</code> is used to provide eltype. Thus <code>SA</code> must be static sized.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/convert.jl#L39-L78">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.deleteat-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}" href="#StaticArrays.deleteat-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.deleteat</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">deleteat(vec::StaticVector, index::Integer)</code></pre><p>Return a new vector with the item at the given <code>index</code> removed.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; deleteat(@SVector[6, 5, 4, 3, 2, 1], 2)
+5-element SVector{5, Int64} with indices SOneTo(5):
+ 6
+ 4
+ 3
+ 2
+ 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L130-L145">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.dimmatch" href="#StaticArrays.dimmatch"><code>StaticArrays.dimmatch</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">dimmatch(x::StaticDimension, y::StaticDimension)</code></pre><p>Return whether dimensions <code>x</code> and <code>y</code> match at compile time, that is:</p><ul><li>if <code>x</code> and <code>y</code> are both <code>Int</code>s, check that they are equal</li><li>if <code>x</code> or <code>y</code> are <code>Dynamic()</code>, return true</li></ul></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/traits.jl#L2-L9">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.gen_by_access" href="#StaticArrays.gen_by_access"><code>StaticArrays.gen_by_access</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">gen_by_access(expr_gen, a::Type{&lt;:AbstractArray}, asym = :wrapped_a)</code></pre><p>Statically generate outer code for fully unrolled multiplication loops. Returned code does wrapper-specific tests (for example if a symmetric matrix view is <code>U</code> or <code>L</code>) and the body of the if expression is then generated by function <code>expr_gen</code>. The function <code>expr_gen</code> receives access pattern description symbol as its argument and this symbol is then consumed by uplo_access to generate the right code for matrix element access.</p><p>The name of the matrix to test is indicated by <code>asym</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L33-L44">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.gen_by_access-Tuple{Any, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:(StaticArray{Tuple{N, M}, T, 2} where {N, M, T}), Type}" href="#StaticArrays.gen_by_access-Tuple{Any, Type{var&quot;#s24&quot;} where var&quot;#s24&quot;&lt;:(StaticArray{Tuple{N, M}, T, 2} where {N, M, T}), Type}"><code>StaticArrays.gen_by_access</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">gen_by_access(expr_gen, a::Type{&lt;:AbstractArray}, b::Type{&lt;:AbstractArray})</code></pre><p>Similar to gen<em>by</em>access with only one type argument. The difference is that tests for both arrays of type <code>a</code> and <code>b</code> are generated and <code>expr_gen</code> receives two access arguments, first for matrix <code>a</code> and the second for matrix <code>b</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L87-L93">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.insert-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any, Any}" href="#StaticArrays.insert-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any, Any}"><code>StaticArrays.insert</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">insert(vec::StaticVector, index::Integer, item)</code></pre><p>Return a new vector with <code>item</code> inserted into <code>vec</code> at the given <code>index</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; insert(@SVector[6, 5, 4, 2, 1], 4, 3)
+6-element SVector{6, Int64} with indices SOneTo(6):
+ 6
+ 5
+ 4
+ 3
+ 2
+ 1</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L52-L68">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.mul_result_structure-Tuple{Any, Any}" href="#StaticArrays.mul_result_structure-Tuple{Any, Any}"><code>StaticArrays.mul_result_structure</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">mul_result_structure(a::Type, b::Type)</code></pre><p>Get a structure wrapper that should be applied to the result of multiplication of matrices of given types (a*b). </p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply.jl#L18-L23">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.multiplied_dimension-Tuple{Type{var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T), Type{var&quot;#s22&quot;} where var&quot;#s22&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T)}" href="#StaticArrays.multiplied_dimension-Tuple{Type{var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T), Type{var&quot;#s22&quot;} where var&quot;#s22&quot;&lt;:(Union{LinearAlgebra.Adjoint{T, var&quot;#s5&quot;} where var&quot;#s5&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.Diagonal{T, var&quot;#s12&quot;} where var&quot;#s12&quot;&lt;:(StaticArray{Tuple{var&quot;#s13&quot;}, T, 1} where var&quot;#s13&quot;), LinearAlgebra.Hermitian{T, var&quot;#s9&quot;} where var&quot;#s9&quot;&lt;:(StaticArray{Tuple{var&quot;#s10&quot;, var&quot;#s11&quot;}, T, 2} where {var&quot;#s10&quot;, var&quot;#s11&quot;}), LinearAlgebra.LowerTriangular{T, var&quot;#s17&quot;} where var&quot;#s17&quot;&lt;:(StaticArray{Tuple{var&quot;#s18&quot;, var&quot;#s19&quot;}, T, 2} where {var&quot;#s18&quot;, var&quot;#s19&quot;}), LinearAlgebra.Symmetric{T, var&quot;#s6&quot;} where var&quot;#s6&quot;&lt;:(StaticArray{Tuple{var&quot;#s7&quot;, var&quot;#s8&quot;}, T, 2} where {var&quot;#s7&quot;, var&quot;#s8&quot;}), LinearAlgebra.Transpose{T, var&quot;#s4&quot;} where var&quot;#s4&quot;&lt;:Union{StaticArray{Tuple{var&quot;#s2&quot;}, T, 1} where var&quot;#s2&quot;, StaticArray{Tuple{var&quot;#s3&quot;, var&quot;#s4&quot;}, T, 2} where {var&quot;#s3&quot;, var&quot;#s4&quot;}}, LinearAlgebra.UnitLowerTriangular{T, var&quot;#s23&quot;} where var&quot;#s23&quot;&lt;:(StaticArray{Tuple{var&quot;#s24&quot;, var&quot;#s25&quot;}, T, 2} where {var&quot;#s24&quot;, var&quot;#s25&quot;}), LinearAlgebra.UnitUpperTriangular{T, var&quot;#s20&quot;} where var&quot;#s20&quot;&lt;:(StaticArray{Tuple{var&quot;#s21&quot;, var&quot;#s22&quot;}, T, 2} where {var&quot;#s21&quot;, var&quot;#s22&quot;}), LinearAlgebra.UpperTriangular{T, var&quot;#s14&quot;} where var&quot;#s14&quot;&lt;:(StaticArray{Tuple{var&quot;#s15&quot;, var&quot;#s16&quot;}, T, 2} where {var&quot;#s15&quot;, var&quot;#s16&quot;}), StaticArray{Tuple{var&quot;#s25&quot;}, T, 1} where var&quot;#s25&quot;, StaticArray{Tuple{var&quot;#s1&quot;, var&quot;#s3&quot;}, T, 2} where {var&quot;#s1&quot;, var&quot;#s3&quot;}} where T)}"><code>StaticArrays.multiplied_dimension</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Calculate the product of the dimensions being multiplied. Useful as a heuristic for unrolling.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L248">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.pop-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}" href="#StaticArrays.pop-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}"><code>StaticArrays.pop</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">pop(vec::StaticVector)</code></pre><p>Return a new vector with the last item in <code>vec</code> removed.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; pop(@SVector[1,2,3])
+2-element SVector{2, Int64} with indices SOneTo(2):
+ 1
+ 2</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L84-L96">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.popfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}" href="#StaticArrays.popfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}"><code>StaticArrays.popfirst</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">popfirst(vec::StaticVector)</code></pre><p>Return a new vector with the first item in <code>vec</code> removed.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; popfirst(@SVector[1,2,3])
+2-element SVector{2, Int64} with indices SOneTo(2):
+ 2
+ 3</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L107-L119">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.push-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}" href="#StaticArrays.push-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.push</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">push(vec::StaticVector, item)</code></pre><p>Return a new <code>StaticVector</code> with <code>item</code> inserted on the end of <code>vec</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; push(@SVector[1, 2, 3], 4)
+4-element SVector{4, Int64} with indices SOneTo(4):
+ 1
+ 2
+ 3
+ 4</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L1-L15">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.pushfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}" href="#StaticArrays.pushfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}"><code>StaticArrays.pushfirst</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">pushfirst(vec::StaticVector, item)</code></pre><p>Return a new <code>StaticVector</code> with <code>item</code> inserted at the beginning of <code>vec</code>.</p><p><strong>Examples</strong></p><pre><code class="language-julia-repl hljs">julia&gt; pushfirst(@SVector[1, 2, 3, 4], 5)
+5-element SVector{5, Int64} with indices SOneTo(5):
+ 5
+ 1
+ 2
+ 3
+ 4</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/deque.jl#L26-L41">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.sacollect" href="#StaticArrays.sacollect"><code>StaticArrays.sacollect</code></a> — <span class="docstring-category">Function</span></header><section><div><p>sacollect(SA, gen)</p><p>Construct a statically-sized vector of type <code>SA</code>.from a generator <code>gen</code>. <code>SA</code> needs to have a size parameter since the length of <code>vec</code> is unknown to the compiler. <code>SA</code> can optionally specify the element type as well.</p><p>Example:</p><pre><code class="nohighlight hljs">sacollect(SVector{3, Int}, 2i+1 for i in 1:3)
+sacollect(SMatrix{2, 3}, i+j for i in 1:2, j in 1:3)
+sacollect(SArray{2, 3}, i+j for i in 1:2, j in 1:3)</code></pre><p>This creates the same statically-sized vector as if the generator were collected in an array, but is more efficient since no array is allocated.</p><p>Equivalent:</p><pre><code class="nohighlight hljs">SVector{3, Int}([2i+1 for i in 1:3])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SArray.jl#L30-L51">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.same_size-Tuple" href="#StaticArrays.same_size-Tuple"><code>StaticArrays.same_size</code></a> — <span class="docstring-category">Method</span></header><section><div><p>Returns the common Size of the inputs (or else throws a DimensionMismatch)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/traits.jl#L102-L104">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.sizematch-Union{Tuple{S2}, Tuple{S1}, Tuple{Size{S1}, Size{S2}}} where {S1, S2}" href="#StaticArrays.sizematch-Union{Tuple{S2}, Tuple{S1}, Tuple{Size{S1}, Size{S2}}} where {S1, S2}"><code>StaticArrays.sizematch</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">sizematch(::Size, ::Size)
+sizematch(::Tuple, ::Tuple)</code></pre><p>Determine whether two sizes match, in the sense that they have the same number of dimensions, and their dimensions match as determined by <a href="#StaticArrays.dimmatch"><code>dimmatch</code></a>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/traits.jl#L68-L74">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.sizematch-Union{Tuple{S}, Tuple{Size{S}, StaticArray}} where S" href="#StaticArrays.sizematch-Union{Tuple{S}, Tuple{Size{S}, StaticArray}} where S"><code>StaticArrays.sizematch</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">sizematch(::Size, A::AbstractArray)</code></pre><p>Determine whether array <code>A</code> matches the given size. If <code>A</code> is a <code>StaticArray</code>, the check is performed at compile time, otherwise, the check is performed at runtime.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/traits.jl#L81-L87">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.uplo_access-NTuple{5, Any}" href="#StaticArrays.uplo_access-NTuple{5, Any}"><code>StaticArrays.uplo_access</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">uplo_access(sa, asym, k, j, uplo)</code></pre><p>Generate code for matrix element access, for a matrix of size <code>sa</code> locally referred to as <code>asym</code> in the context where the result will be used. Both indices <code>k</code> and <code>j</code> need to be statically known for this function to work. <code>uplo</code> is the access pattern mode generated by the <code>gen_by_access</code> function.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/matrix_multiply_add.jl#L266-L273">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@MArray-Tuple{Any}" href="#StaticArrays.@MArray-Tuple{Any}"><code>StaticArrays.@MArray</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@MArray [a b; c d]
+@MArray [[a, b];[c, d]]
+@MArray [i+j for i in 1:2, j in 1:2]
+@MArray ones(2, 2, 2)</code></pre><p>A convenience macro to construct <code>MArray</code> with arbitrary dimension. See <a href="#StaticArrays.@SArray-Tuple{Any}"><code>@SArray</code></a> for detailed features.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/MArray.jl#L53-L61">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@MMatrix-Tuple{Any}" href="#StaticArrays.@MMatrix-Tuple{Any}"><code>StaticArrays.@MMatrix</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@MMatrix [a b c d]
+@MMatrix [[a, b];[c, d]]
+@MMatrix [i+j for i in 1:2, j in 1:2]
+@MMatrix ones(2, 2)</code></pre><p>A convenience macro to construct <code>MMatrix</code>. See <a href="#StaticArrays.@SArray-Tuple{Any}"><code>@SArray</code></a> for detailed features.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/MMatrix.jl#L17-L25">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@MVector-Tuple{Any}" href="#StaticArrays.@MVector-Tuple{Any}"><code>StaticArrays.@MVector</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@MVector [a, b, c, d]
+@MVector [i for i in 1:2]
+@MVector ones(2)</code></pre><p>A convenience macro to construct <code>MVector</code>. See <a href="#StaticArrays.@SArray-Tuple{Any}"><code>@SArray</code></a> for detailed features.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/MVector.jl#L4-L11">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@SArray-Tuple{Any}" href="#StaticArrays.@SArray-Tuple{Any}"><code>StaticArrays.@SArray</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@SArray [a b; c d]
+@SArray [[a, b];[c, d]]
+@SArray [i+j for i in 1:2, j in 1:2]
+@SArray ones(2, 2, 2)</code></pre><p>A convenience macro to construct <code>SArray</code> with arbitrary dimension. It supports:</p><ol><li>(typed) array literals.</li></ol><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Every argument inside the square brackets is treated as a scalar during expansion. Thus <code>@SArray[a; b]</code> always forms a <code>SVector{2}</code> and <code>@SArray [a b; c]</code> always throws an error.</p></div></div><ol><li>comprehensions</li></ol><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>The range of a comprehension is evaluated at global scope by the macro, and must be made of combinations of literal values, functions, or global variables.</p></div></div><ol><li>initialization functions</li></ol><div class="admonition is-info"><header class="admonition-header">Note</header><div class="admonition-body"><p>Only support <code>zeros()</code>, <code>ones()</code>, <code>fill()</code>, <code>rand()</code>, <code>randn()</code>, and <code>randexp()</code></p></div></div></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SArray.jl#L298-L320">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@SMatrix-Tuple{Any}" href="#StaticArrays.@SMatrix-Tuple{Any}"><code>StaticArrays.@SMatrix</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@SMatrix [a b c d]
+@SMatrix [[a, b];[c, d]]
+@SMatrix [i+j for i in 1:2, j in 1:2]
+@SMatrix ones(2, 2)</code></pre><p>A convenience macro to construct <code>SMatrix</code>. See <a href="#StaticArrays.@SArray-Tuple{Any}"><code>@SArray</code></a> for detailed features.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SMatrix.jl#L139-L147">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArrays.@SVector-Tuple{Any}" href="#StaticArrays.@SVector-Tuple{Any}"><code>StaticArrays.@SVector</code></a> — <span class="docstring-category">Macro</span></header><section><div><pre><code class="language-julia hljs">@SVector [a, b, c, d]
+@SVector [i for i in 1:2]
+@SVector ones(2)</code></pre><p>A convenience macro to construct <code>SVector</code>. See <a href="#StaticArrays.@SArray-Tuple{Any}"><code>@SArray</code></a> for detailed features.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/c4092a1a8866313d0cc0d93f0bb870e5d82a2070/src/SVector.jl#L143-L150">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.Dynamic" href="#StaticArraysCore.Dynamic"><code>StaticArraysCore.Dynamic</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">Dynamic()</code></pre><p>Used to signify that a dimension of an array is not known statically.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L422-L426">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.FieldArray" href="#StaticArraysCore.FieldArray"><code>StaticArraysCore.FieldArray</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">abstract FieldArray{N, T, D} &lt;: StaticArray{N, T, D}</code></pre><p>Inheriting from this type will make it easy to create your own rank-D tensor types. A <code>FieldArray</code> will automatically define <code>getindex</code> and <code>setindex!</code> appropriately. An immutable <code>FieldArray</code> will be as performant as an <code>SArray</code> of similar length and element type, while a mutable <code>FieldArray</code> will behave similarly to an <code>MArray</code>.</p><p>Note that you must define the fields of any <code>FieldArray</code> subtype in column major order. If you want to use an alternative ordering you will need to pay special attention in providing your own definitions of <code>getindex</code>, <code>setindex!</code> and tuple conversion.</p><p>If you define a <code>FieldArray</code> which is parametric on the element type you should consider defining <code>similar_type</code> as in the <code>FieldVector</code> example.</p><p><strong>Example</strong></p><pre><code class="nohighlight hljs">struct Stiffness &lt;: FieldArray{Tuple{2,2,2,2}, Float64, 4}
+    xxxx::Float64
+    yxxx::Float64
+    xyxx::Float64
+    yyxx::Float64
+    xxyx::Float64
+    yxyx::Float64
+    xyyx::Float64
+    yyyx::Float64
+    xxxy::Float64
+    yxxy::Float64
+    xyxy::Float64
+    yyxy::Float64
+    xxyy::Float64
+    yxyy::Float64
+    xyyy::Float64
+    yyyy::Float64
+end</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L283-L319">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.FieldMatrix" href="#StaticArraysCore.FieldMatrix"><code>StaticArraysCore.FieldMatrix</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">abstract FieldMatrix{N1, N2, T} &lt;: FieldArray{Tuple{N1, N2}, 2}</code></pre><p>Inheriting from this type will make it easy to create your own rank-two tensor types. A <code>FieldMatrix</code> will automatically define <code>getindex</code> and <code>setindex!</code> appropriately. An immutable <code>FieldMatrix</code> will be as performant as an <code>SMatrix</code> of similar length and element type, while a mutable <code>FieldMatrix</code> will behave similarly to an <code>MMatrix</code>.</p><p>Note that the fields of any subtype of <code>FieldMatrix</code> must be defined in column major order unless you are willing to implement your own <code>getindex</code>.</p><p>If you define a <code>FieldMatrix</code> which is parametric on the element type you should consider defining <code>similar_type</code> as in the <code>FieldVector</code> example.</p><p><strong>Example</strong></p><pre><code class="nohighlight hljs">struct Stress &lt;: FieldMatrix{3, 3, Float64}
+    xx::Float64
+    yx::Float64
+    zx::Float64
+    xy::Float64
+    yy::Float64
+    zy::Float64
+    xz::Float64
+    yz::Float64
+    zz::Float64
+end</code></pre><p>Note that the fields of any subtype of <code>FieldMatrix</code> must be defined in column major order.  This means that formatting of constructors for literal <code>FieldMatrix</code> can be confusing. For example</p><pre><code class="nohighlight hljs">sigma = Stress(1.0, 2.0, 3.0,
+               4.0, 5.0, 6.0,
+               7.0, 8.0, 9.0)
+
+3×3 Stress:
+ 1.0  4.0  7.0
+ 2.0  5.0  8.0
+ 3.0  6.0  9.0</code></pre><p>will give you the transpose of what the multi-argument formatting suggests. For clarity, you may consider using the alternative</p><pre><code class="nohighlight hljs">sigma = Stress(SA[1.0 2.0 3.0;
+                  4.0 5.0 6.0;
+                  7.0 8.0 9.0])</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L322-L368">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.FieldVector" href="#StaticArraysCore.FieldVector"><code>StaticArraysCore.FieldVector</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">abstract FieldVector{N, T} &lt;: FieldArray{Tuple{N}, 1}</code></pre><p>Inheriting from this type will make it easy to create your own vector types. A <code>FieldVector</code> will automatically define <code>getindex</code> and <code>setindex!</code> appropriately. An immutable <code>FieldVector</code> will be as performant as an <code>SVector</code> of similar length and element type, while a mutable <code>FieldVector</code> will behave similarly to an <code>MVector</code>.</p><p>If you define a <code>FieldVector</code> which is parametric on the element type you should consider defining <code>similar_type</code> to preserve your array type through array operations as in the example below.</p><p><strong>Example</strong></p><pre><code class="nohighlight hljs">struct Vec3D{T} &lt;: FieldVector{3, T}
+    x::T
+    y::T
+    z::T
+end
+
+StaticArrays.similar_type(::Type{&lt;:Vec3D}, ::Type{T}, s::Size{(3,)}) where {T} = Vec3D{T}</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L371-L392">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.MArray" href="#StaticArraysCore.MArray"><code>StaticArraysCore.MArray</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">MArray{S, T, N, L}(undef)
+MArray{S, T, N, L}(x::NTuple{L})
+MArray{S, T, N, L}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized, mutable array <code>MArray</code>. The data may optionally be provided upon construction and can be mutated later. The <code>S</code> parameter is a Tuple-type specifying the dimensions, or size, of the array - such as <code>Tuple{3,4,5}</code> for a 3×4×5-sized array. The <code>N</code> parameter is the dimension of the array; the <code>L</code> parameter is the <code>length</code> of the array and is always equal to <code>prod(S)</code>. Constructors may drop the <code>L</code>, <code>N</code> and <code>T</code> parameters if they are inferrable from the input (e.g. <code>L</code> is always inferrable from <code>S</code>).</p><pre><code class="nohighlight hljs">MArray{S}(a::Array)</code></pre><p>Construct a statically-sized, mutable array of dimensions <code>S</code> (expressed as a <code>Tuple{...}</code>) using the data from <code>a</code>. The <code>S</code> parameter is mandatory since the size of <code>a</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L163-L181">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.MMatrix" href="#StaticArraysCore.MMatrix"><code>StaticArraysCore.MMatrix</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">MMatrix{S1, S2, T, L}(undef)
+MMatrix{S1, S2, T, L}(x::NTuple{L, T})
+MMatrix{S1, S2, T, L}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized, mutable matrix <code>MMatrix</code>. The data may optionally be provided upon construction and can be mutated later. The <code>L</code> parameter is the <code>length</code> of the array and is always equal to <code>S1 * S2</code>. Constructors may drop the <code>L</code>, <code>T</code> and even <code>S2</code> parameters if they are inferrable from the input (e.g. <code>L</code> is always inferrable from <code>S1</code> and <code>S2</code>).</p><pre><code class="nohighlight hljs">MMatrix{S1, S2}(mat::Matrix)</code></pre><p>Construct a statically-sized, mutable matrix of dimensions <code>S1 × S2</code> using the data from <code>mat</code>. The parameters <code>S1</code> and <code>S2</code> are mandatory since the size of <code>mat</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L221-L237">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.MVector" href="#StaticArraysCore.MVector"><code>StaticArraysCore.MVector</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">MVector{S,T}(undef)
+MVector{S,T}(x::NTuple{S, T})
+MVector{S,T}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized, mutable vector <code>MVector</code>. Data may optionally be provided upon construction, and can be mutated later. Constructors may drop the <code>T</code> and <code>S</code> parameters if they are inferrable from the input (e.g. <code>MVector(1,2,3)</code> constructs an <code>MVector{3, Int}</code>).</p><pre><code class="nohighlight hljs">MVector{S}(vec::Vector)</code></pre><p>Construct a statically-sized, mutable vector of length <code>S</code> using the data from <code>vec</code>. The parameter <code>S</code> is mandatory since the length of <code>vec</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L203-L218">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.SArray" href="#StaticArraysCore.SArray"><code>StaticArraysCore.SArray</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SArray{S, T, N, L}(x::NTuple{L})
+SArray{S, T, N, L}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized array <code>SArray</code>. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. The <code>S</code> parameter is a Tuple-type specifying the dimensions, or size, of the array - such as <code>Tuple{3,4,5}</code> for a 3×4×5-sized array. The <code>N</code> parameter is the dimension of the array; the <code>L</code> parameter is the <code>length</code> of the array and is always equal to <code>prod(S)</code>. Constructors may drop the <code>L</code>, <code>N</code> and <code>T</code> parameters if they are inferrable from the input (e.g. <code>L</code> is always inferrable from <code>S</code>).</p><pre><code class="nohighlight hljs">SArray{S}(a::Array)</code></pre><p>Construct a statically-sized array of dimensions <code>S</code> (expressed as a <code>Tuple{...}</code>) using the data from <code>a</code>. The <code>S</code> parameter is mandatory since the size of <code>a</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L93-L109">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.SMatrix" href="#StaticArraysCore.SMatrix"><code>StaticArraysCore.SMatrix</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SMatrix{S1, S2, T, L}(x::NTuple{L, T})
+SMatrix{S1, S2, T, L}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized matrix <code>SMatrix</code>. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. The <code>L</code> parameter is the <code>length</code> of the array and is always equal to <code>S1 * S2</code>. Constructors may drop the <code>L</code>, <code>T</code> and even <code>S2</code> parameters if they are inferrable from the input (e.g. <code>L</code> is always inferrable from <code>S1</code> and <code>S2</code>).</p><pre><code class="nohighlight hljs">SMatrix{S1, S2}(mat::Matrix)</code></pre><p>Construct a statically-sized matrix of dimensions <code>S1 × S2</code> using the data from <code>mat</code>. The parameters <code>S1</code> and <code>S2</code> are mandatory since the size of <code>mat</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L143-L158">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.SVector" href="#StaticArraysCore.SVector"><code>StaticArraysCore.SVector</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SVector{S, T}(x::NTuple{S, T})
+SVector{S, T}(x1, x2, x3, ...)</code></pre><p>Construct a statically-sized vector <code>SVector</code>. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. Constructors may drop the <code>T</code> and <code>S</code> parameters if they are inferrable from the input (e.g. <code>SVector(1,2,3)</code> constructs an <code>SVector{3, Int}</code>).</p><pre><code class="nohighlight hljs">SVector{S}(vec::Vector)</code></pre><p>Construct a statically-sized vector of length <code>S</code> using the data from <code>vec</code>. The parameter <code>S</code> is mandatory since the length of <code>vec</code> is unknown to the compiler (the element type may optionally also be specified).</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L126-L140">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.Size" href="#StaticArraysCore.Size"><code>StaticArraysCore.Size</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">Size(dims::Int...)</code></pre><p><code>Size</code> is used extensively throughout the <code>StaticArrays</code> API to describe <em>compile-time</em> knowledge of the size of an array. The dimensions are stored as a type parameter and are statically propagated by the compiler, resulting in efficient, type-inferrable code. For example, to create a static matrix of zeros, use <code>A = zeros(SMatrix{3,3})</code>. The static size of <code>A</code> can be obtained by <code>Size(A)</code>. (rather than <code>size(zeros(3,3))</code>, which returns <code>Base.Tuple{2,Int}</code>).</p><p>Note that if dimensions are not known statically (e.g., for standard <code>Array</code>s), <a href="#StaticArraysCore.Dynamic"><code>Dynamic()</code></a> should be used instead of an <code>Int</code>.</p><pre><code class="nohighlight hljs">Size(a::AbstractArray)
+Size(::Type{T&lt;:AbstractArray})</code></pre><p>The <code>Size</code> constructor can be used to extract static dimension information from a given array. For example:</p><pre><code class="language-julia-repl hljs">julia&gt; Size(zeros(SMatrix{3, 4}))
+Size(3, 4)
+
+julia&gt; Size(zeros(3, 4))
+Size(StaticArrays.Dynamic(), StaticArrays.Dynamic())</code></pre><p>This has multiple uses, including &quot;trait&quot;-based dispatch on the size of a statically-sized array. For example:</p><pre><code class="language-julia hljs">det(x::StaticMatrix) = _det(Size(x), x)
+_det(::Size{(1,1)}, x::StaticMatrix) = x[1,1]
+_det(::Size{(2,2)}, x::StaticMatrix) = x[1,1]*x[2,2] - x[1,2]*x[2,1]
+# and other definitions as necessary</code></pre></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L431-L468">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.SizedArray" href="#StaticArraysCore.SizedArray"><code>StaticArraysCore.SizedArray</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">SizedArray{Tuple{dims...}}(array)</code></pre><p>Wraps an <code>AbstractArray</code> with a static size, so to take advantage of the (faster) methods defined by the static array package. The size is checked once upon construction to determine if the number of elements (<code>length</code>) match, but the array may be reshaped.</p><p>The aliases <code>SizedVector{N}</code> and <code>SizedMatrix{N,M}</code> are provided as more convenient names for one and two dimensional <code>SizedArray</code>s. For example, to wrap a 2x3 array <code>a</code> in a <code>SizedArray</code>, use <code>SizedMatrix{2,3}(a)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L246-L257">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.StaticArray" href="#StaticArraysCore.StaticArray"><code>StaticArraysCore.StaticArray</code></a> — <span class="docstring-category">Type</span></header><section><div><pre><code class="language-julia hljs">abstract type StaticArray{S, T, N} &lt;: AbstractArray{T, N} end
+StaticScalar{T}     = StaticArray{Tuple{}, T, 0}
+StaticVector{N,T}   = StaticArray{Tuple{N}, T, 1}
+StaticMatrix{N,M,T} = StaticArray{Tuple{N,M}, T, 2}</code></pre><p><code>StaticArray</code>s are Julia arrays with fixed, known size.</p><p><strong>Dev docs</strong></p><p>They must define the following methods:</p><ul><li>Constructors that accept a flat tuple of data.</li><li><code>getindex()</code> with an integer (linear indexing) (preferably <code>@inline</code> with <code>@boundscheck</code>).</li><li><code>Tuple()</code>, returning the data in a flat Tuple.</li></ul><p>It may be useful to implement:</p><ul><li><code>similar_type(::Type{MyStaticArray}, ::Type{NewElType}, ::Size{NewSize})</code>, returning a type (or type constructor) that accepts a flat tuple of data.</li></ul><p>For mutable containers you may also need to define the following:</p><ul><li><code>setindex!</code> for a single element (linear indexing).</li><li><code>similar(::Type{MyStaticArray}, ::Type{NewElType}, ::Size{NewSize})</code>.</li><li>In some cases, a zero-parameter constructor, <code>MyStaticArray{...}()</code> for unintialized data is assumed to exist.</li></ul><p>(see also <code>SVector</code>, <code>SMatrix</code>, <code>SArray</code>, <code>MVector</code>, <code>MMatrix</code>, <code>MArray</code>, <code>SizedArray</code>, <code>FieldVector</code>, <code>FieldMatrix</code> and <code>FieldArray</code>)</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L9-L37">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.similar_type" href="#StaticArraysCore.similar_type"><code>StaticArraysCore.similar_type</code></a> — <span class="docstring-category">Function</span></header><section><div><pre><code class="language-julia hljs">similar_type(static_array)
+similar_type(static_array, T)
+similar_type(array, ::Size)
+similar_type(array, T, ::Size)</code></pre><p>Returns a constructor for a statically-sized array similar to the input array (or type) <code>static_array</code>/<code>array</code>, optionally with different element type <code>T</code> or size <code>Size</code>. If the input <code>array</code> is not a <code>StaticArray</code> then the <code>Size</code> is mandatory.</p><p>This differs from <code>similar()</code> in that the resulting array type may not be mutable (or define <code>setindex!()</code>), and therefore the returned type may need to be <em>constructed</em> with its data.</p><p>Note that the (optional) size <em>must</em> be specified as a static <code>Size</code> object (so the compiler can infer the result statically).</p><p>New types should define the signature <code>similar_type(::Type{A},::Type{T},::Size{S}) where {A&lt;:MyType,T,S}</code> if they wish to overload the default behavior.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L400-L419">source</a></section></article><article class="docstring"><header><a class="docstring-article-toggle-button fa-solid fa-chevron-down" href="javascript:;" title="Collapse docstring"></a><a class="docstring-binding" id="StaticArraysCore.size_to_tuple-Union{Tuple{Type{T}}, Tuple{T}} where T&lt;:Tuple" href="#StaticArraysCore.size_to_tuple-Union{Tuple{Type{T}}, Tuple{T}} where T&lt;:Tuple"><code>StaticArraysCore.size_to_tuple</code></a> — <span class="docstring-category">Method</span></header><section><div><pre><code class="language-julia hljs">size_to_tuple(::Type{S}) where S&lt;:Tuple</code></pre><p>Converts a size given by <code>Tuple{N, M, ...}</code> into a tuple <code>(N, M, ...)</code>.</p></div><a class="docs-sourcelink" target="_blank" href="https://github.com/JuliaArrays/StaticArraysCore.jl/blob/v1.4.2/src/StaticArraysCore.jl#L63-L67">source</a></section></article></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../../">« Home</a><a class="docs-footer-nextpage" href="../quickstart/">Quick Start »</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><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> version 1.4.1 on <span class="colophon-date" title="Thursday 16 May 2024 17:37">Thursday 16 May 2024</span>. Using Julia version 1.6.7.</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>Quick Start · StaticArrays.jl</title><meta name="title" content="Quick Start · StaticArrays.jl"/><meta property="og:title" content="Quick Start · StaticArrays.jl"/><meta property="twitter:title" content="Quick Start · StaticArrays.jl"/><meta name="description" content="Documentation for StaticArrays.jl."/><meta property="og:description" content="Documentation for StaticArrays.jl."/><meta property="twitter:description" content="Documentation for StaticArrays.jl."/><meta property="og:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/quickstart/"/><meta property="twitter:url" content="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/quickstart/"/><link rel="canonical" href="https://JuliaArrays.github.io/StaticArrays.jl/stable/pages/quickstart/"/><script data-outdated-warner src="../../assets/warner.js"></script><link href="https://cdnjs.cloudflare.com/ajax/libs/lato-font/3.0.0/css/lato-font.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/juliamono/0.050/juliamono.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/fontawesome.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/solid.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/font-awesome/6.4.2/css/brands.min.css" rel="stylesheet" type="text/css"/><link href="https://cdnjs.cloudflare.com/ajax/libs/KaTeX/0.16.8/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="../../search_index.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" data-theme-primary-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><link href="../../assets/favicon.ico" rel="icon" type="image/x-icon"/></head><body><div id="documenter"><nav class="docs-sidebar"><div class="docs-package-name"><span class="docs-autofit"><a href="../../">StaticArrays.jl</a></span></div><button class="docs-search-query input is-rounded is-small is-clickable my-2 mx-auto py-1 px-2" id="documenter-search-query">Search docs (Ctrl + /)</button><ul class="docs-menu"><li><a class="tocitem" href="../../">Home</a></li><li><a class="tocitem" href="../api/">API</a></li><li class="is-active"><a class="tocitem" href>Quick Start</a></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"><a class="docs-sidebar-button docs-navbar-link fa-solid fa-bars is-hidden-desktop" id="documenter-sidebar-button" href="#"></a><nav class="breadcrumb"><ul class="is-hidden-mobile"><li class="is-active"><a href>Quick Start</a></li></ul><ul class="is-hidden-tablet"><li class="is-active"><a href>Quick Start</a></li></ul></nav><div class="docs-right"><a class="docs-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl" title="View the repository on GitHub"><span class="docs-icon fa-brands"></span><span class="docs-label is-hidden-touch">GitHub</span></a><a class="docs-navbar-link" href="https://github.com/JuliaArrays/StaticArrays.jl/blob/master/docs/src/pages/quickstart.md" title="Edit source on GitHub"><span class="docs-icon fa-solid"></span></a><a class="docs-settings-button docs-navbar-link fa-solid fa-gear" id="documenter-settings-button" href="#" title="Settings"></a><a class="docs-article-toggle-button fa-solid fa-chevron-up" id="documenter-article-toggle-button" href="javascript:;" title="Collapse all docstrings"></a></div></header><article class="content" id="documenter-page"><h1 id="Quick-Start"><a class="docs-heading-anchor" href="#Quick-Start">Quick Start</a><a id="Quick-Start-1"></a><a class="docs-heading-anchor-permalink" href="#Quick-Start" title="Permalink"></a></h1><pre><code class="language-julia hljs">Pkg.add(&quot;StaticArrays&quot;)  # or Pkg.clone(&quot;https://github.com/JuliaArrays/StaticArrays.jl&quot;)
+using StaticArrays
+using LinearAlgebra
+
+# Use the convenience constructor type `SA` to create vectors and matrices
+SA[1, 2, 3]     isa SVector{3,Int}
+SA_F64[1, 2, 3] isa SVector{3,Float64}
+SA_F32[1, 2, 3] isa SVector{3,Float32}
+SA[1 2; 3 4]     isa SMatrix{2,2,Int}
+SA_F64[1 2; 3 4] isa SMatrix{2,2,Float64}
+
+# Create an SVector using various forms, using constructors, functions or macros
+v1 = SVector(1, 2, 3)
+v1.data === (1, 2, 3) # SVector uses a tuple for internal storage
+v2 = SVector{3,Float64}(1, 2, 3) # length 3, eltype Float64
+v3 = @SVector [1, 2, 3]
+v4 = @SVector [i^2 for i = 1:10] # arbitrary comprehensions (range is evaluated at global scope)
+v5 = zeros(SVector{3}) # defaults to Float64
+v6 = @SVector zeros(3)
+v7 = SVector{3}([1, 2, 3]) # Array conversions must specify size
+
+# Can get size() from instance or type
+size(v1) == (3,)
+size(typeof(v1)) == (3,)
+
+# Similar constructor syntax for matrices
+m1 = SMatrix{2,2}(1, 2, 3, 4) # flat, column-major storage, equal to m2:
+m2 = @SMatrix [ 1  3 ;
+                2  4 ]
+m3 = SMatrix{3,3}(1I)
+m4 = @SMatrix randn(4,4)
+m5 = SMatrix{2,2}([1 3 ; 2 4]) # Array conversions must specify size
+
+# Higher-dimensional support
+a = @SArray randn(2, 2, 2, 2, 2, 2)
+
+# Supports all the common operations of AbstractArray
+v7 = v1 + v2
+v8 = sin.(v3)
+v3 == m3 * v3 # recall that m3 = SMatrix{3,3}(1I)
+# map, reduce, broadcast, map!, broadcast!, etc...
+
+# Indexing can also be done using static arrays of integers
+v1[1] === 1
+v1[SVector(3,2,1)] === @SVector [3, 2, 1]
+v1[:] === v1
+typeof(v1[[1,2,3]]) &lt;: Vector # Can&#39;t determine size from the type of [1,2,3]
+
+# For geometric and computer graphics applications in dimensions 1 to 4, the
+# conventional dimension names x,y,z,w can be used to access elements of the
+# vector:
+
+u = SA[1,2,3,4]
+
+u.x === u[1]
+u.y === u[2]
+u.z === u[3]
+u.w === u[4]
+
+# The x,y,z and w properties also work to set values in those dimensions:
+m6 = MVector(1,2)
+m6.x = 10
+# The following is now true
+m6[1] === 10
+
+# Is (partially) hooked into BLAS, LAPACK, etc:
+rand(MMatrix{20,20}) * rand(MMatrix{20,20}) # large matrices can use BLAS
+eigen(m3) # eigen(), etc uses specialized algorithms up to 3×3, or else LAPACK
+
+# Static arrays stay statically sized, even when used by Base functions, etc:
+typeof(eigen(m3)) == Eigen{Float64,Float64,SArray{Tuple{3,3},Float64,2,9},SArray{Tuple{3},Float64,1,3}}
+
+# similar() returns a mutable container, while similar_type() returns a constructor:
+typeof(similar(m3)) == MArray{Tuple{3,3},Int64,2,9} # (final parameter is length = 9)
+similar_type(m3) == SArray{Tuple{3,3},Int64,2,9}
+
+# The Size trait is a compile-time constant representing the size
+Size(m3) === Size(3,3)
+
+# A standard Array can be wrapped into a SizedArray
+m4 = SizedMatrix{3,3}(rand(3,3))
+inv(m4) # Take advantage of specialized fast methods
+
+# reshape() uses Size() or types to specify size:
+reshape([1,2,3,4], Size(2,2)) == @SMatrix [ 1  3 ;
+                                            2  4 ]
+typeof(reshape([1,2,3,4], Size(2,2))) === SizedArray{Tuple{2, 2},Int64,2,1}
+</code></pre></article><nav class="docs-footer"><a class="docs-footer-prevpage" href="../api/">« API</a><div class="flexbox-break"></div><p class="footer-message">Powered by <a href="https://github.com/JuliaDocs/Documenter.jl">Documenter.jl</a> and the <a href="https://julialang.org/">Julia Programming Language</a>.</p></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="auto">Automatic (OS)</option><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> version 1.4.1 on <span class="colophon-date" title="Thursday 16 May 2024 17:37">Thursday 16 May 2024</span>. Using Julia version 1.6.7.</p></section><footer class="modal-card-foot"></footer></div></div></div></body></html>
diff --git a/v1.9.4/search_index.js b/v1.9.4/search_index.js
new file mode 100644
index 00000000..4a87b06f
--- /dev/null
+++ b/v1.9.4/search_index.js
@@ -0,0 +1,3 @@
+var documenterSearchIndex = {"docs":
+[{"location":"pages/api/#API","page":"API","title":"API","text":"","category":"section"},{"location":"pages/api/#Guide","page":"API","title":"Guide","text":"","category":"section"},{"location":"pages/api/#SVector","page":"API","title":"SVector","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"The simplest static array is the type SVector{N,T}, which provides an immutable vector of fixed length N and type T.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"SVector defines a series of convenience constructors, so you can just type e.g. SVector(1,2,3). Alternatively there is an intelligent @SVector macro where you can use native Julia array literals syntax, comprehensions, and the zeros(), ones(), fill(), rand() and randn() functions, such as @SVector [1,2,3], @SVector Float64[1,2,3], @SVector [f(i) for i = 1:10], @SVector zeros(3), @SVector randn(Float32, 4), etc (Note: the range of a comprehension is evaluated at global scope by the macro, and must be made of combinations of literal values, functions, or global variables, but is not limited to just simple ranges. Extending this to (hopefully statically known by type-inference) local-scope variables is hoped for the future. The zeros(), ones(), fill(), rand(), randn(), and randexp() functions do not have this limitation.)","category":"page"},{"location":"pages/api/#SMatrix","page":"API","title":"SMatrix","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Statically sized N×M matrices are provided by SMatrix{N,M,T,L}.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Here L is the length of the matrix, such that N × M = L. However, convenience constructors are provided, so that L, T and even M are unnecessary. At minimum, you can type SMatrix{2}(1,2,3,4) to create a 2×2 matrix (the total number of elements must divide evenly into N). A convenience macro @SMatrix [1 2; 3 4] is provided (which also accepts comprehensions and the zeros(), ones(), fill(), rand(), randn(), and randexp() functions).","category":"page"},{"location":"pages/api/#SArray","page":"API","title":"SArray","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"A container with arbitrarily many dimensions is defined as struct SArray{Size,T,N,L} <: StaticArray{Size,T,N}, where Size = Tuple{S1, S2, ...} is a tuple of Ints. You can easily construct one with the @SArray macro, supporting all the features of @SVector and @SMatrix (but with arbitrary dimension).","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"The main reason SVector and SMatrix are defined is to make it easier to define the types without the extra tuple characters (compare SVector{3} to SArray{Tuple{3}}).","category":"page"},{"location":"pages/api/#Scalar","page":"API","title":"Scalar","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Sometimes you want to broadcast an operation, but not over one of your inputs. A classic example is attempting to displace a collection of vectors by the same vector. We can now do this with the Scalar type:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"[[1,2,3], [4,5,6]] .+ Scalar([1,0,-1]) # [[2,2,2], [5,5,5]]","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Scalar is simply an implementation of an immutable, 0-dimensional StaticArray.","category":"page"},{"location":"pages/api/#The-Size-trait","page":"API","title":"The Size trait","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"The size of a statically sized array is a static parameter associated with the type of the array. The Size trait is provided as an abstract representation of the dimensions of a static array. An array sa::SA of size (dims...) is associated with Size{(dims...)}(). The following are equivalent constructors:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Size{(dims...,)}()\nSize(dims...)\nSize(sa::StaticArray)\nSize(SA) # SA <: StaticArray","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"This is extremely useful for (a) performing dispatch depending on the size of an array, and (b) passing array dimensions that the compiler can reason about.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"An example of size-based dispatch for the determinant of a matrix would be:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"det(x::StaticMatrix) = _det(Size(x), x)\n_det(::Size{(1,1)}, x::StaticMatrix) = x[1,1]\n_det(::Size{(2,2)}, x::StaticMatrix) = x[1,1]*x[2,2] - x[1,2]*x[2,1]\n# and other definitions as necessary","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Examples of using Size as a compile-time constant include","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"reshape(svector, Size(2,2))  # Convert SVector{4} to SMatrix{2,2}\nSizedMatrix{3,3}(rand(3,3))  # Construct a random 3×3 SizedArray (see below)","category":"page"},{"location":"pages/api/#Indexing","page":"API","title":"Indexing","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Statically sized indexing can be realized by indexing each dimension by a scalar, a StaticVector or :. Indexing in this way will result a statically sized array (even if the input was dynamically sized, in the case of StaticVector indices) of the closest type (as defined by similar_type).","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Conversely, indexing a statically sized array with a dynamically sized index (such as a Vector{Integer} or UnitRange{Integer}) will result in a standard (dynamically sized) Array.","category":"page"},{"location":"pages/api/#similar_type()","page":"API","title":"similar_type()","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Since immutable arrays need to be constructed \"all-at-once\", we need a way of obtaining an appropriate constructor if the element type or dimensions of the output array differs from the input. To this end, similar_type is introduced, behaving just like similar, except that it returns a type. Relevant methods are:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"similar_type(::Type{A}) where {A <: StaticArray} # defaults to A\nsimilar_type(::Type{A}, ::Type{ElType}) where {A <: StaticArray, ElType} # Change element type\nsimilar_type(::Type{A}, size::Size) where {A <: AbstractArray} # Change size\nsimilar_type(::Type{A}, ::Type{ElType}, size::Size) where {A <: AbstractArray, ElType} # Change both","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"These setting will affect everything, from indexing, to matrix multiplication and broadcast. Users wanting introduce a new array type should only overload the last method in the above.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Use of similar will fall back to a mutable container, such as a MVector (see below), and it requires use of the Size trait if you wish to set a new static size (or else a dynamically sized Array will be generated when specifying the size as plain integers).","category":"page"},{"location":"pages/api/#Collecting-directly-into-static-arrays","page":"API","title":"Collecting directly into static arrays","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"You can collect iterators into static arrays directly with StaticArrays.sacollect. The size needs to be specified, but the element type is optional.","category":"page"},{"location":"pages/api/#Mutable-arrays:-MVector,-MMatrix-and-MArray","page":"API","title":"Mutable arrays: MVector, MMatrix and MArray","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"These statically sized arrays are identical to the above, but are defined as mutable structs, instead of immutable structs. Because they are mutable, they allow setindex! to be defined (achieved through pointer manipulation, into a tuple).","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"As a consequence of Julia's internal implementation, these mutable containers live on the heap, not the stack. Their memory must be allocated and tracked by the garbage collector. Nevertheless, there is opportunity for speed improvements relative to Base.Array because (a) there may be one less pointer indirection, (b) their (typically small) static size allows for additional loop unrolling and inlining, and consequentially (c) their mutating methods like map! are extremely fast. Benchmarking shows that operations such as addition and matrix multiplication are faster for MMatrix than Matrix, at least for sizes up to 14 × 14, though keep in mind that optimal speed will be obtained by using mutating functions (like map! or A_mul_B!) where possible, rather than reallocating new memory.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Mutable static arrays also happen to be very useful containers that can be constructed on the heap (with the ability to use setindex!, etc), and later copied as e.g. an immutable SVector to the stack for use, or into e.g. an Array{SVector} for storage.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Convenience macros @MVector, @MMatrix and @MArray are provided.","category":"page"},{"location":"pages/api/#SizedArray:-a-decorate-size-wrapper-for-Array","page":"API","title":"SizedArray: a decorate size wrapper for Array","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Another convenient mutable type is the SizedArray, which is just a wrapper-type about a standard Julia Array which declares its known size. For example, if we knew that a was a 2×2 Matrix, then we can type sa = SizedArray{Tuple{2,2}}(a) to construct a new object which knows the type (the size will be verified automatically). For one and two dimensions, a more convenient syntax for obtaining a SizedArray is by using the SizedMatrix and SizedVector aliases, e.g. sa = SizedMatrix{2,2}(a).","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Then, methods on sa will use the specialized code provided by the StaticArrays package, which in many cases will be much, much faster. For example, calling eigen(sa) will be significantly faster than eigen(a) since it will perform a specialized 2×2 matrix diagonalization rather than a general algorithm provided by Julia and LAPACK.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"In some cases it will make more sense to use a SizedArray, and in other cases an MArray might be preferable.","category":"page"},{"location":"pages/api/#FieldVector","page":"API","title":"FieldVector","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Sometimes it is useful to give your own struct types the properties of a vector. StaticArrays can take care of this for you by allowing you to inherit from FieldVector{N, T}. For example, consider:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"struct Point3D <: FieldVector{3, Float64}\n    x::Float64\n    y::Float64\n    z::Float64\nend","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"With this type, users can easily access fields to p = Point3D(x,y,z) using p.x, p.y or p.z, or alternatively via p[1], p[2], or p[3]. You may even permute the coordinates with p[SVector(3,2,1)]). Furthermore, Point3D is a complete AbstractVector implementation where you can add, subtract or scale vectors, multiply them by matrices, etc.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Note: the three components of an ordinary v::SVector{3} can also be accessed as v.x, v.y, and v.z, so there is no need for a FieldVector to use this convention.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"It is also worth noting that FieldVectors may be mutable or immutable, and that setindex! is defined for use on mutable types. For immutable containers, you may want to define a method for similar_type so that operations leave the type constant (otherwise they may fall back to SVector). For mutable containers, you may want to define a default constructor (no inputs) and an appropriate method for similar,","category":"page"},{"location":"pages/api/#Implementing-your-own-types","page":"API","title":"Implementing your own types","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"You can easily create your own StaticArray type, by defining linear getindex (and optionally setindex! for mutable types –- see setindex!(::MArray, val, i) in MArray.jl for an example of how to achieve this through pointer manipulation). Your type should define a constructor that takes a tuple of the data (and mutable containers may want to define a default constructor).","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Other useful functions to overload may be similar_type (and similar for mutable containers).","category":"page"},{"location":"pages/api/#Conversions-from-Array","page":"API","title":"Conversions from Array","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"In order to convert from a dynamically sized AbstractArray to one of the statically sized array types, you must specify the size explicitly.  For example,","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"v = [1,2]\n\nm = [1 2;\n     3 4]\n\n# ... a lot of intervening code\n\nsv = SVector{2}(v)\nsm = SMatrix{2,2}(m)\nsa = SArray{Tuple{2,2}}(m)\n\nsized_v = SizedVector{2}(v)\nsized_m = SizedMatrix{2,2}(m)","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"We have avoided adding SVector(v::AbstractVector) as a valid constructor to help users avoid the type instability (and potential performance disaster, if used without care) of this innocuous looking expression.","category":"page"},{"location":"pages/api/#Arrays-of-static-arrays","page":"API","title":"Arrays of static arrays","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Storing a large number of static arrays is convenient as an array of static arrays. For example, a collection of positions (3D coordinates –- SVector{3,Float64}) could be represented as a Vector{SVector{3,Float64}}.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Another common way of storing the same data is as a 3×N Matrix{Float64}. Rather conveniently, such types have exactly the same binary layout in memory, and therefore we can use reinterpret to convert between the two formats","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"function svectors(x::Matrix{T}, ::Val{N}) where {T,N}\n    size(x,1) == N || error(\"sizes mismatch\")\n    isbitstype(T) || error(\"use for bitstypes only\")\n    reinterpret(SVector{N,T}, vec(x))\nend","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Such a conversion does not copy the data, rather it refers to the same memory. Arguably, a Vector of SVectors is often preferable to a Matrix because it provides a better abstraction of the objects contained in the array and it allows the fast StaticArrays methods to act on elements.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"However, the resulting object is a Base.ReinterpretArray, not an Array, which carries some runtime penalty on every single access. If you can afford the memory for a copy and can live with the non-shared mutation semantics, then it is better to pull a copy by e.g.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"function svectorscopy(x::Matrix{T}, ::Val{N}) where {T,N}\n    size(x,1) == N || error(\"sizes mismatch\")\n    isbitstype(T) || error(\"use for bitstypes only\")\n    copy(reinterpret(SVector{N,T}, vec(x)))\nend","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"For example:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"julia> M=reshape(collect(1:6), (2,3))\n2×3 Array{Int64,2}:\n 1  3  5\n 2  4  6\n\njulia> svectors(M, Val{2}())\n3-element reinterpret(SArray{Tuple{2},Int64,1,2}, ::Array{Int64,1}):\n [1, 2]\n [3, 4]\n [5, 6]\n\njulia> svectorscopy(M, Val{2}())\n3-element Array{SArray{Tuple{2},Int64,1,2},1}:\n [1, 2]\n [3, 4]\n [5, 6]","category":"page"},{"location":"pages/api/#Working-with-mutable-and-immutable-arrays","page":"API","title":"Working with mutable and immutable arrays","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Generally, it is performant to rebind an immutable array, such as","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"function average_position(positions::Vector{SVector{3,Float64}})\n    x = zeros(SVector{3,Float64})\n    for pos ∈ positions\n        x = x + pos\n    end\n    return x / length(positions)\nend","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"so long as the Type of the rebound variable (x, above) does not change.","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"On the other hand, the above code for mutable containers like Array, MArray or SizedArray is not very efficient. Mutable containers must be allocated and later garbage collected, and for small, fixed-size arrays this can be a leading contribution to the cost. In the above code, a new array will be instantiated and allocated on each iteration of the loop. In order to avoid unnecessary allocations, it is best to allocate an array only once and apply mutating functions to it:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"function average_position(positions::Vector{SVector{3,Float64}})\n    x = zeros(MVector{3,Float64})\n    for pos ∈ positions\n        x .+= pos\n    end\n    x ./= length(positions)\n    return x\nend","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"The functions setindex, push, pop, pushfirst, popfirst, insert and deleteat are provided for performing certain specific operations on static arrays, in analogy with the standard functions setindex!, push!, pop!, etc. (Note that if the size of the static array changes, the type of the output will differ from the input.)","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"When building static arrays iteratively, it is usually efficient to build up an MArray first and then convert. The allocation will be elided by recent Julia compilers, resulting in very efficient code:","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"function standard_basis_vector(T, ::Val{I}, ::Val{N}) where {I,N}\n    v = zero(MVector{N,T})\n    v[I] = one(T)\n    SVector(v)\nend","category":"page"},{"location":"pages/api/#SIMD-optimizations","page":"API","title":"SIMD optimizations","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"It seems Julia and LLVM are smart enough to use processor vectorization extensions like SSE and AVX - however they are currently partially disabled by default. Run Julia with julia -O or julia -O3 to enable these optimizations, and many of your (immutable) StaticArray methods should become significantly faster!","category":"page"},{"location":"pages/api/#Docstrings","page":"API","title":"Docstrings","text":"","category":"section"},{"location":"pages/api/","page":"API","title":"API","text":"Pages   = [\"api.md\"]","category":"page"},{"location":"pages/api/","page":"API","title":"API","text":"Modules = [StaticArrays, StaticArraysCore]","category":"page"},{"location":"pages/api/#StaticArrays.StaticMatMulLike","page":"API","title":"StaticArrays.StaticMatMulLike","text":"StaticMatMulLike\n\nStatic wrappers used for multiplication dispatch.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.Args","page":"API","title":"StaticArrays.Args","text":"Args\n\nA help wrapper to distinguish SA(x...) and SA((x...,))\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.SA","page":"API","title":"StaticArrays.SA","text":"SA[ elements ]\nSA{T}[ elements ]\n\nCreate SArray literals using array construction syntax. The element type is inferred by promoting elements to a common type or set to T when T is provided explicitly.\n\nExamples:\n\nSA[1.0, 2.0] creates a length-2 SVector of Float64 elements.\nSA[1 2; 3 4] creates a 2×2 SMatrix of Ints.\nSA[1 2] creates a 1×2 SMatrix of Ints.\nSA{Float32}[1, 2] creates a length-2 SVector of Float32 elements.\n\nA couple of helpful type aliases are also provided:\n\nSA_F64[1, 2] creates a length-2 SVector of Float64 elements\nSA_F32[1, 2] creates a length-2 SVector of Float32 elements\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.SHermitianCompact","page":"API","title":"StaticArrays.SHermitianCompact","text":"SHermitianCompact{N, T, L} <: StaticMatrix{N, N, T}\n\nA StaticArray subtype that represents a Hermitian matrix. Unlike LinearAlgebra.Hermitian, SHermitianCompact stores only the lower triangle of the matrix (as an SVector). The lower triangle is stored in column-major order. For example, for an SHermitianCompact{3}, the indices of the stored elements can be visualized as follows:\n\n┌ 1 ⋅ ⋅ ┐\n| 2 4 ⋅ |\n└ 3 5 6 ┘\n\nType parameters:\n\nN: matrix dimension;\nT: element type for lower triangle;\nL: length of the SVector storing the lower triangular elements.\n\nNote that L is always the Nth triangular number.\n\nAn SHermitianCompact may be constructed either:\n\nfrom an AbstractVector containing the lower triangular elements; or\nfrom a Tuple containing both upper and lower triangular elements in column major order; or\nfrom another StaticMatrix.\n\nFor the latter two cases, only the lower triangular elements are used; the upper triangular elements are ignored.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.SOneTo","page":"API","title":"StaticArrays.SOneTo","text":"SOneTo(n)\n\nReturn a statically-sized AbstractUnitRange starting at 1, functioning as the axes of a StaticArray.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.Scalar","page":"API","title":"StaticArrays.Scalar","text":"Scalar{T}(x::T)\n\nConstruct a statically-sized 0-dimensional array that contains a single element, x. This type is particularly useful for influencing broadcasting operations.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays.TSize","page":"API","title":"StaticArrays.TSize","text":"Size that stores whether a Matrix is a Transpose Useful when selecting multiplication methods, and avoiding allocations when dealing with the Transpose type by passing around the original matrix. Should pair with parent.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArrays._InitialValue","page":"API","title":"StaticArrays._InitialValue","text":"_InitialValue\n\nA singleton type for representing \"universal\" initial value (identity element).\n\nThe idea is that, given op for mapfoldl, virtually, we define an \"extended\" version of it by\n\nop′(::_InitialValue, x) = x\nop′(acc, x) = op(acc, x)\n\nThis is just a conceptually useful model to have in mind and we don't actually define op′ here  (yet?).  But see Base.BottomRF for how it might work in action.\n\n(It is related to that you can always turn a semigroup without an identity into a monoid by \"adjoining\" an element that acts as the identity.)\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#Base.setindex-Tuple{StaticArray, Any, Int64}","page":"API","title":"Base.setindex","text":"setindex(vec::StaticArray, x, index::Int)\n\nReturn a new array with the item at index replaced by x.\n\nExamples\n\njulia> setindex(@SVector[1,2,3], 4, 2)\n3-element SVector{3, Int64} with indices SOneTo(3):\n 1\n 4\n 3\n\njulia> setindex(@SMatrix[2 4; 6 8], 1, 2)\n2×2 SMatrix{2, 2, Int64, 4} with indices SOneTo(2)×SOneTo(2):\n 2  4\n 1  8\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#Base.similar-Tuple{SA} where SA<:StaticArray","page":"API","title":"Base.similar","text":"similar(static_array)\nsimilar(static_array, T)\nsimilar(array, ::Size)\nsimilar(array, T, ::Size)\n\nConstructs and returns a mutable but statically-sized array (i.e. a StaticArray). If the input array is not a StaticArray, then the Size is required to determine the output size (or else a dynamically sized array will be returned).\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#LinearAlgebra.qr-Tuple{StaticArray{Tuple{N, M}, T, 2} where {N, M, T}}","page":"API","title":"LinearAlgebra.qr","text":"qr(A::StaticMatrix,\n   pivot::Union{Val{true}, Val{false}, LinearAlgebra.PivotingStrategy} = Val(false))\n\nCompute the QR factorization of A. The factors can be obtained by iteration:\n\njulia> A = @SMatrix rand(3,4);\n\njulia> Q, R = qr(A);\n\njulia> Q * R ≈ A\ntrue\n\nor by using getfield:\n\njulia> F = qr(A);\n\njulia> F.Q * F.R ≈ A\ntrue\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays._construct_similar-Union{Tuple{ET}, Tuple{L}, Tuple{Any, Size, Tuple{ET, Vararg{ET, L}}}} where {L, ET}","page":"API","title":"StaticArrays._construct_similar","text":"_construct_similar(a, ::Size, elements::NTuple)\n\nConstruct a static array of similar type to a with the given elements.\n\nWhen a is an instance or a concrete type the element type eltype(a) is used. However, when a is a UnionAll type such as SMatrix{2,2}, the promoted type of elements is used instead.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays._lind-Union{Tuple{tA}, Tuple{sa}, Tuple{Symbol, Type{StaticArrays.TSize{sa, tA}}, Int64, Int64}} where {sa, tA}","page":"API","title":"StaticArrays._lind","text":"Obtain an expression for the linear index of var[k,j], taking transposes into account\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays._muladd_expr-Tuple{Array{Expr, N} where N, Array{Expr, N} where N, Type{var\"#s24\"} where var\"#s24\"<:StaticArrays.AlphaBeta}","page":"API","title":"StaticArrays._muladd_expr","text":"Combine left and right sides of an assignment expression, short-cutting         lhs = α * rhs + β * lhs,     element-wise. If α = 1, the multiplication by α is removed. If β = 0, the second rhs term is removed.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays._size-Tuple{Any}","page":"API","title":"StaticArrays._size","text":"Return either the statically known Size() or runtime size()\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.arithmetic_closure-Union{Tuple{Type{T}}, Tuple{T}} where T","page":"API","title":"StaticArrays.arithmetic_closure","text":"arithmetic_closure(T)\n\nReturn the type which values of type T will promote to under a combination of the arithmetic operations +, -, * and /.\n\njulia> import StaticArrays.arithmetic_closure\n\njulia> arithmetic_closure(Bool)\nFloat64\n\njulia> arithmetic_closure(Int32)\nFloat64\n\njulia> arithmetic_closure(BigFloat)\nBigFloat\n\njulia> arithmetic_closure(BigInt)\nBigFloat\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.check_dims-Union{Tuple{sc}, Tuple{sb}, Tuple{sa}, Tuple{Size{sc}, Size{sa}, Size{sb}}} where {sa, sb, sc}","page":"API","title":"StaticArrays.check_dims","text":"Validate the dimensions of a matrix multiplication, including matrix-vector products\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.construct_type-Union{Tuple{SA}, Tuple{Type{SA}, Any}} where SA<:StaticArray","page":"API","title":"StaticArrays.construct_type","text":"SA′ = construct_type(::Type{SA}, x) where {SA<:StaticArray}\n\nPick a proper constructor SA′ based on x if SA(x)/SA(x...) has no specific definition. The default returned SA′ is SA itself for user defined StaticArrays. This differs from  similar_type() in that SA′ should always be a subtype of SA.\n\nnote: Note\nTo distinguish SA(x...) and SA(x::Tuple), the former calls  construct_type(SA, StaticArrays.Args(x)) instead of construct_type(SA, x).\n\nnote: Note\nPlease make sure SA'(x) has a specific definition if the default behavior is overloaded.  Otherwise construction might fall into infinite recursion.\n\n\n\nThe adaption rules for official StaticArrays could be summarized as:\n\nSA <: FieldArray: eltype adaptable\n\nFieldArrays are always static-sized. We only derive SA′'s eltype using type promotion if needed.\n\nSA <: Union{SArray, MArray, SHermitianCompact, SizedArray}: size/eltype adaptable\n\nSA(x::Tuple)\n\nIf SA is fully static-sized, then we first try to fill SA with x's elements.  If failed and length(SA) == 1, then we try to fill SA with x itself.\n\nIf SA is not fully static-sized, then we always try to fill SA with x's elements,  and the constructor's Size is derived based on:\n\nIf SA <: StaticVector, then we use length(x) as the output Length \nIf SA <: StaticMatrix{M}, then we use (M, N) (N = length(x) ÷ M) as the output Size\nIf SA <: StaticMatrix{M,M} where M, then we use (N, N) (N = sqrt(length(x)) as the output Size.\n\nSA(x...)\n\nSimilar to Tuple, but we never fill SA with x itself.\n\nSA(x::StaticArray)\n\nWe treat x as Tuple whenever possible. If failed, then try to inherit x's Size.\n\nSA(x::AbstractArray)\n\nx is used to provide eltype. Thus SA must be static sized.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.deleteat-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}","page":"API","title":"StaticArrays.deleteat","text":"deleteat(vec::StaticVector, index::Integer)\n\nReturn a new vector with the item at the given index removed.\n\nExamples\n\njulia> deleteat(@SVector[6, 5, 4, 3, 2, 1], 2)\n5-element SVector{5, Int64} with indices SOneTo(5):\n 6\n 4\n 3\n 2\n 1\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.dimmatch","page":"API","title":"StaticArrays.dimmatch","text":"dimmatch(x::StaticDimension, y::StaticDimension)\n\nReturn whether dimensions x and y match at compile time, that is:\n\nif x and y are both Ints, check that they are equal\nif x or y are Dynamic(), return true\n\n\n\n\n\n","category":"function"},{"location":"pages/api/#StaticArrays.gen_by_access","page":"API","title":"StaticArrays.gen_by_access","text":"gen_by_access(expr_gen, a::Type{<:AbstractArray}, asym = :wrapped_a)\n\nStatically generate outer code for fully unrolled multiplication loops. Returned code does wrapper-specific tests (for example if a symmetric matrix view is U or L) and the body of the if expression is then generated by function expr_gen. The function expr_gen receives access pattern description symbol as its argument and this symbol is then consumed by uplo_access to generate the right code for matrix element access.\n\nThe name of the matrix to test is indicated by asym.\n\n\n\n\n\n","category":"function"},{"location":"pages/api/#StaticArrays.gen_by_access-Tuple{Any, Type{var\"#s24\"} where var\"#s24\"<:(StaticArray{Tuple{N, M}, T, 2} where {N, M, T}), Type}","page":"API","title":"StaticArrays.gen_by_access","text":"gen_by_access(expr_gen, a::Type{<:AbstractArray}, b::Type{<:AbstractArray})\n\nSimilar to genbyaccess with only one type argument. The difference is that tests for both arrays of type a and b are generated and expr_gen receives two access arguments, first for matrix a and the second for matrix b.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.insert-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any, Any}","page":"API","title":"StaticArrays.insert","text":"insert(vec::StaticVector, index::Integer, item)\n\nReturn a new vector with item inserted into vec at the given index.\n\nExamples\n\njulia> insert(@SVector[6, 5, 4, 2, 1], 4, 3)\n6-element SVector{6, Int64} with indices SOneTo(6):\n 6\n 5\n 4\n 3\n 2\n 1\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.mul_result_structure-Tuple{Any, Any}","page":"API","title":"StaticArrays.mul_result_structure","text":"mul_result_structure(a::Type, b::Type)\n\nGet a structure wrapper that should be applied to the result of multiplication of matrices of given types (a*b). \n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.multiplied_dimension-Tuple{Type{var\"#s23\"} where var\"#s23\"<:(Union{LinearAlgebra.Adjoint{T, var\"#s5\"} where var\"#s5\"<:Union{StaticArray{Tuple{var\"#s2\"}, T, 1} where var\"#s2\", StaticArray{Tuple{var\"#s3\", var\"#s4\"}, T, 2} where {var\"#s3\", var\"#s4\"}}, LinearAlgebra.Diagonal{T, var\"#s12\"} where var\"#s12\"<:(StaticArray{Tuple{var\"#s13\"}, T, 1} where var\"#s13\"), LinearAlgebra.Hermitian{T, var\"#s9\"} where var\"#s9\"<:(StaticArray{Tuple{var\"#s10\", var\"#s11\"}, T, 2} where {var\"#s10\", var\"#s11\"}), LinearAlgebra.LowerTriangular{T, var\"#s17\"} where var\"#s17\"<:(StaticArray{Tuple{var\"#s18\", var\"#s19\"}, T, 2} where {var\"#s18\", var\"#s19\"}), LinearAlgebra.Symmetric{T, var\"#s6\"} where var\"#s6\"<:(StaticArray{Tuple{var\"#s7\", var\"#s8\"}, T, 2} where {var\"#s7\", var\"#s8\"}), LinearAlgebra.Transpose{T, var\"#s4\"} where var\"#s4\"<:Union{StaticArray{Tuple{var\"#s2\"}, T, 1} where var\"#s2\", StaticArray{Tuple{var\"#s3\", var\"#s4\"}, T, 2} where {var\"#s3\", var\"#s4\"}}, LinearAlgebra.UnitLowerTriangular{T, var\"#s23\"} where var\"#s23\"<:(StaticArray{Tuple{var\"#s24\", var\"#s25\"}, T, 2} where {var\"#s24\", var\"#s25\"}), LinearAlgebra.UnitUpperTriangular{T, var\"#s20\"} where var\"#s20\"<:(StaticArray{Tuple{var\"#s21\", var\"#s22\"}, T, 2} where {var\"#s21\", var\"#s22\"}), LinearAlgebra.UpperTriangular{T, var\"#s14\"} where var\"#s14\"<:(StaticArray{Tuple{var\"#s15\", var\"#s16\"}, T, 2} where {var\"#s15\", var\"#s16\"}), StaticArray{Tuple{var\"#s25\"}, T, 1} where var\"#s25\", StaticArray{Tuple{var\"#s1\", var\"#s3\"}, T, 2} where {var\"#s1\", var\"#s3\"}} where T), Type{var\"#s22\"} where var\"#s22\"<:(Union{LinearAlgebra.Adjoint{T, var\"#s5\"} where var\"#s5\"<:Union{StaticArray{Tuple{var\"#s2\"}, T, 1} where var\"#s2\", StaticArray{Tuple{var\"#s3\", var\"#s4\"}, T, 2} where {var\"#s3\", var\"#s4\"}}, LinearAlgebra.Diagonal{T, var\"#s12\"} where var\"#s12\"<:(StaticArray{Tuple{var\"#s13\"}, T, 1} where var\"#s13\"), LinearAlgebra.Hermitian{T, var\"#s9\"} where var\"#s9\"<:(StaticArray{Tuple{var\"#s10\", var\"#s11\"}, T, 2} where {var\"#s10\", var\"#s11\"}), LinearAlgebra.LowerTriangular{T, var\"#s17\"} where var\"#s17\"<:(StaticArray{Tuple{var\"#s18\", var\"#s19\"}, T, 2} where {var\"#s18\", var\"#s19\"}), LinearAlgebra.Symmetric{T, var\"#s6\"} where var\"#s6\"<:(StaticArray{Tuple{var\"#s7\", var\"#s8\"}, T, 2} where {var\"#s7\", var\"#s8\"}), LinearAlgebra.Transpose{T, var\"#s4\"} where var\"#s4\"<:Union{StaticArray{Tuple{var\"#s2\"}, T, 1} where var\"#s2\", StaticArray{Tuple{var\"#s3\", var\"#s4\"}, T, 2} where {var\"#s3\", var\"#s4\"}}, LinearAlgebra.UnitLowerTriangular{T, var\"#s23\"} where var\"#s23\"<:(StaticArray{Tuple{var\"#s24\", var\"#s25\"}, T, 2} where {var\"#s24\", var\"#s25\"}), LinearAlgebra.UnitUpperTriangular{T, var\"#s20\"} where var\"#s20\"<:(StaticArray{Tuple{var\"#s21\", var\"#s22\"}, T, 2} where {var\"#s21\", var\"#s22\"}), LinearAlgebra.UpperTriangular{T, var\"#s14\"} where var\"#s14\"<:(StaticArray{Tuple{var\"#s15\", var\"#s16\"}, T, 2} where {var\"#s15\", var\"#s16\"}), StaticArray{Tuple{var\"#s25\"}, T, 1} where var\"#s25\", StaticArray{Tuple{var\"#s1\", var\"#s3\"}, T, 2} where {var\"#s1\", var\"#s3\"}} where T)}","page":"API","title":"StaticArrays.multiplied_dimension","text":"Calculate the product of the dimensions being multiplied. Useful as a heuristic for unrolling.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.pop-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}","page":"API","title":"StaticArrays.pop","text":"pop(vec::StaticVector)\n\nReturn a new vector with the last item in vec removed.\n\nExamples\n\njulia> pop(@SVector[1,2,3])\n2-element SVector{2, Int64} with indices SOneTo(2):\n 1\n 2\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.popfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}}","page":"API","title":"StaticArrays.popfirst","text":"popfirst(vec::StaticVector)\n\nReturn a new vector with the first item in vec removed.\n\nExamples\n\njulia> popfirst(@SVector[1,2,3])\n2-element SVector{2, Int64} with indices SOneTo(2):\n 2\n 3\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.push-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}","page":"API","title":"StaticArrays.push","text":"push(vec::StaticVector, item)\n\nReturn a new StaticVector with item inserted on the end of vec.\n\nExamples\n\njulia> push(@SVector[1, 2, 3], 4)\n4-element SVector{4, Int64} with indices SOneTo(4):\n 1\n 2\n 3\n 4\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.pushfirst-Tuple{StaticArray{Tuple{N}, T, 1} where {N, T}, Any}","page":"API","title":"StaticArrays.pushfirst","text":"pushfirst(vec::StaticVector, item)\n\nReturn a new StaticVector with item inserted at the beginning of vec.\n\nExamples\n\njulia> pushfirst(@SVector[1, 2, 3, 4], 5)\n5-element SVector{5, Int64} with indices SOneTo(5):\n 5\n 1\n 2\n 3\n 4\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.sacollect","page":"API","title":"StaticArrays.sacollect","text":"sacollect(SA, gen)\n\nConstruct a statically-sized vector of type SA.from a generator gen. SA needs to have a size parameter since the length of vec is unknown to the compiler. SA can optionally specify the element type as well.\n\nExample:\n\nsacollect(SVector{3, Int}, 2i+1 for i in 1:3)\nsacollect(SMatrix{2, 3}, i+j for i in 1:2, j in 1:3)\nsacollect(SArray{2, 3}, i+j for i in 1:2, j in 1:3)\n\nThis creates the same statically-sized vector as if the generator were collected in an array, but is more efficient since no array is allocated.\n\nEquivalent:\n\nSVector{3, Int}([2i+1 for i in 1:3])\n\n\n\n\n\n","category":"function"},{"location":"pages/api/#StaticArrays.same_size-Tuple","page":"API","title":"StaticArrays.same_size","text":"Returns the common Size of the inputs (or else throws a DimensionMismatch)\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.sizematch-Union{Tuple{S2}, Tuple{S1}, Tuple{Size{S1}, Size{S2}}} where {S1, S2}","page":"API","title":"StaticArrays.sizematch","text":"sizematch(::Size, ::Size)\nsizematch(::Tuple, ::Tuple)\n\nDetermine whether two sizes match, in the sense that they have the same number of dimensions, and their dimensions match as determined by dimmatch.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.sizematch-Union{Tuple{S}, Tuple{Size{S}, StaticArray}} where S","page":"API","title":"StaticArrays.sizematch","text":"sizematch(::Size, A::AbstractArray)\n\nDetermine whether array A matches the given size. If A is a StaticArray, the check is performed at compile time, otherwise, the check is performed at runtime.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.uplo_access-NTuple{5, Any}","page":"API","title":"StaticArrays.uplo_access","text":"uplo_access(sa, asym, k, j, uplo)\n\nGenerate code for matrix element access, for a matrix of size sa locally referred to as asym in the context where the result will be used. Both indices k and j need to be statically known for this function to work. uplo is the access pattern mode generated by the gen_by_access function.\n\n\n\n\n\n","category":"method"},{"location":"pages/api/#StaticArrays.@MArray-Tuple{Any}","page":"API","title":"StaticArrays.@MArray","text":"@MArray [a b; c d]\n@MArray [[a, b];[c, d]]\n@MArray [i+j for i in 1:2, j in 1:2]\n@MArray ones(2, 2, 2)\n\nA convenience macro to construct MArray with arbitrary dimension. See @SArray for detailed features.\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArrays.@MMatrix-Tuple{Any}","page":"API","title":"StaticArrays.@MMatrix","text":"@MMatrix [a b c d]\n@MMatrix [[a, b];[c, d]]\n@MMatrix [i+j for i in 1:2, j in 1:2]\n@MMatrix ones(2, 2)\n\nA convenience macro to construct MMatrix. See @SArray for detailed features.\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArrays.@MVector-Tuple{Any}","page":"API","title":"StaticArrays.@MVector","text":"@MVector [a, b, c, d]\n@MVector [i for i in 1:2]\n@MVector ones(2)\n\nA convenience macro to construct MVector. See @SArray for detailed features.\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArrays.@SArray-Tuple{Any}","page":"API","title":"StaticArrays.@SArray","text":"@SArray [a b; c d]\n@SArray [[a, b];[c, d]]\n@SArray [i+j for i in 1:2, j in 1:2]\n@SArray ones(2, 2, 2)\n\nA convenience macro to construct SArray with arbitrary dimension. It supports:\n\n(typed) array literals.\n\nnote: Note\nEvery argument inside the square brackets is treated as a scalar during expansion. Thus @SArray[a; b] always forms a SVector{2} and @SArray [a b; c] always throws an error.\n\ncomprehensions\n\nnote: Note\nThe range of a comprehension is evaluated at global scope by the macro, and must be made of combinations of literal values, functions, or global variables.\n\ninitialization functions\n\nnote: Note\nOnly support zeros(), ones(), fill(), rand(), randn(), and randexp()\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArrays.@SMatrix-Tuple{Any}","page":"API","title":"StaticArrays.@SMatrix","text":"@SMatrix [a b c d]\n@SMatrix [[a, b];[c, d]]\n@SMatrix [i+j for i in 1:2, j in 1:2]\n@SMatrix ones(2, 2)\n\nA convenience macro to construct SMatrix. See @SArray for detailed features.\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArrays.@SVector-Tuple{Any}","page":"API","title":"StaticArrays.@SVector","text":"@SVector [a, b, c, d]\n@SVector [i for i in 1:2]\n@SVector ones(2)\n\nA convenience macro to construct SVector. See @SArray for detailed features.\n\n\n\n\n\n","category":"macro"},{"location":"pages/api/#StaticArraysCore.Dynamic","page":"API","title":"StaticArraysCore.Dynamic","text":"Dynamic()\n\nUsed to signify that a dimension of an array is not known statically.\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.FieldArray","page":"API","title":"StaticArraysCore.FieldArray","text":"abstract FieldArray{N, T, D} <: StaticArray{N, T, D}\n\nInheriting from this type will make it easy to create your own rank-D tensor types. A FieldArray will automatically define getindex and setindex! appropriately. An immutable FieldArray will be as performant as an SArray of similar length and element type, while a mutable FieldArray will behave similarly to an MArray.\n\nNote that you must define the fields of any FieldArray subtype in column major order. If you want to use an alternative ordering you will need to pay special attention in providing your own definitions of getindex, setindex! and tuple conversion.\n\nIf you define a FieldArray which is parametric on the element type you should consider defining similar_type as in the FieldVector example.\n\nExample\n\nstruct Stiffness <: FieldArray{Tuple{2,2,2,2}, Float64, 4}\n    xxxx::Float64\n    yxxx::Float64\n    xyxx::Float64\n    yyxx::Float64\n    xxyx::Float64\n    yxyx::Float64\n    xyyx::Float64\n    yyyx::Float64\n    xxxy::Float64\n    yxxy::Float64\n    xyxy::Float64\n    yyxy::Float64\n    xxyy::Float64\n    yxyy::Float64\n    xyyy::Float64\n    yyyy::Float64\nend\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.FieldMatrix","page":"API","title":"StaticArraysCore.FieldMatrix","text":"abstract FieldMatrix{N1, N2, T} <: FieldArray{Tuple{N1, N2}, 2}\n\nInheriting from this type will make it easy to create your own rank-two tensor types. A FieldMatrix will automatically define getindex and setindex! appropriately. An immutable FieldMatrix will be as performant as an SMatrix of similar length and element type, while a mutable FieldMatrix will behave similarly to an MMatrix.\n\nNote that the fields of any subtype of FieldMatrix must be defined in column major order unless you are willing to implement your own getindex.\n\nIf you define a FieldMatrix which is parametric on the element type you should consider defining similar_type as in the FieldVector example.\n\nExample\n\nstruct Stress <: FieldMatrix{3, 3, Float64}\n    xx::Float64\n    yx::Float64\n    zx::Float64\n    xy::Float64\n    yy::Float64\n    zy::Float64\n    xz::Float64\n    yz::Float64\n    zz::Float64\nend\n\nNote that the fields of any subtype of FieldMatrix must be defined in column major order.  This means that formatting of constructors for literal FieldMatrix can be confusing. For example\n\nsigma = Stress(1.0, 2.0, 3.0,\n               4.0, 5.0, 6.0,\n               7.0, 8.0, 9.0)\n\n3×3 Stress:\n 1.0  4.0  7.0\n 2.0  5.0  8.0\n 3.0  6.0  9.0\n\nwill give you the transpose of what the multi-argument formatting suggests. For clarity, you may consider using the alternative\n\nsigma = Stress(SA[1.0 2.0 3.0;\n                  4.0 5.0 6.0;\n                  7.0 8.0 9.0])\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.FieldVector","page":"API","title":"StaticArraysCore.FieldVector","text":"abstract FieldVector{N, T} <: FieldArray{Tuple{N}, 1}\n\nInheriting from this type will make it easy to create your own vector types. A FieldVector will automatically define getindex and setindex! appropriately. An immutable FieldVector will be as performant as an SVector of similar length and element type, while a mutable FieldVector will behave similarly to an MVector.\n\nIf you define a FieldVector which is parametric on the element type you should consider defining similar_type to preserve your array type through array operations as in the example below.\n\nExample\n\nstruct Vec3D{T} <: FieldVector{3, T}\n    x::T\n    y::T\n    z::T\nend\n\nStaticArrays.similar_type(::Type{<:Vec3D}, ::Type{T}, s::Size{(3,)}) where {T} = Vec3D{T}\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.MArray","page":"API","title":"StaticArraysCore.MArray","text":"MArray{S, T, N, L}(undef)\nMArray{S, T, N, L}(x::NTuple{L})\nMArray{S, T, N, L}(x1, x2, x3, ...)\n\nConstruct a statically-sized, mutable array MArray. The data may optionally be provided upon construction and can be mutated later. The S parameter is a Tuple-type specifying the dimensions, or size, of the array - such as Tuple{3,4,5} for a 3×4×5-sized array. The N parameter is the dimension of the array; the L parameter is the length of the array and is always equal to prod(S). Constructors may drop the L, N and T parameters if they are inferrable from the input (e.g. L is always inferrable from S).\n\nMArray{S}(a::Array)\n\nConstruct a statically-sized, mutable array of dimensions S (expressed as a Tuple{...}) using the data from a. The S parameter is mandatory since the size of a is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.MMatrix","page":"API","title":"StaticArraysCore.MMatrix","text":"MMatrix{S1, S2, T, L}(undef)\nMMatrix{S1, S2, T, L}(x::NTuple{L, T})\nMMatrix{S1, S2, T, L}(x1, x2, x3, ...)\n\nConstruct a statically-sized, mutable matrix MMatrix. The data may optionally be provided upon construction and can be mutated later. The L parameter is the length of the array and is always equal to S1 * S2. Constructors may drop the L, T and even S2 parameters if they are inferrable from the input (e.g. L is always inferrable from S1 and S2).\n\nMMatrix{S1, S2}(mat::Matrix)\n\nConstruct a statically-sized, mutable matrix of dimensions S1 × S2 using the data from mat. The parameters S1 and S2 are mandatory since the size of mat is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.MVector","page":"API","title":"StaticArraysCore.MVector","text":"MVector{S,T}(undef)\nMVector{S,T}(x::NTuple{S, T})\nMVector{S,T}(x1, x2, x3, ...)\n\nConstruct a statically-sized, mutable vector MVector. Data may optionally be provided upon construction, and can be mutated later. Constructors may drop the T and S parameters if they are inferrable from the input (e.g. MVector(1,2,3) constructs an MVector{3, Int}).\n\nMVector{S}(vec::Vector)\n\nConstruct a statically-sized, mutable vector of length S using the data from vec. The parameter S is mandatory since the length of vec is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.SArray","page":"API","title":"StaticArraysCore.SArray","text":"SArray{S, T, N, L}(x::NTuple{L})\nSArray{S, T, N, L}(x1, x2, x3, ...)\n\nConstruct a statically-sized array SArray. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. The S parameter is a Tuple-type specifying the dimensions, or size, of the array - such as Tuple{3,4,5} for a 3×4×5-sized array. The N parameter is the dimension of the array; the L parameter is the length of the array and is always equal to prod(S). Constructors may drop the L, N and T parameters if they are inferrable from the input (e.g. L is always inferrable from S).\n\nSArray{S}(a::Array)\n\nConstruct a statically-sized array of dimensions S (expressed as a Tuple{...}) using the data from a. The S parameter is mandatory since the size of a is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.SMatrix","page":"API","title":"StaticArraysCore.SMatrix","text":"SMatrix{S1, S2, T, L}(x::NTuple{L, T})\nSMatrix{S1, S2, T, L}(x1, x2, x3, ...)\n\nConstruct a statically-sized matrix SMatrix. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. The L parameter is the length of the array and is always equal to S1 * S2. Constructors may drop the L, T and even S2 parameters if they are inferrable from the input (e.g. L is always inferrable from S1 and S2).\n\nSMatrix{S1, S2}(mat::Matrix)\n\nConstruct a statically-sized matrix of dimensions S1 × S2 using the data from mat. The parameters S1 and S2 are mandatory since the size of mat is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.SVector","page":"API","title":"StaticArraysCore.SVector","text":"SVector{S, T}(x::NTuple{S, T})\nSVector{S, T}(x1, x2, x3, ...)\n\nConstruct a statically-sized vector SVector. Since this type is immutable, the data must be provided upon construction and cannot be mutated later. Constructors may drop the T and S parameters if they are inferrable from the input (e.g. SVector(1,2,3) constructs an SVector{3, Int}).\n\nSVector{S}(vec::Vector)\n\nConstruct a statically-sized vector of length S using the data from vec. The parameter S is mandatory since the length of vec is unknown to the compiler (the element type may optionally also be specified).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.Size","page":"API","title":"StaticArraysCore.Size","text":"Size(dims::Int...)\n\nSize is used extensively throughout the StaticArrays API to describe compile-time knowledge of the size of an array. The dimensions are stored as a type parameter and are statically propagated by the compiler, resulting in efficient, type-inferrable code. For example, to create a static matrix of zeros, use A = zeros(SMatrix{3,3}). The static size of A can be obtained by Size(A). (rather than size(zeros(3,3)), which returns Base.Tuple{2,Int}).\n\nNote that if dimensions are not known statically (e.g., for standard Arrays), Dynamic() should be used instead of an Int.\n\nSize(a::AbstractArray)\nSize(::Type{T<:AbstractArray})\n\nThe Size constructor can be used to extract static dimension information from a given array. For example:\n\njulia> Size(zeros(SMatrix{3, 4}))\nSize(3, 4)\n\njulia> Size(zeros(3, 4))\nSize(StaticArrays.Dynamic(), StaticArrays.Dynamic())\n\nThis has multiple uses, including \"trait\"-based dispatch on the size of a statically-sized array. For example:\n\ndet(x::StaticMatrix) = _det(Size(x), x)\n_det(::Size{(1,1)}, x::StaticMatrix) = x[1,1]\n_det(::Size{(2,2)}, x::StaticMatrix) = x[1,1]*x[2,2] - x[1,2]*x[2,1]\n# and other definitions as necessary\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.SizedArray","page":"API","title":"StaticArraysCore.SizedArray","text":"SizedArray{Tuple{dims...}}(array)\n\nWraps an AbstractArray with a static size, so to take advantage of the (faster) methods defined by the static array package. The size is checked once upon construction to determine if the number of elements (length) match, but the array may be reshaped.\n\nThe aliases SizedVector{N} and SizedMatrix{N,M} are provided as more convenient names for one and two dimensional SizedArrays. For example, to wrap a 2x3 array a in a SizedArray, use SizedMatrix{2,3}(a).\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.StaticArray","page":"API","title":"StaticArraysCore.StaticArray","text":"abstract type StaticArray{S, T, N} <: AbstractArray{T, N} end\nStaticScalar{T}     = StaticArray{Tuple{}, T, 0}\nStaticVector{N,T}   = StaticArray{Tuple{N}, T, 1}\nStaticMatrix{N,M,T} = StaticArray{Tuple{N,M}, T, 2}\n\nStaticArrays are Julia arrays with fixed, known size.\n\nDev docs\n\nThey must define the following methods:\n\nConstructors that accept a flat tuple of data.\ngetindex() with an integer (linear indexing) (preferably @inline with @boundscheck).\nTuple(), returning the data in a flat Tuple.\n\nIt may be useful to implement:\n\nsimilar_type(::Type{MyStaticArray}, ::Type{NewElType}, ::Size{NewSize}), returning a type (or type constructor) that accepts a flat tuple of data.\n\nFor mutable containers you may also need to define the following:\n\nsetindex! for a single element (linear indexing).\nsimilar(::Type{MyStaticArray}, ::Type{NewElType}, ::Size{NewSize}).\nIn some cases, a zero-parameter constructor, MyStaticArray{...}() for unintialized data is assumed to exist.\n\n(see also SVector, SMatrix, SArray, MVector, MMatrix, MArray, SizedArray, FieldVector, FieldMatrix and FieldArray)\n\n\n\n\n\n","category":"type"},{"location":"pages/api/#StaticArraysCore.similar_type","page":"API","title":"StaticArraysCore.similar_type","text":"similar_type(static_array)\nsimilar_type(static_array, T)\nsimilar_type(array, ::Size)\nsimilar_type(array, T, ::Size)\n\nReturns a constructor for a statically-sized array similar to the input array (or type) static_array/array, optionally with different element type T or size Size. If the input array is not a StaticArray then the Size is mandatory.\n\nThis differs from similar() in that the resulting array type may not be mutable (or define setindex!()), and therefore the returned type may need to be constructed with its data.\n\nNote that the (optional) size must be specified as a static Size object (so the compiler can infer the result statically).\n\nNew types should define the signature similar_type(::Type{A},::Type{T},::Size{S}) where {A<:MyType,T,S} if they wish to overload the default behavior.\n\n\n\n\n\n","category":"function"},{"location":"pages/api/#StaticArraysCore.size_to_tuple-Union{Tuple{Type{T}}, Tuple{T}} where T<:Tuple","page":"API","title":"StaticArraysCore.size_to_tuple","text":"size_to_tuple(::Type{S}) where S<:Tuple\n\nConverts a size given by Tuple{N, M, ...} into a tuple (N, M, ...).\n\n\n\n\n\n","category":"method"},{"location":"pages/quickstart/#Quick-Start","page":"Quick Start","title":"Quick Start","text":"","category":"section"},{"location":"pages/quickstart/","page":"Quick Start","title":"Quick Start","text":"Pkg.add(\"StaticArrays\")  # or Pkg.clone(\"https://github.com/JuliaArrays/StaticArrays.jl\")\nusing StaticArrays\nusing LinearAlgebra\n\n# Use the convenience constructor type `SA` to create vectors and matrices\nSA[1, 2, 3]     isa SVector{3,Int}\nSA_F64[1, 2, 3] isa SVector{3,Float64}\nSA_F32[1, 2, 3] isa SVector{3,Float32}\nSA[1 2; 3 4]     isa SMatrix{2,2,Int}\nSA_F64[1 2; 3 4] isa SMatrix{2,2,Float64}\n\n# Create an SVector using various forms, using constructors, functions or macros\nv1 = SVector(1, 2, 3)\nv1.data === (1, 2, 3) # SVector uses a tuple for internal storage\nv2 = SVector{3,Float64}(1, 2, 3) # length 3, eltype Float64\nv3 = @SVector [1, 2, 3]\nv4 = @SVector [i^2 for i = 1:10] # arbitrary comprehensions (range is evaluated at global scope)\nv5 = zeros(SVector{3}) # defaults to Float64\nv6 = @SVector zeros(3)\nv7 = SVector{3}([1, 2, 3]) # Array conversions must specify size\n\n# Can get size() from instance or type\nsize(v1) == (3,)\nsize(typeof(v1)) == (3,)\n\n# Similar constructor syntax for matrices\nm1 = SMatrix{2,2}(1, 2, 3, 4) # flat, column-major storage, equal to m2:\nm2 = @SMatrix [ 1  3 ;\n                2  4 ]\nm3 = SMatrix{3,3}(1I)\nm4 = @SMatrix randn(4,4)\nm5 = SMatrix{2,2}([1 3 ; 2 4]) # Array conversions must specify size\n\n# Higher-dimensional support\na = @SArray randn(2, 2, 2, 2, 2, 2)\n\n# Supports all the common operations of AbstractArray\nv7 = v1 + v2\nv8 = sin.(v3)\nv3 == m3 * v3 # recall that m3 = SMatrix{3,3}(1I)\n# map, reduce, broadcast, map!, broadcast!, etc...\n\n# Indexing can also be done using static arrays of integers\nv1[1] === 1\nv1[SVector(3,2,1)] === @SVector [3, 2, 1]\nv1[:] === v1\ntypeof(v1[[1,2,3]]) <: Vector # Can't determine size from the type of [1,2,3]\n\n# For geometric and computer graphics applications in dimensions 1 to 4, the\n# conventional dimension names x,y,z,w can be used to access elements of the\n# vector:\n\nu = SA[1,2,3,4]\n\nu.x === u[1]\nu.y === u[2]\nu.z === u[3]\nu.w === u[4]\n\n# The x,y,z and w properties also work to set values in those dimensions:\nm6 = MVector(1,2)\nm6.x = 10\n# The following is now true\nm6[1] === 10\n\n# Is (partially) hooked into BLAS, LAPACK, etc:\nrand(MMatrix{20,20}) * rand(MMatrix{20,20}) # large matrices can use BLAS\neigen(m3) # eigen(), etc uses specialized algorithms up to 3×3, or else LAPACK\n\n# Static arrays stay statically sized, even when used by Base functions, etc:\ntypeof(eigen(m3)) == Eigen{Float64,Float64,SArray{Tuple{3,3},Float64,2,9},SArray{Tuple{3},Float64,1,3}}\n\n# similar() returns a mutable container, while similar_type() returns a constructor:\ntypeof(similar(m3)) == MArray{Tuple{3,3},Int64,2,9} # (final parameter is length = 9)\nsimilar_type(m3) == SArray{Tuple{3,3},Int64,2,9}\n\n# The Size trait is a compile-time constant representing the size\nSize(m3) === Size(3,3)\n\n# A standard Array can be wrapped into a SizedArray\nm4 = SizedMatrix{3,3}(rand(3,3))\ninv(m4) # Take advantage of specialized fast methods\n\n# reshape() uses Size() or types to specify size:\nreshape([1,2,3,4], Size(2,2)) == @SMatrix [ 1  3 ;\n                                            2  4 ]\ntypeof(reshape([1,2,3,4], Size(2,2))) === SizedArray{Tuple{2, 2},Int64,2,1}\n","category":"page"},{"location":"#Static-Arrays","page":"Home","title":"Static Arrays","text":"","category":"section"},{"location":"","page":"Home","title":"Home","text":"Statically sized arrays for Julia","category":"page"},{"location":"","page":"Home","title":"Home","text":"StaticArrays provides a framework for implementing statically sized arrays in Julia, using the abstract type StaticArray{Size,T,N} <: AbstractArray{T,N}. Subtypes of StaticArray will provide fast implementations of common array and linear algebra operations. Note that here \"statically sized\" means that the size can be determined from the type, and \"static\" does not necessarily imply immutable.","category":"page"},{"location":"","page":"Home","title":"Home","text":"The package also provides some concrete static array types: SVector, SMatrix and SArray, which may be used as-is (or else embedded in your own type). Mutable versions MVector, MMatrix and MArray are also exported, as well as SizedArray for annotating standard Arrays with static size information. Further, the abstract FieldVector can be used to make fast static vectors out of any uniform Julia \"struct\".","category":"page"}]
+}
diff --git a/v1.9.4/siteinfo.js b/v1.9.4/siteinfo.js
new file mode 100644
index 00000000..dd71dbc0
--- /dev/null
+++ b/v1.9.4/siteinfo.js
@@ -0,0 +1 @@
+var DOCUMENTER_CURRENT_VERSION = "v1.9.4";
diff --git a/versions.js b/versions.js
index 4a9fc1dd..209b2bf4 100644
--- a/versions.js
+++ b/versions.js
@@ -17,5 +17,5 @@ var DOC_VERSIONS = [
   "v0.6",
   "dev",
 ];
-var DOCUMENTER_NEWEST = "v1.9.3";
+var DOCUMENTER_NEWEST = "v1.9.4";
 var DOCUMENTER_STABLE = "stable";