From 716ac773a6d0918a42bfd4336e94ef16f8ac5514 Mon Sep 17 00:00:00 2001 From: GenerateMe Date: Fri, 29 Sep 2023 14:13:37 +0200 Subject: [PATCH] linear optimization --- CHANGELOG.md | 1 + README.md | 2 +- docs/fastmath.clustering.html | 78 ++-- docs/fastmath.complex.html | 118 ++--- docs/fastmath.core.html | 593 +++++++++++++------------ docs/fastmath.curves.html | 2 +- docs/fastmath.distance.html | 2 +- docs/fastmath.easings.html | 2 +- docs/fastmath.efloat.html | 6 +- docs/fastmath.fields.html | 130 +++--- docs/fastmath.gp.html | 82 ++-- docs/fastmath.grid.html | 2 +- docs/fastmath.interpolation.html | 63 +-- docs/fastmath.kernel.html | 46 +- docs/fastmath.matrix.html | 201 +++++---- docs/fastmath.optimization.html | 140 +++--- docs/fastmath.optimization.lbfgsb.html | 4 +- docs/fastmath.protocols.html | 19 +- docs/fastmath.protocols.matrix.html | 2 +- docs/fastmath.quaternion.html | 43 ++ docs/fastmath.random.html | 221 ++++----- docs/fastmath.signal.html | 12 +- docs/fastmath.solver.html | 5 +- docs/fastmath.stats.bootstrap.html | 24 +- docs/fastmath.stats.html | 170 +++---- docs/fastmath.transform.html | 4 +- docs/fastmath.vector.html | 294 ++++++------ docs/index.html | 18 +- src/fastmath/optimization.clj | 123 ++++- test/fastmath/optimization_test.clj | 28 ++ 30 files changed, 1320 insertions(+), 1115 deletions(-) create mode 100644 docs/fastmath.quaternion.html create mode 100644 test/fastmath/optimization_test.clj diff --git a/CHANGELOG.md b/CHANGELOG.md index 0694002a..dc4e64ed 100755 --- a/CHANGELOG.md +++ b/CHANGELOG.md @@ -14,6 +14,7 @@ All notable changes to this project will be documented in this file. This change * `fastmath.quaternion` namespace * Cholesky decomposition for fixed size matrices * `negative-zero?` tests for `-0.0` value +* `linear-optimizer` - linear optimization ### Changed diff --git a/README.md b/README.md index a47831f5..8451d868 100644 --- a/README.md +++ b/README.md @@ -168,7 +168,7 @@ Various clustering algorithms including K-Means++, DBSCAN, CLARANS, DENCLUE, MEC ### Optimization -L-BFGS-B, Gradient, Nelder-Mead, Simplex, Powell, BOBYQA, CMAES, BayesianOptimizer +L-BFGS-B, Gradient, Nelder-Mead, Simplex, Powell, BOBYQA, CMAES, BayesianOptimizer, Linear optimizer ### Grids diff --git a/docs/fastmath.clustering.html b/docs/fastmath.clustering.html index 6dc179ea..dd7268e2 100644 --- a/docs/fastmath.clustering.html +++ b/docs/fastmath.clustering.html @@ -1,6 +1,6 @@ -fastmath.clustering documentation

Project

Namespaces

Public Vars

fastmath.clustering

Clustering.

+fastmath.clustering documentation

Project

Namespaces

Public Vars

fastmath.clustering

Clustering.

Various clustering algrorithms backed by SMILE library.

Only partition clustering is implemented.

Input data

@@ -58,9 +58,9 @@

Regrouping

:data :clustering :obj :predict) ;;=> {:clusters 2, -;;=> :info {:distortion 11522.0}, -;;=> :representatives ((1.0) (124.0)), -;;=> :sizes (106 894 0), +;;=> :info {:distortion 11442.0}, +;;=> :representatives ((1.0) (125.0)), +;;=> :sizes (109 891 0), ;;=> :type :clarans}
view source

clustering-methods-list

List of clustering methods.

Examples

List of methods

clustering-methods-list
@@ -92,7 +92,7 @@ 
Regrouping

 ;;=> {:clusters 8,
 ;;=>  :info {},
 ;;=>  :representatives nil,
-;;=>  :sizes (131 1147 1169 1125 1092 122 93 121 0),
+;;=>  :sizes (1119 1128 1129 1129 147 108 120 120 0),
 ;;=>  :type :dbscan}
view source

denclue

(denclue data sigma m)(denclue data sigma m tolerance)(denclue data sigma m tolerance min-pts)

DENsity CLUstering algorithm.

Input:

    @@ -136,18 +136,18 @@

    Regrouping

    (r/randval (r/grand) (r/grand 5 1.0))))) (deterministic-annealing 4 0.5) (regroup))) -;;=> ({:key 1, -;;=> :representative (0.08901912095860125 5.05141457324412), -;;=> :size 231} -;;=> {:key 3, -;;=> :representative (4.949899452159327 4.998411798416555), -;;=> :size 252} +;;=> ({:key 3, +;;=> :representative (4.981128559374225 4.917380239304928), +;;=> :size 242} +;;=> {:key 1, +;;=> :representative (0.0240693616013261 4.906708467338807), +;;=> :size 246} ;;=> {:key 2, -;;=> :representative (5.169817768215978 -0.04166862180388523), -;;=> :size 256} +;;=> :representative (4.927300741141155 0.06848813585858737), +;;=> :size 263} ;;=> {:key 0, -;;=> :representative (-0.07634736991709429 -0.19863728536737843), -;;=> :size 261})
view source

g-means

(g-means data clusters)(g-means data clusters max-iter)(g-means data clusters max-iter tolerance)

G-Means

+;;=> :representative (0.12708107663316356 -0.14485027403046535), +;;=> :size 249})
view source

g-means

(g-means data clusters)(g-means data clusters max-iter)(g-means data clusters max-iter tolerance)

G-Means

Input:

  • data - sequence of samples
    • @@ -160,7 +160,7 @@

    Regrouping

    ((juxt :clusters :sizes :representatives)
  (g-means (repeatedly 100 (fn* [] (r/randval (r/drand) (r/drand 5 6))))
           4))
-;;=> [2 (51 49 0) ((0.4772938178957185) (5.477688669526616))]
view source

k-means

(k-means data clusters)(k-means data clusters max-iter)(k-means data clusters max-iter tolerance)

K-Means++ algorithm.

+;;=> [2 (46 54 0) ((5.530726228077052) (0.4718967556076599))]
view source

k-means

(k-means data clusters)(k-means data clusters max-iter)(k-means data clusters max-iter tolerance)

K-Means++ algorithm.

Input:

  • data - sequence of samples
    • @@ -177,11 +177,11 @@

    Regrouping

    ;;=> :data [1 2 3 -1 -1 2 -1 11 111], ;;=> :info {:distortion 2.0000000000000004}, ;;=> :obj -;;=> #object[smile.clustering.KMeans 0x618519cf "Cluster distortion: 2.00000\nCluster size of 9 data points:\nCluster 1 3 (33.3%)\nCluster 2 1 (11.1%)\nCluster 3 1 (11.1%)\nCluster 4 4 (44.4%)\n"], -;;=> :predict #, +;;=> #object[smile.clustering.KMeans 0x3d678abb "Cluster distortion: 2.00000\nCluster size of 9 data points:\nCluster 1 3 (33.3%)\nCluster 2 1 (11.1%)\nCluster 3 1 (11.1%)\nCluster 4 4 (44.4%)\n"], +;;=> :predict #, ;;=> :representatives ((-1.0) (111.0) (11.0) (2.0)), ;;=> :sizes (3 1 1 4 0), -;;=> :type :k-means}

Clusters group into separate maps.

+;;=> :type :k-means}

Clusters group into separate maps.

(regroup (k-means [1 2 3 -1 -1 2 -1 11 111] 4))
 ;;=> ({:data (1 2 3 2), :key 3, :representative (2.0), :size 4}
 ;;=>  {:data (-1 -1 -1), :key 0, :representative (-1.0), :size 3}
@@ -219,10 +219,10 @@ 
Regrouping

              20)
         :data :clustering
         :obj :predict)
-;;=> {:clusters 4,
-;;=>  :info {:entropy 0.0},
+;;=> {:clusters 5,
+;;=>  :info {:entropy 123.76475896122787},
 ;;=>  :representatives nil,
-;;=>  :sizes (263 2287 2204 246 0),
+;;=>  :sizes (1067 255 2242 253 1183 0),
 ;;=>  :type :mec}
view source

outlier-id

const

;;=> 2147483647

Id of the cluster which contain outliers.

view source

predict

(predict cluster in)

Predict cluster for given vector

view source

regroup

(regroup {:keys [clustering data representatives sizes]})

Transform clustering result into list of clusters as separate maps.

@@ -238,25 +238,25 @@

Regrouping

Examples

Result of clustering with regrouping

(k-means [1 2 3 -1 -1 2 -1 11 111] 7)
 ;;=> #fastmath.clustering.ClusteringResult
-;;=>  {:clustering (4 0 5 3 3 0 3 2 1),
+;;=>  {:clustering (5 3 4 1 1 3 1 0 2),
 ;;=>   :clusters 7,
 ;;=>   :data [1 2 3 -1 -1 2 -1 11 111],
 ;;=>   :info {:distortion 0.0},
 ;;=>   :obj
-;;=>   #object[smile.clustering.KMeans 0x543ca0a1 "Cluster distortion: 0.00000\nCluster size of 9 data points:\nCluster    1      2 (22.2%)\nCluster    2      1 (11.1%)\nCluster    3      1 (11.1%)\nCluster    4      3 (33.3%)\nCluster    5      1 (11.1%)\nCluster    6      1 (11.1%)\nCluster    7      0 ( 0.0%)\n"],
-;;=>   :predict #,
-;;=>   :representatives ((2.0) (111.0) (11.0) (-1.0) (1.0) (3.0) (##NaN)),
-;;=>   :sizes (2 1 1 3 1 1 0 0),
+;;=>   #object[smile.clustering.KMeans 0x197da505 "Cluster distortion: 0.00000\nCluster size of 9 data points:\nCluster    1      1 (11.1%)\nCluster    2      3 (33.3%)\nCluster    3      1 (11.1%)\nCluster    4      2 (22.2%)\nCluster    5      1 (11.1%)\nCluster    6      1 (11.1%)\nCluster    7      0 ( 0.0%)\n"],
+;;=>   :predict #,
+;;=>   :representatives ((11.0) (-1.0) (111.0) (2.0) (3.0) (1.0) (##NaN)),
+;;=>   :sizes (1 3 1 2 1 1 0 0),
 ;;=>   :type :k-means}
 (regroup (k-means [1 2 3 -1 -1 2 -1 11 111] 7))
 ;;=> ({:data (1), :key 5, :representative (1.0), :size 1}
-;;=>  {:data (2 2), :key 3, :representative (2.0), :size 2}
+;;=>  {:data (2 2), :key 0, :representative (2.0), :size 2}
 ;;=>  {:data (3), :key 4, :representative (3.0), :size 1}
-;;=>  {:data (-1 -1 -1), :key 0, :representative (-1.0), :size 3}
+;;=>  {:data (-1 -1 -1), :key 3, :representative (-1.0), :size 3}
 ;;=>  {:data (11), :key 2, :representative (11.0), :size 1}
 ;;=>  {:data (111), :key 1, :representative (111.0), :size 1})
 (count (regroup (k-means [1 2 3 -1 -1 2 -1 11 111] 7)))
-;;=> 6
view source

spectral

(spectral data clusters sigma)(spectral data clusters sigma max-iters tolerance)(spectral data clusters samples sigma)(spectral data clusters samples sigma max-iters tolerance)

Spectral clustering

+;;=> 6
view source

spectral

(spectral data clusters sigma)(spectral data clusters sigma max-iters tolerance)(spectral data clusters samples sigma)(spectral data clusters samples sigma max-iters tolerance)

Spectral clustering

Input:

  • data - sequence of samples
    • @@ -279,9 +279,9 @@

    Regrouping

    :data :clustering :obj :predict) ;;=> {:clusters 4, -;;=> :info {:distortion 32.57089991186055}, +;;=> :info {:distortion 35.370075541146754}, ;;=> :representatives nil, -;;=> :sizes (133 264 81 22 0), +;;=> :sizes (132 268 96 4 0), ;;=> :type :spectral}

2d vectors

(dissoc (lloyd
          (repeatedly
@@ -294,12 +294,12 @@ 
Regrouping

         :data :clustering
         :obj :predict)
 ;;=> {:clusters 4,
-;;=>  :info {:distortion 319781.50713524147},
-;;=>  :representatives ((121.62222222222222 124.56888888888889)
-;;=>                    (-0.3235294117647059 47.1764705882353)
-;;=>                    (138.4607843137255 0.23529411764705882)
-;;=>                    (115.3021582733813 -0.26618705035971224)),
-;;=>  :sizes (225 34 102 139 0),
+;;=>  :info {:distortion 150979.2782140331},
+;;=>  :representatives ((124.51690821256038 123.1304347826087)
+;;=>                    (-1.7142857142857142 130.17857142857142)
+;;=>                    (-0.5806451612903226 0.0)
+;;=>                    (123.24358974358974 0.13675213675213677)),
+;;=>  :sizes (207 28 31 234 0),
 ;;=>  :type :lloyd}
view source

x-means

(x-means data clusters)(x-means data clusters max-iter)(x-means data clusters max-iter tolerance)

X-Means

Input:

    @@ -314,4 +314,4 @@

    Regrouping

    (x-means (repeatedly 10000 (fn* [] (r/randval (r/grand) (r/grand 5 1.0)))) 4)) -;;=> [2 (4924 5076 0) ((5.005016732578154) (-0.01610911384093022))]
view source
\ No newline at end of file +;;=> [2 (4997 5003 0) ((5.030492889086659) (-0.009684743016128554))]
view source
\ No newline at end of file diff --git a/docs/fastmath.complex.html b/docs/fastmath.complex.html index 8512c2bc..ebd3bd3f 100644 --- a/docs/fastmath.complex.html +++ b/docs/fastmath.complex.html @@ -1,133 +1,141 @@ -fastmath.complex documentation

Project

Namespaces

Public Vars

fastmath.complex

Complex numbers functions.

+fastmath.complex documentation

Project

Namespaces

Public Vars

fastmath.complex

Complex numbers functions.

Complex number is represented as Vec2 type (from clojure2d.math.vector namespace).

To create complex number use complex, vec2 or ->Vec2.

-

Simplified implementation based on Apache Commons Math. Functions don’t check NaNs or INF values.

-

Complex plane (identity) looks as follows:

-

identity

-

Categories

    Other vars: -I I I- ONE TWO ZERO abs acos acosech acosh acoth acsch add arg asech asin asinh atan atanh complex conjugate cos cosh coth csc csch div exp flip im log mult mult-I mult-I- neg pow re reciprocal scale sec sech sin sinh sq sqrt sqrt1z sub tan tanh

    -I

    view source

    abs

    Absolute value

    +

    Implementation checks for ##Inf, ##NaN and some of the function distinguish +0.0 and -0.0

    +

    Categories

      Other vars: -I I I- ONE TWO ZERO abs acos acosh acot acoth acsc acsch add arg asec asech asin asinh atan atanh complex conjugate cos cosh cot coth csc csch csgn delta-eq div exp flip im imaginary? inf? log logb mult mult-I mult-I- nan? neg norm pow re real? reciprocal scale sec sech sin sinh sq sqrt sqrt1z sub tan tanh zero?

      -I

      view source

      abs

      (abs z)

      Absolute value, magnitude

      Examples

      Abs

      (abs (complex 1 -3))
-;;=> 3.1622776601683795
      view source

      acos

      (acos z)

      acos

      +;;=> 3.1622776601683795
      view source

      acos

      (acos z)

      acos

      Examples

      acos(z)

      (acos (complex 2 -1))
-;;=> [0.5073563032171449 1.4693517443681863]

      Plot of acos

      -
      view source

      acosech

      (acosech z)

      acosech

      -
      view source

      acosh

      (acosh z)

      acosh

      -
      view source

      acoth

      (acoth z)

      sech

      -
      view source

      acsch

      (acsch z)

      sech

      -
      view source

      add

      Sum of two complex numbers.

      +;;=> [0.5073563032171444 1.4693517443681854]

      Plot of acos

      +
      view source

      acosh

      (acosh z)

      acosh

      +
      view source

      acot

      (acot z)

      acot

      +
      view source

      acoth

      (acoth z)
      view source

      acsc

      (acsc z)

      acsc

      +
      view source

      acsch

      (acsch z)
      view source

      add

      (add z1 z2)

      Sum of two complex numbers

      Examples

      Sum

      (add I ONE)
-;;=> [1.0 1.0]
      view source

      arg

      Argument (angle) of complex number.

      +;;=> [1.0 1.0]
      view source

      arg

      (arg z)

      Argument (angle) of the complex number

      Examples

      Argument

      (m/degrees (arg I-))
-;;=> -90.0
      view source

      asech

      (asech z)

      sech

      -
      view source

      asin

      (asin z)

      asin

      +;;=> -90.0
      view source

      asec

      (asec z)

      asec

      +
      view source

      asech

      (asech z)
      view source

      asin

      (asin z)

      asin

      Examples

      asin(z)

      (asin (complex 2 -1))
-;;=> [1.0634400235777521 -1.4693517443681852]

      Plot of asin

      -
      view source

      asinh

      (asinh z)

      asinh

      -
      view source

      atan

      (atan z)

      atan

      +;;=> [1.0634400235777521 -1.4693517443681854]

      Plot of asin

      +
      view source

      asinh

      (asinh z)

      asinh

      +
      view source

      atan

      (atan z)

      atan

      Examples

      atan(z)

      (atan (complex 2 -1))
-;;=> [1.1780972450961724 -0.1732867951399863]

      Plot of atan

      -
      view source

      atanh

      (atanh z)

      atanh

      -
      view source

      complex

      (complex a b)(complex a)(complex)

      Create complex number. Represented as Vec2.

      +;;=> [1.1780972450961724 -0.17328679513998632]

      Plot of atan

      +
      view source

      atanh

      (atanh z)

      atanh

      +
      view source

      complex

      (complex a b)(complex a)(complex)

      Create complex number. Represented as Vec2.

      Examples

      New complex number.

      (complex 2 -1)
-;;=> [2.0 -1.0]
      view source

      conjugate

      (conjugate z)

      Complex conjugate. \(\bar{z}\)

      +;;=> [2.0 -1.0]
      view source

      conjugate

      (conjugate z)

      Complex conjugate. \(\bar{z}\)

      Examples

      Conjugate

      (conjugate I)
-;;=> [0.0 -1.0]
      view source

      cos

      (cos z)

      cos

      +;;=> [0.0 -1.0]
      view source

      cos

      (cos z)

      cos

      Examples

      cos(z)

      (cos (complex 2 -1))
 ;;=> [-0.6421481247155197 1.0686074213827785]

      Plot of cos

      -
      view source

      cosh

      (cosh z)

      cosh

      +
      view source

      cosh

      (cosh z)

      cosh

      Examples

      cosh(z)

      (cosh (complex 2 -1))
 ;;=> [2.0327230070196656 -3.0518977991517997]

      Plot of cosh

      -
      view source

      coth

      (coth z)

      coth

      -
      view source

      csc

      (csc z)

      cosecant

      +
      view source

      cot

      (cot z)

      csc

      +
      view source

      coth

      (coth z)

      coth

      +
      view source

      csc

      (csc z)

      csc

      Examples

      csc(z)

      (csc (complex 2 -1))
-;;=> [0.6354937992539001 -0.22150093085050934]

      Plot of csc

      -
      view source

      csch

      (csch z)

      cosech

      -
      view source

      div

      (div z1 z2)

      Divide two complex numbers.

      +;;=> [0.6354937992538998 -0.22150093085050923]

      Plot of csc

      +
      view source

      csch

      (csch z)

      csch

      +
      view source

      csgn

      (csgn re im)(csgn z)

      Complex sgn.

      +

      Returns 0 for 0+0i or calls m/sgn on real part otherwise.

      +
      view source

      delta-eq

      (delta-eq q1 q2)(delta-eq q1 q2 accuracy)

      Compare complex numbers with given accuracy (10e-6 by default)

      +
      view source

      div

      (div z1 z2)

      Divide two complex numbers.

      Examples

      Divide

      (div (complex 1 2) (complex 3 4))
-;;=> [0.44 0.08]
      view source

      exp

      (exp z)

      exp

      +;;=> [0.44 0.08]
      view source

      exp

      (exp z)

      exp

      Examples

      exp(z)

      (exp (complex 2 -1))
 ;;=> [3.992324048441272 -6.217676312367968]

      \(e^{i\pi}+1\)

      (add (exp (complex 0 m/PI)) ONE)
 ;;=> [0.0 1.224646799076922E-16]

      Plot of exp

      -
      view source

      flip

      (flip z)

      Exchange imaginary and real parts

      -
      view source

      I-

      view source

      im

      (im z)

      Imaginary part

      -
      view source

      log

      (log z)

      log

      +
      view source

      flip

      (flip z)

      Exchange imaginary and real parts

      +
      view source

      I-

      view source

      im

      (im z)

      Imaginary part

      +
      view source

      imaginary?

      (imaginary? z)

      Is z is a pure imaginary number?

      +
      view source

      inf?

      (inf? z)

      Is infinite?

      +
      view source

      log

      (log z)

      log, principal value

      Examples

      log(z)

      (log (complex 2 -1))
-;;=> [0.8047189562170503 -0.4636476090008061]

      log(e)

      +;;=> [0.8047189562170501 -0.4636476090008061]

      log(e)

      (log (complex m/E 0))
 ;;=> [1.0 0.0]

      Plot of log

      -
      view source

      mult

      (mult z1 z2)

      Multiply two complex numbers.

      +
      view source

      logb

      (logb z b)

      log with base b

      +
      view source

      mult

      (mult z1 z2)

      Multiply two complex numbers.

      Examples

      Multiply

      (mult (complex 1 2) (complex 3 4))
-;;=> [-5.0 10.0]
      view source

      mult-I

      (mult-I z)
      view source

      mult-I-

      (mult-I- z)
      view source

      neg

      (neg z)

      Negate complex number. \(-z\)

      +;;=> [-5.0 10.0]
      view source

      mult-I

      (mult-I z)
      view source

      mult-I-

      (mult-I- z)
      view source

      nan?

      (nan? z)

      Is NaN?

      +
      view source

      neg

      (neg z)

      Negate complex number. \(-z\)

      Examples

      Negate.

      (neg (complex 1 2))
-;;=> [-1.0 -2.0]
      view source

      pow

      (pow z1 z2)

      Power. \(z_1^{z_2}\)

      +;;=> [-1.0 -2.0]
      view source

      norm

      (norm z)

      Norm (Guass) of the complex number, absolute value squared

      +
      view source

      pow

      (pow z1 z2)

      Power. \(z_1^{z_2}\)

      Examples

      \(\sqrt{2}\)

      (pow TWO (complex 0.5 0.0))
 ;;=> [1.4142135623730951 0.0]

      Complex power

      (pow (complex 1 2) (complex 3 4))
-;;=> [0.12900959407446697 0.03392409290517014]
      view source

      re

      (re z)

      Real part

      -
      view source

      reciprocal

      (reciprocal z)

      \(\frac{1}{z}\)

      +;;=> [0.12900959407446694 0.03392409290517002]
      view source

      re

      (re z)

      Real part

      +
      view source

      real?

      (real? z)

      Is z is a real number?

      +
      view source

      reciprocal

      (reciprocal z)

      \(\frac{1}{z}\)

      Examples

      Reciprocal of real

      (reciprocal TWO)
-;;=> [0.5 0.0]

      Reciprocal of complex

      +;;=> [0.5 -0.0]

      Reciprocal of complex

      (reciprocal (complex 0 2))
 ;;=> [0.0 -0.5]

      Plot of reciprocal

      -
      view source

      scale

      Scale number

      -
      view source

      sec

      (sec z)

      secant

      +
      view source

      scale

      (scale z v)

      Multiply by real number

      +
      view source

      sec

      (sec z)

      sec

      Examples

      sec(z)

      (sec (complex 2 -1))
-;;=> [-0.41314934426693994 -0.6875274386554792]

      Plot of sec

      -
      view source

      sech

      (sech z)

      sech

      -
      view source

      sin

      (sin z)

      sin

      +;;=> [-0.4131493442669398 -0.687527438655479]

      Plot of sec

      +
      view source

      sech

      (sech z)

      sech

      +
      view source

      sin

      (sin z)

      sin

      Examples

      sin(z)

      (sin (complex 2 -1))
 ;;=> [1.403119250622041 0.4890562590412935]

      Plot of sin

      -
      view source

      sinh

      (sinh z)

      sinh

      +
      view source

      sinh

      (sinh z)

      sinh

      Examples

      sinh(z)

      (sinh (complex 2 -1))
 ;;=> [1.9596010414216063 -3.1657785132161678]

      Plot of sinh

      -
      view source

      sq

      (sq z)

      Square complex number. \(z^2\)

      +
      view source

      sq

      (sq z)

      Square complex number. \(z^2\)

      Examples

      Square.

      (sq (complex 1 2))
 ;;=> [-3.0 4.0]

      \(i^2\)

      (sq I)
 ;;=> [-1.0 0.0]

      Plot of sq

      -
      view source

      sqrt

      (sqrt z)

      Sqrt of complex number. \(\sqrt{z}\)

      +
      view source

      sqrt

      (sqrt z)

      Sqrt of complex number. \(\sqrt{z}\)

      Examples

      Square root of real.

      (sqrt (complex 2 0))
 ;;=> [1.4142135623730951 0.0]

      Square root of complex.

      (sqrt (complex 2 2))
 ;;=> [1.5537739740300376 0.6435942529055827]

      Plot of sqrt

      -
      view source

      sqrt1z

      (sqrt1z z)

      \(\sqrt{1-z^2}\)

      +
      view source

      sqrt1z

      (sqrt1z z)

      \(\sqrt{1-z^2}\)

      Examples

      Example 1

      (sqrt1z (complex 2 3))
 ;;=> [3.115799084103365 -1.9256697360916721]

      Plot of sqrt1z

      -
      view source

      sub

      Subtraction of two complex numbers.

      +
      view source

      sub

      (sub z1 z2)

      Difference of two complex numbers

      Examples

      Subtract

      (sub ONE I-)
-;;=> [1.0 1.0]
      view source

      tan

      (tan z)

      tan

      +;;=> [1.0 1.0]
      view source

      tan

      (tan z)

      tan

      Examples

      tan(z)

      (tan (complex 2 -1))
-;;=> [-0.2434582011857252 -1.1667362572409201]

      Plot of tan

      -
      view source

      tanh

      (tanh z)

      tanh

      +;;=> [-0.24345820118572514 -1.16673625724092]

      Plot of tan

      +
      view source

      tanh

      (tanh z)

      tanh

      Examples

      tanh(z)

      (tanh (complex 2 -1))
-;;=> [1.0147936161466335 -0.0338128260798967]

      Plot of tanh

      -
      view source
      \ No newline at end of file +;;=> [1.0147936161466335 -0.033812826079896684]

      Plot of tanh

      +
      view source

      zero?

      (zero? z)

      Is zero?

      +
      view source
      \ No newline at end of file diff --git a/docs/fastmath.core.html b/docs/fastmath.core.html index f39e8285..f9084ba6 100644 --- a/docs/fastmath.core.html +++ b/docs/fastmath.core.html @@ -1,6 +1,6 @@ -fastmath.core documentation

      Project

      Namespaces

      Public Vars

      fastmath.core

      Collection of fast math functions and plethora of constants known from other math libraries.

      +fastmath.core documentation

      Project

      Namespaces

      Public Vars

      fastmath.core

      Collection of fast math functions and plethora of constants known from other math libraries.

      Primitive math operators

      Based on Primitive Math by Zach Tellman several operators are introduced and replace clojure.core functions. All operators are macros and can’t be used as functions. List includes:

      Known from Clojure: * + - / > < >= <= == rem quot mod bit-or bit-and bit-xor bit-and-not bit-set bit-clear bit-test bit-flip bit-not bit-shift-left bit-shift-right unsigned-bit-shift-right inc dec zero? neg? pos? min max even? odd? abs

      @@ -17,17 +17,17 @@

      Fast Math

      Almost all math functions are backed by FastMath library. Most of them are macros. Some of them are wrapped in Clojure functions. Almost all operates on primitive double and returns double (with an exception round or qround which returns long).

      Other functions

      Additionally namespace contains functions which are common in frameworks like OpenFrameworks and Processing.

      -

      Categories

        Other vars: * + - / < << <= == > >= >> >>> Ci I0 Si abs acos acosh acot acoth acovercos acoversin acrd acsc acsch aexcsc aexsec ahacovercos ahacoversin ahavercos ahaversin approx approx-eq approx= asec asech asin asinh atan atan2 atanh avercos aversin bessel-j between-? between? bit-and bit-and-not bit-clear bit-flip bit-not bit-or bit-set bit-shift-left bit-shift-right bit-test bit-xor bits->double bool-and bool-not bool-or bool-xor cb cbrt ceil cexpexp cloglog cnorm co-intervals combinations constrain copy-sign cos cos-interpolation cosh cot coth covercos coversin crd csc csch cut dec degrees delta-eq delta= difference-of-products digamma dist double-array->seq double-bits double-double-array->seq double-high-bits double-low-bits eq erf erfc evalpoly even? excsc exp expm1 exsec factorial factorial20 fast* fast+ fast- fast-identity fast-max fast-min floor fma fpow frac gamma gcd group-by-intervals hacovercos hacoversin havercos haversin haversine haversine-dist high-2-exp high-exp hypot hypot-sqrt iabs inc inf? inv-erf inv-erfc inv-gamma-1pm1 invalid-double? itrunc jinc lcm lerp ln log log-I0 log-beta log-combinations log-factorial log-gamma log-gamma-1p log10 log1mexp log1p log1pexp log1pmx log1psq log2 log2mexp logaddexp logb logcosh logexpm1 logistic logit logmxp1 logsubexp logsumexp low-2-exp low-exp make-norm makepoly max mevalpoly min minkowski mlerp mnorm mod muladd nan? neg-inf? neg? negmuladd next-double norm not-neg? not-pos? not== odd? one? order pos-inf? pos? pow pow2 pow3 prev-double qceil qcos qdist qexp qfloor qlog qpow qround qsin qsqrt quad-interpolation quot radians rank rank1 regularized-beta regularized-gamma-p regularized-gamma-q rem remainder rint round round-even round-up-pow2 rqsqrt safe-sqrt sample sec sech seq->double-array seq->double-double-array sfrac sgn sigmoid signum sin sinc sinh slice-range smooth-interpolation smoothstep sq sqrt sum-of-products tan tanh trigamma trunc unsigned-bit-shift-right unuse-primitive-operators use-primitive-operators valid-double? vercos versin wrap xexpx xexpy xlog1py xlogx xlogy zero?

        Constants

        *

        macro

        (* x)(* x y)(* x y & rest)

        A primitive math version of *

        +

        Categories

          Other vars: * + - / < << <= == > >= >> >>> Ci I0 Si abs acos acosh acot acoth acovercos acoversin acrd acsc acsch aexcsc aexsec ahacovercos ahacoversin ahavercos ahaversin approx approx-eq approx= asec asech asin asinh atan atan2 atanh avercos aversin bessel-j between-? between? bit-and bit-and-not bit-clear bit-flip bit-not bit-or bit-set bit-shift-left bit-shift-right bit-test bit-xor bits->double bool-and bool-not bool-or bool-xor cb cbrt ceil cexpexp cloglog cnorm co-intervals combinations constrain copy-sign cos cos-interpolation cosh cot coth covercos coversin crd csc csch cut dec degrees delta-eq delta= difference-of-products digamma dist double-array->seq double-bits double-double-array->seq double-exponent double-high-bits double-low-bits double-significand eq erf erfc evalpoly even? excsc exp expm1 exsec factorial factorial20 fast* fast+ fast- fast-identity fast-max fast-min floor fma fpow frac gamma gcd group-by-intervals hacovercos hacoversin havercos haversin haversine haversine-dist high-2-exp high-exp hypot hypot-sqrt iabs inc inf? inv-erf inv-erfc inv-gamma-1pm1 invalid-double? itrunc jinc lcm lerp ln log log-I0 log-beta log-combinations log-factorial log-gamma log-gamma-1p log10 log1mexp log1p log1pexp log1pmx log1psq log2 log2int log2mexp logaddexp logb logcosh logexpm1 logistic logit logmxp1 logsubexp logsumexp low-2-exp low-exp make-norm makepoly max mevalpoly min minkowski mlerp mnorm mod muladd nan? neg-inf? neg? negative-zero? negmuladd next-double norm not-neg? not-pos? not== odd? one? order pos-inf? pos? pow pow2 pow3 prev-double qceil qcos qdist qexp qfloor qlog qpow qround qsin qsqrt quad-interpolation quot radians rank rank1 regularized-beta regularized-gamma-p regularized-gamma-q rem remainder rint round round-even round-up-pow2 rqsqrt safe-sqrt sample sec sech seq->double-array seq->double-double-array sfrac sgn sigmoid signum sin sinc sinh slice-range smooth-interpolation smoothstep sq sqrt sum-of-products tan tanh trigamma trunc ulp unsigned-bit-shift-right unuse-primitive-operators use-primitive-operators valid-double? vercos versin wrap xexpx xexpy xlog1py xlogx xlogy zero?

          Constants

          *

          macro

          (* x)(* x y)(* x y & rest)

          A primitive math version of *

          view source

          +

          macro

          (+ x)(+ x y)(+ x y & rest)

          A primitive math version of +

          view source

          -

          macro

          (- x)(- x y)(- x y & rest)

          A primitive math version of -

          view source

          -E

          const

          ;;=> -2.718281828459045

          Value of \(-e\)

          -
          view source

          -HALF_PI

          const

          ;;=> -1.5707963267948966

          Value of \(-\frac{\pi}{2}\)

          -
          view source

          -PI

          const

          ;;=> -3.141592653589793

          Value of \(-\pi\)

          -
          view source

          -QUARTER_PI

          const

          ;;=> -0.7853981633974483

          Value of \(-\frac{\pi}{4}\)

          -
          view source

          -TAU

          const

          ;;=> -6.283185307179586

          Alias for TWO_PI-

          -
          view source

          -THIRD_PI

          const

          ;;=> 1.0471975511965976

          Value of \(-\frac{\pi}{3}\)

          -
          view source

          -TWO_PI

          const

          ;;=> -6.283185307179586

          Value of \(-2 {\pi}\)

          -
          view source

          /

          macro

          (/ x)(/ x y)(/ x y & rest)

          A primitive math version of /

          +
          view source

          -HALF_PI

          const

          ;;=> -1.5707963267948966

          Value of \(-\frac{\pi}{2}\)

          +
          view source

          -PI

          const

          ;;=> -3.141592653589793

          Value of \(-\pi\)

          +
          view source

          -QUARTER_PI

          const

          ;;=> -0.7853981633974483

          Value of \(-\frac{\pi}{4}\)

          +
          view source

          -TAU

          const

          ;;=> -6.283185307179586

          Alias for TWO_PI-

          +
          view source

          -THIRD_PI

          const

          ;;=> 1.0471975511965976

          Value of \(-\frac{\pi}{3}\)

          +
          view source

          -TWO_PI

          const

          ;;=> -6.283185307179586

          Value of \(-2 {\pi}\)

          +
          view source

          /

          macro

          (/ x)(/ x y)(/ x y & rest)

          A primitive math version of /

          view source

          <

          macro

          (< x)(< x y)(< x y & rest)

          A primitive math version of <

          view source

          <<

          macro

          (<< x y)

          fastmath.java.PrimitiveMath/shiftLeft function wrapped in macro.

          view source

          <=

          macro

          (<= x)(<= x y)(<= x y & rest)

          A primitive math version of <=

          @@ -40,73 +40,73 @@

          Other functions

          Examples

          Usage

          (fastmath.core/abs 1.0)
 ;;=> 1.0

          Plot of abs

          -
          view source

          acos

          macro

          (acos x)

          net.jafama.FastMath/acos function wrapped in macro.

          +
          view source

          acos

          macro

          (acos x)

          net.jafama.FastMath/acos function wrapped in macro.

          Examples

          Usage

          (fastmath.core/acos 1.0)
 ;;=> 0.0

          Plot of acos

          -
          view source

          acosh

          macro

          (acosh x)

          net.jafama.FastMath/acosh function wrapped in macro.

          +
          view source

          acosh

          macro

          (acosh x)

          net.jafama.FastMath/acosh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/acosh 1.0)
 ;;=> 0.0

          Plot of acosh

          -
          view source

          acot

          (acot v)

          Arccotangent

          +
          view source

          acot

          (acot v)

          Arccotangent

          Examples

          Usage

          (fastmath.core/acot 1.0)
 ;;=> 0.7853981633974483

          Plot of acot

          -
          view source

          acoth

          (acoth v)

          Area hyperbolic cotangent

          +
          view source

          acoth

          (acoth v)

          Area hyperbolic cotangent

          Examples

          Usage

          (fastmath.core/acoth 1.0)
 ;;=> Infinity

          Plot of acoth

          -
          view source

          acovercos

          (acovercos v)

          Arc covercosine

          -
          view source

          acoversin

          (acoversin v)

          Arc coversine

          -
          view source

          acrd

          (acrd v)

          Inverse chord

          -
          view source

          acsc

          (acsc v)

          Arcosecant

          +
          view source

          acovercos

          (acovercos v)

          Arc covercosine

          +
          view source

          acoversin

          (acoversin v)

          Arc coversine

          +
          view source

          acrd

          (acrd v)

          Inverse chord

          +
          view source

          acsc

          (acsc v)

          Arcosecant

          Examples

          Usage

          (fastmath.core/acsc 1.0)
 ;;=> 1.5707963267948966

          Plot of acsc

          -
          view source

          acsch

          (acsch v)

          Area hyperbolic cosecant

          +
          view source

          acsch

          (acsch v)

          Area hyperbolic cosecant

          Examples

          Usage

          (fastmath.core/acsch 1.0)
 ;;=> 0.8813735870195429

          Plot of acsch

          -
          view source

          aexcsc

          (aexcsc v)

          Arc excosecant

          -
          view source

          aexsec

          (aexsec v)

          Arc exsecant

          -
          view source

          ahacovercos

          (ahacovercos v)

          Arc hacovercosine

          -
          view source

          ahacoversin

          (ahacoversin v)

          Arc hacoversine

          -
          view source

          ahavercos

          (ahavercos v)

          Arc havecosine

          -
          view source

          ahaversin

          (ahaversin v)

          Arc haversine

          -
          view source

          approx

          (approx v)(approx v digits)

          Round v to specified (default: 2) decimal places. Be aware of double number accuracy.

          +
          view source

          aexcsc

          (aexcsc v)

          Arc excosecant

          +
          view source

          aexsec

          (aexsec v)

          Arc exsecant

          +
          view source

          ahacovercos

          (ahacovercos v)

          Arc hacovercosine

          +
          view source

          ahacoversin

          (ahacoversin v)

          Arc hacoversine

          +
          view source

          ahavercos

          (ahavercos v)

          Arc havecosine

          +
          view source

          ahaversin

          (ahaversin v)

          Arc haversine

          +
          view source

          approx

          (approx v)(approx v digits)

          Round v to specified (default: 2) decimal places. Be aware of double number accuracy.

          Examples

          Default rounding (2 digits).

          (approx 1.232323)
 ;;=> 1.23

          Rounding up to 4 digits.

          (approx 1.232323 4)
-;;=> 1.2323
          view source

          approx-eq

          (approx-eq a b)(approx-eq a b digits)

          Checks equality approximately. See approx.

          +;;=> 1.2323
          view source

          approx-eq

          (approx-eq a b)(approx-eq a b digits)

          Checks equality approximately. See approx.

          Examples

          Default rounding (2 digits).

          (approx-eq 1.232323 1.231999)
 ;;=> true

          Rounding up to 4 digits.

          (approx-eq 1.232323 1.23231999 4)
 ;;=> true

          Keep an eye on rounding

          (approx-eq 1.2349 1.235)
-;;=> false
          view source

          approx=

          Alias for approx-eq

          -
          view source

          asec

          (asec v)

          Arcsecant

          +;;=> false
          view source

          approx=

          Alias for approx-eq

          +
          view source

          asec

          (asec v)

          Arcsecant

          Examples

          Usage

          (fastmath.core/asec 1.0)
 ;;=> 0.0

          Plot of asec

          -
          view source

          asech

          (asech v)

          Area hyperbolic secant

          +
          view source

          asech

          (asech v)

          Area hyperbolic secant

          Examples

          Usage

          (fastmath.core/asech 1.0)
 ;;=> 0.0

          Plot of asech

          -
          view source

          asin

          macro

          (asin x)

          net.jafama.FastMath/asin function wrapped in macro.

          +
          view source

          asin

          macro

          (asin x)

          net.jafama.FastMath/asin function wrapped in macro.

          Examples

          Usage

          (fastmath.core/asin 1.0)
 ;;=> 1.5707963267948966

          Plot of asin

          -
          view source

          asinh

          macro

          (asinh x)

          net.jafama.FastMath/asinh function wrapped in macro.

          +
          view source

          asinh

          macro

          (asinh x)

          net.jafama.FastMath/asinh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/asinh 1.0)
 ;;=> 0.8813735870195429

          Plot of asinh

          -
          view source

          atan

          macro

          (atan x)

          net.jafama.FastMath/atan function wrapped in macro.

          +
          view source

          atan

          macro

          (atan x)

          net.jafama.FastMath/atan function wrapped in macro.

          Examples

          Usage

          (fastmath.core/atan 1.0)
 ;;=> 0.7853981633974483

          Plot of atan

          -
          view source

          atan2

          macro

          (atan2 x y)

          net.jafama.FastMath/atan2 function wrapped in macro.

          +
          view source

          atan2

          macro

          (atan2 x y)

          net.jafama.FastMath/atan2 function wrapped in macro.

          Examples

          atan2 values

          (degrees (atan2 1 1))
 ;;=> 45.0
@@ -114,13 +114,13 @@ 
          Other functions
          
 ;;=> 0.0
 (degrees (atan2 0 -1))
 ;;=> 180.0

          Plot of atan2

          -
          view source

          atanh

          macro

          (atanh x)

          net.jafama.FastMath/atanh function wrapped in macro.

          +
          view source

          atanh

          macro

          (atanh x)

          net.jafama.FastMath/atanh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/atanh 1.0)
 ;;=> Infinity

          Plot of atanh

          -
          view source

          avercos

          (avercos v)

          Arc vecosine

          -
          view source

          aversin

          (aversin v)

          Arc versine

          -
          view source

          bessel-j

          macro

          (bessel-j x y)

          Bessel J function value for given order and argument.

          +
          view source

          avercos

          (avercos v)

          Arc vecosine

          +
          view source

          aversin

          (aversin v)

          Arc versine

          +
          view source

          bessel-j

          macro

          (bessel-j x y)

          Bessel J function value for given order and argument.

          Examples

          bessel-j values

          (bessel-j 1 1)
 ;;=> 0.44005058574493355
@@ -128,8 +128,8 @@ 
          Other functions
          
 ;;=> 0.7651976865579666
 (bessel-j 0 10)
 ;;=> -0.24593576445134827

          Plot of bessel-j

          -
          view source

          between-?

          (between-? [x y] v)(between-? x y v)

          Check if given number is within the range (x,y].

          -
          view source

          between?

          (between? [x y] v)(between? x y v)

          Check if given number is within the range x,y.

          +
          view source

          between-?

          (between-? [x y] v)(between-? x y v)

          Check if given number is within the range (x,y].

          +
          view source

          between?

          (between? [x y] v)(between? x y v)

          Check if given number is within the range x,y.

          Examples

          Examples

          (between? [1 4] 2)
 ;;=> true
@@ -148,7 +148,7 @@ 
          Other functions
          
 (between? 1 4 1)
 ;;=> true
 
-;; Test: ok.
          view source

          bit-and

          macro

          (bit-and x)(bit-and x y)(bit-and x y & rest)

          A primitive math version of bit-and

          +;; Test: ok.
          view source

          bit-and

          macro

          (bit-and x)(bit-and x y)(bit-and x y & rest)

          A primitive math version of bit-and

          view source

          bit-and-not

          macro

          (bit-and-not x)(bit-and-not x y)(bit-and-not x y & rest)

          A primitive math version of bit-and-not

          view source

          bit-clear

          macro

          (bit-clear x y)

          fastmath.java.PrimitiveMath/bitClear function wrapped in macro.

          view source

          bit-flip

          macro

          (bit-flip x y)

          fastmath.java.PrimitiveMath/bitFlip function wrapped in macro.

          @@ -160,20 +160,20 @@

          Other functions

          view source

          bit-test

          macro

          (bit-test x y)

          fastmath.java.PrimitiveMath/bitTest function wrapped in macro.

          view source

          bit-xor

          macro

          (bit-xor x)(bit-xor x y)(bit-xor x y & rest)

          A primitive math version of bit-xor

          view source

          bits->double

          (bits->double v)

          Convert 64 bits to double

          -
          view source

          bool-and

          macro

          deprecated

          (bool-and x)(bool-and x y)(bool-and x y & rest)

          A primitive math version of bool-and

          +
          view source

          bool-and

          macro

          deprecated

          (bool-and x)(bool-and x y)(bool-and x y & rest)

          A primitive math version of bool-and

          view source

          bool-not

          macro

          (bool-not x)

          fastmath.java.PrimitiveMath/not function wrapped in macro.

          view source

          bool-or

          macro

          deprecated

          (bool-or x)(bool-or x y)(bool-or x y & rest)

          A primitive math version of bool-or

          view source

          bool-xor

          macro

          deprecated

          (bool-xor x)(bool-xor x y)(bool-xor x y & rest)

          A primitive math version of bool-xor

          view source

          CATALAN_G

          const

          ;;=> 0.915965594177219

          Catalan G

          -
          view source

          cb

          (cb x)

          \(x^3\)

          +
          view source

          cb

          (cb x)

          \(x^3\)

          Examples

          Usage

          (fastmath.core/cb 1.0)
 ;;=> 1.0

          Plot of cb

          -
          view source

          cbrt

          macro

          (cbrt x)

          \(\sqrt3{x}\)

          +
          view source

          cbrt

          macro

          (cbrt x)

          \(\sqrt3{x}\)

          Examples

          Usage

          (fastmath.core/cbrt 1.0)
 ;;=> 1.0

          Plot of cbrt

          -
          view source

          ceil

          (ceil x)(ceil x scale)

          \(\lceil x \rceil\). See: qceil.

          +
          view source

          ceil

          (ceil x)(ceil x scale)

          \(\lceil x \rceil\). See: qceil.

          Rounding is done to a multiply of scale value (when provided).

          Examples

          Scaled ceil

          (ceil 234.312 10)
@@ -184,120 +184,122 @@ 
          Other functions
          
 ;; Test: ok.

          Usage

          (fastmath.core/ceil 1.0)
 ;;=> 1.0

          Plot of ceil

          -
          view source

          cexpexp

          (cexpexp x)

          1-exp(-exp(x))

          -
          view source

          Ci

          (Ci x)

          Negative of integral of cos(t)/t from x to inf

          -
          view source

          cloglog

          (cloglog x)

          log(-log(1-x))

          -
          view source

          cnorm

          (cnorm v start1 stop1 start2 stop2)(cnorm v start stop)

          Constrained version of norm. Result of norm is applied to constrain to [0,1] or [start2,stop2] ranges.

          +
          view source

          cexpexp

          (cexpexp x)

          1-exp(-exp(x))

          +
          view source

          Ci

          (Ci x)

          Negative of integral of cos(t)/t from x to inf

          +
          view source

          cloglog

          (cloglog x)

          log(-log(1-x))

          +
          view source

          cnorm

          (cnorm v start1 stop1 start2 stop2)(cnorm v start stop)

          Constrained version of norm. Result of norm is applied to constrain to [0,1] or [start2,stop2] ranges.

          Examples

          Constrain result of norm.

          (cnorm 1.5 0 1 100 200)
 ;;=> 200.0
 (cnorm 555 200 500)
-;;=> 1.0
          view source

          co-intervals

          (co-intervals data)(co-intervals data number)(co-intervals data number overlap)

          Divide sequence to overlaping intervals containing similar number of values. Same as R’s co.intervals()

          +;;=> 1.0
          view source

          co-intervals

          (co-intervals data)(co-intervals data number)(co-intervals data number overlap)

          Divide sequence to overlaping intervals containing similar number of values. Same as R’s co.intervals()

          Examples

          Usage

          (co-intervals [1 2 3 1 2 3 4 5 6 1 2 3 4 5 6 7 1 1 1 1 -1])
 ;;=> ([-1.5 1.5] [0.5 2.5] [0.5 3.5] [1.5 4.5] [2.5 5.5] [3.5 7.5])

          Higher overlap

          (co-intervals [1 2 3 1 2 3 4 5 6 1 2 3 4 5 6 7 1 1 1 1 -1] 5 0.95)
-;;=> ([-1.5 5.5] [0.5 5.5] [0.5 6.5] [0.5 7.5])
          view source

          combinations

          (combinations n k)

          Binomial coefficient (n choose k)

          -
          view source

          constrain

          macro

          (constrain value mn mx)

          Clamp value to the range [mn,mx].

          +;;=> ([-1.5 5.5] [0.5 5.5] [0.5 6.5] [0.5 7.5])
          view source

          combinations

          (combinations n k)

          Binomial coefficient (n choose k)

          +
          view source

          constrain

          macro

          (constrain value mn mx)

          Clamp value to the range [mn,mx].

          Examples

          Examples

          (constrain 0.5 1 2)
 ;;=> 1.0
 (constrain 1.5 1 2)
 ;;=> 1.5
 (constrain 2.5 1 2)
-;;=> 2.0
          view source

          copy-sign

          macro

          (copy-sign x y)

          Returns a value with a magnitude of first argument and sign of second.

          -
          view source

          cos

          macro

          (cos x)

          net.jafama.FastMath/cos function wrapped in macro.

          +;;=> 2.0
          view source

          copy-sign

          macro

          (copy-sign x y)

          Returns a value with a magnitude of first argument and sign of second.

          +
          view source

          cos

          macro

          (cos x)

          net.jafama.FastMath/cos function wrapped in macro.

          Examples

          Usage

          (fastmath.core/cos 1.0)
 ;;=> 0.5403023058681398

          Plot of cos

          -
          view source

          cos-interpolation

          (cos-interpolation start stop t)

          oF interpolateCosine interpolation. See also lerp/mlerp, quad-interpolation or smooth-interpolation.

          +
          view source

          cos-interpolation

          (cos-interpolation start stop t)

          oF interpolateCosine interpolation. See also lerp/mlerp, quad-interpolation or smooth-interpolation.

          Examples

          Example

          (cos-interpolation 0.0 1.0 0.123)
 ;;=> 0.03686712449046664

          Plot of cos-interpolation

          -
          view source

          cosh

          macro

          (cosh x)

          net.jafama.FastMath/cosh function wrapped in macro.

          +
          view source

          cosh

          macro

          (cosh x)

          net.jafama.FastMath/cosh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/cosh 1.0)
 ;;=> 1.543080634815244

          Plot of cosh

          -
          view source

          cot

          (cot v)

          Cotangent

          +
          view source

          cot

          (cot v)

          Cotangent

          Examples

          Usage

          (fastmath.core/cot 1.0)
-;;=> 0.6420926159343308

          Plot of cot

          -
          view source

          coth

          (coth v)

          Hyperbolic cotangent

          +;;=> 0.6420926159343309

          Plot of cot

          +
          view source

          coth

          (coth v)

          Hyperbolic cotangent

          Examples

          Usage

          (fastmath.core/coth 1.0)
 ;;=> 1.3130352854993315

          Plot of coth

          -
          view source

          covercos

          (covercos v)

          Covercosine

          -
          view source

          coversin

          (coversin v)

          Coversine

          -
          view source

          crd

          (crd v)

          Chord

          -
          view source

          csc

          (csc v)

          Cosecant

          +
          view source

          covercos

          (covercos v)

          Covercosine

          +
          view source

          coversin

          (coversin v)

          Coversine

          +
          view source

          crd

          (crd v)

          Chord

          +
          view source

          csc

          (csc v)

          Cosecant

          Examples

          Usage

          (fastmath.core/csc 1.0)
 ;;=> 1.1883951057781215

          Plot of csc

          -
          view source

          csch

          (csch v)

          Hyperbilic cosecant

          +
          view source

          csch

          (csch v)

          Hyperbilic cosecant

          Examples

          Usage

          (fastmath.core/csch 1.0)
 ;;=> 0.8509181282393214

          Plot of csch

          -
          view source

          cut

          (cut data breaks)(cut x1 x2 breaks)

          Cut range or sequence into intervals

          -
          view source

          dec

          macro

          (dec x)

          fastmath.java.PrimitiveMath/dec function wrapped in macro.

          +
          view source

          cut

          (cut data breaks)(cut x1 x2 breaks)

          Cut range or sequence into intervals

          +
          view source

          dec

          macro

          (dec x)

          fastmath.java.PrimitiveMath/dec function wrapped in macro.

          view source

          deg-in-rad

          const

          ;;=> 0.017453292519943295

          \(\frac{\pi}{180}\)

          -
          view source

          degrees

          (degrees rad)

          Convert radians into degrees.

          +
          view source

          degrees

          (degrees rad)

          Convert radians into degrees.

          Examples

          Let’s convert \(\pi\) radians to degrees.

          (degrees PI)
-;;=> 180.0
          view source

          delta-eq

          (delta-eq a b)(delta-eq a b accuracy)

          Checks equality for given accuracy (default 1.0e-6).

          -
          view source

          delta=

          Alias for delta-eq

          -
          view source

          difference-of-products

          (difference-of-products a b c d)

          Kahan’s algorithm for (ab)-(cd) to avoid catastrophic cancellation.

          -
          view source

          digamma

          macro

          (digamma x)

          Logarithmic derivative of \(\Gamma\).

          +;;=> 180.0
          view source

          delta-eq

          (delta-eq a b)(delta-eq a b accuracy)

          Checks equality for given accuracy (default 1.0e-6).

          +
          view source

          delta=

          Alias for delta-eq

          +
          view source

          difference-of-products

          (difference-of-products a b c d)

          Kahan’s algorithm for (ab)-(cd) to avoid catastrophic cancellation.

          +
          view source

          digamma

          macro

          (digamma x)

          Logarithmic derivative of \(\Gamma\).

          Examples

          Usage

          (fastmath.core/digamma 1.0)
 ;;=> -0.5772156677920679

          Plot of digamma

          -
          view source

          dist

          (dist [x1 y1] [x2 y2])(dist x1 y1 x2 y2)

          Euclidean distance between points (x1,y1) and (x2,y2). See fastmath.vector namespace to see other metrics which work on vectors.

          +
          view source

          dist

          (dist [x1 y1] [x2 y2])(dist x1 y1 x2 y2)

          Euclidean distance between points (x1,y1) and (x2,y2). See fastmath.vector namespace to see other metrics which work on vectors.

          Examples

          Distance between two points.

          (dist 1 3 -2 10)
-;;=> 7.615773105863909
          view source

          double-array->seq

          Convert double array into sequence.

          +;;=> 7.615773105863909
          view source

          double-array->seq

          Convert double array into sequence.

          Alias for seq.

          Examples

          Convert

          (double-array->seq (seq->double-array [4 3 2]))
-;;=> (4.0 3.0 2.0)
          view source

          double-array-type

          const

          ;;=> class [D
          view source

          double-bits

          (double-bits v)

          Returns double as 64-bits (long)

          -
          view source

          double-double-array->seq

          (double-double-array->seq res)

          Convert double array of double arrays into sequence of sequences.

          +;;=> (4.0 3.0 2.0)
          view source

          double-array-type

          const

          ;;=> class [D
          view source

          double-bits

          (double-bits v)

          Returns double as 64-bits (long)

          +
          view source

          double-double-array->seq

          (double-double-array->seq res)

          Convert double array of double arrays into sequence of sequences.

          Examples

          Convert

          (double-double-array->seq (seq->double-double-array
                            [[4 3 2] (double-array [1 2 3])]))
-;;=> ((4.0 3.0 2.0) (1.0 2.0 3.0))
          view source

          double-double-array-type

          const

          ;;=> class [[D
          view source

          double-high-bits

          (double-high-bits v)

          Returns high word from double as bits

          -
          view source

          double-low-bits

          (double-low-bits v)

          Returns low word from double as bits

          -
          view source

          double-one-minus-epsilon

          const

          ;;=> 0.9999999999999999

          Value of 0x1.fffffffffffffp-1d = 0.(9)

          -
          view source

          E

          const

          ;;=> 2.718281828459045

          Value of \(e\)

          -
          view source

          EPSILON

          const

          ;;=> 1.0E-10

          Very small number \(\varepsilon\)

          -
          view source

          eq

          (eq _)(eq a b)(eq a b c)(eq a b c d)

          Primitive math equality function for doubles. See ==.

          -
          view source

          erf

          macro

          (erf x)(erf x y)

          Error function. For two arguments return difference between (erf x) and (erf y).

          +;;=> ((4.0 3.0 2.0) (1.0 2.0 3.0))
          view source

          double-double-array-type

          const

          ;;=> class [[D
          view source

          double-exponent

          (double-exponent v)

          Extract exponent information from double

          +
          view source

          double-high-bits

          (double-high-bits v)

          Returns high word from double as bits

          +
          view source

          double-low-bits

          (double-low-bits v)

          Returns low word from double as bits

          +
          view source

          double-one-minus-epsilon

          const

          ;;=> 0.9999999999999999

          Value of 0x1.fffffffffffffp-1d = 0.(9)

          +
          view source

          double-significand

          (double-significand v)

          Extract significand from double

          +
          view source

          E

          const

          ;;=> 2.718281828459045

          Value of \(e\)

          +
          view source

          EPSILON

          const

          ;;=> 1.0E-10

          Very small number \(\varepsilon\)

          +
          view source

          eq

          (eq _)(eq a b)(eq a b c)(eq a b c d)

          Primitive math equality function for doubles. See ==.

          +
          view source

          erf

          macro

          (erf x)(erf x y)

          Error function. For two arguments return difference between (erf x) and (erf y).

          Examples

          Usage

          (fastmath.core/erf 1.0)
 ;;=> 0.8427007929497151

          Plot of erf

          Plort of 2d erf

          -
          view source

          erfc

          macro

          (erfc x)

          Complementary error function.

          +
          view source

          erfc

          macro

          (erfc x)

          Complementary error function.

          Examples

          Usage

          (fastmath.core/erfc 1.0)
 ;;=> 0.15729920705028488

          Plot of erfc

          -
          view source

          evalpoly

          (evalpoly x & coeffs)

          Evaluate polynomial

          -
          view source

          even?

          macro

          (even? x)

          fastmath.java.PrimitiveMath/isEven function wrapped in macro.

          +
          view source

          evalpoly

          (evalpoly x & coeffs)

          Evaluate polynomial

          +
          view source

          even?

          macro

          (even? x)

          fastmath.java.PrimitiveMath/isEven function wrapped in macro.

          view source

          excsc

          (excsc v)

          Excosecant

          -
          view source

          exp

          macro

          (exp x)

          net.jafama.FastMath/exp function wrapped in macro.

          +
          view source

          exp

          macro

          (exp x)

          net.jafama.FastMath/exp function wrapped in macro.

          Examples

          Usage

          (fastmath.core/exp 1.0)
 ;;=> 2.7182818284590455

          Plot of exp

          -
          view source

          expm1

          macro

          (expm1 x)

          net.jafama.FastMath/expm1 function wrapped in macro.

          +
          view source

          expm1

          macro

          (expm1 x)

          net.jafama.FastMath/expm1 function wrapped in macro.

          Examples

          Usage

          (fastmath.core/expm1 1.0)
 ;;=> 1.7182818284590455

          Plot of expm1

          -
          view source

          exsec

          (exsec v)

          Exsecant

          -
          view source

          factorial

          (factorial n)

          Factorial

          -
          view source

          factorial20

          (factorial20 n)

          Factorial table up to 20!

          -
          view source

          fast*

          (fast* a b)

          Primitive * for two doubles as function.

          -
          view source

          fast+

          (fast+ a b)

          Primitive + for two doubles as function.

          -
          view source

          fast-

          (fast- a b)

          Primitive - for two doubles as function.

          -
          view source

          fast-identity

          (fast-identity a)

          Identity on double.

          -
          view source

          fast-max

          (fast-max a b)

          Primitive max for two doubles as function.

          -
          view source

          fast-min

          (fast-min a b)

          Primitive min for two doubles as function

          -
          view source

          floor

          (floor x)(floor x scale)

          \(\lfloor x \rfloor\). See: qfloor.

          +
          view source

          exsec

          (exsec v)

          Exsecant

          +
          view source

          factorial

          (factorial n)

          Factorial

          +
          view source

          factorial20

          (factorial20 n)

          Factorial table up to 20!

          +
          view source

          fast*

          (fast* a b)

          Primitive * for two doubles as function.

          +
          view source

          fast+

          (fast+ a b)

          Primitive + for two doubles as function.

          +
          view source

          fast-

          (fast- a b)

          Primitive - for two doubles as function.

          +
          view source

          fast-identity

          (fast-identity a)

          Identity on double.

          +
          view source

          fast-max

          (fast-max a b)

          Primitive max for two doubles as function.

          +
          view source

          fast-min

          (fast-min a b)

          Primitive min for two doubles as function

          +
          view source

          floor

          (floor x)(floor x scale)

          \(\lfloor x \rfloor\). See: qfloor.

          Rounding is done to a multiply of scale value (when provided).

          Examples

          Scaled floor

          (floor 234.312 10)
@@ -308,9 +310,9 @@ 
          Other functions
          
 ;; Test: ok.

          Usage

          (fastmath.core/floor 1.0)
 ;;=> 1.0

          Plot of floor

          -
          view source

          fma

          macro

          (fma x y z)

          [x y z] -> (+ z (* x y)) or Math/fma for java 9+

          -
          view source

          FOUR_INV_PI

          const

          ;;=> 1.2732395447351628

          Value of \(\frac{4}{\pi}\)

          -
          view source

          fpow

          macro

          (fpow x y)

          Fast version of pow where exponent is integer.

          +
          view source

          fma

          macro

          (fma x y z)

          [x y z] -> (+ z (* x y)) or Math/fma for java 9+

          +
          view source

          FOUR_INV_PI

          const

          ;;=> 1.2732395447351628

          Value of \(\frac{4}{\pi}\)

          +
          view source

          fpow

          macro

          (fpow x y)

          Fast version of pow where exponent is integer.

          Examples

          Example

          (fpow 1.23 4)
 ;;=> 2.28886641
@@ -321,7 +323,7 @@ 
          Other functions
          
 (fpow 1.23 5)
 ;;=> 2.8153056842999997
 (fpow 1.23 -2)
-;;=> 0.6609822195782934
          view source

          frac

          (frac v)

          Fractional part, always returns values from 0.0 to 1.0 (exclusive). See sfrac for signed version.

          +;;=> 0.6609822195782934
          view source

          frac

          (frac v)

          Fractional part, always returns values from 0.0 to 1.0 (exclusive). See sfrac for signed version.

          Examples

          Examples

          (frac 0.555)
 ;;=> 0.555
@@ -329,19 +331,19 @@ 
          Other functions
          
 ;;=> 0.555

          Usage

          (fastmath.core/frac 1.0)
 ;;=> 0.0

          Plot of frac

          -
          view source

          GAMMA

          const

          ;;=> 0.5772156649015329

          Euler-Mascheroni constant

          -
          view source

          gamma

          macro

          (gamma x)

          Gamma function \(\Gamma(x)\)

          +
          view source

          GAMMA

          const

          ;;=> 0.5772156649015329

          Euler-Mascheroni constant

          +
          view source

          gamma

          macro

          (gamma x)

          Gamma function \(\Gamma(x)\)

          Examples

          Usage

          (fastmath.core/gamma 1.0)
 ;;=> 1.0

          Plot of gamma

          -
          view source

          gcd

          (gcd a b)

          Fast binary greatest common divisor (Stein’s algorithm)

          +
          view source

          gcd

          (gcd a b)

          Fast binary greatest common divisor (Stein’s algorithm)

          Examples

          Usage

          (gcd 340 440)
 ;;=> 20
 (gcd (* 123 5544331) (* 123 123))
 ;;=> 123
 (gcd -234 -432)
-;;=> 18
          view source

          group-by-intervals

          (group-by-intervals coll)(group-by-intervals intervals coll)

          Group sequence of values into given intervals.

          +;;=> 18
          view source

          group-by-intervals

          (group-by-intervals coll)(group-by-intervals intervals coll)

          Group sequence of values into given intervals.

          If intervals are missing, use co-intervals to find some.

          Examples

          Examples

          (group-by-intervals [1 2 3 4 1 2 3 4 5 1 -2])
@@ -351,12 +353,12 @@ 
          Other functions
          
 ;;=>  [2.5 4.5] (3 4 3 4),
 ;;=>  [3.5 5.5] (4 4 5)}
 (group-by-intervals [[1 2] [3 4]] [1 2 3 4 1 2 3 4 5 1 -2])
-;;=> {[1 2] (2 2), [3 4] (4 4)}
          view source

          hacovercos

          (hacovercos v)

          Hacovercosine

          -
          view source

          hacoversin

          (hacoversin v)

          Hacoversine

          -
          view source

          HALF_PI

          const

          ;;=> 1.5707963267948966

          Value of \(\frac{\pi}{2}\)

          -
          view source

          havercos

          (havercos v)

          Havercosine

          -
          view source

          haversin

          (haversin v)(haversin [lat1 lon1] [lat2 lon2])(haversin lat1 lon1 lat2 lon2)

          Haversine formula for value or lattitude and longitude pairs.

          -
          view source

          haversine

          Haversine (haversin alias)

          +;;=> {[1 2] (2 2), [3 4] (4 4)}
          view source

          hacovercos

          (hacovercos v)

          Hacovercosine

          +
          view source

          hacoversin

          (hacoversin v)

          Hacoversine

          +
          view source

          HALF_PI

          const

          ;;=> 1.5707963267948966

          Value of \(\frac{\pi}{2}\)

          +
          view source

          havercos

          (havercos v)

          Havercosine

          +
          view source

          haversin

          (haversin v)(haversin [lat1 lon1] [lat2 lon2])(haversin lat1 lon1 lat2 lon2)

          Haversine formula for value or lattitude and longitude pairs.

          +
          view source

          haversine

          Haversine (haversin alias)

          Examples

          Usage

          (haversine 10)
 ;;=> 0.9195357645382263
@@ -366,12 +368,12 @@ 
          Other functions
          
 ;;=> 0.17694529423473296

          Usage

          (fastmath.core/haversine 1.0)
 ;;=> 0.22984884706593012

          Plot of haversine

          -
          view source

          haversine-dist

          (haversine-dist [lat1 lon1] [lat2 lon2])(haversine-dist lat1 lon1 lat2 lon2)

          Haversine distance d for r=1

          +
          view source

          haversine-dist

          (haversine-dist [lat1 lon1] [lat2 lon2])(haversine-dist lat1 lon1 lat2 lon2)

          Haversine distance d for r=1

          Examples

          Usage

          (haversine-dist [10 20] [30 10])
 ;;=> 0.8683203900985386
 (haversine-dist 10 20 30 10)
-;;=> 0.8683203900985386
          view source

          high-2-exp

          (high-2-exp v)

          Find lowest exponent (power of 2) which is greater or equal x. See low-2-exp.

          +;;=> 0.8683203900985386
          view source

          high-2-exp

          (high-2-exp v)

          Find lowest exponent (power of 2) which is greater or equal x. See low-2-exp.

          Examples

          Result 5 means, that \(2^5=32\) is greater than 23.11. Lower exponent (4) gives lower value (16).

          (high-2-exp 23.11)
 ;;=> 5

          For x less than 1.0 gives negative exponent.

          @@ -379,21 +381,21 @@

          Other functions

          ;;=> -3

          Usage

          (fastmath.core/high-2-exp 1.0)
 ;;=> 0

          Plot of high-2-exp

          -
          view source

          high-exp

          (high-exp b x)

          Find lowest exponent for base b which is higher or equalx. See also low-exp.

          +
          view source

          high-exp

          (high-exp b x)

          Find lowest exponent for base b which is higher or equalx. See also low-exp.

          Examples

          Result 2 means, that \(9^2=81\) is greater than 23.11. Lower exponent 1 gives lower value 9.

          (high-exp 9 23.11)
 ;;=> 2

          For x less than 1.0 gives negative exponent.

          (high-exp 10 0.011)
-;;=> -1
          view source

          hypot

          (hypot x y)(hypot x y z)

          Hypot. See also hypot-sqrt.

          +;;=> -1
          view source

          hypot

          (hypot x y)(hypot x y z)

          Hypot. See also hypot-sqrt.

          Examples

          Plot of hypot

          -
          view source

          hypot-sqrt

          (hypot-sqrt x y)(hypot-sqrt x y z)

          Hypot, sqrt version: \(\sqrt{x^2+y^2}\) or \(\sqrt{x^2+y^2+z^2}\). Should be faster than hypot.

          +
          view source

          hypot-sqrt

          (hypot-sqrt x y)(hypot-sqrt x y z)

          Hypot, sqrt version: \(\sqrt{x^2+y^2}\) or \(\sqrt{x^2+y^2+z^2}\). Should be faster than hypot.

          Examples

          Plot of hypot-sqrt

          -
          view source

          I0

          (I0 x)

          Modified Bessel function of the first kind, order 0.

          -
          view source

          iabs

          (iabs x)

          \(|x|\) - long version. See abs.

          +
          view source

          I0

          (I0 x)

          Modified Bessel function of the first kind, order 0.

          +
          view source

          iabs

          (iabs x)

          \(|x|\) - long version. See abs.

          Examples

          Usage

          (fastmath.core/iabs 1.0)
 ;;=> 1

          Plot of iabs

          -
          view source

          inc

          macro

          (inc x)

          fastmath.java.PrimitiveMath/inc function wrapped in macro.

          +
          view source

          inc

          macro

          (inc x)

          fastmath.java.PrimitiveMath/inc function wrapped in macro.

          view source

          inf?

          (inf? v)

          Check if number is infinite

          Examples

          Usage

          (inf? ##Inf)
@@ -407,25 +409,26 @@ 
          Other functions
          
 (inf? ##NaN)
 ;;=> false
 
-;; Test: ok.
          view source

          inv-erf

          macro

          (inv-erf x)

          Inverse erf.

          +;; Test: ok.
          view source

          inv-erf

          macro

          (inv-erf x)

          Inverse erf.

          Examples

          Usage

          (fastmath.core/inv-erf 1.0)
 ;;=> Infinity

          Plot of inv-erf

          -
          view source

          inv-erfc

          macro

          (inv-erfc x)

          Inverse erfc.

          +
          view source

          inv-erfc

          macro

          (inv-erfc x)

          Inverse erfc.

          Examples

          Usage

          (fastmath.core/inv-erfc 1.0)
 ;;=> 0.0

          Plot of inv-erfc

          -
          view source

          inv-gamma-1pm1

          macro

          (inv-gamma-1pm1 x)

          \(\frac{1}{\Gamma(1+x)}-1\).

          +
          view source

          inv-gamma-1pm1

          macro

          (inv-gamma-1pm1 x)

          \(\frac{1}{\Gamma(1+x)}-1\).

          Examples

          Usage

          (fastmath.core/inv-gamma-1pm1 1.0)
 ;;=> -0.0

          Plot of inv-gamma-1pm1

          -
          view source

          INV_LN2

          const

          ;;=> 1.4426950408889634

          \(\frac{1}{\ln{2}}\)

          -
          view source

          INV_LOG_HALF

          const

          ;;=> -1.4426950408889634

          \(\frac{1}{\ln{0.5}}\)

          -
          view source

          INV_PI

          const

          ;;=> 0.3183098861837907

          Value of \(\frac{1}{\pi}\)

          -
          view source

          INV_SQRT2PI

          const

          ;;=> 0.3989422804014327

          \(\frac{1}{\sqrt\pi}\)

          -
          view source

          INV_SQRT_2

          const

          ;;=> 0.7071067811865475

          \(\frac{1}{\sqrt{2}}\)

          -
          view source

          INV_TWO_PI

          const

          ;;=> 0.15915494309189535

          Value of \(\frac{1}{2 \pi}\)

          -
          view source

          invalid-double?

          (invalid-double? v)

          Check if number is invalid

          +
          view source

          INV_FOUR_PI

          const

          ;;=> 0.07957747154594767

          Value of \(\frac{1}{4 \pi}\)

          +
          view source

          INV_LN2

          const

          ;;=> 1.4426950408889634

          \(\frac{1}{\ln{2}}\)

          +
          view source

          INV_LOG_HALF

          const

          ;;=> -1.4426950408889634

          \(\frac{1}{\ln{0.5}}\)

          +
          view source

          INV_PI

          const

          ;;=> 0.3183098861837907

          Value of \(\frac{1}{\pi}\)

          +
          view source

          INV_SQRT2PI

          const

          ;;=> 0.3989422804014327

          \(\frac{1}{\sqrt\pi}\)

          +
          view source

          INV_SQRT_2

          const

          ;;=> 0.7071067811865475

          \(\frac{1}{\sqrt{2}}\)

          +
          view source

          INV_TWO_PI

          const

          ;;=> 0.15915494309189535

          Value of \(\frac{1}{2 \pi}\)

          +
          view source

          invalid-double?

          (invalid-double? v)

          Check if number is invalid

          Examples

          Usage

          (invalid-double? ##Inf)
 ;;=> true
@@ -438,7 +441,7 @@ 
          Other functions
          
 (invalid-double? ##NaN)
 ;;=> true
 
-;; Test: ok.
          view source

          itrunc

          (itrunc v)

          Truncate fractional part, keep sign. Returns long.

          +;; Test: ok.
          view source

          itrunc

          (itrunc v)

          Truncate fractional part, keep sign. Returns long.

          Examples

          Examples

          (itrunc 1.234)
 ;;=> 1
@@ -446,9 +449,9 @@ 
          Other functions
          
 ;;=> -1

          Usage

          (fastmath.core/itrunc 1.0)
 ;;=> 1

          Plot of itrunc

          -
          view source

          jinc

          (jinc x)

          Besselj1 devided by x

          -
          view source

          jvm-version

          const

          ;;=> 19
          view source

          LANCZOS_G

          const

          ;;=> 4.7421875

          Lanchos approximation g constant

          -
          view source

          lcm

          (lcm a b)

          Fast binary least common multiplier.

          +
          view source

          jinc

          (jinc x)

          Besselj1 devided by x

          +
          view source

          jvm-version

          const

          ;;=> 21
          view source

          LANCZOS_G

          const

          ;;=> 4.7421875

          Lanchos approximation g constant

          +
          view source

          lcm

          (lcm a b)

          Fast binary least common multiplier.

          Examples

          Usage

          (lcm 340 440)
 ;;=> 7480
@@ -457,7 +460,7 @@ 
          Other functions
          
 (lcm 331 (* 123 123))
 ;;=> 5007699
 (lcm -234 -432)
-;;=> 5616
          view source

          lerp

          (lerp start stop t)

          Linear interpolation between start and stop for amount t. See also mlerp, cos-interpolation, quad-interpolation or smooth-interpolation.

          +;;=> 5616
          view source

          lerp

          (lerp start stop t)

          Linear interpolation between start and stop for amount t. See also mlerp, cos-interpolation, quad-interpolation or smooth-interpolation.

          Examples

          Examples

          (lerp 0.0 1.0 0.123)
 ;;=> 0.123
@@ -467,70 +470,71 @@ 
          Other functions
          
 ;;=> 150.0

          Interpolate outside given range.

          (lerp -1.0 1.0 1.5)
 ;;=> 2.0

          Plot of lerp

          -
          view source

          ln

          macro

          (ln x)

          net.jafama.FastMath/log function wrapped in macro.

          +
          view source

          ln

          macro

          (ln x)

          net.jafama.FastMath/log function wrapped in macro.

          Examples

          Usage

          (fastmath.core/ln 1.0)
 ;;=> 0.0

          Plot of ln

          -
          view source

          LN10

          const

          ;;=> 2.302585092994046

          \(\ln{10}\)

          -
          view source

          LN2

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          -
          view source

          LN2_2

          const

          ;;=> 0.34657359027997264

          \(\frac{\ln{2}}{2}\)

          -
          view source

          log

          macro

          (log x)

          net.jafama.FastMath/log function wrapped in macro.

          +
          view source

          LN10

          const

          ;;=> 2.302585092994046

          \(\ln{10}\)

          +
          view source

          LN2

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          +
          view source

          LN2_2

          const

          ;;=> 0.34657359027997264

          \(\frac{\ln{2}}{2}\)

          +
          view source

          log

          macro

          (log x)

          net.jafama.FastMath/log function wrapped in macro.

          Examples

          Usage

          (fastmath.core/log 1.0)
 ;;=> 0.0

          Plot of log

          -
          view source

          log-beta

          macro

          (log-beta x y)

          Logarithm of Beta function.

          +
          view source

          log-beta

          macro

          (log-beta x y)

          Logarithm of Beta function.

          Examples

          Plot of log-beta

          -
          view source

          log-combinations

          (log-combinations n k)

          Log of binomial coefficient (n choose k)

          -
          view source

          log-factorial

          (log-factorial x)

          Log factorial, alias to log-gamma

          -
          view source

          log-gamma

          macro

          (log-gamma x)

          Log of Gamma function \(\ln\Gamma(x)\)

          +
          view source

          log-combinations

          (log-combinations n k)

          Log of binomial coefficient (n choose k)

          +
          view source

          log-factorial

          (log-factorial x)

          Log factorial, alias to log-gamma

          +
          view source

          log-gamma

          macro

          (log-gamma x)

          Log of Gamma function \(\ln\Gamma(x)\)

          Examples

          Usage

          (fastmath.core/log-gamma 1.0)
 ;;=> -0.0

          Plot of log-gamma

          -
          view source

          log-gamma-1p

          macro

          (log-gamma-1p x)

          Log of Gamma function \(\ln\Gamma(1+x)\)

          +
          view source

          log-gamma-1p

          macro

          (log-gamma-1p x)

          Log of Gamma function \(\ln\Gamma(1+x)\)

          Examples

          Usage

          (fastmath.core/log-gamma-1p 1.0)
 ;;=> 0.0

          Plot of log-gamma-1p

          -
          view source

          log-I0

          (log-I0 x)

          Log of I0.

          -
          view source

          log10

          macro

          (log10 x)

          \(\ln_{10}{x}\)

          +
          view source

          log-I0

          (log-I0 x)

          Log of I0.

          +
          view source

          log10

          macro

          (log10 x)

          \(\ln_{10}{x}\)

          Examples

          Usage

          (fastmath.core/log10 1.0)
 ;;=> 0.0

          Plot of log10

          -
          view source

          LOG10E

          const

          ;;=> 0.4342944819032518

          \(\log_{10}{e}\)

          -
          view source

          log1mexp

          (log1mexp x)

          log(1-exp(x))

          -
          view source

          log1p

          macro

          (log1p x)

          net.jafama.FastMath/log1p function wrapped in macro.

          +
          view source

          LOG10E

          const

          ;;=> 0.4342944819032518

          \(\log_{10}{e}\)

          +
          view source

          log1mexp

          (log1mexp x)

          log(1-exp(x))

          +
          view source

          log1p

          macro

          (log1p x)

          net.jafama.FastMath/log1p function wrapped in macro.

          Examples

          Usage

          (fastmath.core/log1p 1.0)
 ;;=> 0.6931471805599453

          Plot of log1p

          -
          view source

          log1pexp

          (log1pexp x)

          log(1+exp(x))

          +
          view source

          log1pexp

          (log1pexp x)

          log(1+exp(x))

          Examples

          Usage

          (fastmath.core/log1pexp 1.0)
 ;;=> 1.3132616875182228

          Plot of log1pexp

          -
          view source

          log1pmx

          (log1pmx x)

          log(1+x)-x

          -
          view source

          log1psq

          (log1psq x)

          log(1+x^2))

          -
          view source

          log2

          (log2 x)

          Logarithm with base 2.

          +
          view source

          log1pmx

          (log1pmx x)

          log(1+x)-x

          +
          view source

          log1psq

          (log1psq x)

          log(1+x^2))

          +
          view source

          log2

          (log2 x)

          Logarithm with base 2.

          \(\ln_2{x}\)

          Examples

          Usage

          (fastmath.core/log2 1.0)
 ;;=> 0.0

          Plot of log2

          -
          view source

          LOG2E

          const

          ;;=> 1.4426950408889634

          \(\log_{2}{e}\)

          -
          view source

          log2mexp

          (log2mexp x)

          log(2-exp(x))

          -
          view source

          LOG_HALF

          const

          ;;=> -0.6931471805599453

          \(\ln{0.5}\)

          -
          view source

          LOG_PI

          const

          ;;=> 1.1447298858494002

          \(\ln{\pi}\)

          -
          view source

          LOG_TWO_PI

          const

          ;;=> 1.8378770664093453

          \(\ln{2 \pi}\)

          -
          view source

          logaddexp

          (logaddexp x y)

          log(exp(x)+exp(y))

          -
          view source

          logb

          (logb b x)

          Logarithm with base b.

          +
          view source

          LOG2E

          const

          ;;=> 1.4426950408889634

          \(\log_{2}{e}\)

          +
          view source

          log2int

          (log2int v)

          Fast and integer version of log2, returns long

          +
          view source

          log2mexp

          (log2mexp x)

          log(2-exp(x))

          +
          view source

          LOG_HALF

          const

          ;;=> -0.6931471805599453

          \(\ln{0.5}\)

          +
          view source

          LOG_PI

          const

          ;;=> 1.1447298858494002

          \(\ln{\pi}\)

          +
          view source

          LOG_TWO_PI

          const

          ;;=> 1.8378770664093453

          \(\ln{2 \pi}\)

          +
          view source

          logaddexp

          (logaddexp x y)

          log(exp(x)+exp(y))

          +
          view source

          logb

          (logb b x)

          Logarithm with base b.

          \(\ln_b{x}\)

          -
          view source

          logcosh

          (logcosh x)

          log(cosh(x))

          -
          view source

          logexpm1

          (logexpm1 x)

          log(exp(x)-1))

          -
          view source

          logistic

          Alias for sigmoid

          -
          view source

          logit

          (logit x)

          Logit function

          +
          view source

          logcosh

          (logcosh x)

          log(cosh(x))

          +
          view source

          logexpm1

          (logexpm1 x)

          log(exp(x)-1))

          +
          view source

          logistic

          Alias for sigmoid

          +
          view source

          logit

          (logit x)

          Logit function

          Examples

          Usage

          (fastmath.core/logit 1.0)
 ;;=> Infinity

          Plot of logit

          -
          view source

          logmxp1

          (logmxp1 x)

          log(x)-x+1

          -
          view source

          logsubexp

          (logsubexp x y)

          log(abs(exp(x)-exp(y)))

          -
          view source

          logsumexp

          (logsumexp xs)

          log(exp(x1)+…+exp(xn))

          -
          view source

          low-2-exp

          (low-2-exp x)

          Find greatest exponent (power of 2) which is lower or equal x. See high-2-exp.

          +
          view source

          logmxp1

          (logmxp1 x)

          log(x)-x+1

          +
          view source

          logsubexp

          (logsubexp x y)

          log(abs(exp(x)-exp(y)))

          +
          view source

          logsumexp

          (logsumexp xs)

          log(exp(x1)+…+exp(xn))

          +
          view source

          low-2-exp

          (low-2-exp x)

          Find greatest exponent (power of 2) which is lower or equal x. See high-2-exp.

          Examples

          Result 4 means, that \(2^4=16\) is lower than 23.11. Next exponent (5) gives greater value (32).

          (low-2-exp 23.11)
 ;;=> 4

          For x less than 1.0 gives negative exponent.

          @@ -538,44 +542,44 @@

          Other functions

          ;;=> -4

          Usage

          (fastmath.core/low-2-exp 1.0)
 ;;=> 0

          Plot of low-2-exp

          -
          view source

          low-exp

          (low-exp b x)

          Find greatest exponent for base b which is lower or equal x. See also high-exp.

          +
          view source

          low-exp

          (low-exp b x)

          Find greatest exponent for base b which is lower or equal x. See also high-exp.

          Examples

          Result 1 means, that \(9^1=9\) is lower than 23.11. Next exponent 2 gives greater value 82.

          (low-exp 9 23.11)
 ;;=> 1

          For x less than 1.0 gives negative exponent.

          (low-exp 10 0.011)
-;;=> -2
          view source

          M_1_PI

          const

          ;;=> 0.3183098861837907

          \(\frac{1}{\pi}\)

          -
          view source

          M_2_PI

          const

          ;;=> 0.6366197723675814

          \(\frac{2}{\pi}\)

          -
          view source

          M_2_SQRTPI

          const

          ;;=> 1.1283791670955126

          \(\frac{2}{\sqrt\pi}\)

          -
          view source

          M_3PI_4

          const

          ;;=> 2.356194490192345

          \(\frac{3\pi}{4}\)

          -
          view source

          M_E

          const

          ;;=> 2.718281828459045

          \(e\)

          -
          view source

          M_INVLN2

          const

          ;;=> 1.4426950408889634

          \(\frac{1}{\ln{2}}\)

          -
          view source

          M_IVLN10

          const

          ;;=> 0.43429448190325176

          \(\frac{1}{\ln{10}}\)

          -
          view source

          M_LN10

          const

          ;;=> 2.302585092994046

          \(\ln{10}\)

          -
          view source

          M_LN2

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          -
          view source

          M_LOG10E

          const

          ;;=> 0.4342944819032518

          \(\log_{10}{e}\)

          -
          view source

          M_LOG2_E

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          -
          view source

          M_LOG2E

          const

          ;;=> 1.4426950408889634

          \(\log_{2}{e}\)

          -
          view source

          M_PI

          const

          ;;=> 3.141592653589793

          \(\pi\)

          -
          view source

          M_PI_2

          const

          ;;=> 1.5707963267948966

          \(\frac{\pi}{2}\)

          -
          view source

          M_PI_4

          const

          ;;=> 0.7853981633974483

          \(\frac{\pi}{4}\)

          -
          view source

          M_SQRT1_2

          const

          ;;=> 0.7071067811865475

          \(\frac{1}{\sqrt{2}}\)

          -
          view source

          M_SQRT2

          const

          ;;=> 1.4142135623730951

          \(\sqrt{2}\)

          -
          view source

          M_SQRT3

          const

          ;;=> 1.7320508075688772

          \(\sqrt{3}\)

          -
          view source

          M_SQRT_PI

          const

          ;;=> 1.7724538509055159

          \(\sqrt\pi\)

          -
          view source

          M_TWOPI

          const

          ;;=> 6.283185307179586

          \(2\pi\)

          -
          view source

          MACHINE-EPSILON

          const

          ;;=> 1.1102230246251565E-16

          Smallest machine number. Value is calculated during evaluation and may differ on different processors.

          -
          view source

          make-norm

          (make-norm start stop)(make-norm start stop dstart dstop)

          Make norm function for given range. Resulting function accepts double value (with optional target [dstart,dstop] range) and returns double.

          +;;=> -2
          view source

          M_1_PI

          const

          ;;=> 0.3183098861837907

          \(\frac{1}{\pi}\)

          +
          view source

          M_2_PI

          const

          ;;=> 0.6366197723675814

          \(\frac{2}{\pi}\)

          +
          view source

          M_2_SQRTPI

          const

          ;;=> 1.1283791670955126

          \(\frac{2}{\sqrt\pi}\)

          +
          view source

          M_3PI_4

          const

          ;;=> 2.356194490192345

          \(\frac{3\pi}{4}\)

          +
          view source

          M_E

          const

          ;;=> 2.718281828459045

          \(e\)

          +
          view source

          M_INVLN2

          const

          ;;=> 1.4426950408889634

          \(\frac{1}{\ln{2}}\)

          +
          view source

          M_IVLN10

          const

          ;;=> 0.43429448190325176

          \(\frac{1}{\ln{10}}\)

          +
          view source

          M_LN10

          const

          ;;=> 2.302585092994046

          \(\ln{10}\)

          +
          view source

          M_LN2

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          +
          view source

          M_LOG10E

          const

          ;;=> 0.4342944819032518

          \(\log_{10}{e}\)

          +
          view source

          M_LOG2_E

          const

          ;;=> 0.6931471805599453

          \(\ln{2}\)

          +
          view source

          M_LOG2E

          const

          ;;=> 1.4426950408889634

          \(\log_{2}{e}\)

          +
          view source

          M_PI

          const

          ;;=> 3.141592653589793

          \(\pi\)

          +
          view source

          M_PI_2

          const

          ;;=> 1.5707963267948966

          \(\frac{\pi}{2}\)

          +
          view source

          M_PI_4

          const

          ;;=> 0.7853981633974483

          \(\frac{\pi}{4}\)

          +
          view source

          M_SQRT1_2

          const

          ;;=> 0.7071067811865475

          \(\frac{1}{\sqrt{2}}\)

          +
          view source

          M_SQRT2

          const

          ;;=> 1.4142135623730951

          \(\sqrt{2}\)

          +
          view source

          M_SQRT3

          const

          ;;=> 1.7320508075688772

          \(\sqrt{3}\)

          +
          view source

          M_SQRT_PI

          const

          ;;=> 1.7724538509055159

          \(\sqrt\pi\)

          +
          view source

          M_TWOPI

          const

          ;;=> 6.283185307179586

          \(2\pi\)

          +
          view source

          MACHINE-EPSILON

          const

          ;;=> 1.1102230246251565E-16

          Smallest machine number. Value is calculated during evaluation and may differ on different processors.

          +
          view source

          make-norm

          (make-norm start stop)(make-norm start stop dstart dstop)

          Make norm function for given range. Resulting function accepts double value (with optional target [dstart,dstop] range) and returns double.

          Examples

          Make cos() normalizer from -1.0,1.0 to 0.0, 1.0.

          (let [norm-cos (make-norm -1.0 1.0 0.0 1.0)] (norm-cos (cos 2.0)))
 ;;=> 0.29192658172642894

          Make normalizer from 0,255 to any range.

          (let [norm-0-255 (make-norm 0 255)]
   [(norm-0-255 123 -10 -20) (norm-0-255 123 20 10)])
-;;=> [-14.823529411764707 15.176470588235293]
          view source

          makepoly

          (makepoly coeffs)

          Create polynomial function for given coefficients

          -
          view source

          max

          macro

          (max x)(max x y)(max x y & rest)

          A primitive math version of max

          +;;=> [-14.823529411764707 15.176470588235293]
          view source

          makepoly

          (makepoly coeffs)

          Create polynomial function for given coefficients

          +
          view source

          max

          macro

          (max x)(max x y)(max x y & rest)

          A primitive math version of max

          view source

          mevalpoly

          macro

          (mevalpoly x & coeffs)

          Evaluate polynomial macro version in the form coeffs0+coeffs1*x+coeffs2*x^2+….

          -
          view source

          min

          macro

          (min x)(min x y)(min x y & rest)

          A primitive math version of min

          +
          view source

          min

          macro

          (min x)(min x y)(min x y & rest)

          A primitive math version of min

          view source

          minkowski

          (minkowski x)

          Minkowski’s question mark function ?(x)

          -
          view source

          mlerp

          macro

          (mlerp start stop t)

          lerp as macro. For inline code. See also lerp, cos-interpolation, quad-interpolation or smooth-interpolation.

          +
          view source

          mlerp

          macro

          (mlerp start stop t)

          lerp as macro. For inline code. See also lerp, cos-interpolation, quad-interpolation or smooth-interpolation.

          Examples

          Examples

          (mlerp 0.0 1.0 0.123)
 ;;=> 0.123
@@ -584,7 +588,7 @@ 
          Other functions
          
 (mlerp 100 200 0.5)
 ;;=> 150.0

          Interpolate outside given range.

          (mlerp -1.0 1.0 1.5)
-;;=> 2.0
          view source

          mnorm

          macro

          (mnorm v start stop)(mnorm v start1 stop1 start2 stop2)

          Macro version of norm.

          +;;=> 2.0
          view source

          mnorm

          macro

          (mnorm v start stop)(mnorm v start1 stop1 start2 stop2)

          Macro version of norm.

          Examples

          Normalize from 1,-1 to 0,1

          (mnorm 0.234 -1.0 1.0)
 ;;=> 0.617

          Normalize from -1,1 to 0,1

          @@ -593,7 +597,7 @@

          Other functions

          (mnorm (cos HALF_PI) -1.0 1.0 0.0 255.0)
 ;;=> 127.5

          Normalize cos() to 255,0

          (mnorm (cos HALF_PI) -1.0 1.0 255.0 0.0)
-;;=> 127.5
          view source

          mod

          macro

          (mod x y)

          fastmath.java.PrimitiveMath/modulus function wrapped in macro.

          +;;=> 127.5
          view source

          mod

          macro

          (mod x y)

          fastmath.java.PrimitiveMath/modulus function wrapped in macro.

          Examples

          Modulus (compared to clojure.core version).

          (mod 3.123 0.333)
 ;;=> 0.12600000000000006
@@ -611,7 +615,7 @@ 
          Other functions
          
 ;;=> -0.1259999999999999
 (clojure.core/mod 3.123 -0.333)
 ;;=> -0.20700000000000013
          view source

          muladd

          macro

          (muladd x y z)

          [x y z] -> (+ z (* x y)) or Math/fma for java 9+

          -
          view source

          nan?

          (nan? v)

          Check if number is NaN

          +
          view source

          nan?

          (nan? v)

          Check if number is NaN

          Examples

          Usage

          (nan? ##Inf)
 ;;=> false
@@ -624,7 +628,7 @@ 
          Other functions
          
 (nan? ##NaN)
 ;;=> true
 
-;; Test: ok.
          view source

          neg-inf?

          (neg-inf? v)

          Check if number is negatively infinite

          +;; Test: ok.
          view source

          neg-inf?

          (neg-inf? v)

          Check if number is negatively infinite

          Examples

          Usage

          (neg-inf? ##Inf)
 ;;=> false
@@ -637,14 +641,15 @@ 
          Other functions
          
 (neg-inf? ##NaN)
 ;;=> false
 
-;; Test: ok.
          view source

          neg?

          macro

          (neg? x)

          fastmath.java.PrimitiveMath/isNeg function wrapped in macro.

          -
          view source

          negmuladd

          macro

          (negmuladd x y z)

          [x y z] -> (+ z (* -1.0 x y)

          -
          view source

          next-double

          (next-double v)(next-double v delta)

          Next double value. Optional value delta sets step amount.

          +;; Test: ok.
          view source

          neg?

          macro

          (neg? x)

          fastmath.java.PrimitiveMath/isNeg function wrapped in macro.

          +
          view source

          negative-zero?

          (negative-zero? x)

          Check if zero is negative, ie. -0.0

          +
          view source

          negmuladd

          macro

          (negmuladd x y z)

          [x y z] -> (+ z (* -1.0 x y)

          +
          view source

          next-double

          (next-double v)(next-double v delta)

          Next double value. Optional value delta sets step amount.

          Examples

          Next double.

          (next-double 1234.56789)
 ;;=> 1234.5678900000003

          Next double with delta.

          (next-double 1234.56789 1000)
-;;=> 1234.5678900002274
          view source

          norm

          (norm v start stop)(norm v start1 stop1 start2 stop2)

          Normalize v from the range [start,stop] to the range [0,1] or map v from the range [start1,stop1] to the range [start2,stop2]. See also make-norm.

          +;;=> 1234.5678900002274
          view source

          norm

          (norm v start stop)(norm v start1 stop1 start2 stop2)

          Normalize v from the range [start,stop] to the range [0,1] or map v from the range [start1,stop1] to the range [start2,stop2]. See also make-norm.

          Examples

          Normalize from 1,-1 to 0,1

          (norm 0.234 -1.0 1.0)
 ;;=> 0.617

          Normalize from -1,1 to 0,1

          @@ -653,7 +658,7 @@

          Other functions

          (norm (cos HALF_PI) -1.0 1.0 0.0 255.0)
 ;;=> 127.5

          Normalize cos() to 255,0

          (norm (cos HALF_PI) -1.0 1.0 255.0 0.0)
-;;=> 127.5
          view source

          not-neg?

          macro

          (not-neg? x)

          fastmath.java.PrimitiveMath/isNNeg function wrapped in macro.

          +;;=> 127.5
          view source

          not-neg?

          macro

          (not-neg? x)

          fastmath.java.PrimitiveMath/isNNeg function wrapped in macro.

          view source

          not-pos?

          macro

          (not-pos? x)

          fastmath.java.PrimitiveMath/isNPos function wrapped in macro.

          view source

          not==

          macro

          (not== x)(not== x y)(not== x y & rest)

          A primitive math version of not==

          view source

          odd?

          macro

          (odd? x)

          fastmath.java.PrimitiveMath/isOdd function wrapped in macro.

          @@ -668,9 +673,9 @@

          Other functions

          (order [1 1 3 2 1 1 2 3 4 3] true)
 ;;=> (8 2 7 9 3 6 0 1 4 5)
 
-;; Test: ok.
          view source

          PHI

          const

          ;;=> 1.618033988749895

          Golden ratio \(\phi\)

          -
          view source

          PI

          const

          ;;=> 3.141592653589793

          Value of \(\pi\)

          -
          view source

          pos-inf?

          (pos-inf? v)

          Check if number is positively infinite

          +;; Test: ok.
          view source

          PHI

          const

          ;;=> 1.618033988749895

          Golden ratio \(\phi\)

          +
          view source

          PI

          const

          ;;=> 3.141592653589793

          Value of \(\pi\)

          +
          view source

          pos-inf?

          (pos-inf? v)

          Check if number is positively infinite

          Examples

          Usage

          (pos-inf? ##Inf)
 ;;=> true
@@ -683,23 +688,23 @@ 
          Other functions
          
 (pos-inf? ##NaN)
 ;;=> false
 
-;; Test: ok.
          view source

          pos?

          macro

          (pos? x)

          fastmath.java.PrimitiveMath/isPos function wrapped in macro.

          +;; Test: ok.
          view source

          pos?

          macro

          (pos? x)

          fastmath.java.PrimitiveMath/isPos function wrapped in macro.

          view source

          pow

          macro

          (pow x y)

          net.jafama.FastMath/pow function wrapped in macro.

          -
          view source

          pow2

          (pow2 x)

          Same as sq. \(x^2\)

          +
          view source

          pow2

          (pow2 x)

          Same as sq. \(x^2\)

          Examples

          Usage

          (fastmath.core/pow2 1.0)
 ;;=> 1.0

          Plot of pow2

          -
          view source

          pow3

          (pow3 x)

          \(x^3\)

          +
          view source

          pow3

          (pow3 x)

          \(x^3\)

          Examples

          Usage

          (fastmath.core/pow3 1.0)
 ;;=> 1.0

          Plot of pow3

          -
          view source

          prev-double

          (prev-double v)(prev-double v delta)

          Next double value. Optional value delta sets step amount.

          +
          view source

          prev-double

          (prev-double v)(prev-double v delta)

          Next double value. Optional value delta sets step amount.

          Examples

          Prev double.

          (prev-double 1234.56789)
 ;;=> 1234.5678899999998

          Prev double with delta.

          (prev-double 1234.56789 1000)
-;;=> 1234.5678899997727
          view source

          qceil

          macro

          (qceil x)

          Fast version of ceil. Returns long. See: ceil.

          -
          view source

          qcos

          macro

          (qcos x)

          Fast and less accurate cos.

          +;;=> 1234.5678899997727
          view source

          qceil

          macro

          (qceil x)

          Fast version of ceil. Returns long. See: ceil.

          +
          view source

          qcos

          macro

          (qcos x)

          Fast and less accurate cos.

          Examples

          Compare cos and qcos.

          (cos 1.123)
 ;;=> 0.43298018843109504
@@ -707,12 +712,12 @@ 
          Other functions
          
 ;;=> 0.433093818853152

          Usage

          (fastmath.core/qcos 1.0)
 ;;=> 0.540171472729893

          Plot of qcos

          -
          view source

          qdist

          (qdist [x1 y1] [x2 y2])(qdist x1 y1 x2 y2)

          Quick version of Euclidean distance between points. qsqrt is used instead of sqrt.

          +
          view source

          qdist

          (qdist [x1 y1] [x2 y2])(qdist x1 y1 x2 y2)

          Quick version of Euclidean distance between points. qsqrt is used instead of sqrt.

          Examples

          Distance between two points (quick version).

          (qdist 1 3 -2 10)
 ;;=> 7.481406462931432

          Distance between two points (accurate version).

          (dist 1 3 -2 10)
-;;=> 7.615773105863909
          view source

          qexp

          macro

          (qexp x)

          Quick and less accurate version of exp.

          +;;=> 7.615773105863909
          view source

          qexp

          macro

          (qexp x)

          Quick and less accurate version of exp.

          Examples

          Compare exp and qexp.

          (exp 1.123)
 ;;=> 3.07406257154899
@@ -720,8 +725,8 @@ 
          Other functions
          
 ;;=> 3.1542205810546875

          Usage

          (fastmath.core/qexp 1.0)
 ;;=> 2.799318313598633

          Plot of qexp

          -
          view source

          qfloor

          macro

          (qfloor x)

          Fast version of floor. Returns long. See: floor.

          -
          view source

          qlog

          macro

          (qlog x)

          Fast and less accurate version of log.

          +
          view source

          qfloor

          macro

          (qfloor x)

          Fast version of floor. Returns long. See: floor.

          +
          view source

          qlog

          macro

          (qlog x)

          Fast and less accurate version of log.

          Examples

          Compare log and qlog.

          (log 23.123)
 ;;=> 3.1408277931718307
@@ -729,13 +734,13 @@ 
          Other functions
          
 ;;=> 3.1407453502111626

          Usage

          (fastmath.core/qlog 1.0)
 ;;=> 0.0

          Plot of qlog

          -
          view source

          qpow

          macro

          (qpow x y)

          Fast and less accurate version of pow.

          +
          view source

          qpow

          macro

          (qpow x y)

          Fast and less accurate version of pow.

          Examples

          Compare pow and qpow.

          (pow 1.23 43.3)
 ;;=> 7814.322402338249
 (qpow 1.23 43.3)
-;;=> 7808.951363383271
          view source

          qround

          macro

          (qround x)

          Fast version of round. Returns long. See: rint, round.

          -
          view source

          qsin

          macro

          (qsin x)

          Fast and less accurate sin.

          +;;=> 7808.951363383271
          view source

          qround

          macro

          (qround x)

          Fast version of round. Returns long. See: rint, round.

          +
          view source

          qsin

          macro

          (qsin x)

          Fast and less accurate sin.

          Examples

          Compare sin and qsin.

          (sin 1.123)
 ;;=> 0.901403437105813
@@ -743,7 +748,7 @@ 
          Other functions
          
 ;;=> 0.901348847046022

          Usage

          (fastmath.core/qsin 1.0)
 ;;=> 0.8415549774368984

          Plot of qsin

          -
          view source

          qsqrt

          macro

          (qsqrt x)

          Approximated sqrt using binary operations with error 1.0E-2.

          +
          view source

          qsqrt

          macro

          (qsqrt x)

          Approximated sqrt using binary operations with error 1.0E-2.

          Examples

          Compare sqrt and qsqrt.

          (sqrt 23.123)
 ;;=> 4.808638060823459
@@ -751,12 +756,12 @@ 
          Other functions
          
 ;;=> 4.746781462931431

          Usage

          (fastmath.core/qsqrt 1.0)
 ;;=> 0.982050807866429

          Plot of qsqrt

          -
          view source

          quad-interpolation

          (quad-interpolation start stop t)

          Quad interpolation. See also lerp/mlerp, cos-interpolation or smooth-interpolation.

          +
          view source

          quad-interpolation

          (quad-interpolation start stop t)

          Quad interpolation. See also lerp/mlerp, cos-interpolation or smooth-interpolation.

          Examples

          Example

          (quad-interpolation 0.0 1.0 0.123)
 ;;=> 0.030258

          Plot of quad-interpolation

          -
          view source

          QUARTER_PI

          const

          ;;=> 0.7853981633974483

          Value of \(\frac{\pi}{4}\)

          -
          view source

          quot

          macro

          (quot x y)

          fastmath.java.PrimitiveMath/quotient function wrapped in macro.

          +
          view source

          QUARTER_PI

          const

          ;;=> 0.7853981633974483

          Value of \(\frac{\pi}{4}\)

          +
          view source

          quot

          macro

          (quot x y)

          fastmath.java.PrimitiveMath/quotient function wrapped in macro.

          Examples

          Quotient (compared to clojure.core version).

          (quot 3.123 0.333)
 ;;=> 9.0
@@ -774,10 +779,10 @@ 
          Other functions
          
 ;;=> 9.0
 (clojure.core/quot 3.123 -0.333)
 ;;=> -9.0
          view source

          rad-in-deg

          const

          ;;=> 57.29577951308232

          \(\frac{180}{\pi}\)

          -
          view source

          radians

          (radians deg)

          Convert degrees into radians.

          +
          view source

          radians

          (radians deg)

          Convert degrees into radians.

          Examples

          Let’s convert 180 degrees to radians.

          (radians 180)
-;;=> 3.141592653589793
          view source

          rank

          (rank vs)(rank vs ties)(rank vs ties desc?)

          Sample ranks. See R docs.

          +;;=> 3.141592653589793
          view source

          rank

          (rank vs)(rank vs ties)(rank vs ties desc?)

          Sample ranks. See R docs.

          Rank uses 0 based indexing.

          Possible tie strategies: :average, :first, :last, :random, :min, :max, :dense.

          :dense is the same as in data.table::frank from R

          @@ -799,16 +804,16 @@

          Other functions

          ;; Test: ok.

          Random ties

          (rank [3 1 4 1 5 9 2 6 5 3 5] :random)
-;;=> [3 1 5 0 8 10 2 9 6 4 7]
+;;=> [4 1 5 0 6 10 2 9 7 3 8]
 (rank [3 1 4 1 5 9 2 6 5 3 5] :random)
-;;=> [3 1 5 0 7 10 2 9 8 4 6]
+;;=> [4 1 5 0 7 10 2 9 6 3 8]
 (rank [3 1 4 1 5 9 2 6 5 3 5] :random)
-;;=> [4 0 5 1 6 10 2 9 8 3 7]
+;;=> [3 1 5 0 6 10 2 9 7 4 8]
 (rank [3 1 4 1 5 9 2 6 5 3 5] :random)
-;;=> [4 0 5 1 6 10 2 9 7 3 8]
          view source

          regularized-beta

          macro

          (regularized-beta x y z)

          Regularized Beta.

          -
          view source

          regularized-gamma-p

          macro

          (regularized-gamma-p x y)

          Regularized gamma P

          -
          view source

          regularized-gamma-q

          macro

          (regularized-gamma-q x y)

          Regularized gamma Q

          -
          view source

          rem

          macro

          (rem x y)

          fastmath.java.PrimitiveMath/remainder function wrapped in macro.

          +;;=> [3 0 5 1 6 10 2 9 8 4 7]
          view source

          regularized-beta

          macro

          (regularized-beta x y z)

          Regularized Beta.

          +
          view source

          regularized-gamma-p

          macro

          (regularized-gamma-p x y)

          Regularized gamma P

          +
          view source

          regularized-gamma-q

          macro

          (regularized-gamma-q x y)

          Regularized gamma Q

          +
          view source

          rem

          macro

          (rem x y)

          fastmath.java.PrimitiveMath/remainder function wrapped in macro.

          Examples

          Remainder (compared to clojure.core version).

          (rem 3.123 0.333)
 ;;=> 0.12600000000000006
@@ -832,20 +837,21 @@ 
          Other functions
          
 (rem 3.123 0.2)
 ;;=> 0.12300000000000005
 (mod 3.123 0.2)
-;;=> 0.12300000000000005
          view source

          rint

          (rint x)

          Round to double. See round, qround.

          +;;=> 0.12300000000000005
          view source

          rint

          (rint x)(rint x scale)

          Round to double. See round, qround.

          +

          Rounding is done to a multiply of scale value (when provided).

          Examples

          Round to double.

          (rint PI)
 ;;=> 3.0

          Usage

          (fastmath.core/rint 1.0)
 ;;=> 1.0

          Plot of rint

          -
          view source

          round

          (round x)

          Round to long. See: rint, qround.

          +
          view source

          round

          (round x)

          Round to long. See: rint, qround.

          Examples

          Round to long.

          (round PI)
 ;;=> 3

          Usage

          (fastmath.core/round 1.0)
 ;;=> 1

          Plot of round

          -
          view source

          round-even

          (round-even x)

          Round evenly (like in round in R), IEEE / IEC rounding

          -
          view source

          round-up-pow2

          (round-up-pow2 v)

          Round long to the next power of 2

          +
          view source

          round-even

          (round-even x)

          Round evenly (like in round in R), IEEE / IEC rounding

          +
          view source

          round-up-pow2

          (round-up-pow2 v)

          Round long to the next power of 2

          Examples

          Examples

          (round-up-pow2 1023)
 ;;=> 1024
@@ -855,16 +861,16 @@ 
          Other functions
          
 ;;=> 2048

          Usage

          (fastmath.core/round-up-pow2 1.0)
 ;;=> 1

          Plot of round-up-pow2

          -
          view source

          rqsqrt

          macro

          (rqsqrt x)

          Inversed version of qsqrt. Quick and less accurate.

          +
          view source

          rqsqrt

          macro

          (rqsqrt x)

          Inversed version of qsqrt. Quick and less accurate.

          Examples

          Usage

          (fastmath.core/rqsqrt 1.0)
 ;;=> 0.9662250423950712

          Plot of rqsqrt

          -
          view source

          safe-sqrt

          (safe-sqrt value)

          Safe sqrt, for value <= 0 result is 0.

          +
          view source

          safe-sqrt

          (safe-sqrt value)

          Safe sqrt, for value <= 0 result is 0.

          \( \left\{ \begin{array}{lr} 0 & : x \leq 0\\ \sqrt{x} & : x > 0 \end{array} \right. \)

          Examples

          Usage

          (fastmath.core/safe-sqrt 1.0)
 ;;=> 1.0

          Plot of safe-sqrt

          -
          view source

          sample

          (sample f number-of-values)(sample f number-of-values domain?)(sample f domain-min domain-max number-of-values)(sample f domain-min domain-max number-of-values domain?)

          Sample function f and return sequence of values.

          +
          view source

          sample

          (sample f number-of-values)(sample f number-of-values domain?)(sample f domain-min domain-max number-of-values)(sample f domain-min domain-max number-of-values domain?)

          Sample function f and return sequence of values.

          range-min defaults to 0.0, range-max to 1.0.

          Range is inclusive.

          When optional domain? is set to true (default: false) function returns pairs [x,(f x)].

          @@ -885,32 +891,32 @@

          Other functions

          (sample sq 1 5 5) ;;=> (1.0 4.0 9.0 16.0 25.0) (sample sq 1 5 5 true) -;;=> ([1.0 1.0] [2.0 4.0] [3.0 9.0] [4.0 16.0] [5.0 25.0])
          view source

          sec

          (sec v)

          Secant

          +;;=> ([1.0 1.0] [2.0 4.0] [3.0 9.0] [4.0 16.0] [5.0 25.0])
          view source

          sec

          (sec v)

          Secant

          Examples

          Usage

          (fastmath.core/sec 1.0)
 ;;=> 1.8508157176809255

          Plot of sec

          -
          view source

          sech

          (sech v)

          Hyperbolic secant

          +
          view source

          sech

          (sech v)

          Hyperbolic secant

          Examples

          Usage

          (fastmath.core/sech 1.0)
 ;;=> 0.6480542736638853

          Plot of sech

          -
          view source

          seq->double-array

          (seq->double-array vs)

          Convert sequence to double array. Returns input if vs is double array already.

          +
          view source

          seq->double-array

          (seq->double-array vs)

          Convert sequence to double array. Returns input if vs is double array already.

          Examples

          Convert

          (seq->double-array [1 2 3])
-;;=> [D@3d219ef1
+;;=> [D@70fc098e
 (seq (seq->double-array [1 2 3]))
 ;;=> (1.0 2.0 3.0)
 (double-array->seq (seq->double-array [1 2 3]))
 ;;=> (1.0 2.0 3.0)

          Also works on number (treated as one element list).

          (seq (seq->double-array 1))
-;;=> (1.0)
          view source

          seq->double-double-array

          (seq->double-double-array vss)

          Convert sequence to double-array of double-arrays.

          +;;=> (1.0)
          view source

          seq->double-double-array

          (seq->double-double-array vss)

          Convert sequence to double-array of double-arrays.

          If sequence is double-array of double-arrays returns vss

          Examples

          Convert

          (seq->double-double-array [[1 2] [3 4]])
-;;=> [[D@7d01a6fa
+;;=> [[D@76f969bf
 (double-double-array->seq (seq->double-double-array [[1 2] [3 4]]))
 ;;=> ((1.0 2.0) (3.0 4.0))

          Also works on seq of numbers

          (seq (second (seq->double-double-array [1 2 3])))
-;;=> (2.0)
          view source

          sfrac

          (sfrac v)

          Fractional part, always returns values from -1.0 to 1.0 (exclusive). See frac for unsigned version.

          +;;=> (2.0)
          view source

          sfrac

          (sfrac v)

          Fractional part, always returns values from -1.0 to 1.0 (exclusive). See frac for unsigned version.

          Examples

          Examples

          (sfrac 0.555)
 ;;=> 0.555
@@ -918,82 +924,82 @@ 
          Other functions
          
 ;;=> -0.555

          Usage

          (fastmath.core/sfrac 1.0)
 ;;=> 0.0

          Plot of sfrac

          -
          view source

          sgn

          (sgn value)

          Return -1 when value is negative, 1 otherwise. See also signum.

          +
          view source

          sgn

          (sgn value)

          Return -1 when value is negative, 1 otherwise. See also signum.

          \( \left\{ \begin{array}{lr} 1.0 & : x \geq 0\\ -1.0 & : x < 0\\ \end{array} \right. \)

          Examples

          Usage

          (fastmath.core/sgn 1.0)
 ;;=> 1.0

          Plot of sgn

          -
          view source

          Si

          (Si x)

          Integral of sin(t)/t from 0 to x

          -
          view source

          sigmoid

          (sigmoid x)

          Sigmoid function

          +
          view source

          Si

          (Si x)

          Integral of sin(t)/t from 0 to x

          +
          view source

          sigmoid

          (sigmoid x)

          Sigmoid function

          Examples

          Usage

          (fastmath.core/sigmoid 1.0)
 ;;=> 0.7310585786300049

          Plot of sigmoid

          -
          view source

          signum

          (signum value)

          Return 1 if value is > 0, 0 if it is 0, -1 otherwise. See also sgn.

          +
          view source

          signum

          (signum value)

          Return 1 if value is > 0, 0 if it is 0, -1 otherwise. See also sgn.

          \( \left\{ \begin{array}{lr} 1.0 & : x > 0\\ -1.0 & : x < 0\\ 0.0 & : x = 0 \end{array} \right. \)

          Examples

          Usage

          (fastmath.core/signum 1.0)
 ;;=> 1.0

          Plot of signum

          -
          view source

          SILVER

          const

          ;;=> 2.414213562373095

          Silver ratio \(\delta_S\)

          -
          view source

          sin

          macro

          (sin x)

          net.jafama.FastMath/sin function wrapped in macro.

          +
          view source

          SILVER

          const

          ;;=> 2.414213562373095

          Silver ratio \(\delta_S\)

          +
          view source

          sin

          macro

          (sin x)

          net.jafama.FastMath/sin function wrapped in macro.

          Examples

          Usage

          (fastmath.core/sin 1.0)
 ;;=> 0.8414709848078964

          Plot of sin

          -
          view source

          sinc

          (sinc v)

          Sinc function.

          +
          view source

          sinc

          (sinc v)

          Sinc function.

          Examples

          Usage

          (fastmath.core/sinc 1.0)
 ;;=> 3.898171832295186E-17

          Plot of sinc

          -
          view source

          sinh

          macro

          (sinh x)

          net.jafama.FastMath/sinh function wrapped in macro.

          +
          view source

          sinh

          macro

          (sinh x)

          net.jafama.FastMath/sinh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/sinh 1.0)
 ;;=> 1.1752011936438016

          Plot of sinh

          -
          view source

          SIXTH

          const

          ;;=> 0.16666666666666666

          Value of \(\frac{1}{6}\)

          -
          view source

          slice-range

          (slice-range start end cnt)(slice-range cnt)

          Slice range to get cnt number of points evenly distanced.

          -
          view source

          smooth-interpolation

          (smooth-interpolation start stop t)

          Smoothstep based interpolation. See also lerp/mlerp, quad-interpolation or cos-interpolation.

          +
          view source

          SIXTH

          const

          ;;=> 0.16666666666666666

          Value of \(\frac{1}{6}\)

          +
          view source

          slice-range

          (slice-range start end cnt)(slice-range cnt)

          Slice range to get cnt number of points evenly distanced.

          +
          view source

          smooth-interpolation

          (smooth-interpolation start stop t)

          Smoothstep based interpolation. See also lerp/mlerp, quad-interpolation or cos-interpolation.

          Examples

          Example

          (smooth-interpolation 0.0 1.0 0.123)
 ;;=> 0.041665266

          Plot of smooth-interpolation

          -
          view source

          smoothstep

          (smoothstep edge0 edge1 x)

          GL smoothstep.

          +
          view source

          smoothstep

          (smoothstep edge0 edge1 x)

          GL smoothstep.

          Examples

          x from range.

          (smoothstep 100 200 120)
 ;;=> 0.10400000000000002

          corner case (< x edge0)

          (smoothstep 100 200 50)
 ;;=> 0.0

          corner case (> x edge1)

          (smoothstep 100 200 250)
-;;=> 1.0
          view source

          sq

          (sq x)

          Same as pow2. \(x^2\)

          +;;=> 1.0
          view source

          sq

          (sq x)

          Same as pow2. \(x^2\)

          Examples

          Usage

          (fastmath.core/sq 1.0)
 ;;=> 1.0

          Plot of sq

          -
          view source

          sqrt

          macro

          (sqrt x)

          \(\sqrt{x}\)

          +
          view source

          sqrt

          macro

          (sqrt x)

          \(\sqrt{x}\)

          Examples

          Usage

          (fastmath.core/sqrt 1.0)
 ;;=> 1.0

          Plot of sqrt

          -
          view source

          SQRT2

          const

          ;;=> 1.4142135623730951

          \(\sqrt{2}\)

          -
          view source

          SQRT2_2

          const

          ;;=> 0.7071067811865476

          \(\frac{\sqrt{2}}{2}\)

          -
          view source

          SQRT2PI

          const

          ;;=> 2.5066282746310002

          \(\sqrt{2\pi}\)

          -
          view source

          SQRT3

          const

          ;;=> 1.7320508075688772

          \(\sqrt{3}\)

          -
          view source

          SQRT3_2

          const

          ;;=> 0.8660254037844386

          \(\frac{\sqrt{3}}{2}\)

          -
          view source

          SQRT3_3

          const

          ;;=> 0.5773502691896257

          \(\frac{\sqrt{3}}{3}\)

          -
          view source

          SQRT3_4

          const

          ;;=> 0.4330127018922193

          \(\frac{\sqrt{3}}{4}\)

          -
          view source

          SQRT5

          const

          ;;=> 2.23606797749979

          \(\sqrt{5}\)

          -
          view source

          SQRT_HALFPI

          const

          ;;=> 1.2533141373155001

          \(\sqrt{\frac{1}{2}\pi}\)

          -
          view source

          SQRTPI

          const

          ;;=> 1.7724538509055159

          \(\sqrt{\pi}\)

          -
          view source

          sum-of-products

          (sum-of-products a b c d)

          Kahan’s algorithm for (ab)+(cd) to avoid catastrophic cancellation.

          -
          view source

          tan

          macro

          (tan x)

          net.jafama.FastMath/tan function wrapped in macro.

          +
          view source

          SQRT2

          const

          ;;=> 1.4142135623730951

          \(\sqrt{2}\)

          +
          view source

          SQRT2_2

          const

          ;;=> 0.7071067811865476

          \(\frac{\sqrt{2}}{2}\)

          +
          view source

          SQRT2PI

          const

          ;;=> 2.5066282746310002

          \(\sqrt{2\pi}\)

          +
          view source

          SQRT3

          const

          ;;=> 1.7320508075688772

          \(\sqrt{3}\)

          +
          view source

          SQRT3_2

          const

          ;;=> 0.8660254037844386

          \(\frac{\sqrt{3}}{2}\)

          +
          view source

          SQRT3_3

          const

          ;;=> 0.5773502691896257

          \(\frac{\sqrt{3}}{3}\)

          +
          view source

          SQRT3_4

          const

          ;;=> 0.4330127018922193

          \(\frac{\sqrt{3}}{4}\)

          +
          view source

          SQRT5

          const

          ;;=> 2.23606797749979

          \(\sqrt{5}\)

          +
          view source

          SQRT_HALFPI

          const

          ;;=> 1.2533141373155001

          \(\sqrt{\frac{1}{2}\pi}\)

          +
          view source

          SQRTPI

          const

          ;;=> 1.7724538509055159

          \(\sqrt{\pi}\)

          +
          view source

          sum-of-products

          (sum-of-products a b c d)

          Kahan’s algorithm for (ab)+(cd) to avoid catastrophic cancellation.

          +
          view source

          tan

          macro

          (tan x)

          net.jafama.FastMath/tan function wrapped in macro.

          Examples

          Usage

          (fastmath.core/tan 1.0)
 ;;=> 1.5574077246549018

          Plot of tan

          -
          view source

          tanh

          macro

          (tanh x)

          net.jafama.FastMath/tanh function wrapped in macro.

          +
          view source

          tanh

          macro

          (tanh x)

          net.jafama.FastMath/tanh function wrapped in macro.

          Examples

          Usage

          (fastmath.core/tanh 1.0)
 ;;=> 0.7615941559557649

          Plot of tanh

          -
          view source

          TAU

          const

          ;;=> 6.283185307179586

          Alias for TWO_PI

          -
          view source

          THIRD

          const

          ;;=> 0.3333333333333333

          Value of \(\frac{1}{3}\)

          -
          view source

          THIRD_PI

          const

          ;;=> 1.0471975511965976

          Value of \(\frac{\pi}{3}\)

          -
          view source

          trigamma

          macro

          (trigamma x)

          Derivative of digamma.

          +
          view source

          TAU

          const

          ;;=> 6.283185307179586

          Alias for TWO_PI

          +
          view source

          THIRD

          const

          ;;=> 0.3333333333333333

          Value of \(\frac{1}{3}\)

          +
          view source

          THIRD_PI

          const

          ;;=> 1.0471975511965976

          Value of \(\frac{\pi}{3}\)

          +
          view source

          trigamma

          macro

          (trigamma x)

          Derivative of digamma.

          Examples

          Usage

          (fastmath.core/trigamma 1.0)
 ;;=> 1.6449340668481562

          Plot of trigamma

          -
          view source

          trunc

          (trunc v)

          Truncate fractional part, keep sign. Returns double.

          +
          view source

          trunc

          (trunc v)

          Truncate fractional part, keep sign. Returns double.

          Examples

          Examples

          (trunc 1.234)
 ;;=> 1.0
@@ -1001,13 +1007,14 @@ 
          Other functions
          
 ;;=> -1.0

          Usage

          (fastmath.core/trunc 1.0)
 ;;=> 1.0

          Plot of trunc

          -
          view source

          TWO_INV_PI

          const

          ;;=> 0.6366197723675814

          Value of \(\frac{2}{\pi}\)

          -
          view source

          TWO_PI

          const

          ;;=> 6.283185307179586

          Value of \(2 {\pi}\)

          -
          view source

          TWO_THIRD

          const

          ;;=> 0.6666666666666666

          Value of \(\frac{2}{3}\)

          -
          view source

          unsigned-bit-shift-right

          macro

          (unsigned-bit-shift-right x y)

          fastmath.java.PrimitiveMath/unsignedShiftRight function wrapped in macro.

          +
          view source

          TWO_INV_PI

          const

          ;;=> 0.6366197723675814

          Value of \(\frac{2}{\pi}\)

          +
          view source

          TWO_PI

          const

          ;;=> 6.283185307179586

          Value of \(2 {\pi}\)

          +
          view source

          TWO_THIRD

          const

          ;;=> 0.6666666666666666

          Value of \(\frac{2}{3}\)

          +
          view source

          ulp

          (ulp v)

          Unit in the Last Place, distance between next value larger than v and v

          +
          view source

          unsigned-bit-shift-right

          macro

          (unsigned-bit-shift-right x y)

          fastmath.java.PrimitiveMath/unsignedShiftRight function wrapped in macro.

          view source

          unuse-primitive-operators

          (unuse-primitive-operators)

          Undoes the work of use-primitive-operators. This is idempotent.

          -
          view source

          use-primitive-operators

          (use-primitive-operators)(use-primitive-operators skip-set)

          Replaces Clojure’s arithmetic and number coercion functions with primitive equivalents. These are defined as macros, so they cannot be used as higher-order functions. This is an idempotent operation. Undo with unuse-primitive-operators.

          -
          view source

          valid-double?

          (valid-double? v)

          Check if number is invalid

          +
          view source

          use-primitive-operators

          (use-primitive-operators)(use-primitive-operators skip-set)

          Replaces Clojure’s arithmetic and number coercion functions with primitive equivalents. These are defined as macros, so they cannot be used as higher-order functions. This is an idempotent operation. Undo with unuse-primitive-operators.

          +
          view source

          valid-double?

          (valid-double? v)

          Check if number is invalid

          Examples

          Usage

          (valid-double? ##Inf)
 ;;=> false
@@ -1020,9 +1027,9 @@ 
          Other functions
          
 (valid-double? ##NaN)
 ;;=> false
 
-;; Test: ok.
          view source

          vercos

          (vercos v)

          Vercosine

          -
          view source

          versin

          (versin v)

          Versine

          -
          view source

          wrap

          (wrap [start stop] value)(wrap start stop value)

          Wrap overflowed value into the range, similar to ofWrap.

          +;; Test: ok.
          view source

          vercos

          (vercos v)

          Vercosine

          +
          view source

          versin

          (versin v)

          Versine

          +
          view source

          wrap

          (wrap [start stop] value)(wrap start stop value)

          Wrap overflowed value into the range, similar to ofWrap.

          Examples

          Example 1

          (wrap 0 -1 1)
 ;;=> -1.0

          Example 2 (value outside range)

          @@ -1030,10 +1037,10 @@

          Other functions

          ;;=> -1.0000000000000022

          Example 3 (reversed range)

          (wrap 0.7 0.5 1.0)
 ;;=> 0.6000000000000001

          Plot of wrap

          -
          view source

          xexpx

          (xexpx x)

          x * exp(x)

          -
          view source

          xexpy

          (xexpy x y)

          x * exp(x)

          -
          view source

          xlog1py

          (xlog1py x y)

          x * log(1+y)

          -
          view source

          xlogx

          (xlogx x)

          x * log(x)

          -
          view source

          xlogy

          (xlogy x y)

          x * log(y)

          -
          view source

          zero?

          macro

          (zero? x)

          fastmath.java.PrimitiveMath/isZero function wrapped in macro.

          +
          view source

          xexpx

          (xexpx x)

          x * exp(x)

          +
          view source

          xexpy

          (xexpy x y)

          x * exp(x)

          +
          view source

          xlog1py

          (xlog1py x y)

          x * log(1+y)

          +
          view source

          xlogx

          (xlogx x)

          x * log(x)

          +
          view source

          xlogy

          (xlogy x y)

          x * log(y)

          +
          view source

          zero?

          macro

          (zero? x)

          fastmath.java.PrimitiveMath/isZero function wrapped in macro.

          view source
          \ No newline at end of file diff --git a/docs/fastmath.curves.html b/docs/fastmath.curves.html index c092d465..021812d5 100644 --- a/docs/fastmath.curves.html +++ b/docs/fastmath.curves.html @@ -1,6 +1,6 @@ -fastmath.curves documentation

          Project

          Namespaces

          Public Vars

          fastmath.curves

          Collection of parametric curves

          +fastmath.curves documentation

          Project

          Namespaces

          Public Vars

          fastmath.curves

          Collection of parametric curves

          Categories

            Other vars: add curve curves-list mult parametrization

            add

            (add c1 c2)

            Add two curves (by adding resulting vectors).

            view source

            curve

            multimethod

            Return vector field for given name and parametrization.

            Default parametrization is random.

            diff --git a/docs/fastmath.distance.html b/docs/fastmath.distance.html index 0742e472..45b15047 100644 --- a/docs/fastmath.distance.html +++ b/docs/fastmath.distance.html @@ -1,6 +1,6 @@ -fastmath.distance documentation

            Project

            Namespaces

            Public Vars

            fastmath.distance

            Distance objects.

            +fastmath.distance documentation

            Project

            Namespaces

            Public Vars

            fastmath.distance

            Distance objects.

            Objects implement IFn, Smile and Apache Commons Math distance interfaces.

            Categories

              Other vars: angular canberra chebyshev correlation cosine discrete earth-movers euclidean euclidean-sq jensen-shannon make-mahalanobis make-minkowski manhattan

              angular

              Angular distance

              Examples

              Usage

              diff --git a/docs/fastmath.easings.html b/docs/fastmath.easings.html index b51be7ad..bbe602ca 100644 --- a/docs/fastmath.easings.html +++ b/docs/fastmath.easings.html @@ -1,6 +1,6 @@ -fastmath.easings documentation

              Project

              Namespaces

              Public Vars

              fastmath.easings

              Easing functions.

              +fastmath.easings documentation

              Project

              Namespaces

              Public Vars

              fastmath.easings

              Easing functions.

              List of all are in easings-list.

              Categories

                Other vars: back-in back-in-out back-out bounce-in bounce-in-out bounce-out circle-in circle-in-out circle-out cubic-in cubic-in-out cubic-out easings-list elastic-in elastic-in-out elastic-out exp-in exp-in-out exp-out in-out linear out poly-in poly-in-out poly-out quad-in quad-in-out quad-out reflect sin-in sin-in-out sin-out

                back-in

                (back-in t)(back-in s t)

                BackIn easing.

                Parameter s (default: 1.70158) defines overshoot.

                diff --git a/docs/fastmath.efloat.html b/docs/fastmath.efloat.html index a9280ae4..b01412b9 100644 --- a/docs/fastmath.efloat.html +++ b/docs/fastmath.efloat.html @@ -1,6 +1,6 @@ -fastmath.efloat documentation

                Project

                Namespaces

                Public Vars

                fastmath.efloat

                (re)Implementation of EFloat/Interval from pbrt-v3/pbrt-v4.

                +fastmath.efloat documentation

                Project

                Namespaces

                Public Vars

                fastmath.efloat

                (re)Implementation of EFloat/Interval from pbrt-v3/pbrt-v4.

                A floating point number structure which keeps a track of error caused by operations.

                -

                Categories

                  Other vars: ->EFloat ->Pair ->double abs absolute-error acos add addf ceil cos difference-of-products div divf efloat equals? floor fma in-range? lower-bound map->EFloat map->Pair max mid-point min mul mulf neg quadratic relative-error sin sq sqrt sub subf sum-of-products upper-bound width

                  ->double

                  (->double ev)
                  view source

                  abs

                  (abs ev)
                  view source

                  absolute-error

                  (absolute-error ev)
                  view source

                  acos

                  (acos ev)
                  view source

                  add

                  (add ev1 ev2)
                  view source

                  addf

                  (addf ev v)
                  view source

                  ceil

                  (ceil ev)
                  view source

                  cos

                  (cos ev)
                  view source

                  difference-of-products

                  (difference-of-products a b c d)
                  view source

                  div

                  (div ev1 ev2)
                  view source

                  divf

                  (divf ev v)
                  view source

                  efloat

                  (efloat v)(efloat v err)(efloat v low high)

                  Create EFloat object from a single value or low and high values.

                  -
                  view source

                  equals?

                  (equals? ev v)
                  view source

                  floor

                  (floor ev)
                  view source

                  fma

                  (fma ev1 ev2 ev3)
                  view source

                  in-range?

                  (in-range? ev v)
                  view source

                  lower-bound

                  (lower-bound ev)
                  view source

                  max

                  (max ev1 ev2)
                  view source

                  mid-point

                  (mid-point ev)
                  view source

                  min

                  (min ev1 ev2)
                  view source

                  mul

                  (mul ev1 ev2)
                  view source

                  mulf

                  (mulf ev v)
                  view source

                  neg

                  (neg ev)
                  view source

                  quadratic

                  (quadratic a b c)
                  view source

                  relative-error

                  (relative-error ev)
                  view source

                  sin

                  (sin ev)
                  view source

                  sq

                  (sq ev)
                  view source

                  sqrt

                  (sqrt ev)
                  view source

                  sub

                  (sub ev1 ev2)
                  view source

                  subf

                  (subf ev v)
                  view source

                  sum-of-products

                  (sum-of-products a b c d)
                  view source

                  upper-bound

                  (upper-bound ev)
                  view source

                  width

                  (width ev)
                  view source
                  \ No newline at end of file +

                  Categories

                    Other vars: ->EFloat ->Pair ->double abs absolute-error acos add addf ceil cos difference-of-products div divf efloat equals? floor fma in-range? lower-bound map->EFloat map->Pair max mid-point min mul mulf neg quadratic relative-error sin sq sqrt sub subf sum-of-products upper-bound width

                    ->double

                    (->double ev)
                    view source

                    abs

                    (abs ev)
                    view source

                    absolute-error

                    (absolute-error ev)
                    view source

                    acos

                    (acos ev)
                    view source

                    add

                    (add ev1 ev2)
                    view source

                    addf

                    (addf ev v)
                    view source

                    ceil

                    (ceil ev)
                    view source

                    cos

                    (cos ev)
                    view source

                    difference-of-products

                    (difference-of-products a b c d)
                    view source

                    div

                    (div ev1 ev2)
                    view source

                    divf

                    (divf ev v)
                    view source

                    efloat

                    (efloat v)(efloat v err)(efloat v low high)

                    Create EFloat object from a single value or low and high values.

                    +
                    view source

                    equals?

                    (equals? ev v)
                    view source

                    floor

                    (floor ev)
                    view source

                    fma

                    (fma ev1 ev2 ev3)
                    view source

                    in-range?

                    (in-range? ev v)
                    view source

                    lower-bound

                    (lower-bound ev)
                    view source

                    max

                    (max ev1 ev2)
                    view source

                    mid-point

                    (mid-point ev)
                    view source

                    min

                    (min ev1 ev2)
                    view source

                    mul

                    (mul ev1 ev2)
                    view source

                    mulf

                    (mulf ev v)
                    view source

                    neg

                    (neg ev)
                    view source

                    quadratic

                    (quadratic a b c)
                    view source

                    relative-error

                    (relative-error ev)
                    view source

                    sin

                    (sin ev)
                    view source

                    sq

                    (sq ev)
                    view source

                    sqrt

                    (sqrt ev)
                    view source

                    sub

                    (sub ev1 ev2)
                    view source

                    subf

                    (subf ev v)
                    view source

                    sum-of-products

                    (sum-of-products a b c d)
                    view source

                    upper-bound

                    (upper-bound ev)
                    view source

                    width

                    (width ev)
                    view source
                    \ No newline at end of file diff --git a/docs/fastmath.fields.html b/docs/fastmath.fields.html index 1ba96a5e..cf35572f 100644 --- a/docs/fastmath.fields.html +++ b/docs/fastmath.fields.html @@ -1,6 +1,6 @@ -fastmath.fields documentation

                    Project

                    Namespaces

                    Public Vars

                    fastmath.fields

                    Vector field functions.

                    +fastmath.fields documentation

                    Project

                    Namespaces

                    Public Vars

                    fastmath.fields

                    Vector field functions.

                    Vector fields are functions R^2->R^2.

                    Names are taken from fractal flames world where such fields are call variations. Most implementations are taken from JWildfire software.

                    Creation

                    @@ -33,7 +33,7 @@

                    Combinations

                  • randomize-configuration - change parametrization for given configuration.

                    • Categories

                      Other vars: *skip-random-fields* angle-between combine composition cross curl derivative divergence dot field fields-list fields-list-not-random fields-list-random fields-map grad-x grad-y heading jacobian magnitude multiplication parametrization random-configuration random-field randomize-configuration scalar->vector-field sum

                      *skip-random-fields*

                      dynamic

                      When random configuration for combine is used. Skip vector fields which are random.

                      -
                      view source

                      angle-between

                      Angle between input vector and result of the vector field.

                      +
                      view source

                      angle-between

                      Angle between input vector and result of the vector field.

                      In case when two vector fields are given, cross product is taken from result of vector fields.

                      Resulting value is from range [-PI,PI].

                      Examples

                      Usage

                      @@ -41,7 +41,7 @@

                      Combinations

                      ;;=> 0.42920367320510344

                      Usage (two fields)

                      (let [f (angle-between (field :sinusoidal) (field :swirl))]
   (f (v/vec2 1 1)))
-;;=> 0.42920367320510255
                      view source

                      combine

                      (combine {:keys [type name amount config var step var1 var2]})(combine)

                      Create composite vector field function based on configuration

                      +;;=> 0.42920367320510255
                      view source

                      combine

                      (combine {:keys [type name amount config var step var1 var2]})(combine)

                      Create composite vector field function based on configuration

                      Call without argument to get random vector field.

                      Configuration is a tree structure where nodes are one of the following

                      Examples

                      Create random combination

                      (let [f (combine)] (f (v/vec2 -0.5 0.5)))
-;;=> [-1.6783534698442983 -0.06029950436770843]

                      Create combination for given configuration

                      +;;=> [-0.5217406307918071 -0.12663102804343862]

                      Create combination for given configuration

                      (let [conf {:type :operation,
             :name :comp,
             :var1 {:type :variation,
@@ -89,55 +89,55 @@ 
                      Combinations
                      
             :amount 1.0}
       f (combine conf)]
   (f (v/vec2 -0.5 0.5)))
-;;=> [0.18532823300678739 0.437177284257253]
                      view source

                      composition

                      (composition f1 f2 amount)(composition f1 f2)

                      Compose two vector fields.

                      +;;=> [0.18532823300678739 0.437177284257253]
                      view source

                      composition

                      (composition f1 f2 amount)(composition f1 f2)

                      Compose two vector fields.

                      Examples

                      Usage

                      (let [field-1 (field :sinusoidal)
       field-2 (field :swirl)
       field-comp (composition field-1 field-2)]
   (field-comp (v/vec2 0.5 0.3)))
-;;=> [-0.11582232201566794 0.5408299143217236]
                      view source

                      cross

                      2d cross product (det of the 2x2 matrix) of the input vector and result of the vector field.

                      +;;=> [-0.11582232201566794 0.5408299143217236]
                      view source

                      cross

                      2d cross product (det of the 2x2 matrix) of the input vector and result of the vector field.

                      In case when two vector fields are given, cross product is taken from results of vector fields.

                      Examples

                      Usage

                      (let [f (cross (field :swirl))] (f (v/vec2 1 1)))
 ;;=> 0.8322936730942845

                      Usage (two fields)

                      (let [f (cross (field :sinusoidal) (field :swirl))] (f (v/vec2 1 1)))
-;;=> -0.7003509767480289
                      view source

                      curl

                      (curl f)(curl f h)

                      Curl (2d version) of the field.

                      +;;=> -0.7003509767480289
                      view source

                      curl

                      (curl f)(curl f h)

                      Curl (2d version) of the field.

                      See: https://youtu.be/rB83DpBJQsE?t=855

                      Examples

                      Usage

                      (let [f (curl (field :swirl) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> -2.0
                      view source

                      derivative

                      (derivative f amount h)(derivative f h)(derivative f)

                      Calculate directional derivative of fn. Derivative is calculated along 1,1 vector with h as a step (default 1.0e-6).

                      +;;=> -2.0
                      view source

                      derivative

                      (derivative f amount h)(derivative f h)(derivative f)

                      Calculate directional derivative of fn. Derivative is calculated along 1,1 vector with h as a step (default 1.0e-6).

                      Examples

                      Usage

                      (let [f (derivative (field :sinusoidal) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> [1.0 1.0]
                      view source

                      divergence

                      (divergence f)(divergence f h)

                      Divergence of the field.

                      +;;=> [1.0 1.0]
                      view source

                      divergence

                      (divergence f)(divergence f h)

                      Divergence of the field.

                      See: https://youtu.be/rB83DpBJQsE?t=855

                      Examples

                      Usage

                      (let [f (divergence (field :sinusoidal) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> 2.0
                      view source

                      dot

                      Dot product of the input vector and result of the vector field.

                      +;;=> 2.0
                      view source

                      dot

                      Dot product of the input vector and result of the vector field.

                      In case when two vector fields are given, cross product is taken from result of vector fields.

                      Examples

                      Usage

                      (let [f (dot (field :swirl))] (f (v/vec2 1 1)))
 ;;=> 1.8185948536513636

                      Usage (two fields)

                      (let [f (dot (field :sinusoidal) (field :swirl))] (f (v/vec2 1 1)))
-;;=> 1.5302948024685854
                      view source

                      field

                      multimethod

                      Return vector field for given name and options: amount (scaling factor) and parametrization.

                      +;;=> 1.5302948024685854
                      view source

                      field

                      multimethod

                      Return vector field for given name and options: amount (scaling factor) and parametrization.

                      Default scaling factor is 1.0, default parametrization is random.

                      Resulting function operates on Vec2 type.

                      Examples

                      Get vector field by name

                      (field :sinusoidal)
-;;=> fastmath.fields.s$sinusoidal$fn__29997@158c442a
+;;=> fastmath.fields.s$sinusoidal$fn__30073@274c6ddd
 ((field :sinusoidal) (v/vec2 m/HALF_PI m/HALF_PI))
 ;;=> [1.0 1.0]

                      Get vector field by name and scale

                      (field :sinusoidal 0.5)
-;;=> fastmath.fields.s$sinusoidal$fn__29997@5e3efdb9
+;;=> fastmath.fields.s$sinusoidal$fn__30073@6358c9ae
 ((field :sinusoidal 0.5) (v/vec2 m/HALF_PI m/HALF_PI))
 ;;=> [0.5 0.5]

                      Apply parametrization

                      (let [params (parametrization :cpow3)
       f (field :cpow3 1.0 params)]
   {:parametrization params, :value (f (v/vec2 -1.0 1.0))})
-;;=> {:parametrization {:d 13.550332230506799,
-;;=>                    :divisor -1.4008224545855428,
-;;=>                    :r 0.9210964153948565,
-;;=>                    :spread 1.5706529922073926},
-;;=>  :value [1.0944626140632712 3.4694309860675565]}
                      view source

                      fields-list

                      Examples

                      List of all vector field names.

                      +;;=> {:parametrization {:d -14.084455698606515, +;;=> :divisor -1.2957732414050445, +;;=> :r 0.8931076301162941, +;;=> :spread 2.8389757614011772}, +;;=> :value [-0.02294518426545013 0.4561549708802658]}
                      view source

                      fields-list

                      Examples

                      List of all vector field names.

                      (sort fields-list)
 ;;=> (:acosech
 ;;=>  :acosh
@@ -332,7 +332,7 @@ 
                      Combinations
                      
 ;;=>  :woggle :x
 ;;=>  :xheart :xtrb
 ;;=>  :y :yinyang
-;;=>  :z :zsymmetry)
                      view source

                      fields-list-not-random

                      Examples

                      List of all vector fields which are not random.

                      +;;=> :z :zsymmetry)
                      view source

                      fields-list-not-random

                      Examples

                      List of all vector fields which are not random.

                      (sort fields-list-not-random)
 ;;=> (:acoth
 ;;=>  :anamorphcyl :arcsech2
@@ -466,7 +466,7 @@ 
                      Combinations
                      
 ;;=>  :wedge :wedgesph
 ;;=>  :whorl :x
 ;;=>  :xheart :y
-;;=>  :z :zsymmetry)
                      view source

                      fields-list-random

                      Examples

                      List of all vector fields which give random results.

                      +;;=> :z :zsymmetry)
                      view source

                      fields-list-random

                      Examples

                      List of all vector fields which give random results.

                      (sort fields-list-random)
 ;;=> (:acosech
 ;;=>  :acosh :apocarpet
@@ -528,81 +528,73 @@ 
                      Combinations
                      
 ;;=>  :truchethexfill :twintrian
 ;;=>  :vogel :wallpaper
 ;;=>  :wedgejulia :woggle
-;;=>  :xtrb :yinyang)
                      view source

                      fields-map

                      view source

                      grad-x

                      (grad-x f amount h)(grad-x f h)(grad-x f)

                      Calculate gradient along x axis.

                      +;;=> :xtrb :yinyang)
                      view source

                      fields-map

                      view source

                      grad-x

                      (grad-x f amount h)(grad-x f h)(grad-x f)

                      Calculate gradient along x axis.

                      Examples

                      Usage

                      (let [f (grad-x (field :sinusoidal) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> [1.0 0.0]
                      view source

                      grad-y

                      (grad-y f amount h)(grad-y f h)(grad-y f)

                      Calculate gradient along y axis.

                      +;;=> [1.0 0.0]
                      view source

                      grad-y

                      (grad-y f amount h)(grad-y f h)(grad-y f)

                      Calculate gradient along y axis.

                      Examples

                      Usage

                      (let [f (grad-y (field :sinusoidal) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> [0.0 1.0]
                      view source

                      heading

                      (heading f)

                      Angle of the vectors from field.

                      +;;=> [0.0 1.0]
                      view source

                      heading

                      (heading f)

                      Angle of the vectors from field.

                      Examples

                      Usage

                      (let [f (heading (field :sinusoidal))]
   (m/degrees (f (v/vec2 m/HALF_PI m/HALF_PI))))
-;;=> 45.0
                      view source

                      jacobian

                      (jacobian f)(jacobian f h)

                      Det of Jacobian of the field

                      +;;=> 45.0
                      view source

                      jacobian

                      (jacobian f)(jacobian f h)

                      Det of Jacobian of the field

                      Examples

                      Usage

                      (let [f (jacobian (field :sinusoidal) 1.0E-8)] (f (v/vec2 0.0 0.0)))
-;;=> 1.0
                      view source

                      magnitude

                      (magnitude f)

                      Magnitude of the vectors from field.

                      +;;=> 1.0
                      view source

                      magnitude

                      (magnitude f)

                      Magnitude of the vectors from field.

                      Examples

                      Usage

                      (let [f (magnitude (field :sinusoidal))]
   (f (v/vec2 m/HALF_PI m/HALF_PI)))
-;;=> 1.4142135623730951
                      view source

                      multiplication

                      (multiplication f1 f2 amount)(multiplication f1 f2)

                      Multiply two vector fields (as a element-wise multiplication of results).

                      +;;=> 1.4142135623730951
                      view source

                      multiplication

                      (multiplication f1 f2 amount)(multiplication f1 f2)

                      Multiply two vector fields (as a element-wise multiplication of results).

                      Examples

                      Usage

                      (let [field-1 (field :sinusoidal)
       field-2 (field :swirl)
       field-multiplication (multiplication field-1 field-2)]
   (field-multiplication (v/vec2 0.5 0.3)))
-;;=> [-0.05565308460418609 0.1688671791104423]
                      view source

                      parametrization

                      multimethod

                      Return random parametrization map for given field.

                      +;;=> [-0.05565308460418609 0.1688671791104423]
                      view source

                      parametrization

                      multimethod

                      Return random parametrization map for given field.

                      Optinally you can pass part of the parametrization. In this case function will add remaining keys with randomly generated values.

                      If field doesn’t have parametrization, empty map will be returned.

                      See field.

                      Examples

                      Get random parametrization for given field

                      (parametrization :auger)
-;;=> {:freq -2.7581161401981023,
-;;=>  :scale 1.5185071494571902,
-;;=>  :sym 1.6604261172323973,
-;;=>  :weight -0.03224849866297275}

                      Add lacking fields

                      +;;=> {:freq 2.5825461333040565, +;;=> :scale -1.5130389003393934, +;;=> :sym 1.133320717504653, +;;=> :weight 0.11842671408241556}

                      Add lacking fields

                      (parametrization :auger {:scale 1.0, :freq 1.0})
 ;;=> {:freq 1.0,
 ;;=>  :scale 1.0,
-;;=>  :sym -1.780967830401293,
-;;=>  :weight -0.2100609105377551}

                      Returns empty map when field doesn’t have parametrization

                      +;;=> :sym 1.2115684744663069, +;;=> :weight 0.26201326923916457}

                      Returns empty map when field doesn’t have parametrization

                      (parametrization :sinusoidal)
 ;;=> {}
                      view source

                      random-configuration

                      (random-configuration)(random-configuration depth)(random-configuration depth f)

                      Create random configuration for combine function. Optionally with depth (0 = only root is created).

                      See combine for structure.

                      Bind *skip-random-fields* to true to exclude fields which are random.

                      Examples

                      Generate random configuration

                      (random-configuration)
-;;=> {:amount 1.0,
-;;=>  :config {:rot 2.6181978084699455, :twist -5.154127002205628},
-;;=>  :name :disc2,
-;;=>  :type :variation}

                      One node configuration

                      +;;=> {:amount 1.0, :config {}, :name :squircular, :type :variation}

                      One node configuration

                      (random-configuration 0)
-;;=> {:amount 1.0, :config {}, :name :sqrt-asinh, :type :variation}

                      Configuration with depth 2

                      +;;=> {:amount 1.0, :config {}, :name :diamond, :type :variation}

                      Configuration with depth 2

                      (random-configuration 2)
 ;;=> {:amount 1.0,
-;;=>  :name :deriv,
-;;=>  :step 0.2168858796955329,
+;;=>  :name :comp,
 ;;=>  :type :operation,
-;;=>  :var {:amount 1.0,
-;;=>        :name :comp,
-;;=>        :type :operation,
-;;=>        :var1 {:amount 1.0,
-;;=>               :config {:contrast 0.07274760605121522,
-;;=>                        :phi1 354.2573549924269,
-;;=>                        :phi2 17.20000230260112,
-;;=>                        :pow 2.9714988331436114,
-;;=>                        :radius 1.0567259159882174,
-;;=>                        :thickness 0.7105285279534599},
-;;=>               :name :glynnsim2,
-;;=>               :type :variation},
-;;=>        :var2 {:amount 1.0,
-;;=>               :config {:x1 0.1664017937624582,
-;;=>                        :x2 1.2050407496891395,
-;;=>                        :y1 1.8475285003941921,
-;;=>                        :y2 0.584446148926949},
-;;=>               :name :cosh2bs,
-;;=>               :type :variation}}}
                      view source

                      random-field

                      (random-field)(random-field depth)

                      Create randomized field (optional depth can be provided).

                      -
                      view source

                      randomize-configuration

                      (randomize-configuration f)

                      Randomize values for given configuration. Keeps structure untouched.

                      +;;=> :var1 {:amount 1.0, +;;=> :name :deriv, +;;=> :step 0.9667944074740565, +;;=> :type :operation, +;;=> :var {:amount 1.0, +;;=> :config {:a -0.8525853754431658, +;;=> :b 0.7772607155299691, +;;=> :c 0.7170063828409245, +;;=> :d -0.7067016229715266, +;;=> :e -0.9102525466961031, +;;=> :f 0.26099060732035717, +;;=> :mode true}, +;;=> :name :chunk, +;;=> :type :variation}}, +;;=> :var2 {:amount 1.0, :config {}, :name :invpolar, :type :variation}}
                      view source

                      random-field

                      (random-field)(random-field depth)

                      Create randomized field (optional depth can be provided).

                      +
                      view source

                      randomize-configuration

                      (randomize-configuration f)

                      Randomize values for given configuration. Keeps structure untouched.

                      Examples

                      Usage

                      (let [conf {:type :variation,
             :name :blocky,
@@ -610,17 +602,17 @@ 
                      Combinations
                      
             :config {:x -1.4, :y 0.9, :mp 2.6}}]
   [(randomize-configuration conf) (randomize-configuration conf)])
 ;;=> [{:amount 1.0,
-;;=>   :config {:mp 1.7953356115794685,
-;;=>            :x -1.0069950566912558,
-;;=>            :y -0.913306464273377},
+;;=>   :config {:mp 0.8986513423304683,
+;;=>            :x 1.1904936014304281,
+;;=>            :y -0.6462182660765559},
 ;;=>   :name :blocky,
 ;;=>   :type :variation}
 ;;=>  {:amount 1.0,
-;;=>   :config {:mp 1.4403319180575245,
-;;=>            :x -0.985190457995947,
-;;=>            :y 0.6687955091301594},
+;;=>   :config {:mp 1.9154806023569149,
+;;=>            :x 0.9869828060465601,
+;;=>            :y -1.160872986608712},
 ;;=>   :name :blocky,
-;;=>   :type :variation}]
                      view source

                      scalar->vector-field

                      (scalar->vector-field scalar f)(scalar->vector-field scalar f1 f2)

                      Returns vector field build from scalar fields of the input vector and result of the vector field.

                      +;;=> :type :variation}]
                      view source

                      scalar->vector-field

                      (scalar->vector-field scalar f)(scalar->vector-field scalar f1 f2)

                      Returns vector field build from scalar fields of the input vector and result of the vector field.

                      Examples

                      Usage

                      (let [f (scalar->vector-field v/heading (field :sinusoidal))]
   (v/applyf (f (v/vec2 m/HALF_PI m/HALF_PI)) m/degrees))
@@ -629,10 +621,10 @@ 
                      Combinations
                      
                               (field :sinusoidal)
                               (field :julia))]
   (v/applyf (f (v/vec2 m/HALF_PI m/HALF_PI)) m/degrees))
-;;=> [45.0 22.500000000000004]
                      view source

                      sum

                      (sum f1 f2 amount)(sum f1 f2)

                      Add two vector fields.

                      +;;=> [45.0 -157.50000000000003]
                      view source

                      sum

                      (sum f1 f2 amount)(sum f1 f2)

                      Add two vector fields.

                      Examples

                      Usage

                      (let [field-1 (field :sinusoidal)
       field-2 (field :swirl)
       field-sum (sum field-1 field-2)]
   (field-sum (v/vec2 0.5 0.3)))
-;;=> [0.3633426850161062 0.866943667067757]
                      view source
                      \ No newline at end of file +;;=> [0.3633426850161062 0.866943667067757]
                      view source
                      \ No newline at end of file diff --git a/docs/fastmath.gp.html b/docs/fastmath.gp.html index 1affca87..c20339da 100644 --- a/docs/fastmath.gp.html +++ b/docs/fastmath.gp.html @@ -1,42 +1,42 @@ -fastmath.gp documentation

                      Project

                      Namespaces

                      Public Vars

                      fastmath.gp

                      Gaussian Processes

                      +fastmath.gp documentation

                      Project

                      Namespaces

                      Public Vars

                      fastmath.gp

                      Gaussian Processes

                      See more here

                      Categories

                        Other vars: ->GaussianProcess L gaussian-process posterior-samples predict predict-all prior-samples

                        gaussian-process

                        (gaussian-process xss ys)(gaussian-process xss ys {:keys [kscale kernel noise normalize? L?], :or {kscale 1.0, kernel (k/kernel :gaussian 1.0), normalize? false, noise 1.0E-8, L? true}})

                        Examples

                        Object creation

                        (gaussian-process [1 2 3] [-1 2 1])
-;;=> fastmath.gp.GaussianProcess@2e8a0ea8
+;;=> fastmath.gp.GaussianProcess@7014908d
 (gaussian-process [1 2 3]
                   [-1 2 1]
                   {:normalize? true,
                    :kernel (k/kernel :gaussian 0.5),
                    :kscale 2.0,
                    :noise 0.1})
-;;=> fastmath.gp.GaussianProcess@7c6f6097
                        view source

                        L

                        (L ys w chol n)(L gp-object)
                        view source

                        posterior-samples

                        (posterior-samples gp-object xvals)(posterior-samples gp-object xvals stddev?)

                        Examples

                        With gaussian kernel

                        +;;=> fastmath.gp.GaussianProcess@7c5fba85
                        view source

                        L

                        (L ys w chol n)(L gp-object)
                        view source

                        posterior-samples

                        (posterior-samples gp-object xvals)(posterior-samples gp-object xvals stddev?)

                        Examples

                        With gaussian kernel

                        (let [gp (gaussian-process [-5 1 2]
                            [17 10 12]
                            {:kernel (k/kernel :gaussian 0.5)})]
   (posterior-samples gp (range -5 2 0.9)))
-;;=> (17.00000382183717
-;;=>  3.469134911744126
-;;=>  0.05639732263679262
-;;=>  0.4407898012542572
-;;=>  -1.1822643945486515
-;;=>  1.7996161405577882
-;;=>  4.432909454920831
-;;=>  11.175489507479758)

                        Plot of 10 posteriors (with gaussian kernel)

                        +;;=> (16.999911271700068 +;;=> 1.4396261676852156 +;;=> -0.5662562350658056 +;;=> -0.26381866980281693 +;;=> -0.5616964300404151 +;;=> 0.32780559947465765 +;;=> 5.603781510038106 +;;=> 9.397793642342432)

                        Plot of 10 posteriors (with gaussian kernel)

                        With periodic kernel

                        (let [gp (gaussian-process [-5 1 2]
                            [17 10 12]
                            {:kernel (k/kernel :periodic 0.2 6.5)})]
   (posterior-samples gp (range -5 2 0.9)))
-;;=> (16.999957394562713
-;;=>  0.39918841594982335
-;;=>  0.6947387524410465
-;;=>  0.8668027797681881
-;;=>  -0.30261928761149637
-;;=>  1.53149857822521
-;;=>  -0.6431299741943961
-;;=>  14.112061105415885)

                        Plot of 10 posteriors (with periodic kernel)

                        +;;=> (17.00003848656039 +;;=> 4.275540849613845 +;;=> 0.9307956232029831 +;;=> -1.8504644482052286 +;;=> 0.29385792463691496 +;;=> 0.47311529931052004 +;;=> 0.27135029649557507 +;;=> 13.501674596943719)

                        Plot of 10 posteriors (with periodic kernel)

                        view source

                        predict

                        (predict gp-object xval)(predict gp-object xval stddev?)

                        Examples

                        Usage

                        (let [gp (gaussian-process [-5 1 2] [17 10 12])]
   [(gp 1.1) (predict gp 1.1)])
@@ -67,30 +67,30 @@
 ;;=>  [6.277135459489308 0.739305317305734])
                        view source

                        prior-samples

                        (prior-samples gp-object xvals)

                        Examples

                        Usage

                        (let [gp (gaussian-process [0 1 -2 -2.001] [-2 3 0.5 -0.6])]
   (prior-samples gp (range 0 1 0.1)))
-;;=> (0.6169941324989417
-;;=>  0.7417796225662417
-;;=>  0.8573053364748918
-;;=>  0.9637098017534088
-;;=>  1.0605747005533621
-;;=>  1.1468076303547878
-;;=>  1.2206802441175801
-;;=>  1.280013808525612
-;;=>  1.322481015514251
-;;=>  1.345971476764109
-;;=>  1.3489626436116557)

                        Plot of 10 priors

                        +;;=> (0.5513335229785846 +;;=> 0.5012297169060579 +;;=> 0.4385817858195753 +;;=> 0.36437646639668436 +;;=> 0.2804423584423929 +;;=> 0.18914414674256888 +;;=> 0.09304839529620974 +;;=> -0.005376263636502346 +;;=> -0.10397293800368286 +;;=> -0.20099438784565596 +;;=> -0.2950807811768326)

                        Plot of 10 priors

                        With added noise

                        (let [gp
       (gaussian-process [0 1 -2 -2.001] [-2 3 0.5 -0.6] {:noise 0.1})]
   (prior-samples gp (range 0 1 0.1)))
-;;=> (0.4666480150602599
-;;=>  0.42741472858998836
-;;=>  0.3627654448154403
-;;=>  0.27308195820743597
-;;=>  0.16030445319322284
-;;=>  0.027659566848698178
-;;=>  -0.12067661975798452
-;;=>  -0.279941560519676
-;;=>  -0.4451428187970916
-;;=>  -0.611379745903101
-;;=>  -0.7741132697704154)

                        Plot of 10 priors (with noise)

                        +;;=> (-0.08439228071890412 +;;=> -0.13608678909072633 +;;=> -0.19293817674278546 +;;=> -0.2559562744697197 +;;=> -0.32611484009258196 +;;=> -0.40411339705714877 +;;=> -0.49013874945984665 +;;=> -0.5836576095416394 +;;=> -0.6832733741851441 +;;=> -0.7866755749316164 +;;=> -0.8907035794074853)

                        Plot of 10 priors (with noise)

                        view source
                        \ No newline at end of file diff --git a/docs/fastmath.grid.html b/docs/fastmath.grid.html index 8ff0dcf7..6e8bbb41 100644 --- a/docs/fastmath.grid.html +++ b/docs/fastmath.grid.html @@ -1,6 +1,6 @@ -fastmath.grid documentation

                        Project

                        Namespaces

                        Public Vars

                        fastmath.grid

                        Grid calculation functions.

                        +fastmath.grid documentation

                        Project

                        Namespaces

                        Public Vars

                        fastmath.grid

                        Grid calculation functions.

                        Convert 2d coordinates into various grid coordinates and back.

                        Terms used:

                        view source

                        b-spline

                        (b-spline xs ys)(b-spline degree-or-knots xs ys)

                        B-spline for given points, default degree equals samples count - 1.

                        more

                        Examples

                        Usage

                        (interpolate b-spline ...)
 ;;=> 0.5600852765013091

                        B-Spline plot

                        B-Spline plot (degree=1)

                        B-Spline plot (with knots)

                        -
                        view source

                        b-spline-interp

                        (b-spline-interp xs ys)(b-spline-interp degree xs ys)(b-spline-interp degree h xs ys)

                        B-spline interpolation.

                        +
                        view source

                        b-spline-interp

                        (b-spline-interp xs ys)(b-spline-interp degree xs ys)(b-spline-interp degree h xs ys)

                        B-spline interpolation.

                        See:

                        • 2 or 3 arity - exact interpolation using b-spline, default degree = 3 (more)
                          • @@ -71,41 +72,41 @@

                          2d

                          ;;=> 0.6903406231405653

                        B-Spline interpolation plot

                        B-Spline interpolation plot (degree=5)

                        B-Spline interpolation plot (degree=3, h=6)

                        -
                        view source

                        bicubic

                        (bicubic xs ys vs)

                        Bicubic 2d.

                        +
                        view source

                        bicubic

                        (bicubic xs ys vs)

                        Bicubic 2d.

                        Grid based.

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate2d bicubic ...)
 ;;=> 0.07081337259133846

                        Bicubic plot

                        -
                        view source

                        bicubic-smile

                        (bicubic-smile xs ys vs)

                        Bicubic 2d.

                        +
                        view source

                        bicubic-smile

                        (bicubic-smile xs ys vs)

                        Bicubic 2d.

                        Grid based.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate2d bicubic-smile ...)
 ;;=> 0.07081337259133846

                        Bicubic (Smile) plot

                        -
                        view source

                        bilinear

                        (bilinear xs ys vs)

                        Bilinear 2d.

                        +
                        view source

                        bilinear

                        (bilinear xs ys vs)

                        Bilinear 2d.

                        Grid based.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate2d bilinear ...)
 ;;=> 0.062068616254939334

                        Bilinear plot

                        -
                        view source

                        cubic-2d

                        (cubic-2d xs ys vs)

                        Cubic spline 2d.

                        +
                        view source

                        cubic-2d

                        (cubic-2d xs ys vs)

                        Cubic spline 2d.

                        Grid based.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate2d cubic-2d ...)
 ;;=> 0.053984474655155074

                        Cubic-2d plot

                        -
                        view source

                        cubic-spline

                        (cubic-spline xs ys)

                        Cubic spline interpolation.

                        +
                        view source

                        cubic-spline

                        (cubic-spline xs ys)

                        Cubic spline interpolation.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate cubic-spline ...)
 ;;=> 0.6809644344471792

                        Cubic spline plot

                        -
                        view source

                        divided-difference

                        (divided-difference xs ys)

                        Create Divided Difference Algorithm for interpolation.

                        +
                        view source

                        divided-difference

                        (divided-difference xs ys)

                        Create Divided Difference Algorithm for interpolation.

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate divided-difference ...)
 ;;=> 0.6789478287835669

                        Divided difference plot

                        -
                        view source

                        interpolators-1d-list

                        Map of 1d interpolation functions

                        +
                        view source

                        interpolators-1d-list

                        Map of 1d interpolation functions

                        Examples

                        List of names

                        (keys interpolators-1d-list)
 ;;=> (:linear-smile :divided-difference :rbf
@@ -116,27 +117,27 @@ 
                        2d
                        
 ;;=>                :polynomial :shepard
 ;;=>                :linear :microsphere
 ;;=>                :monotone :step
-;;=>                :b-spline-interp :akima)
                        view source

                        interpolators-2d-list

                        Map of 2d interpolation functions

                        +;;=> :b-spline-interp :akima)
                        view source

                        interpolators-2d-list

                        Map of 2d interpolation functions

                        Examples

                        List of names

                        (keys interpolators-2d-list)
 ;;=> (:bicubic :piecewise-bicubic
 ;;=>           :microsphere-2d :bilinear
-;;=>           :bicubic-smile :cubic-2d)
                        view source

                        kriging-spline

                        (kriging-spline xs ys)

                        Kriging interpolation.

                        +;;=> :bicubic-smile :cubic-2d)
                        view source

                        kriging-spline

                        (kriging-spline xs ys)

                        Kriging interpolation.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate kriging-spline ...)
 ;;=> 0.6863915017789624

                        Kriging spline plot

                        -
                        view source

                        linear

                        (linear xs ys)

                        Create Divided Difference Algorithm for inqterpolation.

                        +
                        view source

                        linear

                        (linear xs ys)

                        Create Divided Difference Algorithm for inqterpolation.

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate linear ...)
 ;;=> 0.6843915831251183

                        Linear (Apache) plot

                        -
                        view source

                        linear-smile

                        (linear-smile xs ys)

                        Linear interpolation from Smile library.

                        +
                        view source

                        linear-smile

                        (linear-smile xs ys)

                        Linear interpolation from Smile library.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate linear-smile ...)
 ;;=> 0.6843915831251183

                        Linear (Smile) plot

                        -
                        view source

                        loess

                        (loess xs ys)(loess bandwidth robustness-iters xs ys)(loess bandwidth robustness-iters accuracy xs ys)

                        Local Regression Algorithm

                        +
                        view source

                        loess

                        (loess xs ys)(loess bandwidth robustness-iters xs ys)(loess bandwidth robustness-iters accuracy xs ys)

                        Local Regression Algorithm

                        • bandwidth: 0.2-1.0 (optimal: 0.25-0.5, default: 0.4)
                        • robustness-iters: 0-4 (optimal: 0, default: 2)
                          • @@ -152,7 +153,7 @@

                          2d

                        Usage (0.2, 1.0)

                        (interpolate loess 0.2 1 ...)
 ;;=> 0.6809644344471794

                        Loess (0.2, 1.0) plot

                        -
                        view source

                        microsphere-2d-projection

                        (microsphere-2d-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys vs)

                        Microsphere projection interpolator - 2d version

                        +
                        view source

                        microsphere-2d-projection

                        (microsphere-2d-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys vs)

                        Microsphere projection interpolator - 2d version

                        Grid based.

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        @@ -161,34 +162,34 @@

                        2d

                        1.0E-4 0.5 1.5 false 0.1 ...) -;;=> 0.12273607821725575

                        Microsphere 2d plot

                        -
                        view source

                        microsphere-projection

                        (microsphere-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys)

                        Microsphere projection interpolator - 1d version

                        +;;=> 0.02860557409286495

                        Microsphere 2d plot

                        +
                        view source

                        microsphere-projection

                        (microsphere-projection elements max-dark-friction dark-threshold background exponent shared-sphere? no-interpolation-tolerance xs ys)

                        Microsphere projection interpolator - 1d version

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate microsphere-projection 6 0.1 0.1 0.1 1.5 false 0.01 ...)
-;;=> 0.5898304448413348

                        Microsphere plot

                        -
                        view source

                        monotone

                        (monotone xs ys)

                        Monotone interpolation

                        +;;=> 0.6885033102791858

                        Microsphere plot

                        +
                        view source

                        monotone

                        (monotone xs ys)

                        Monotone interpolation

                        https://gist.github.com/lecho/7627739

                        Examples

                        Usage

                        (interpolate monotone ...)
 ;;=> 0.7094972531399422

                        Monotone plot

                        -
                        view source

                        neville

                        (neville xs ys)

                        Neville algorithm

                        +
                        view source

                        neville

                        (neville xs ys)

                        Neville algorithm

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate neville ...)
 ;;=> 0.6789478287835672

                        Neville plot

                        -
                        view source

                        piecewise-bicubic

                        (piecewise-bicubic xs ys vs)

                        Piecewise bicubic 2d.

                        +
                        view source

                        piecewise-bicubic

                        (piecewise-bicubic xs ys vs)

                        Piecewise bicubic 2d.

                        Grid based.

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate2d piecewise-bicubic ...)
 ;;=> 0.06876424996210916

                        Piecewise bicubic plot

                        -
                        view source

                        polynomial

                        (polynomial xs ys)

                        Polynomial interpolation.

                        +
                        view source

                        polynomial

                        (polynomial xs ys)

                        Polynomial interpolation.

                        more

                        Examples

                        Usage

                        (interpolate polynomial ...)
 ;;=> 0.6789478287861641

                        Polynomial plot

                        -
                        view source

                        rbf

                        (rbf xs ys)(rbf rbf-fn normalize? xs ys)(rbf rbf-fn xs ys)

                        RBF (Radial Basis Function) interpolation.

                        +
                        view source

                        rbf

                        (rbf xs ys)(rbf rbf-fn normalize? xs ys)(rbf rbf-fn xs ys)

                        RBF (Radial Basis Function) interpolation.

                        Default kernel: :gaussian

                        Source: Smile

                        Examples

                        Usage

                        @@ -206,7 +207,7 @@

                        2d

                        Usage (wendland-53 kernel)

                        (interpolate rbf (k/rbf :wendland-53) ...)
 ;;=> 0.74837576670325

                        Rbf (wendland-53 kernel) plot

                        -
                        view source

                        shepard

                        (shepard xs ys)(shepard p xs ys)

                        Shepard interpolation.

                        +
                        view source

                        shepard

                        (shepard xs ys)(shepard p xs ys)

                        Shepard interpolation.

                        Source: Smile.

                        Examples

                        Usage

                        (interpolate shepard ...)
@@ -214,21 +215,21 @@ 
                        2d

                        Usage (0.9)

                        (interpolate shepard 0.9 ...)
 ;;=> 0.5225345022349268

                        Shepard (0.9) plot

                        -
                        view source

                        spline

                        (spline xs ys)

                        Cubic spline interpolation

                        +
                        view source

                        spline

                        (spline xs ys)

                        Cubic spline interpolation

                        Source: Apache Commons Math.

                        Examples

                        Usage

                        (interpolate spline ...)
 ;;=> 0.6809644344471794

                        Spline plot

                        -
                        view source

                        step

                        (step xs ys)

                        Step function.

                        +
                        view source

                        step

                        (step xs ys)

                        Step function.

                        Examples

                        Usage

                        (interpolate step ...)
 ;;=> 0.8165378262982225

                        Step plot

                        -
                        view source

                        step-after

                        (step-after xs ys)

                        Step function.

                        +
                        view source

                        step-after

                        (step-after xs ys)

                        Step function.

                        Examples

                        Usage

                        (interpolate step-after ...)
 ;;=> 0.8165378262982225

                        Step (after) plot

                        -
                        view source

                        step-before

                        (step-before xs ys)

                        Step function.

                        +
                        view source

                        step-before

                        (step-before xs ys)

                        Step function.

                        Examples

                        Usage

                        (interpolate step-before ...)
 ;;=> 0.5357270595553765

                        Step (before) plot

                        -
                        view source
                        \ No newline at end of file +
                        view source
                        \ No newline at end of file diff --git a/docs/fastmath.kernel.html b/docs/fastmath.kernel.html index b5a6586e..db4da88a 100644 --- a/docs/fastmath.kernel.html +++ b/docs/fastmath.kernel.html @@ -1,6 +1,6 @@ -fastmath.kernel documentation

                        Project

                        Namespaces

                        Public Vars

                        fastmath.kernel

                        Various kernel functions.

                        +fastmath.kernel documentation

                        Project

                        Namespaces

                        Public Vars

                        fastmath.kernel

                        Various kernel functions.

                        • RBF (double -> double functions)
                        • vector kernels (vector x vector -> double function; may be positive definite, conditional positive definite, positive semi-definite, mercer)
                          • @@ -13,25 +13,25 @@ ;;=> 0.02 (let [ak (approx (kernel :gaussian) 6)] (ak [1 2] [3 4])) ;;=> 0.018316

                        Plot of :gaussian kernel pproximated to one decimal place.

                        -
                        view source

                        cauchy-density-kernel

                        (cauchy-density-kernel x)
                        view source

                        cosine-density-kernel

                        (cosine-density-kernel x)
                        view source

                        cpd->pd

                        (cpd->pd k)

                        Convert conditionally positive definite kernel into positive definite.

                        +
                        view source

                        cauchy-density-kernel

                        (cauchy-density-kernel x)
                        view source

                        cosine-density-kernel

                        (cosine-density-kernel x)
                        view source

                        cpd->pd

                        (cpd->pd k)

                        Convert conditionally positive definite kernel into positive definite.

                        Formula is based on this SO answer. x0 is equal 0.

                        Doesn’t work well.

                        Examples

                        Usage

                        (let [k (kernel :circular) pd (cpd->pd k)] (pd [0.0 -0.1] [0.2 0.4]))
 ;;=> 0.013011305

                        Plot of :periodic kernel converted with cpd->pd function.

                        -
                        view source

                        epanechnikov-density-kernel

                        (epanechnikov-density-kernel x)
                        view source

                        exp

                        (exp k)(exp k t)

                        Kernel wraper. exp of kernel k with optional scaling value t.

                        +
                        view source

                        epanechnikov-density-kernel

                        (epanechnikov-density-kernel x)
                        view source

                        exp

                        (exp k)(exp k t)

                        Kernel wraper. exp of kernel k with optional scaling value t.

                        Examples

                        Usage

                        (let [k (exp (kernel :laplacian))] (k [1 2] [3 4]))
 ;;=> 1.060887420006057

                        Exp with scale=0.5

                        (let [k (exp (kernel :laplacian) 0.5)] (k [1 2] [3 4]))
 ;;=> 1.0299938931887205

                        Plot of exp of :dirichlet kernel with scaling=5.0

                        -
                        view source

                        fields

                        (fields k f)(fields k f1 f2)

                        Kernel wrapper. Apply vector field for each input before applying kernel function.

                        +
                        view source

                        fields

                        (fields k f)(fields k f1 f2)

                        Kernel wrapper. Apply vector field for each input before applying kernel function.

                        Examples

                        Usage

                        (let [k (kernel :laplacian)
       fld (fields/field :horseshoe)
       kf (fields k fld)]
   (kf (v/vec2 2 3) (v/vec2 1 2)))
-;;=> 0.21437946979352915
                        view source

                        gaussian-density-kernel

                        (gaussian-density-kernel x)
                        view source

                        kernel

                        multimethod

                        Crated vector kernel.

                        +;;=> 0.21437946979352915
                        view source

                        gaussian-density-kernel

                        (gaussian-density-kernel x)
                        view source

                        kernel

                        multimethod

                        Crated vector kernel.

                        Kernels can be Mercer, positive definite, conditional positive definite, positive semi-definite or other.

                        Optional parameters:

                        For :gaussian, :exponential, :laplacian, :rational-quadratic, :multiquadratic, :inverse-multiquadratic, :circular, :spherical, :wave, :power, :log, :cauchy, :generalized-t-student, :hyperbolic-secant, :thin-plate, :mattern-12, :mattern-32, :mattern-52 and ::hyperbolic-secant you can provide scaling parameter and distance (see fastmath.distance, default is euclidean).

                        @@ -95,10 +95,10 @@

                        Plot of thin-plate

                        Plot of variance-function

                        Plot of wave

                        -
                        view source

                        kernel->rbf

                        (kernel->rbf k)(kernel->rbf k center)

                        Convert vector kernel to RBF kernel. center is fixed y vector (default contains EPSILON values).

                        +
                        view source

                        kernel->rbf

                        (kernel->rbf k)(kernel->rbf k center)

                        Convert vector kernel to RBF kernel. center is fixed y vector (default contains EPSILON values).

                        Examples

                        Usage

                        (let [k (kernel :mattern-52) r (kernel->rbf k)] (r 0.234))
-;;=> 0.9567485662415672
                        view source

                        kernel-density

                        multimethod

                        Create kernel density estimator.

                        +;;=> 0.9567485662415672
                        view source

                        kernel-density

                        multimethod

                        Create kernel density estimator.

                        Parameters:

                        Examples

                        Usage

                        (let [k (kernel-density :epanechnikov (repeatedly 1000 rand))] (k 0.5))
-;;=> 0.9183374186479187
+;;=> 1.117963173775483
 (let [k (kernel-density :gaussian (repeatedly 1000 rand) 2)] (k 0.5))
-;;=> 0.19727139631330753

                        Plot of cauchy

                        +;;=> 0.1974205108544589

                        Plot of cauchy

                        Plot of cosine

                        Plot of default

                        Plot of epanechnikov

                        @@ -125,7 +125,7 @@

                        Plot of triweight

                        Plot of uniform

                        Plot of wigner

                        -
                        view source

                        kernel-density-ci

                        (kernel-density-ci method data)(kernel-density-ci method data bandwidth)(kernel-density-ci method data bandwidth alpha)

                        Create function which returns confidence intervals for given kde method.

                        +
                        view source

                        kernel-density-ci

                        (kernel-density-ci method data)(kernel-density-ci method data bandwidth)(kernel-density-ci method data bandwidth alpha)

                        Create function which returns confidence intervals for given kde method.

                        Check 6.1.5 http://sfb649.wiwi.hu-berlin.de/fedc_homepage/xplore/tutorials/xlghtmlnode33.html

                        Parameters:

                          @@ -138,10 +138,10 @@

                        Examples

                        Usage

                        (let [k (kernel-density-ci :epanechnikov (repeatedly 1000 rand))]
   (k 0.5))
-;;=> [0.9688370602070584 0.7995779565431819 1.138096163870935]
+;;=> [1.0980476125749297 0.9158708086785848 1.2802244164712744]
 (let [k (kernel-density-ci :gaussian (repeatedly 1000 rand) 2)] (k 0.5))
-;;=> [0.19739560420073257 0.18705372725971706 0.2077374811417481]

                        Kernel density with confidence intervals

                        -
                        view source

                        kernel-density-list

                        Examples

                        List of density kernels

                        +;;=> [0.19738297405101762 0.18704142797234344 0.2077245201296918]

                        Kernel density with confidence intervals

                        +
                        view source

                        kernel-density-list

                        Examples

                        List of density kernels

                        kernel-density-list
 ;;=> (:cauchy :cosine
 ;;=>          :default :epanechnikov
@@ -150,7 +150,7 @@
 ;;=>          :sigmoid :silverman
 ;;=>          :smile :triangular
 ;;=>          :tricube :triweight
-;;=>          :uniform :wigner)
                        view source

                        kernels-list

                        Examples

                        List of vector kernels

                        +;;=> :uniform :wigner)
                        view source

                        kernels-list

                        Examples

                        List of vector kernels

                        kernels-list
 ;;=> (:anova
 ;;=>  :bessel
@@ -169,14 +169,14 @@
 ;;=>  :power :rational-quadratic
 ;;=>  :scalar-functions :spherical
 ;;=>  :spline :thin-plate
-;;=>  :variance-function :wave)
                        view source

                        laplace-density-kernel

                        (laplace-density-kernel x)
                        view source

                        logistic-density-kernel

                        (logistic-density-kernel x)
                        view source

                        mult

                        (mult k1)(mult k1 k2)(mult k1 k2 k3)(mult k1 k2 k3 & r)

                        Kernel wrapper. Multiply two or more kernels.

                        +;;=> :variance-function :wave)
                        view source

                        laplace-density-kernel

                        (laplace-density-kernel x)
                        view source

                        logistic-density-kernel

                        (logistic-density-kernel x)
                        view source

                        mult

                        (mult k1)(mult k1 k2)(mult k1 k2 k3)(mult k1 k2 k3 & r)

                        Kernel wrapper. Multiply two or more kernels.

                        Examples

                        Usage

                        (let [k1 (kernel :laplacian)
       k2 (kernel :periodic)
       res (mult k1 k2)]
   (res [1 2 3 4] [-1 2 3 5]))
 ;;=> 0.042910348739392076

                        Product of two kernels

                        -
                        view source

                        quartic-density-kernel

                        (quartic-density-kernel x)
                        view source

                        rbf

                        multimethod

                        RBF kernel creator. RBF is double->double function.

                        +
                        view source

                        quartic-density-kernel

                        (quartic-density-kernel x)
                        view source

                        rbf

                        multimethod

                        RBF kernel creator. RBF is double->double function.

                        Parameters:

                        All kernels accept scale parameter (as last parameter).

                        Following kernels also accept beta: :multiquadratic, :inverse-multiquadratic, :truncated-power, :radial-powers and :thin-plate.

                        @@ -228,10 +228,10 @@

                        Plot of wu-31

                        Plot of wu-32

                        Plot of wu-33

                        -
                        view source

                        rbf->kernel

                        (rbf->kernel rbf-kernel)(rbf->kernel rbf-kernel distance)

                        Treat RBF kernel as vector kernel using distance function (default euclidean.

                        +
                        view source

                        rbf->kernel

                        (rbf->kernel rbf-kernel)(rbf->kernel rbf-kernel distance)

                        Treat RBF kernel as vector kernel using distance function (default euclidean.

                        Examples

                        Usage

                        (let [r (rbf :mattern-c4) k (rbf->kernel r)] (k [1 2 3 4] [-1 2 3 5]))
-;;=> 1.5719823264954609
                        view source

                        rbf-list

                        Examples

                        List of RBF kernels

                        +;;=> 1.5719823264954609
                        view source

                        rbf-list

                        Examples

                        List of RBF kernels

                        rbf-list
 ;;=> (:gaussian
 ;;=>  :gaussians-laguerre-11 :gaussians-laguerre-12
@@ -253,21 +253,21 @@
 ;;=>  :wu-11 :wu-20
 ;;=>  :wu-21 :wu-22
 ;;=>  :wu-30 :wu-31
-;;=>  :wu-32 :wu-33)
                        view source

                        scale

                        (scale k scale)

                        Kernel wrapper. Scale kernel result.

                        +;;=> :wu-32 :wu-33)
                        view source

                        scale

                        (scale k scale)

                        Kernel wrapper. Scale kernel result.

                        Examples

                        Usage

                        (let [k (kernel :laplacian)
       sk (scale k 2.0)]
   {:kernel (k [1 2 3 4] [-1 2 3 5]),
    :scaled-kernel (sk [1 2 3 4] [-1 2 3 5])})
-;;=> {:kernel 0.10687792566038574, :scaled-kernel 0.2137558513207715}
                        view source

                        sigmoid-density-kernel

                        (sigmoid-density-kernel x)
                        view source

                        silverman-density-kernel

                        (silverman-density-kernel x)
                        view source

                        smile-mercer

                        (smile-mercer k)

                        Create Smile Mercer Kernel object

                        +;;=> {:kernel 0.10687792566038574, :scaled-kernel 0.2137558513207715}
                        view source

                        sigmoid-density-kernel

                        (sigmoid-density-kernel x)
                        view source

                        silverman-density-kernel

                        (silverman-density-kernel x)
                        view source

                        smile-mercer

                        (smile-mercer k)

                        Create Smile Mercer Kernel object

                        Used to pass to Smile constructors/functions.

                        Examples

                        Usage

                        (smile-mercer (kernel :mattern-52))
-;;=> fastmath.kernel$smile_mercer$reify__19944@6aba6d59
                        view source

                        smile-rbf

                        (smile-rbf rbf-fn)

                        Create RBF Smile object.

                        +;;=> fastmath.kernel$smile_mercer$reify__19969@1c4f7000
                        view source

                        smile-rbf

                        (smile-rbf rbf-fn)

                        Create RBF Smile object.

                        Used to pass to Smile constructors/functions.

                        Examples

                        Usage

                        (smile-rbf (rbf :mattern-c2))
-;;=> fastmath.kernel$smile_rbf$reify__19682@2550b98a
                        view source

                        triangular-density-kernel

                        (triangular-density-kernel x)
                        view source

                        tricube-density-kernel

                        (tricube-density-kernel x)
                        view source

                        triweight-density-kernel

                        (triweight-density-kernel x)
                        view source

                        uniform-density-kernel

                        (uniform-density-kernel x)
                        view source

                        wadd

                        (wadd kernels)(wadd weights kernels)

                        Kernel wrapper. Add kernels (weighted).

                        +;;=> fastmath.kernel$smile_rbf$reify__19707@49cfb519
                        view source

                        triangular-density-kernel

                        (triangular-density-kernel x)
                        view source

                        tricube-density-kernel

                        (tricube-density-kernel x)
                        view source

                        triweight-density-kernel

                        (triweight-density-kernel x)
                        view source

                        uniform-density-kernel

                        (uniform-density-kernel x)
                        view source

                        wadd

                        (wadd kernels)(wadd weights kernels)

                        Kernel wrapper. Add kernels (weighted).

                        Examples

                        Usage

                        (let [k1 (kernel :laplacian)
       k2 (kernel :periodic)
@@ -279,4 +279,4 @@
       res (wadd [0.2 0.8] [k1 k2])]
   (res [1 2 3 4] [-1 2 3 5]))
 ;;=> 0.3425670639094149

                        Weighted sum of two kernels

                        -
                        view source

                        wigner-density-kernel

                        (wigner-density-kernel x)
                        view source
                        \ No newline at end of file +
                        view source

                        wigner-density-kernel

                        (wigner-density-kernel x)
                        view source
                        \ No newline at end of file diff --git a/docs/fastmath.matrix.html b/docs/fastmath.matrix.html index 26abe9a4..29085bac 100644 --- a/docs/fastmath.matrix.html +++ b/docs/fastmath.matrix.html @@ -1,119 +1,126 @@ -fastmath.matrix documentation

                        Project

                        Namespaces

                        Public Vars

                        fastmath.matrix

                        Fixed size (2x2, 3x3, 4x4) matrix types.

                        -

                        Categories

                          Other vars: ->Mat2x2 ->Mat3x3 ->Mat4x4 acos acosh acot acoth acsc add adds asec asech asin asinh atan atanh cbrt ceil col cols cols->mat2x2 cols->mat3x3 cols->mat4x4 cos cosh cot coth csc csch degrees det diag diagonal emulm exp expm1 eye floor fmap frac inverse jinc ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmxp1 mat->RealMatrix mat->array2d mat2x2 mat3x3 mat4x4 mulm mulmt muls mulv ncol negate nrow outer radians rint round row rows rows->mat2x2 rows->mat3x3 rows->mat4x4 safe-sqrt sec sech sfrac sgn sigmoid signum sin sinc sinh solve sq sqrt sub symmetric? tan tanh tmulm tmulmt trace transpose trunc vtmul xlogx zero

                          acos

                          (acos vector)

                          Apply acos to matrix elements.

                          -
                          view source

                          acosh

                          (acosh vector)

                          Apply acosh to matrix elements.

                          -
                          view source

                          acot

                          (acot vector)

                          Apply acot to matrix elements.

                          -
                          view source

                          acoth

                          (acoth vector)

                          Apply acoth to matrix elements.

                          -
                          view source

                          acsc

                          (acsc vector)

                          Apply acsc to matrix elements.

                          -
                          view source

                          add

                          (add A)(add A B)

                          Add matrices, C=A+B.

                          -
                          view source

                          adds

                          (adds A s)

                          Add scalar to all matrix elements

                          -
                          view source

                          asec

                          (asec vector)

                          Apply asec to matrix elements.

                          -
                          view source

                          asech

                          (asech vector)

                          Apply asech to matrix elements.

                          -
                          view source

                          asin

                          (asin vector)

                          Apply asin to matrix elements.

                          -
                          view source

                          asinh

                          (asinh vector)

                          Apply asinh to matrix elements.

                          -
                          view source

                          atan

                          (atan vector)

                          Apply atan to matrix elements.

                          -
                          view source

                          atanh

                          (atanh vector)

                          Apply atanh to matrix elements.

                          -
                          view source

                          cbrt

                          (cbrt vector)

                          Apply cbrt to matrix elements.

                          -
                          view source

                          ceil

                          (ceil vector)

                          Apply ceil to matrix elements.

                          -
                          view source

                          col

                          (col A c)

                          Return column as a vector

                          -
                          view source

                          cols

                          (cols A)

                          Return matrix columns

                          -
                          view source

                          cols->mat2x2

                          (cols->mat2x2 [a00 a10] [a01 a11])

                          Create 2x2 matrix from 2d vectors (columns).

                          -
                          view source

                          cols->mat3x3

                          (cols->mat3x3 [a00 a10 a20] [a01 a11 a21] [a02 a12 a22])

                          Create 3x3 matrix from 3d vectors (columns).

                          -
                          view source

                          cols->mat4x4

                          (cols->mat4x4 [a00 a10 a20 a30] [a01 a11 a21 a31] [a02 a12 a22 a32] [a03 a13 a23 a33])

                          Create 4x4 matrix from 4d vectors (columns).

                          -
                          view source

                          cos

                          (cos vector)

                          Apply cos to matrix elements.

                          -
                          view source

                          cosh

                          (cosh vector)

                          Apply cosh to matrix elements.

                          -
                          view source

                          cot

                          (cot vector)

                          Apply cot to matrix elements.

                          -
                          view source

                          coth

                          (coth vector)

                          Apply coth to matrix elements.

                          -
                          view source

                          csc

                          (csc vector)

                          Apply csc to matrix elements.

                          -
                          view source

                          csch

                          (csch vector)

                          Apply csch to matrix elements.

                          -
                          view source

                          degrees

                          (degrees vector)

                          Apply degrees to matrix elements.

                          -
                          view source

                          det

                          (det A)

                          Return determinant of the matrix.

                          -
                          view source

                          diag

                          (diag A)

                          Return diagonal of the matrix as a vector.

                          -
                          view source

                          diagonal

                          (diagonal diag)

                          Create diagonal matrix

                          -
                          view source

                          emulm

                          (emulm A B)

                          Multiply two matrices element-wise, Hadamard product, C=AoB

                          -
                          view source

                          exp

                          (exp vector)

                          Apply exp to matrix elements.

                          -
                          view source

                          expm1

                          (expm1 vector)

                          Apply expm1 to matrix elements.

                          -
                          view source

                          floor

                          (floor vector)

                          Apply floor to matrix elements.

                          -
                          view source

                          fmap

                          (fmap A f)

                          Apply a function f to each matrix element.

                          -
                          view source

                          frac

                          (frac vector)

                          Apply frac to matrix elements.

                          -
                          view source

                          inverse

                          (inverse m)

                          Matrix inversion.

                          +fastmath.matrix documentation

                          Project

                          Namespaces

                          Public Vars

                          fastmath.matrix

                          Fixed size (2x2, 3x3, 4x4) matrix types.

                          +

                          Categories

                            Other vars: ->Mat2x2 ->Mat3x3 ->Mat4x4 acos acosh acot acoth acsc acsch add adds asec asech asin asinh atan atanh cb cbrt ceil cholesky col cols cols->mat2x2 cols->mat3x3 cols->mat4x4 cos cosh cot coth csc csch degrees det diag diagonal emulm exp expm1 eye floor fmap frac inverse jinc ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmxp1 mat->RealMatrix mat->array mat->array2d mat->float-array mat->float-array2d mat2x2 mat3x3 mat4x4 mulm mulmt muls mulv ncol negate nrow outer radians rint round row rows rows->mat2x2 rows->mat3x3 rows->mat4x4 safe-sqrt sec sech sfrac sgn sigmoid signum sin sinc sinh solve sq sqrt sub symmetric? tan tanh tmulm tmulmt trace transpose trunc vtmul xlogx zero

                            acos

                            (acos vector)

                            Apply acos to matrix elements.

                            +
                            view source

                            acosh

                            (acosh vector)

                            Apply acosh to matrix elements.

                            +
                            view source

                            acot

                            (acot vector)

                            Apply acot to matrix elements.

                            +
                            view source

                            acoth

                            (acoth vector)

                            Apply acoth to matrix elements.

                            +
                            view source

                            acsc

                            (acsc vector)

                            Apply acsc to matrix elements.

                            +
                            view source

                            acsch

                            (acsch vector)

                            Apply acsch to matrix elements.

                            +
                            view source

                            add

                            (add A)(add A B)

                            Add matrices, C=A+B.

                            +
                            view source

                            adds

                            (adds A s)

                            Add scalar to all matrix elements

                            +
                            view source

                            asec

                            (asec vector)

                            Apply asec to matrix elements.

                            +
                            view source

                            asech

                            (asech vector)

                            Apply asech to matrix elements.

                            +
                            view source

                            asin

                            (asin vector)

                            Apply asin to matrix elements.

                            +
                            view source

                            asinh

                            (asinh vector)

                            Apply asinh to matrix elements.

                            +
                            view source

                            atan

                            (atan vector)

                            Apply atan to matrix elements.

                            +
                            view source

                            atanh

                            (atanh vector)

                            Apply atanh to matrix elements.

                            +
                            view source

                            cb

                            (cb vector)

                            Apply cb to matrix elements.

                            +
                            view source

                            cbrt

                            (cbrt vector)

                            Apply cbrt to matrix elements.

                            +
                            view source

                            ceil

                            (ceil vector)

                            Apply ceil to matrix elements.

                            +
                            view source

                            cholesky

                            (cholesky A)(cholesky A upper?)

                            Calculate L (lower by default) triangular for where L * L^T = A.

                            +

                            Checks only for symmetry, can return NaNs when A is not positive-definite.

                            +
                            view source

                            col

                            (col A c)

                            Return column as a vector

                            +
                            view source

                            cols

                            (cols A)

                            Return matrix columns

                            +
                            view source

                            cols->mat2x2

                            (cols->mat2x2 [a00 a10] [a01 a11])

                            Create 2x2 matrix from 2d vectors (columns).

                            +
                            view source

                            cols->mat3x3

                            (cols->mat3x3 [a00 a10 a20] [a01 a11 a21] [a02 a12 a22])

                            Create 3x3 matrix from 3d vectors (columns).

                            +
                            view source

                            cols->mat4x4

                            (cols->mat4x4 [a00 a10 a20 a30] [a01 a11 a21 a31] [a02 a12 a22 a32] [a03 a13 a23 a33])

                            Create 4x4 matrix from 4d vectors (columns).

                            +
                            view source

                            cos

                            (cos vector)

                            Apply cos to matrix elements.

                            +
                            view source

                            cosh

                            (cosh vector)

                            Apply cosh to matrix elements.

                            +
                            view source

                            cot

                            (cot vector)

                            Apply cot to matrix elements.

                            +
                            view source

                            coth

                            (coth vector)

                            Apply coth to matrix elements.

                            +
                            view source

                            csc

                            (csc vector)

                            Apply csc to matrix elements.

                            +
                            view source

                            csch

                            (csch vector)

                            Apply csch to matrix elements.

                            +
                            view source

                            degrees

                            (degrees vector)

                            Apply degrees to matrix elements.

                            +
                            view source

                            det

                            (det A)

                            Return determinant of the matrix.

                            +
                            view source

                            diag

                            (diag A)

                            Return diagonal of the matrix as a vector.

                            +
                            view source

                            diagonal

                            (diagonal diag)

                            Create diagonal matrix

                            +
                            view source

                            emulm

                            (emulm A B)

                            Multiply two matrices element-wise, Hadamard product, C=AoB

                            +
                            view source

                            exp

                            (exp vector)

                            Apply exp to matrix elements.

                            +
                            view source

                            expm1

                            (expm1 vector)

                            Apply expm1 to matrix elements.

                            +
                            view source

                            floor

                            (floor vector)

                            Apply floor to matrix elements.

                            +
                            view source

                            fmap

                            (fmap A f)

                            Apply a function f to each matrix element.

                            +
                            view source

                            frac

                            (frac vector)

                            Apply frac to matrix elements.

                            +
                            view source

                            inverse

                            (inverse m)

                            Matrix inversion.

                            Returns nil if inversion doesn’t exist.

                            -
                            view source

                            jinc

                            (jinc vector)

                            Apply jinc to matrix elements.

                            -
                            view source

                            ln

                            (ln vector)

                            Apply ln to matrix elements.

                            -
                            view source

                            log

                            (log vector)

                            Apply log to matrix elements.

                            -
                            view source

                            log10

                            (log10 vector)

                            Apply log10 to matrix elements.

                            -
                            view source

                            log1mexp

                            (log1mexp vector)

                            Apply log1mexp to matrix elements.

                            -
                            view source

                            log1p

                            (log1p vector)

                            Apply log1p to matrix elements.

                            -
                            view source

                            log1pexp

                            (log1pexp vector)

                            Apply log1pexp to matrix elements.

                            -
                            view source

                            log1pmx

                            (log1pmx vector)

                            Apply log1pmx to matrix elements.

                            -
                            view source

                            log1psq

                            (log1psq vector)

                            Apply log1psq to matrix elements.

                            -
                            view source

                            log2

                            (log2 vector)

                            Apply log2 to matrix elements.

                            -
                            view source

                            logexpm1

                            (logexpm1 vector)

                            Apply logexpm1 to matrix elements.

                            -
                            view source

                            logit

                            (logit vector)

                            Apply logit to matrix elements.

                            -
                            view source

                            logmxp1

                            (logmxp1 vector)

                            Apply logmxp1 to matrix elements.

                            -
                            view source

                            mat->array2d

                            (mat->array2d A)

                            Return doubles of doubles

                            -
                            view source

                            mat->RealMatrix

                            (mat->RealMatrix A)

                            Return Apache Commons Math Array2DRowMatrix

                            -
                            view source

                            mat2x2

                            (mat2x2 v)(mat2x2 d1 d2)(mat2x2 a00 a01 a10 a11)

                            Create 2x2 matrix.

                            +
                            view source

                            jinc

                            (jinc vector)

                            Apply jinc to matrix elements.

                            +
                            view source

                            ln

                            (ln vector)

                            Apply ln to matrix elements.

                            +
                            view source

                            log

                            (log vector)

                            Apply log to matrix elements.

                            +
                            view source

                            log10

                            (log10 vector)

                            Apply log10 to matrix elements.

                            +
                            view source

                            log1mexp

                            (log1mexp vector)

                            Apply log1mexp to matrix elements.

                            +
                            view source

                            log1p

                            (log1p vector)

                            Apply log1p to matrix elements.

                            +
                            view source

                            log1pexp

                            (log1pexp vector)

                            Apply log1pexp to matrix elements.

                            +
                            view source

                            log1pmx

                            (log1pmx vector)

                            Apply log1pmx to matrix elements.

                            +
                            view source

                            log1psq

                            (log1psq vector)

                            Apply log1psq to matrix elements.

                            +
                            view source

                            log2

                            (log2 vector)

                            Apply log2 to matrix elements.

                            +
                            view source

                            logexpm1

                            (logexpm1 vector)

                            Apply logexpm1 to matrix elements.

                            +
                            view source

                            logit

                            (logit vector)

                            Apply logit to matrix elements.

                            +
                            view source

                            logmxp1

                            (logmxp1 vector)

                            Apply logmxp1 to matrix elements.

                            +
                            view source

                            mat->array

                            (mat->array A)

                            Return doubles of doubles

                            +
                            view source

                            mat->array2d

                            (mat->array2d A)

                            Return doubles of doubles

                            +
                            view source

                            mat->float-array

                            (mat->float-array A)

                            Return doubles of doubles

                            +
                            view source

                            mat->float-array2d

                            (mat->float-array2d A)

                            Return doubles of doubles

                            +
                            view source

                            mat->RealMatrix

                            (mat->RealMatrix A)

                            Return Apache Commons Math Array2DRowMatrix

                            +
                            view source

                            mat2x2

                            (mat2x2 v)(mat2x2 d1 d2)(mat2x2 a00 a01 a10 a11)

                            Create 2x2 matrix.

                            Arity:

                            • 1 - fills matrix with given value
                            • 2 - creates diagonal matrix
                            • 4 - creates row ordered matrix
                            -
                            view source

                            mat3x3

                            (mat3x3 v)(mat3x3 d1 d2 d3)(mat3x3 a00 a01 a02 a10 a11 a12 a20 a21 a22)

                            Create 3x3 matrix.

                            +
                            view source

                            mat3x3

                            (mat3x3 v)(mat3x3 d1 d2 d3)(mat3x3 a00 a01 a02 a10 a11 a12 a20 a21 a22)

                            Create 3x3 matrix.

                            Arity:

                            • 1 - fills matrix with given value
                            • 3 - creates diagonal matrix
                            • 9 - creates row ordered matrix
                            -
                            view source

                            mat4x4

                            (mat4x4 v)(mat4x4 d1 d2 d3 d4)(mat4x4 a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33)

                            Create 4x4 matrix.

                            +
                            view source

                            mat4x4

                            (mat4x4 v)(mat4x4 d1 d2 d3 d4)(mat4x4 a00 a01 a02 a03 a10 a11 a12 a13 a20 a21 a22 a23 a30 a31 a32 a33)

                            Create 4x4 matrix.

                            Arity:

                            • 1 - fills matrix with given value
                            • 4 - creates diagonal matrix
                            • 16 - creates row ordered matrix
                            -
                            view source

                            mulm

                            (mulm A B)(mulm A transposeA? B transposeB?)

                            Multiply two matrices, C=AxB.

                            +
                            view source

                            mulm

                            (mulm A B)(mulm A transposeA? B transposeB?)

                            Multiply two matrices, C=AxB.

                            Optionally you can request transposition of matrices.

                            -
                            view source

                            mulmt

                            (mulmt A B)

                            Multiply with transposed matrix, C=AxB^T

                            -
                            view source

                            muls

                            (muls A s)

                            Multply matrix by a scalar, C=sA

                            -
                            view source

                            mulv

                            (mulv A v)

                            Multply matrix by vector, x=Av

                            -
                            view source

                            ncol

                            (ncol A)

                            Return number of rows

                            -
                            view source

                            negate

                            (negate A)

                            Negate all matrix elements, C=-A

                            -
                            view source

                            nrow

                            (nrow A)

                            Return number of rows

                            -
                            view source

                            outer

                            (outer v1 v2)

                            Outer project for two vectors.

                            -
                            view source

                            radians

                            (radians vector)

                            Apply radians to matrix elements.

                            -
                            view source

                            rint

                            (rint vector)

                            Apply rint to matrix elements.

                            -
                            view source

                            round

                            (round vector)

                            Apply round to matrix elements.

                            -
                            view source

                            row

                            (row A r)

                            Return row as a vector

                            -
                            view source

                            rows

                            (rows A)

                            Return matrix rows

                            -
                            view source

                            rows->mat2x2

                            (rows->mat2x2 [a00 a01] [a10 a11])

                            Create 2x2 matrix from 2d vectors (rows).

                            -
                            view source

                            rows->mat3x3

                            (rows->mat3x3 [a00 a01 a02] [a10 a11 a12] [a20 a21 a22])

                            Create 3x3 matrix from 3d vectors (rows).

                            -
                            view source

                            rows->mat4x4

                            (rows->mat4x4 [a00 a01 a02 a03] [a10 a11 a12 a13] [a20 a21 a22 a23] [a30 a31 a32 a33])

                            Create 4x4 matrix from 4d vectors (rows).

                            -
                            view source

                            safe-sqrt

                            (safe-sqrt vector)

                            Apply safe-sqrt to matrix elements.

                            -
                            view source

                            sec

                            (sec vector)

                            Apply sec to matrix elements.

                            -
                            view source

                            sech

                            (sech vector)

                            Apply sech to matrix elements.

                            -
                            view source

                            sfrac

                            (sfrac vector)

                            Apply sfrac to matrix elements.

                            -
                            view source

                            sgn

                            (sgn vector)

                            Apply sgn to matrix elements.

                            -
                            view source

                            sigmoid

                            (sigmoid vector)

                            Apply sigmoid to matrix elements.

                            -
                            view source

                            signum

                            (signum vector)

                            Apply signum to matrix elements.

                            -
                            view source

                            sin

                            (sin vector)

                            Apply sin to matrix elements.

                            -
                            view source

                            sinc

                            (sinc vector)

                            Apply sinc to matrix elements.

                            -
                            view source

                            sinh

                            (sinh vector)

                            Apply sinh to matrix elements.

                            -
                            view source

                            solve

                            (solve A b)

                            Solve linear equation Ax=b

                            -
                            view source

                            sq

                            (sq vector)

                            Apply sq to matrix elements.

                            -
                            view source

                            sqrt

                            (sqrt vector)

                            Apply sqrt to matrix elements.

                            -
                            view source

                            sub

                            (sub A)(sub A B)

                            Subract matrices, C=A-B.

                            -
                            view source

                            symmetric?

                            (symmetric? A)

                            Check if matrix is symmetric

                            -
                            view source

                            tan

                            (tan vector)

                            Apply tan to matrix elements.

                            -
                            view source

                            tanh

                            (tanh vector)

                            Apply tanh to matrix elements.

                            -
                            view source

                            tmulm

                            (tmulm A B)

                            Transpose and multiply, C=A^TxB

                            -
                            view source

                            tmulmt

                            (tmulmt A B)

                            Transpose both and multiply, C=A^TxB^T

                            -
                            view source

                            trace

                            (trace A)

                            Return trace of the matrix (sum of diagonal elements)

                            -
                            view source

                            transpose

                            (transpose A)

                            Transpose matrix, C=A^T

                            -
                            view source

                            trunc

                            (trunc vector)

                            Apply trunc to matrix elements.

                            -
                            view source

                            vtmul

                            (vtmul A v)

                            Multiply transposed vector by matrix, C=v^T A

                            -
                            view source

                            xlogx

                            (xlogx vector)

                            Apply xlogx to matrix elements.

                            -
                            view source
                            \ No newline at end of file +
                            view source

                            mulmt

                            (mulmt A B)

                            Multiply with transposed matrix, C=AxB^T

                            +
                            view source

                            muls

                            (muls A s)

                            Multply matrix by a scalar, C=sA

                            +
                            view source

                            mulv

                            (mulv A v)

                            Multply matrix by vector, x=Av

                            +
                            view source

                            ncol

                            (ncol A)

                            Return number of rows

                            +
                            view source

                            negate

                            (negate A)

                            Negate all matrix elements, C=-A

                            +
                            view source

                            nrow

                            (nrow A)

                            Return number of rows

                            +
                            view source

                            outer

                            (outer v1 v2)

                            Outer project for two vectors.

                            +
                            view source

                            radians

                            (radians vector)

                            Apply radians to matrix elements.

                            +
                            view source

                            rint

                            (rint vector)

                            Apply rint to matrix elements.

                            +
                            view source

                            round

                            (round vector)

                            Apply round to matrix elements.

                            +
                            view source

                            row

                            (row A r)

                            Return row as a vector

                            +
                            view source

                            rows

                            (rows A)

                            Return matrix rows

                            +
                            view source

                            rows->mat2x2

                            (rows->mat2x2 [a00 a01] [a10 a11])

                            Create 2x2 matrix from 2d vectors (rows).

                            +
                            view source

                            rows->mat3x3

                            (rows->mat3x3 [a00 a01 a02] [a10 a11 a12] [a20 a21 a22])

                            Create 3x3 matrix from 3d vectors (rows).

                            +
                            view source

                            rows->mat4x4

                            (rows->mat4x4 [a00 a01 a02 a03] [a10 a11 a12 a13] [a20 a21 a22 a23] [a30 a31 a32 a33])

                            Create 4x4 matrix from 4d vectors (rows).

                            +
                            view source

                            safe-sqrt

                            (safe-sqrt vector)

                            Apply safe-sqrt to matrix elements.

                            +
                            view source

                            sec

                            (sec vector)

                            Apply sec to matrix elements.

                            +
                            view source

                            sech

                            (sech vector)

                            Apply sech to matrix elements.

                            +
                            view source

                            sfrac

                            (sfrac vector)

                            Apply sfrac to matrix elements.

                            +
                            view source

                            sgn

                            (sgn vector)

                            Apply sgn to matrix elements.

                            +
                            view source

                            sigmoid

                            (sigmoid vector)

                            Apply sigmoid to matrix elements.

                            +
                            view source

                            signum

                            (signum vector)

                            Apply signum to matrix elements.

                            +
                            view source

                            sin

                            (sin vector)

                            Apply sin to matrix elements.

                            +
                            view source

                            sinc

                            (sinc vector)

                            Apply sinc to matrix elements.

                            +
                            view source

                            sinh

                            (sinh vector)

                            Apply sinh to matrix elements.

                            +
                            view source

                            solve

                            (solve A b)

                            Solve linear equation Ax=b

                            +
                            view source

                            sq

                            (sq vector)

                            Apply sq to matrix elements.

                            +
                            view source

                            sqrt

                            (sqrt vector)

                            Apply sqrt to matrix elements.

                            +
                            view source

                            sub

                            (sub A)(sub A B)

                            Subract matrices, C=A-B.

                            +
                            view source

                            symmetric?

                            (symmetric? A)

                            Check if matrix is symmetric

                            +
                            view source

                            tan

                            (tan vector)

                            Apply tan to matrix elements.

                            +
                            view source

                            tanh

                            (tanh vector)

                            Apply tanh to matrix elements.

                            +
                            view source

                            tmulm

                            (tmulm A B)

                            Transpose and multiply, C=A^TxB

                            +
                            view source

                            tmulmt

                            (tmulmt A B)

                            Transpose both and multiply, C=A^TxB^T

                            +
                            view source

                            trace

                            (trace A)

                            Return trace of the matrix (sum of diagonal elements)

                            +
                            view source

                            transpose

                            (transpose A)

                            Transpose matrix, C=A^T

                            +
                            view source

                            trunc

                            (trunc vector)

                            Apply trunc to matrix elements.

                            +
                            view source

                            vtmul

                            (vtmul A v)

                            Multiply transposed vector by matrix, C=v^T A

                            +
                            view source

                            xlogx

                            (xlogx vector)

                            Apply xlogx to matrix elements.

                            +
                            view source
                            \ No newline at end of file diff --git a/docs/fastmath.optimization.html b/docs/fastmath.optimization.html index 50f737cf..47467c3f 100644 --- a/docs/fastmath.optimization.html +++ b/docs/fastmath.optimization.html @@ -1,6 +1,6 @@ -fastmath.optimization documentation

                            Project

                            Namespaces

                            Public Vars

                            fastmath.optimization

                            Optimization.

                            +fastmath.optimization documentation

                            Project

                            Namespaces

                            Public Vars

                            fastmath.optimization

                            Optimization.

                            Namespace provides various optimization methods.

                            • Brent (1d functions)
                              • @@ -10,7 +10,9 @@
                            • Multidirectional simplex
                            • CMAES
                            • Gradient
                              • +
                            • L-BFGS-B
                            • Bayesian Optimization (see below)
                              • +
                            • Linear optimization

                            All optimizers require bounds.

                            Optimizers

                            @@ -53,7 +55,8 @@

                            Specific paramet

                            Bayesian Optimization

                            Bayesian optimizer can be used for optimizing expensive to evaluate black box functions. Refer this article or this article

                            -

                            Categories

                              Other vars: bayesian-optimization maximize maximizer minimize minimizer scan-and-maximize scan-and-minimize

                              bayesian-optimization

                              (bayesian-optimization f {:keys [warm-up init-points bounds utility-function-type utility-param kernel kscale jitter noise optimizer optimizer-params normalize?], :or {utility-function-type :ucb, init-points 3, jitter 0.25, noise 1.0E-8, utility-param (if (#{:ei :poi} utility-function-type) 0.001 2.576), warm-up (* (count bounds) 1000), normalize? true, kernel (k/kernel :mattern-52), kscale 1.0}})

                              Bayesian optimizer

                              +

                              Linear optimization

                              +

                              Categories

                                Other vars: bayesian-optimization linear-optimization maximize maximizer minimize minimizer scan-and-maximize scan-and-minimize

                                bayesian-optimization

                                (bayesian-optimization f {:keys [warm-up init-points bounds utility-function-type utility-param kernel kscale jitter noise optimizer optimizer-params normalize?], :or {utility-function-type :ucb, init-points 3, jitter 0.25, noise 1.0E-8, utility-param (if (#{:ei :poi} utility-function-type) 0.001 2.576), warm-up (* (count bounds) 1000), normalize? true, kernel (k/kernel :mattern-52), kscale 1.0}})

                                Bayesian optimizer

                                Parameters are:

                                • :warm-up - number of brute force iterations to find maximum of utility function
                                  • @@ -88,44 +91,67 @@

                                  Bayesian Opt {:bounds bounds, :init-points 5, :utility-function-type :poi}) 10)) ;;=> {:gp -;;=> #object[fastmath.gp.GaussianProcess 0x2c72cb63 "fastmath.gp.GaussianProcess@2c72cb63"], -;;=> :util-best (3.227802177805199 -2.5215316000712362), -;;=> :util-fn #, -;;=> :x (3.227802177805199 -2.5215316000712362), -;;=> :xs ((3.227802177805199 -2.5215316000712362) -;;=> (3.1969880293006945 -2.551635600292198) -;;=> (3.155543590855263 -2.576565723996086) -;;=> (3.1244183338484 -2.5841905038468362) -;;=> (3.1130573810943782 -2.583808025029185) -;;=> (3.0984862396773494 -2.595287075953053) -;;=> (3.0733960553410244 -2.6024720151371135) -;;=> (3.063184009721807 -2.60842917989942) -;;=> (3.0302504001334984 -2.6218246890829806) -;;=> (2.9918072743371567 -2.638563414429271) -;;=> (2.9472770477568027 -2.657641458916429) -;;=> [-2.2719197766030055 -4.11685501735947] -;;=> [-4.50063744330848 2.092209893523737] -;;=> [2.943715371396424 -2.659370952841656] -;;=> [0.23377811830742168 2.9856553624837234] -;;=> [-2.083589336560353 -1.5045868205292168]), -;;=> :y -16.3145229624578, -;;=> :ys (-16.3145229624578 -;;=> -18.427271314071184 -;;=> -20.905706429688372 -;;=> -22.462993118468145 -;;=> -22.932168917049705 -;;=> -23.988952259667855 -;;=> -25.37940412325127 -;;=> -26.073624834174797 -;;=> -28.142801650884138 -;;=> -30.69916455047249 -;;=> -33.77494194500137 -;;=> -158.0365255295933 -;;=> -179.5172422623248 -;;=> -34.035215163034444 -;;=> -67.97024697164709 -;;=> -113.148303721833)}

                                Bayesian optimization points

                                -
                                view source

                                maximize

                                (maximize method f config)

                                Maximize given function.

                                +;;=> #object[fastmath.gp.GaussianProcess 0x34d2a92e "fastmath.gp.GaussianProcess@34d2a92e"], +;;=> :util-best (3.3141987214345434 -2.592010075663022), +;;=> :util-fn #, +;;=> :x (3.3141987214345434 -2.592010075663022), +;;=> :xs ((3.3141987214345434 -2.592010075663022) +;;=> (3.30992762512701 -2.596653048786531) +;;=> (3.278908684956144 -2.6269924745653417) +;;=> (3.2705125757874742 -2.637386077017003) +;;=> (3.2448338138896844 -2.671730136958611) +;;=> (3.1902248200344023 -2.7260638718526145) +;;=> (3.1587157021032857 -2.7452233603103924) +;;=> (3.0912019152796755 -2.771360671770304) +;;=> (3.0568616392253114 -2.7832848673444093) +;;=> (3.0254794263100253 -2.792257257375391) +;;=> (3.0181484109349483 -2.7937673519330035) +;;=> [-1.5162973865171314 -3.138013006830275] +;;=> [-4.559795626206481 2.080373576819847] +;;=> [3.014181669126163 -2.7942294999844366] +;;=> [0.4771670888630597 2.972154631606192] +;;=> [-1.972425173538717 -1.4158273234310959]), +;;=> :y -15.999529485423349, +;;=> :ys (-15.999529485423349 +;;=> -16.293018875754733 +;;=> -18.38232805807585 +;;=> -19.05939382833454 +;;=> -21.321613964051767 +;;=> -25.708403262220124 +;;=> -27.84863433722665 +;;=> -31.998516848853015 +;;=> -34.17055983454501 +;;=> -36.12689000130423 +;;=> -36.562489296028275 +;;=> -141.92959726860622 +;;=> -193.24651956856653 +;;=> -36.78102142190461 +;;=> -66.18256953291899 +;;=> -121.23291722716954)}

                                Bayesian optimization points

                                +
                                view source

                                linear-optimization

                                (linear-optimization target constraints)(linear-optimization target constraints {:keys [goal epsilon max-ulps cut-off rule non-negative? max-iter stats?], :or {goal :minimize, epsilon 1.0E-6, max-ulps 10, cut-off 1.0E-10, rule :dantzig, non-negative? false, max-iter Integer/MAX_VALUE}})

                                Solves a linear problem.

                                +

                                Target is defined as a vector of coefficients and constant as the last value: [a1 a2 a3 ... c] means f(x1,x2,x3) = a1*x1 + a2*x2 + a3*x3 + ... + c

                                +

                                Constraints are defined as a sequence of one of the following triplets:

                                +
                                  +
                                • [a1 a2 a3 ...] R n - which means a1*x1+a2*x2+a3*x3+... R n
                                  • +
                                • [a1 a2 a3 ... ca] R [b1 b2 b3 ... cb] - which meansa1x1+a2x2+a3x3+…+ca R b1x1+b2x2+b3x3+…+cbwhereRis a relationship and can be one of<=,>=or=as symbol or keyword. Also:leq,:geqand:eq` are valid.
                                  • +
                                +

                                Function returns pair of optimal point and function value. If stat? option is set to true, returns also information about number of iterations.

                                +

                                Possible options:

                                +
                                  +
                                • :goal - :minimize (default) or :maximize
                                  • +
                                • :rule - pivot selection rule, :dantzig (default) or :bland
                                  • +
                                • :max-iter - maximum number of iterations, maximum integer by default
                                  • +
                                • :non-negative? - allow non-negative variables only, default: false
                                  • +
                                • :epsilon - convergence value, default: 1.0e-6:
                                  • +
                                • :max-ulps - floating point comparisons, default: 10 ulp
                                  • +
                                • :cut-off - pivot elements smaller than cut-off are treated as zero, default: 1.0e-10
                                  • +
                                +
                                (linear-optimization [-1 4 0] [[-3 1] :<= 6
+                               [-1 -2] :>= -4
+                               [0 1] :>= -3])
+;; => [(9.999999999999995 -3.0) -21.999999999999993]
+
                                +
                                view source

                                maximize

                                (maximize method f config)

                                Maximize given function.

                                Parameters: optimization method, function and configuration.

                                Examples

                                Usage

                                (let [bounds [[-5.0 5.0]]
@@ -137,7 +163,7 @@ 
                                Bayesian Opt
    :bfgs (maximize :bfgs f {:bounds bounds})})
 ;;=> {:bfgs [(-0.452310691333493) 7.224689671203529],
 ;;=>  :brent [(-0.4523106823170646) 7.224689671203529],
-;;=>  :powell [(-0.4522927913307559) 7.224689666542709]}
                                view source

                                maximizer

                                (maximizer method f config)

                                Create optimizer which maximizer function.

                                +;;=> :powell [(-0.4522927913307559) 7.224689666542709]}
                                view source

                                maximizer

                                (maximizer method f config)

                                Create optimizer which maximizes function.

                                Returns function which performs optimization for optionally given initial point.

                                Examples

                                Usage

                                (let [bounds [[-5.0 5.0]]
@@ -149,10 +175,10 @@ 
                                Bayesian Opt
    :run-1 (optimizer),
    :run-2 (optimizer [4.5]),
    :run-3 (optimizer [-4.5])})
-;;=> {:optimizer #,
+;;=> {:optimizer #,
 ;;=>  :run-1 [(0.0) 6.0],
-;;=>  :run-2 [(-3.8369253615253918) 2.4140475047943664],
-;;=>  :run-3 [(-0.9525047436884773) 6.138618012978813]}
                                view source

                                minimize

                                (minimize method f config)

                                Minimize given function.

                                +;;=> :run-2 [(-0.5881313212519057) 6.978121213364068], +;;=> :run-3 [(-4.5) 2.1239369421519996]}
                                view source

                                minimize

                                (minimize method f config)

                                Minimize given function.

                                Parameters: optimization method, function and configuration.

                                Examples

                                1d function

                                (let [bounds [[-5.0 5.0]]
@@ -177,7 +203,7 @@ 
                                Bayesian Opt
 ;;=>           1.1846390625694734E-19],
 ;;=>  :gradient [(2.999999970870807 2.00000006031274) 5.809729042963462E-14]}

                                With stats

                                (minimize :gradient
-          (fn* [p1__32381#] (m/sin p1__32381#))
+          (fn* [p1__32473#] (m/sin p1__32473#))
           {:bounds [[-5 5]], :stats? true})
 ;;=> {:evaluations 22, :iterations 3, :result [(-1.5707963273466874) -1.0]}

                                min/max of f using :powell optimizer

                                min/max of f using :nelder-mead optimizer

                                @@ -191,7 +217,7 @@

                                Bayesian Opt

                                min/max of f using :cmaes optimizer

                                min/max of f using :gradient optimizer

                                min/max of f using :bobyqa optimizer

                                -
                                view source

                                minimizer

                                (minimizer method f config)

                                Create optimizer which minimizes function.

                                +
                                view source

                                minimizer

                                (minimizer method f config)

                                Create optimizer which minimizes function.

                                Returns function which performs optimization for optionally given initial point.

                                Examples

                                Usage

                                (let [bounds [[-5.0 5.0]]
@@ -203,10 +229,10 @@ 
                                Bayesian Opt
    :run-1 (optimizer),
    :run-2 (optimizer [4.5]),
    :run-3 (optimizer [-4.5])})
-;;=> {:optimizer #,
+;;=> {:optimizer #,
 ;;=>  :run-1 [(-3.947569586073323) 2.2959519482739297],
 ;;=>  :run-2 [(2.357114991599655) -0.2350104692683484],
-;;=>  :run-3 [(-4.570514545168775) 2.074718566761628]}
                                view source

                                scan-and-maximize

                                Examples

                                Usage

                                +;;=> :run-3 [(-4.570514545168775) 2.074718566761628]}
                                view source

                                scan-and-maximize

                                Examples

                                Usage

                                (let [bounds [[-5.0 5.0]]
       f (fn [x]
           (+ (* 0.2 (m/sin (* 10.0 x)))
@@ -214,9 +240,9 @@ 
                                Bayesian Opt
   {:powell (scan-and-maximize :powell f {:bounds bounds}),
    :brent (scan-and-maximize :brent f {:bounds bounds}),
    :bfgs (scan-and-maximize :bfgs f {:bounds bounds})})
-;;=> {:bfgs [(-0.4523106924984993) 7.224689671203531],
-;;=>  :brent [(-0.4523106941608976) 7.224689671203531],
-;;=>  :powell [(-0.45231248621698766) 7.2246896711567805]}
                                view source

                                scan-and-minimize

                                Examples

                                1d function

                                +;;=> {:bfgs [(-0.45231069249866795) 7.224689671203531], +;;=> :brent [(-0.4523106934099928) 7.22468967120353], +;;=> :powell [(-0.45231836815888715) 7.224689670346889]}
                                view source

                                scan-and-minimize

                                Examples

                                1d function

                                (let [bounds [[-5.0 5.0]]
       f (fn [x]
           (+ (* 0.2 (m/sin (* 10.0 x)))
@@ -224,17 +250,17 @@ 
                                Bayesian Opt
   {:powell (scan-and-minimize :powell f {:bounds bounds}),
    :brent (scan-and-minimize :brent f {:bounds bounds}),
    :bfgs (scan-and-minimize :bfgs f {:bounds bounds})})
-;;=> {:bfgs [(2.3571149047757025) -0.2350104692684255],
-;;=>  :brent [(2.3571149057838023) -0.2350104692684255],
-;;=>  :powell [(2.3571125931263115) -0.23501046921408636]}

                                2d function

                                +;;=> {:bfgs [(2.3571149048049227) -0.23501046926842556], +;;=> :brent [(2.3571149066758332) -0.23501046926842525], +;;=> :powell [(2.357114791634838) -0.23501046926829589]}

                                2d function

                                (let [bounds [[-5.0 5.0] [-5.0 5.0]]
       f (fn [x y]
           (+ (m/sq (+ (* x x) y -11.0)) (m/sq (+ x (* y y) -7.0))))]
   {:bobyqa (scan-and-minimize :bobyqa f {:bounds bounds}),
    :gradient (scan-and-minimize :gradient f {:bounds bounds}),
    :bfgs (scan-and-minimize :bfgs f {:bounds bounds})})
-;;=> {:bfgs [(2.9999999995839555 1.999999999938392) 6.981593795980213E-18],
+;;=> {:bfgs [(2.999999999796513 1.9999999988947754) 2.679589659167391E-17],
 ;;=>  :bobyqa [(-2.805118086981481 3.131312518269862)
 ;;=>           4.1058320675767663E-20],
-;;=>  :gradient [(3.5844283403285986 -1.8481265269092102)
-;;=>             4.412799367501478E-20]}
                                view source
                                \ No newline at end of file +;;=> :gradient [(-3.779310253247502 -3.283185991415039) +;;=> 2.19298749248373E-18]}
                                view source
                                \ No newline at end of file diff --git a/docs/fastmath.optimization.lbfgsb.html b/docs/fastmath.optimization.lbfgsb.html index f2c13bcb..beac8017 100644 --- a/docs/fastmath.optimization.lbfgsb.html +++ b/docs/fastmath.optimization.lbfgsb.html @@ -1,4 +1,4 @@ -fastmath.optimization.lbfgsb documentation

                                Project

                                Namespaces

                                Public Vars

                                fastmath.optimization.lbfgsb

                                Categories

                                  Other vars: ->lbfgsb grad-function

                                  ->lbfgsb

                                  (->lbfgsb params)

                                  Create lbfgsb object

                                  -
                                  view source

                                  grad-function

                                  (grad-function f goal)(grad-function f goal tol)
                                  view source
                                  \ No newline at end of file +fastmath.optimization.lbfgsb documentation

                                  Project

                                  Namespaces

                                  Public Vars

                                  fastmath.optimization.lbfgsb

                                  Categories

                                    Other vars: ->lbfgsb grad-function

                                    ->lbfgsb

                                    (->lbfgsb params)

                                    Create lbfgsb object

                                    +
                                    view source

                                    grad-function

                                    (grad-function f goal)(grad-function f goal tol)
                                    view source
                                    \ No newline at end of file diff --git a/docs/fastmath.protocols.html b/docs/fastmath.protocols.html index 09ae7921..2c8b71b3 100644 --- a/docs/fastmath.protocols.html +++ b/docs/fastmath.protocols.html @@ -1,17 +1,17 @@ -fastmath.protocols documentation

                                    Project

                                    Namespaces

                                    Public Vars

                                    fastmath.protocols

                                    Set of protocols for fastmath.

                                    +fastmath.protocols documentation

                                    Project

                                    Namespaces

                                    Public Vars

                                    fastmath.protocols

                                    Set of protocols for fastmath.

                                    Includes:

                                    • random generator protocol
                                    • distribution protocols
                                    • vector protocol
                                    -

                                    Categories

                                      Other vars: ->seq abs add approx as-vec axis-rotate base-from brandom cdf cell->anchor cell->mid continuous? coords->cell coords->mid corners covariance cross dimensions distribution-id distribution-parameters distribution? dot drandom econstrain einterpolate emn emult emx fmap forward-1d forward-2d frandom from-polar grandom grid-type heading icdf interpolate irandom is-near-zero? is-zero? lower-bound lpdf lrandom mag magsq maxdim mean means mindim mn mult mx pdf permute perpendicular probability reciprocal reverse-1d reverse-2d rotate sample set-seed set-seed! shift source-object sub sum to-acm-vec to-polar to-vec transform upper-bound variance

                                      DistributionIdProto

                                      protocol

                                      Get name and parameter names from distribution

                                      +

                                      Categories

                                        Other vars: ->seq abs add approx as-vec axis-rotate base-from brandom cdf cell->anchor cell->mid continuous? coords->cell coords->mid corners covariance cross dimensions distribution-id distribution-parameters distribution? dot drandom econstrain einterpolate emn emult emx fmap forward-1d forward-2d frandom from-polar grandom grid-type heading icdf interpolate irandom is-near-zero? is-zero? lower-bound lpdf lrandom mag magsq maxdim mean means mindim mn mult mx pdf permute perpendicular probability prod reciprocal reverse-1d reverse-2d rotate sample set-seed set-seed! shift source-object sub sum to-acm-vec to-polar to-vec transform upper-bound variance

                                        DistributionIdProto

                                        protocol

                                        Get name and parameter names from distribution

                                        members

                                        distribution-id

                                        (distribution-id d)

                                        Distribution id as keyword

                                        distribution-parameters

                                        (distribution-parameters d)

                                        List of distribution parameter names

                                        distribution?

                                        (distribution? d)

                                        Returns true if the object is distribution

                                        -
                                        view source

                                        DistributionProto

                                        protocol

                                        Get information from distributions.

                                        +
                                        view source

                                        DistributionProto

                                        protocol

                                        Get information from distributions.

                                        members

                                        cdf

                                        (cdf d v)(cdf d v1 v2)

                                        Cumulative probability.

                                        continuous?

                                        (continuous? d)

                                        Does distribution support continuous range?

                                        dimensions

                                        (dimensions d)

                                        Returns dimensions

                                        @@ -21,17 +21,17 @@

                                        probability

                                        (probability d v)

                                        Probability (PMF)

                                        sample

                                        (sample d)

                                        Returns random sample.

                                        source-object

                                        (source-object d)

                                        Returns Java object from backend library

                                        -
                                        view source

                                        GridProto

                                        protocol

                                        Common grid conversion functions.

                                        +
                                        view source

                                        GridProto

                                        protocol

                                        Common grid conversion functions.

                                        members

                                        cell->anchor

                                        (cell->anchor g cell)(cell->anchor g q r)

                                        Converts cell coordinates to anchor coordinates.

                                        cell->mid

                                        (cell->mid g cell)(cell->mid g q r)

                                        Converts cell coordinates to cell midpoint

                                        coords->cell

                                        (coords->cell g coords)(coords->cell g x y)

                                        Converts 2d space coordinates to cell coordinates.

                                        coords->mid

                                        (coords->mid g coords)(coords->mid g x y)

                                        Converts 2d space into cell midpoint.

                                        corners

                                        (corners g coords)(corners g coords scale)(corners g x y scale)

                                        Returns list of cell vertices for given 2d space coordinates.

                                        grid-type

                                        (grid-type g)

                                        Returns type of the cell.

                                        -
                                        view source

                                        MultivariateDistributionProto

                                        protocol

                                        Get information from distributions.

                                        +
                                        view source

                                        MultivariateDistributionProto

                                        protocol

                                        Get information from distributions.

                                        members

                                        covariance

                                        (covariance d)

                                        Variance

                                        means

                                        (means d)

                                        Mean

                                        -
                                        view source

                                        RNGProto

                                        protocol

                                        Defines set of random functions for different RNGs or distributions returning primitive values.

                                        +
                                        view source

                                        RNGProto

                                        protocol

                                        Defines set of random functions for different RNGs or distributions returning primitive values.

                                        members

                                        ->seq

                                        (->seq rng)(->seq rng n)

                                        Returns lazy sequence of random samples (can be limited to optional n values).

                                        brandom

                                        (brandom rng)(brandom rng p)

                                        Boolean random.

                                        Returns true or false with equal probability. You can set p probability for true

                                        @@ -52,11 +52,11 @@

                                        forward-2d

                                        (forward-2d t xss)

                                        Forward transform of sequence of sequences.

                                        reverse-1d

                                        (reverse-1d t xs)

                                        Reverse transform of sequence or array.

                                        reverse-2d

                                        (reverse-2d t xss)

                                        Reverse transform of sequence of sequences.

                                        -
                                        view source

                                        UnivariateDistributionProto

                                        protocol

                                        members

                                        lower-bound

                                        (lower-bound d)

                                        Lower value

                                        +
                                        view source

                                        UnivariateDistributionProto

                                        protocol

                                        members

                                        lower-bound

                                        (lower-bound d)

                                        Lower value

                                        mean

                                        (mean d)

                                        Mean

                                        upper-bound

                                        (upper-bound d)

                                        Higher value

                                        variance

                                        (variance d)

                                        Variance

                                        -
                                        view source

                                        VectorProto

                                        protocol

                                        Vector operations

                                        +
                                        view source

                                        VectorProto

                                        protocol

                                        Vector operations

                                        members

                                        abs

                                        (abs v1)

                                        Absolute value of vector elements

                                        add

                                        (add v1)(add v1 v2)

                                        Sum of two vectors.

                                        approx

                                        (approx v)(approx v d)

                                        Round to 2 (or d) decimal places

                                        @@ -85,6 +85,7 @@

                                        mx

                                        (mx v1)

                                        Maximum value of vector elements

                                        permute

                                        (permute v idxs)

                                        Permute vector elements with given indices.

                                        perpendicular

                                        (perpendicular v1)(perpendicular v1 v2)

                                        Perpendicular vector (only 2d).

                                        +

                                        prod

                                        (prod v1)

                                        Product of elements

                                        reciprocal

                                        (reciprocal v)

                                        Reciprocal of elements.

                                        rotate

                                        (rotate v1 angle)(rotate v1 anglex angley anglez)

                                        Rotate vector

                                        shift

                                        (shift v1 v)

                                        Add v value to every vector element.

                                        @@ -94,4 +95,4 @@

                                        to-polar

                                        (to-polar v1)

                                        To polar coordinates (2d, 3d only), first element is length, the rest angle.

                                        to-vec

                                        (to-vec v)

                                        Convert to Clojure primitive vector Vec.

                                        transform

                                        (transform v1 o vx vy)(transform v1 o vx vy vz)

                                        Transform vector; map point to coordinate system defined by origin, vx and vy (as bases), d and 3d only.

                                        -
                                        view source
                                        \ No newline at end of file +
                                        view source
                                        \ No newline at end of file diff --git a/docs/fastmath.protocols.matrix.html b/docs/fastmath.protocols.matrix.html index 9286806a..8af2c76e 100644 --- a/docs/fastmath.protocols.matrix.html +++ b/docs/fastmath.protocols.matrix.html @@ -1,3 +1,3 @@ -fastmath.protocols.matrix documentation

                                        Project

                                        Namespaces

                                        Public Vars

                                        fastmath.protocols.matrix

                                        Categories

                                          Other vars: add adds cols column det diag emulm fmap inverse mulm muls mulv ncol nrow row rows sub symmetric? to-acm-mat to-array2d trace transpose vtmul

                                          MatrixProto

                                          protocol

                                          members

                                          add

                                          (add m1 m2)

                                          adds

                                          (adds m v)

                                          cols

                                          (cols m)

                                          column

                                          (column m id)

                                          det

                                          (det m)

                                          diag

                                          (diag m)

                                          emulm

                                          (emulm m1 m2)

                                          fmap

                                          (fmap m f)

                                          inverse

                                          (inverse m)

                                          mulm

                                          (mulm m1 m2)(mulm m1 t1? m2 t2?)

                                          muls

                                          (muls m v)

                                          mulv

                                          (mulv m v)

                                          ncol

                                          (ncol m)

                                          nrow

                                          (nrow m)

                                          row

                                          (row m id)

                                          rows

                                          (rows m)

                                          sub

                                          (sub m)(sub m1 m2)

                                          symmetric?

                                          (symmetric? m)

                                          to-acm-mat

                                          (to-acm-mat m)

                                          to-array2d

                                          (to-array2d m)

                                          trace

                                          (trace m)

                                          transpose

                                          (transpose m)

                                          vtmul

                                          (vtmul m v)
                                          view source
                                          \ No newline at end of file +fastmath.protocols.matrix documentation

                                          Project

                                          Namespaces

                                          Public Vars

                                          fastmath.protocols.matrix

                                          Categories

                                            Other vars: add adds cholesky cols column det diag emulm fmap inverse mulm muls mulv ncol nrow row rows sub symmetric? to-double-array to-double-array2d to-float-array to-float-array2d trace transpose vtmul

                                            MatrixProto

                                            protocol

                                            members

                                            add

                                            (add m1 m2)

                                            adds

                                            (adds m v)

                                            cholesky

                                            (cholesky m)

                                            cols

                                            (cols m)

                                            column

                                            (column m id)

                                            det

                                            (det m)

                                            diag

                                            (diag m)

                                            emulm

                                            (emulm m1 m2)

                                            fmap

                                            (fmap m f)

                                            inverse

                                            (inverse m)

                                            mulm

                                            (mulm m1 m2)(mulm m1 t1? m2 t2?)

                                            muls

                                            (muls m v)

                                            mulv

                                            (mulv m v)

                                            ncol

                                            (ncol m)

                                            nrow

                                            (nrow m)

                                            row

                                            (row m id)

                                            rows

                                            (rows m)

                                            sub

                                            (sub m)(sub m1 m2)

                                            symmetric?

                                            (symmetric? m)

                                            to-double-array

                                            (to-double-array m)

                                            to-double-array2d

                                            (to-double-array2d m)

                                            to-float-array

                                            (to-float-array m)

                                            to-float-array2d

                                            (to-float-array2d m)

                                            trace

                                            (trace m)

                                            transpose

                                            (transpose m)

                                            vtmul

                                            (vtmul m v)
                                            view source
                                            \ No newline at end of file diff --git a/docs/fastmath.quaternion.html b/docs/fastmath.quaternion.html new file mode 100644 index 00000000..7d9066be --- /dev/null +++ b/docs/fastmath.quaternion.html @@ -0,0 +1,43 @@ + +fastmath.quaternion documentation

                                            Project

                                            Namespaces

                                            Public Vars

                                            fastmath.quaternion

                                            Categories

                                              Other vars: -I -J -K I J K ONE ZERO acos acosh acot acoth acsc acsch add arg asec asech asin asinh atan atanh complex->quaternion conjugate cos cosh cot coth csc csch delta-eq div exp from-euler im-i im-j im-k imaginary? inf? log logb mult nan? neg norm normalize pow qsgn quaternion re real? reciprocal rotate rotation-quaternion scalar scale sec sech sin sinh slerp sq sqrt sub tan tanh to-euler vector zero?

                                              -I

                                              view source

                                              -J

                                              view source

                                              -K

                                              view source

                                              acos

                                              (acos q)
                                              view source

                                              acosh

                                              (acosh q)
                                              view source

                                              acot

                                              (acot q)
                                              view source

                                              acoth

                                              (acoth q)
                                              view source

                                              acsc

                                              (acsc q)
                                              view source

                                              acsch

                                              (acsch q)
                                              view source

                                              add

                                              (add q1 q2)

                                              Sum of two quaternions

                                              +
                                              view source

                                              arg

                                              (arg quaternion)

                                              Argument of quaternion, atan2(|vector(q)|, re(q))

                                              +
                                              view source

                                              asec

                                              (asec q)
                                              view source

                                              asech

                                              (asech q)
                                              view source

                                              asin

                                              (asin q)
                                              view source

                                              asinh

                                              (asinh q)
                                              view source

                                              atan

                                              (atan q)
                                              view source

                                              atanh

                                              (atanh q)
                                              view source

                                              complex->quaternion

                                              (complex->quaternion z)

                                              Create quaternion from complex number

                                              +
                                              view source

                                              conjugate

                                              (conjugate quaternion)

                                              Returns conjugate of quaternion

                                              +
                                              view source

                                              cos

                                              (cos q)
                                              view source

                                              cosh

                                              (cosh q)
                                              view source

                                              cot

                                              (cot q)
                                              view source

                                              coth

                                              (coth q)
                                              view source

                                              csc

                                              (csc q)
                                              view source

                                              csch

                                              (csch q)
                                              view source

                                              delta-eq

                                              (delta-eq q1 q2)(delta-eq q1 q2 accuracy)

                                              Compare quaternions with given accuracy (10e-6 by default)

                                              +
                                              view source

                                              div

                                              (div q1 q2)

                                              Divide two quaternions

                                              +
                                              view source

                                              exp

                                              (exp q)
                                              view source

                                              from-euler

                                              (from-euler [roll pitch yaw])(from-euler roll pitch yaw)

                                              Convert Euler ZYX (body 3-2-1) representation to quaternion

                                              +

                                              Input should be 3d vector contating roll (x), pitch (y) and yaw (z) angles, or individual values.

                                              +
                                                +
                                              • roll and yaw should be from [-pi, pi] range
                                                • +
                                              • pitch should be from [-pi/2, pi/2] range
                                                • +
                                              +
                                              view source

                                              im-i

                                              (im-i quaternion)

                                              Return i imaginary part

                                              +
                                              view source

                                              im-j

                                              (im-j quaternion)

                                              Return j imaginary part

                                              +
                                              view source

                                              im-k

                                              (im-k quaternion)

                                              Return k imaginary part

                                              +
                                              view source

                                              imaginary?

                                              (imaginary? quaternion)

                                              Is q is a pure imaginary number?

                                              +
                                              view source

                                              inf?

                                              (inf? quaternion)

                                              Is infinitive?

                                              +
                                              view source

                                              log

                                              (log q)
                                              view source

                                              logb

                                              (logb quaternion b)

                                              log with base b

                                              +
                                              view source

                                              mult

                                              (mult q1 q2)

                                              Multiply two quaternions.

                                              +
                                              view source

                                              nan?

                                              (nan? quaternion)

                                              Is NaN?

                                              +
                                              view source

                                              neg

                                              (neg quaternion)

                                              Negation of quaternion.

                                              +
                                              view source

                                              norm

                                              (norm quaternion)

                                              Norm of the quaternion, length of the vector

                                              +
                                              view source

                                              normalize

                                              (normalize quaternion)

                                              Normalize quaternion

                                              +
                                              view source

                                              pow

                                              (pow q p)

                                              Quaternion power

                                              +
                                              view source

                                              qsgn

                                              (qsgn re im-i im-j im-k)(qsgn q)

                                              sgn of the quaternion.

                                              +

                                              Returns 0 for 0+0i+0j+0k or calls m/sgn on real part otherwise.

                                              +
                                              view source

                                              quaternion

                                              (quaternion a b c d)(quaternion scalar [i j k])(quaternion a)

                                              Create quaternion from individual values or scalar and vector parts, reprezented as Vec4.

                                              +
                                              view source

                                              re

                                              (re quaternion)

                                              Returns scalar part of quaternion

                                              +
                                              view source

                                              real?

                                              (real? quaternion)

                                              Is q is a real number?

                                              +
                                              view source

                                              reciprocal

                                              (reciprocal quaternion)
                                              view source

                                              rotate

                                              (rotate in rotq)(rotate in angle u)

                                              Rotate 3d in vector around axis u, the same as fastmath.vector/axis-rotate.

                                              +
                                              view source

                                              rotation-quaternion

                                              (rotation-quaternion angle u)

                                              Create rotation quaternion around vector u and angle alpha

                                              +
                                              view source

                                              scalar

                                              (scalar quaternion)

                                              Returns scalar part of quaternion, double

                                              +
                                              view source

                                              scale

                                              (scale quaternion scale)

                                              Scale the quaternion

                                              +
                                              view source

                                              sec

                                              (sec q)
                                              view source

                                              sech

                                              (sech q)
                                              view source

                                              sin

                                              (sin q)
                                              view source

                                              sinh

                                              (sinh q)
                                              view source

                                              slerp

                                              (slerp q1 q2 t)

                                              Interpolate quaternions

                                              +
                                              view source

                                              sq

                                              (sq quaternion)

                                              Square of quaternion.

                                              +
                                              view source

                                              sqrt

                                              (sqrt q)
                                              view source

                                              sub

                                              (sub q1 q2)

                                              Difference of two quaternions

                                              +
                                              view source

                                              tan

                                              (tan q)
                                              view source

                                              tanh

                                              (tanh q)
                                              view source

                                              to-euler

                                              (to-euler q)

                                              Convert quaternion to Euler ZYX (body 3-2-1). Quaternion will be normalized.

                                              +

                                              Output will contain roll (x), pitch (y) and yaw (z) angles.

                                              +
                                              view source

                                              vector

                                              (vector quaternion)

                                              Returns vector part of quaternion, Vec3 type

                                              +
                                              view source

                                              zero?

                                              (zero? quaternion)

                                              Is zero?

                                              +
                                              view source
                                              \ No newline at end of file diff --git a/docs/fastmath.random.html b/docs/fastmath.random.html index 52fe60d2..6aa5c7ed 100644 --- a/docs/fastmath.random.html +++ b/docs/fastmath.random.html @@ -1,6 +1,6 @@ -fastmath.random documentation

                                              Project

                                              Namespaces

                                              Public Vars

                                              fastmath.random

                                              Various random and noise functions.

                                              +fastmath.random documentation

                                              Project

                                              Namespaces

                                              Public Vars

                                              fastmath.random

                                              Various random and noise functions.

                                              Namespace defines various random number generators (RNGs), different types of random functions, sequence generators and noise functions.

                                              RNGs

                                              You can use a selection of various RNGs defined in Apache Commons Math library.

                                              @@ -82,15 +82,15 @@

                                              Discrete Noise

                                              Distribution

                                              Various real and integer distributions. See DistributionProto and RNGProto for functions.

                                              To create distribution call distribution multimethod with name as a keyword and map as parameters.

                                              -

                                              Categories

                                                Other vars: ->seq ball-random billow-noise brand brandom ccdf cdf continuous? covariance default-normal default-rng dimensions discrete-noise distribution distribution-id distribution-parameters distribution? distributions-list drand drandom fbm-noise flip flipb frand frandom grand grandom icdf integrate-pdf irand irandom jittered-sequence-generator likelihood log-likelihood lower-bound lpdf lrand lrandom mean means noise noise-generators noise-interpolations noise-types observe observe1 pdf probability random-noise-cfg random-noise-fn randval ridgedmulti-noise rng rngs-list sample sequence-generator sequence-generators-list set-seed set-seed! simplex single-noise source-object synced-rng upper-bound variance vnoise warp-noise-fn

                                                ->seq

                                                (->seq)(->seq rng)(->seq rng n)(->seq rng n sampling-method)

                                                Returns lazy sequence of random samples (can be limited to optional n values).

                                                +

                                                Categories

                                                  Other vars: ->seq ball-random billow-noise brand brandom ccdf cdf continuous? covariance default-normal default-rng dimensions discrete-noise distribution distribution-id distribution-parameters distribution? distributions-list drand drandom fbm-noise flip flip-rng flipb flipb-rng frand frandom grand grandom icdf integrate-pdf irand irandom jittered-sequence-generator likelihood log-likelihood lower-bound lpdf lrand lrandom mean means noise noise-generators noise-interpolations noise-types observe observe1 pdf probability random-noise-cfg random-noise-fn randval randval-rng ridgedmulti-noise rng rngs-list roll-a-dice roll-a-dice-rng sample sequence-generator sequence-generators-list set-seed set-seed! simplex single-noise source-object synced-rng upper-bound variance vnoise warp-noise-fn

                                                  ->seq

                                                  (->seq)(->seq rng)(->seq rng n)(->seq rng n sampling-method)

                                                  Returns lazy sequence of random samples (can be limited to optional n values).

                                                  Additionally one of the sampling methods can be provided, ie: :uniform, :antithetic, :systematic and :stratified.

                                                  Examples

                                                  Sequence of random values from distribution

                                                  (->seq (distribution :gamma) 5)
-;;=> (9.338595251977102
-;;=>  0.6447322934022234
-;;=>  2.9546608203555897
-;;=>  2.1361644933461856
-;;=>  2.179096738777491)
+;;=> (3.0067488022135267
+;;=>  1.4020291240773082
+;;=>  13.327457354701531
+;;=>  1.525168177213365
+;;=>  1.4430890050414493)
 (->seq (distribution :gamma) 5 :stratified)
 ;;=> (0.538681218505258
 ;;=>  1.815596109861234
@@ -102,13 +102,13 @@ 
                                                  Distribution
                                                  
 ;;=>  0.366695439109843
 ;;=>  0.566695439109843
 ;;=>  0.7666954391098431
-;;=>  0.9666954391098429)
                                                  view source

                                                  ball-random

                                                  (ball-random dims)(ball-random rng dims)

                                                  Return random vector from a ball

                                                  -
                                                  view source

                                                  billow-noise

                                                  (billow-noise)(billow-noise cfg__20703__auto__)

                                                  Create billow-noise function with optional configuration.

                                                  +;;=> 0.9666954391098429)
                                                  view source

                                                  ball-random

                                                  (ball-random dims)(ball-random rng dims)

                                                  Return random vector from a ball

                                                  +
                                                  view source

                                                  billow-noise

                                                  (billow-noise)(billow-noise cfg__20732__auto__)

                                                  Create billow-noise function with optional configuration.

                                                  Examples

                                                  Usage

                                                  (let [n (billow-noise {:seed 12345, :interpolation :none})]
   (n 0.5 1.1 -1.3))
 ;;=> 0.16031746031746036

                                                  2d noise

                                                  -
                                                  view source

                                                  brand

                                                  Random boolean with default RNG.

                                                  +
                                                  view source

                                                  brand

                                                  Random boolean with default RNG.

                                                  Returns true or false with equal probability. You can set p probability for true

                                                  Examples

                                                  Usage

                                                  (brand)
@@ -116,35 +116,35 @@ 
                                                  Distribution
                                                  
 (brand 0.1)
 ;;=> false

                                                  Count number of true values with probability 0.15

                                                  (count (filter true? (repeatedly 100000 (fn* [] (brand 0.15)))))
-;;=> 14901
                                                  view source

                                                  brandom

                                                  (brandom rng)(brandom rng p)

                                                  Random boolean with provided RNG

                                                  +;;=> 15091
                                                  view source

                                                  brandom

                                                  (brandom rng)(brandom rng p)

                                                  Random boolean with provided RNG

                                                  Examples

                                                  boolean

                                                  (rngproto-snippet brandom ...)
-;;=> true
                                                  view source

                                                  ccdf

                                                  (ccdf d v)

                                                  Complementary cumulative probability.

                                                  -
                                                  view source

                                                  cdf

                                                  (cdf d v)(cdf d v1 v2)

                                                  Cumulative probability.

                                                  +;;=> false
                                                  view source

                                                  ccdf

                                                  (ccdf d v)

                                                  Complementary cumulative probability.

                                                  +
                                                  view source

                                                  cdf

                                                  (cdf d v)(cdf d v1 v2)

                                                  Cumulative probability.

                                                  Examples

                                                  Usage

                                                  (cdf (distribution :gamma) 1)
 ;;=> 0.09020401043104985
 (cdf (distribution :gamma) 1 4)
-;;=> 0.5037901398591113
                                                  view source

                                                  continuous?

                                                  (continuous? d)

                                                  Does distribution support continuous domain?

                                                  +;;=> 0.5037901398591113
                                                  view source

                                                  continuous?

                                                  (continuous? d)

                                                  Does distribution support continuous domain?

                                                  Examples

                                                  Usage

                                                  (continuous? (distribution :gamma))
 ;;=> true
 (continuous? (distribution :pascal))
 ;;=> false
 
-;; Test: ok.
                                                  view source

                                                  covariance

                                                  (covariance d)

                                                  Distribution covariance matrix (for multivariate distributions)

                                                  +;; Test: ok.
                                                  view source

                                                  covariance

                                                  (covariance d)

                                                  Distribution covariance matrix (for multivariate distributions)

                                                  Examples

                                                  Usage

                                                  (covariance (distribution :multi-normal))
 ;;=> ((1.0 0.0) (0.0 1.0))
 (covariance (distribution :dirichlet {:alpha [2 2]}))
 ;;=> [[0.05 -0.05] [-0.05 0.05]]
 
-;; Test: ok.
                                                  view source

                                                  default-normal

                                                  Default normal distribution (u=0.0, sigma=1.0).

                                                  +;; Test: ok.
                                                  view source

                                                  default-normal

                                                  Default normal distribution (u=0.0, sigma=1.0).

                                                  Examples

                                                  Usage

                                                  (sample default-normal)
-;;=> 1.444215875679369
+;;=> -0.4221634035506921
 (set-seed! default-normal 1234)
-;;=> org.apache.commons.math3.distribution.NormalDistribution@7a4204ef
+;;=> org.apache.commons.math3.distribution.NormalDistribution@1f136b88
 (sample default-normal)
 ;;=> 0.14115907833078006
 (irandom default-normal)
@@ -152,18 +152,18 @@ 
                                                  Distribution
                                                  
 (mean default-normal)
 ;;=> 0.0
 (variance default-normal)
-;;=> 1.0
                                                  view source

                                                  default-rng

                                                  Default RNG - JDK

                                                  +;;=> 1.0
                                                  view source

                                                  default-rng

                                                  Default RNG - JDK

                                                  Examples

                                                  Usage

                                                  (set-seed! default-rng 111)
-;;=> org.apache.commons.math3.random.JDKRandomGenerator@74b6c343
+;;=> org.apache.commons.math3.random.JDKRandomGenerator@656d49a1
 (irandom default-rng)
 ;;=> -1196652709
 (set-seed! default-rng 999)
-;;=> org.apache.commons.math3.random.JDKRandomGenerator@74b6c343
+;;=> org.apache.commons.math3.random.JDKRandomGenerator@656d49a1
 (irandom default-rng)
 ;;=> -1242822577
 (set-seed! default-rng 111)
-;;=> org.apache.commons.math3.random.JDKRandomGenerator@74b6c343
+;;=> org.apache.commons.math3.random.JDKRandomGenerator@656d49a1
 (irandom default-rng)
 ;;=> -1196652709
                                                  view source

                                                  dimensions

                                                  (dimensions d)

                                                  Distribution dimensionality

                                                  Examples

                                                  Usage

                                                  @@ -172,7 +172,7 @@

                                                  Distribution

                                                  (dimensions (distribution :dirichlet {:alpha (repeat 30 2.0)})) ;;=> 30 -;; Test: ok.
                                                  view source

                                                  discrete-noise

                                                  (discrete-noise X Y)(discrete-noise X)

                                                  Discrete noise. Parameters:

                                                  +;; Test: ok.
                                                  view source

                                                  discrete-noise

                                                  (discrete-noise X Y)(discrete-noise X)

                                                  Discrete noise. Parameters:

                                                  • X (long)
                                                  • Y (long, optional)
                                                    • @@ -187,7 +187,7 @@

                                                    Distribution

                                                    ;;=> 0.4702831345937602 (discrete-noise 123) ;;=> 0.28831296287864117

                                                  Draw noise for 0-180 range.

                                                  -
                                                  view source

                                                  distribution

                                                  multimethod

                                                  Create distribution object.

                                                  +
                                                  view source

                                                  distribution

                                                  multimethod

                                                  Create distribution object.

                                                  • First parameter is distribution as a :key.
                                                  • Second parameter is a map with configuration.
                                                    • @@ -195,14 +195,14 @@

                                                    Distribution

                                                    All distributions accept rng under :rng key (default: default-rng) and some of them accept inverse-cumm-accuracy (default set to 1e-9).

                                                  Examples

                                                  Usage

                                                  (distribution :beta)
-;;=> org.apache.commons.math3.distribution.BetaDistribution@6692accf
+;;=> org.apache.commons.math3.distribution.BetaDistribution@1be8135f
 (distribution :beta {:alpha 1.0, :beta 1.0})
-;;=> org.apache.commons.math3.distribution.BetaDistribution@51ada4ed

                                                  All parameters

                                                  +;;=> org.apache.commons.math3.distribution.BetaDistribution@344f58d6

                                                  All parameters

                                                  (into (sorted-map)
-      (map (fn* [p1__32715#]
-             (vector p1__32715#
+      (map (fn* [p1__32807#]
+             (vector p1__32807#
                      (sort (distribution-parameters (distribution
-                                                     p1__32715#)))))
+                                                     p1__32807#)))))
            (keys (methods distribution))))
 ;;=> {:anderson-darling ({:n 1.0}),
 ;;=>  :bb (:bd :mu :sigma),
@@ -518,14 +518,14 @@ 
                                                  Distribution

                                                  2d multidimensional normal (mean=0,0, covariances=I)

                                                  2d multidimensional normal (mean=0,0, covariances=[1 -1 -1 2])

                                                  2d dirichlet (alpha=2,0.8)

                                                  -
                                                  view source

                                                  distribution-id

                                                  (distribution-id d)

                                                  Distribution identifier as keyword.

                                                  +
                                                  view source

                                                  distribution-id

                                                  (distribution-id d)

                                                  Distribution identifier as keyword.

                                                  Examples

                                                  Usage

                                                  (distribution-id (distribution :gamma))
 ;;=> :gamma
 (distribution-id default-normal)
 ;;=> :normal
 
-;; Test: ok.
                                                  view source

                                                  distribution-parameters

                                                  (distribution-parameters d)(distribution-parameters d all?)

                                                  Distribution highest supported value.

                                                  +;; Test: ok.
                                                  view source

                                                  distribution-parameters

                                                  (distribution-parameters d)(distribution-parameters d all?)

                                                  Distribution highest supported value.

                                                  When all? is true, technical parameters are included, ie: :rng and :inverser-cumm-accuracy.

                                                  Examples

                                                  Usage

                                                  (distribution-parameters (distribution :gamma))
@@ -535,8 +535,8 @@ 
                                                  Distribution
                                                  
 (distribution-parameters default-normal)
 ;;=> [:sd :mu]
 
-;; Test: ok.
                                                  view source

                                                  distribution?

                                                  (distribution? distr)

                                                  Checks if distr is a distribution object.

                                                  -
                                                  view source

                                                  distributions-list

                                                  List of distributions.

                                                  +;; Test: ok.
                                                  view source

                                                  distribution?

                                                  (distribution? distr)

                                                  Checks if distr is a distribution object.

                                                  +
                                                  view source

                                                  distributions-list

                                                  List of distributions.

                                                  Examples

                                                  Number and list of distributions

                                                  distributions-list
 ;;=> #{:anderson-darling :bb :bernoulli :beta :binomial
@@ -556,7 +556,7 @@ 
                                                  Distribution
                                                  
 ;;=>   :uniform-int :uniform-real :watson-g :watson-u :weibull :zabb :zabi
 ;;=>   :zaga :zanbi :zibb :zibi :zinbi :zip :zip2 :zipf}
 (count distributions-list)
-;;=> 83
                                                  view source

                                                  drand

                                                  (drand)(drand mx)(drand mn mx)

                                                  Random double number with default RNG.

                                                  +;;=> 83
                                                  view source

                                                  drand

                                                  (drand)(drand mx)(drand mn mx)

                                                  Random double number with default RNG.

                                                  As default returns random double from [0,1) range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

                                                  Examples

                                                  Usage

                                                  (drand)
@@ -567,28 +567,30 @@ 
                                                  Distribution
                                                  
 ;;=> 11.178257652282884
                                                  view source

                                                  drandom

                                                  (drandom rng)(drandom rng mx)(drandom rng mn mx)

                                                  Random double number with provided RNG

                                                  Examples

                                                  double

                                                  (rngproto-snippet drandom ...)
-;;=> 0.8690532195659586

                                                  Double random value from distribution

                                                  +;;=> 0.06701962727042732

                                                  Double random value from distribution

                                                  (drandom (distribution :gamma))
-;;=> 3.7980437804625375
                                                  view source

                                                  fbm-noise

                                                  (fbm-noise)(fbm-noise cfg__20703__auto__)

                                                  Create fbm-noise function with optional configuration.

                                                  +;;=> 6.329354086567372
                                                  view source

                                                  fbm-noise

                                                  (fbm-noise)(fbm-noise cfg__20732__auto__)

                                                  Create fbm-noise function with optional configuration.

                                                  Examples

                                                  Usage

                                                  (let [n (fbm-noise {:interpolation :linear, :noise-type :value})]
   (n 0.5 1.1 -1.3))
-;;=> 0.41496425382627966

                                                  2d noise

                                                  -
                                                  view source

                                                  flip

                                                  (flip p)(flip)

                                                  Returns 1 with given probability, 0 otherwise

                                                  +;;=> 0.4168546210033432

                                                  2d noise

                                                  +
                                                  view source

                                                  flip

                                                  (flip p)(flip)

                                                  Returns 1 with given probability, 0 otherwise

                                                  Examples

                                                  Usage

                                                  (flip)
 ;;=> 1
 (flip 0.2)
 ;;=> 0
 (repeatedly 10 (fn* [] (flip 0.1)))
-;;=> (0 1 0 1 0 0 1 0 0 0)
                                                  view source

                                                  flipb

                                                  (flipb p)(flipb)

                                                  Returns true with given probability, false otherwise

                                                  +;;=> (0 1 0 1 0 0 1 0 0 0)
                                                  view source

                                                  flip-rng

                                                  (flip-rng rng p)(flip-rng rng)

                                                  Returns 1 with given probability, 0 otherwise, for given rng

                                                  +
                                                  view source

                                                  flipb

                                                  (flipb p)(flipb)

                                                  Returns true with given probability, false otherwise

                                                  Examples

                                                  Usage

                                                  (flipb)
 ;;=> true
 (flipb 0.2)
 ;;=> false
 (repeatedly 10 (fn* [] (flipb 0.1)))
-;;=> (false false false false false false false false false false)
                                                  view source

                                                  frand

                                                  (frand)(frand mx)(frand mn mx)

                                                  Random double number with default RNG.

                                                  +;;=> (false false false false false false false false false false)
                                                  view source

                                                  flipb-rng

                                                  (flipb-rng rng p)(flipb-rng rng)

                                                  Returns true with given probability, false otherwise, for given rng

                                                  +
                                                  view source

                                                  frand

                                                  (frand)(frand mx)(frand mn mx)

                                                  Random double number with default RNG.

                                                  As default returns random float from [0,1) range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

                                                  Examples

                                                  Usage

                                                  (frand)
@@ -599,9 +601,9 @@ 
                                                  Distribution
                                                  
 ;;=> 15.521044
                                                  view source

                                                  frandom

                                                  (frandom rng)(frandom rng mx)(frandom rng mn mx)

                                                  Random double number with provided RNG

                                                  Examples

                                                  float

                                                  (rngproto-snippet frandom ...)
-;;=> 0.38781476

                                                  Float random value from distribution (sample cast to float)

                                                  +;;=> 0.5313778

                                                  Float random value from distribution (sample cast to float)

                                                  (frandom (distribution :gamma))
-;;=> 2.1697888
                                                  view source

                                                  grand

                                                  (grand)(grand stddev)(grand mean stddev)

                                                  Random gaussian double number with default RNG.

                                                  +;;=> 4.370595
                                                  view source

                                                  grand

                                                  (grand)(grand stddev)(grand mean stddev)

                                                  Random gaussian double number with default RNG.

                                                  As default returns random double from N(0,1). When std is passed, N(0,std) is used. When mean is passed, distribution is set to N(mean, std).

                                                  Examples

                                                  Usage

                                                  (grand)
@@ -612,13 +614,13 @@ 
                                                  Distribution
                                                  
 ;;=> 8.045099200233572
                                                  view source

                                                  grandom

                                                  (grandom rng)(grandom rng stddev)(grandom rng mean stddev)

                                                  Random gaussian double number with provided RNG

                                                  Examples

                                                  gaussian double

                                                  (rngproto-snippet grandom ...)
-;;=> 0.08249794434126573
                                                  view source

                                                  icdf

                                                  (icdf d v)

                                                  Inverse cumulative probability

                                                  +;;=> -0.6728837945388857
                                                  view source

                                                  icdf

                                                  (icdf d v)

                                                  Inverse cumulative probability

                                                  Examples

                                                  Usage

                                                  (icdf (distribution :gamma) 0.5)
-;;=> 3.3566939800333233
                                                  view source

                                                  integrate-pdf

                                                  (integrate-pdf pdf-func mn mx steps)(integrate-pdf pdf-func {:keys [mn mx steps interpolator min-iterations], :or {mn 0.0, mx 1.0, steps 1000, min-iterations 3, interpolator :linear}})

                                                  Integrate PDF function, returns CDF and iCDF

                                                  +;;=> 3.3566939800333233
                                                  view source

                                                  integrate-pdf

                                                  (integrate-pdf pdf-func mn mx steps)(integrate-pdf pdf-func {:keys [mn mx steps interpolator min-iterations], :or {mn 0.0, mx 1.0, steps 1000, min-iterations 3, interpolator :linear}})

                                                  Integrate PDF function, returns CDF and iCDF

                                                  Parameters: * pdf-func - univariate function * mn - lower bound for integration, value of pdf-func should be 0.0 at this point * mx - upper bound for integration * steps - how much subintervals to integrate (default 1000) * min-iterations - minimum iterations for RombergIntegrator (default 3) * interpolator - interpolation method between integrated points (default :spline)

                                                  Possible interpolation methods: :linear (default), :spline, :monotone or any function from fastmath.interpolation

                                                  -
                                                  view source

                                                  irand

                                                  (irand)(irand mx)(irand mn mx)

                                                  Random integer number with default RNG.

                                                  +
                                                  view source

                                                  irand

                                                  (irand)(irand mx)(irand mn mx)

                                                  Random integer number with default RNG.

                                                  As default returns random integer from full integer range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

                                                  Examples

                                                  Usage

                                                  (irand)
@@ -629,9 +631,9 @@ 
                                                  Distribution
                                                  
 ;;=> 16
                                                  view source

                                                  irandom

                                                  (irandom rng)(irandom rng mx)(irandom rng mn mx)

                                                  Random integer number with provided RNG

                                                  Examples

                                                  integer

                                                  (rngproto-snippet irandom ...)
-;;=> -1215083642

                                                  Integer random value from distribution (sample cast to int)

                                                  +;;=> 1455081240

                                                  Integer random value from distribution (sample cast to int)

                                                  (irandom (distribution :gamma))
-;;=> 6
                                                  view source

                                                  jittered-sequence-generator

                                                  (jittered-sequence-generator seq-generator dimensions)(jittered-sequence-generator seq-generator dimensions jitter)

                                                  Create jittered sequence generator.

                                                  +;;=> 4
                                                  view source

                                                  jittered-sequence-generator

                                                  (jittered-sequence-generator seq-generator dimensions)(jittered-sequence-generator seq-generator dimensions jitter)

                                                  Create jittered sequence generator.

                                                  Suitable for :r2, :sobol and :halton sequences.

                                                  jitter parameter range is from 0 (no jitter) to 1 (full jitter). Default: 0.25.

                                                  See also sequence-generator.

                                                  @@ -639,28 +641,28 @@

                                                  Distribution

                                                  (let [gen1 (jittered-sequence-generator :r2 2 0.5)
       gen2 (jittered-sequence-generator :r2 2 0.5)]
   [(first gen1) (first gen2)])
-;;=> [[0.35672590506969504 0.3429804320698949]
-;;=>  [0.3483662837005658 0.30353072436954287]]

                                                  Jittered (0.5) R2 plot (500 samples)

                                                  +;;=> [[0.27411060522326863 0.37253956285622764] +;;=> [0.29572045931878443 0.3284307457115735]]

                                                  Jittered (0.5) R2 plot (500 samples)

                                                  Jittered (0.5) Halton plot (500 samples)

                                                  Jittered (0.5) Sobol plot (500 samples)

                                                  Jittered (0.5) Sphere plot (500 samples)

                                                  Jittered (0.5) Gaussian plot (500 samples)

                                                  Jittered (0.5) Default plot (500 samples)

                                                  -
                                                  view source

                                                  likelihood

                                                  (likelihood d vs)

                                                  Likelihood of samples

                                                  +
                                                  view source

                                                  likelihood

                                                  (likelihood d vs)

                                                  Likelihood of samples

                                                  Examples

                                                  Usage

                                                  (likelihood (distribution :gamma) [10 0.5 0.5 1 2])
-;;=> 4.452548659934162E-6
                                                  view source

                                                  log-likelihood

                                                  (log-likelihood d vs)

                                                  Log likelihood of samples

                                                  +;;=> 4.452548659934162E-6
                                                  view source

                                                  log-likelihood

                                                  (log-likelihood d vs)

                                                  Log likelihood of samples

                                                  Examples

                                                  Usage

                                                  (log-likelihood (distribution :gamma) [10 0.5 0.5 1 2])
-;;=> -12.322033893165353
                                                  view source

                                                  lower-bound

                                                  (lower-bound d)

                                                  Distribution lowest supported value

                                                  +;;=> -12.322033893165353
                                                  view source

                                                  lower-bound

                                                  (lower-bound d)

                                                  Distribution lowest supported value

                                                  Examples

                                                  Usage

                                                  (lower-bound (distribution :gamma))
 ;;=> 0.0
 
-;; Test: ok.
                                                  view source

                                                  lpdf

                                                  (lpdf d v)

                                                  Log density

                                                  +;; Test: ok.
                                                  view source

                                                  lpdf

                                                  (lpdf d v)

                                                  Log density

                                                  Examples

                                                  Usage

                                                  (lpdf (distribution :gamma) 1)
-;;=> -1.8862943611198908
                                                  view source

                                                  lrand

                                                  (lrand)(lrand mx)(lrand mn mx)

                                                  Random long number with default RNG.

                                                  +;;=> -1.8862943611198908
                                                  view source

                                                  lrand

                                                  (lrand)(lrand mx)(lrand mn mx)

                                                  Random long number with default RNG.

                                                  As default returns random long from full integer range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

                                                  Examples

                                                  Usage

                                                  (lrand)
@@ -671,77 +673,77 @@ 
                                                  Distribution
                                                  
 ;;=> 19
                                                  view source

                                                  lrandom

                                                  (lrandom rng)(lrandom rng mx)(lrandom rng mn mx)

                                                  Random long number with provided RNG

                                                  Examples

                                                  long

                                                  (rngproto-snippet lrandom ...)
-;;=> 8255623744776393858

                                                  Long random value from distribution (sample cast to long)

                                                  +;;=> -3175270031798328528

                                                  Long random value from distribution (sample cast to long)

                                                  (lrandom (distribution :gamma))
-;;=> 2
                                                  view source

                                                  mean

                                                  (mean d)

                                                  Distribution mean

                                                  +;;=> 1
                                                  view source

                                                  mean

                                                  (mean d)

                                                  Distribution mean

                                                  Examples

                                                  Usage

                                                  (mean (distribution :gamma))
 ;;=> 4.0
 
-;; Test: ok.
                                                  view source

                                                  means

                                                  (means d)

                                                  Distribution means (for multivariate distributions)

                                                  +;; Test: ok.
                                                  view source

                                                  means

                                                  (means d)

                                                  Distribution means (for multivariate distributions)

                                                  Examples

                                                  Usage

                                                  (means (distribution :multi-normal))
 ;;=> [0.0 0.0]
 (means (distribution :dirichlet {:alpha [2 2]}))
 ;;=> (0.5 0.5)
 
-;; Test: ok.
                                                  view source

                                                  noise

                                                  (noise x)(noise x y)(noise x y z)

                                                  Improved Perlin Noise.

                                                  +;; Test: ok.
                                                  view source

                                                  noise

                                                  (noise x)(noise x y)(noise x y z)

                                                  Improved Perlin Noise.

                                                  6 octaves, quintic interpolation.

                                                  Examples

                                                  Usage

                                                  (noise 3.3)
-;;=> 0.4863771428571427
+;;=> 0.17802717460317485
 (noise 3.3 1.1)
-;;=> 0.5620622179961904
+;;=> 0.46523967878095224
 (noise 3.3 0.0 -0.1)
-;;=> 0.5007101511517461

                                                  2d noise

                                                  -
                                                  view source

                                                  noise-generators

                                                  List of possible noise generators as a map of names and functions.

                                                  +;;=> 0.4567598342501587

                                                  2d noise

                                                  +
                                                  view source

                                                  noise-generators

                                                  List of possible noise generators as a map of names and functions.

                                                  Examples

                                                  List of names (keys)

                                                  (keys noise-generators)
-;;=> (:fbm :single :billow :ridgemulti)
                                                  view source

                                                  noise-interpolations

                                                  List of possible noise interpolations as a map of names and values.

                                                  +;;=> (:fbm :single :billow :ridgemulti)
                                                  view source

                                                  noise-interpolations

                                                  List of possible noise interpolations as a map of names and values.

                                                  Examples

                                                  List of names (keys)

                                                  (keys noise-interpolations)
-;;=> (:none :linear :hermite :quintic)
                                                  view source

                                                  noise-types

                                                  List of possible noise types as a map of names and values.

                                                  +;;=> (:none :linear :hermite :quintic)
                                                  view source

                                                  noise-types

                                                  List of possible noise types as a map of names and values.

                                                  Examples

                                                  List of names (keys)

                                                  (keys noise-types)
-;;=> (:value :gradient :simplex)
                                                  view source

                                                  observe

                                                  macro

                                                  (observe d vs)

                                                  Log likelihood of samples. Alias for log-likelihood.

                                                  +;;=> (:value :gradient :simplex)
                                                  view source

                                                  observe

                                                  macro

                                                  (observe d vs)

                                                  Log likelihood of samples. Alias for log-likelihood.

                                                  Examples

                                                  Usage

                                                  (observe (distribution :gamma) [10 0.5 0.5 1 2])
-;;=> -12.322033893165353
                                                  view source

                                                  observe1

                                                  (observe1 d v)

                                                  Log of probability/density of the value. Alias for lpdf.

                                                  +;;=> -12.322033893165353
                                                  view source

                                                  observe1

                                                  (observe1 d v)

                                                  Log of probability/density of the value. Alias for lpdf.

                                                  Examples

                                                  Usage

                                                  (observe1 (distribution :gamma) 10)
-;;=> -4.083709268125845
                                                  view source

                                                  pdf

                                                  (pdf d v)

                                                  Density

                                                  +;;=> -4.083709268125845
                                                  view source

                                                  pdf

                                                  (pdf d v)

                                                  Density

                                                  Examples

                                                  Usage

                                                  (pdf (distribution :gamma) 1)
 ;;=> 0.15163266492815838
 (pdf (distribution :pascal) 1)
-;;=> 9.5367431640625E-6
                                                  view source

                                                  probability

                                                  (probability d v)

                                                  Probability (PMF)

                                                  +;;=> 9.5367431640625E-6
                                                  view source

                                                  probability

                                                  (probability d v)

                                                  Probability (PMF)

                                                  Examples

                                                  Usage

                                                  (probability (distribution :gamma) 1)
 ;;=> 0.15163266492815838
 (probability (distribution :pascal) 1)
-;;=> 9.5367431640625E-6
                                                  view source

                                                  random-noise-cfg

                                                  (random-noise-cfg pre-config)(random-noise-cfg)

                                                  Create random noise configuration.

                                                  +;;=> 9.5367431640625E-6
                                                  view source

                                                  random-noise-cfg

                                                  (random-noise-cfg pre-config)(random-noise-cfg)

                                                  Create random noise configuration.

                                                  Optional map with fixed values.

                                                  Examples

                                                  Random configuration

                                                  (random-noise-cfg)
-;;=> {:gain 0.322139923164584,
-;;=>  :generator :ridgemulti,
-;;=>  :interpolation :quintic,
-;;=>  :lacunarity 1.9176121136112807,
-;;=>  :noise-type :simplex,
+;;=> {:gain 0.5066632167432485,
+;;=>  :generator :billow,
+;;=>  :interpolation :linear,
+;;=>  :lacunarity 2.1800521196541762,
+;;=>  :noise-type :value,
 ;;=>  :normalize? true,
-;;=>  :octaves 8,
-;;=>  :seed -475178238,
-;;=>  :warp-depth 1,
-;;=>  :warp-scale 0.0}
                                                  view source

                                                  random-noise-fn

                                                  (random-noise-fn cfg)(random-noise-fn)

                                                  Create random noise function from all possible options.

                                                  +;;=> :octaves 4, +;;=> :seed -399001627, +;;=> :warp-depth 2, +;;=> :warp-scale 0.4698011222895738}
                                                  view source

                                                  random-noise-fn

                                                  (random-noise-fn cfg)(random-noise-fn)

                                                  Create random noise function from all possible options.

                                                  Optionally provide own configuration cfg. In this case one of 4 different blending methods will be selected.

                                                  Examples

                                                  Create function

                                                  (random-noise-fn)
-;;=> fastmath.random$billow_noise$fn__20721@30b2f3b5
+;;=> fastmath.random$billow_noise$fn__20750@319cbb18
 (random-noise-fn (random-noise-cfg))
-;;=> fastmath.random$fbm_noise$fn__20717@3a7933a0

                                                  One

                                                  +;;=> fastmath.random$single_noise$fn__20742@8882fd3

                                                  One

                                                  Two

                                                  Three

                                                  -
                                                  view source

                                                  randval

                                                  macro

                                                  (randval v1 v2)(randval prob v1 v2)(randval prob)(randval)

                                                  Return value with given probability (default 0.5)

                                                  +
                                                  view source

                                                  randval

                                                  macro

                                                  (randval v1 v2)(randval prob v1 v2)(randval prob)(randval)

                                                  Return value with given probability (default 0.5)

                                                  Examples

                                                  Usage

                                                  (randval :val-one :val-two)
 ;;=> :val-one
@@ -749,19 +751,20 @@ 
                                                  Distribution
                                                  
 ;;=> :high-probability

                                                  Check probability of nil (should return value around 1000).

                                                  (count (filter nil?
                (repeatedly 1000000 (fn* [] (randval 0.001 nil 101)))))
-;;=> 952
                                                  view source

                                                  ridgedmulti-noise

                                                  (ridgedmulti-noise)(ridgedmulti-noise cfg__20703__auto__)

                                                  Create ridgedmulti-noise function with optional configuration.

                                                  +;;=> 1019
                                                  view source

                                                  randval-rng

                                                  macro

                                                  (randval-rng rng v1 v2)(randval-rng rng prob v1 v2)(randval-rng rng prob)(randval-rng rng)

                                                  Return value with given probability (default 0.5), for given rng

                                                  +
                                                  view source

                                                  ridgedmulti-noise

                                                  (ridgedmulti-noise)(ridgedmulti-noise cfg__20732__auto__)

                                                  Create ridgedmulti-noise function with optional configuration.

                                                  Examples

                                                  Usage

                                                  (let [n
       (ridgedmulti-noise
        {:octaves 3, :lacunarity 2.1, :gain 0.7, :noise-type :simplex})]
   (n 0.5 1.1 -1.3))
-;;=> 0.29206521847895894

                                                  2d noise

                                                  -
                                                  view source

                                                  rng

                                                  multimethod

                                                  Create RNG for given name (as keyword) and optional seed. Return object enhanced with RNGProto. See: rngs-list for names.

                                                  +;;=> 0.35030055891668704

                                                  2d noise

                                                  +
                                                  view source

                                                  rng

                                                  multimethod

                                                  Create RNG for given name (as keyword) and optional seed. Return object enhanced with RNGProto. See: rngs-list for names.

                                                  Examples

                                                  Creation

                                                  (rng :mersenne)
-;;=> org.apache.commons.math3.random.MersenneTwister@98ef834
+;;=> org.apache.commons.math3.random.MersenneTwister@1d0e669b
 (rng :isaac 1234)
-;;=> org.apache.commons.math3.random.ISAACRandom@1ac18537

                                                  Usage

                                                  +;;=> org.apache.commons.math3.random.ISAACRandom@7b033a75

                                                  Usage

                                                  (irandom (rng :mersenne 999) 15 25)
 ;;=> 24
                                                  view source

                                                  rngs-list

                                                  List of all possible RNGs.

                                                  Examples

                                                  Contains

                                                  @@ -769,10 +772,12 @@

                                                  Distribution

                                                  ;;=> (:isaac :jdk :mersenne ;;=> :well1024a :well19937a ;;=> :well19937c :well44497a -;;=> :well44497b :well512a)
                                                  view source

                                                  sample

                                                  (sample d)

                                                  Random sample

                                                  +;;=> :well44497b :well512a)
                                                  view source

                                                  roll-a-dice

                                                  (roll-a-dice sides)(roll-a-dice dices sides)

                                                  Roll a dice with given sides

                                                  +
                                                  view source

                                                  roll-a-dice-rng

                                                  (roll-a-dice-rng rng sides)(roll-a-dice-rng rng dices sides)

                                                  Roll a dice with given sides and given rng

                                                  +
                                                  view source

                                                  sample

                                                  (sample d)

                                                  Random sample

                                                  Examples

                                                  Random value from distribution

                                                  (sample (distribution :gamma))
-;;=> 2.709109155416231
                                                  view source

                                                  sequence-generator

                                                  multimethod

                                                  Create Sequence generator. See sequence-generators-list for names.

                                                  +;;=> 1.2169466036243723
                                                  view source

                                                  sequence-generator

                                                  multimethod

                                                  Create Sequence generator. See sequence-generators-list for names.

                                                  Values:

                                                  • :r2, :halton, :sobol, :default - range [0-1] for each dimension
                                                    • @@ -812,11 +817,11 @@

                                                    Distribution

                                                  Sphere plot (500 samples)

                                                  Gaussian plot (500 samples)

                                                  Default plot (500 samples)

                                                  -
                                                  view source

                                                  sequence-generators-list

                                                  List of random sequence generator. See sequence-generator.

                                                  +
                                                  view source

                                                  sequence-generators-list

                                                  List of random sequence generator. See sequence-generator.

                                                  Examples

                                                  Generator names.

                                                  (sort sequence-generators-list)
-;;=> (:ball :default :gaussian :halton :r2 :sobol :sphere)
                                                  view source

                                                  set-seed

                                                  (set-seed)(set-seed v)(set-seed rng v)

                                                  Create and return new RNG

                                                  -
                                                  view source

                                                  set-seed!

                                                  (set-seed!)(set-seed! v)(set-seed! rng v)

                                                  Sets seed.

                                                  +;;=> (:ball :default :gaussian :halton :r2 :sobol :sphere)
                                                  view source

                                                  set-seed

                                                  (set-seed)(set-seed v)(set-seed rng v)

                                                  Create and return new RNG

                                                  +
                                                  view source

                                                  set-seed!

                                                  (set-seed!)(set-seed! v)(set-seed! rng v)

                                                  Sets seed.

                                                  If rng is :smile calls smile.math.MathEx/setSeed().

                                                  Without rng sets both :smile and default-rng

                                                  Examples

                                                  Set seed for the RNG object

                                                  @@ -835,24 +840,24 @@

                                                  Distribution

                                                  (set-seed! :smile 1234)
 ;;=> nil

                                                  Set seed to both SMILE and fastmath default RNGs

                                                  (set-seed! 1234)
-;;=> org.apache.commons.math3.random.JDKRandomGenerator@74b6c343

                                                  Set to random seed both default RNGs

                                                  +;;=> org.apache.commons.math3.random.JDKRandomGenerator@656d49a1

                                                  Set to random seed both default RNGs

                                                  (set-seed!)
-;;=> org.apache.commons.math3.random.JDKRandomGenerator@74b6c343
                                                  view source

                                                  simplex

                                                  (simplex x)(simplex x y)(simplex x y z)

                                                  Simplex noise. 6 octaves.

                                                  +;;=> org.apache.commons.math3.random.JDKRandomGenerator@656d49a1
                                                  view source

                                                  simplex

                                                  (simplex x)(simplex x y)(simplex x y z)

                                                  Simplex noise. 6 octaves.

                                                  Examples

                                                  Usage

                                                  (simplex 3.3)
-;;=> 0.37317187056
+;;=> 0.6525392810438096
 (simplex 3.3 1.1)
-;;=> 0.33595758451118996
+;;=> 0.4992060978009244
 (simplex 3.3 0.0 -0.1)
-;;=> 0.3157868077601413

                                                  2d noise

                                                  -
                                                  view source

                                                  single-noise

                                                  (single-noise)(single-noise cfg__20703__auto__)

                                                  Create single-noise function with optional configuration.

                                                  +;;=> 0.5027365575805084

                                                  2d noise

                                                  +
                                                  view source

                                                  single-noise

                                                  (single-noise)(single-noise cfg__20732__auto__)

                                                  Create single-noise function with optional configuration.

                                                  Examples

                                                  Usage

                                                  (let [n (single-noise {:interpolation :linear})] (n 0.5 1.1 -1.3))
-;;=> 0.479

                                                  2d noise

                                                  -
                                                  view source

                                                  source-object

                                                  (source-object d)

                                                  Returns Java or proxy object from backend library (if available)

                                                  +;;=> 0.634

                                                  2d noise

                                                  +
                                                  view source

                                                  source-object

                                                  (source-object d)

                                                  Returns Java or proxy object from backend library (if available)

                                                  Examples

                                                  Usage

                                                  (source-object default-normal)
-;;=> org.apache.commons.math3.distribution.NormalDistribution@7a4204ef
                                                  view source

                                                  synced-rng

                                                  (synced-rng m)(synced-rng m seed)

                                                  Create synchronized RNG for given name and optional seed. Wraps rng method.

                                                  +;;=> org.apache.commons.math3.distribution.NormalDistribution@1f136b88
                                                  view source

                                                  synced-rng

                                                  (synced-rng m)(synced-rng m seed)

                                                  Create synchronized RNG for given name and optional seed. Wraps rng method.

                                                  Examples

                                                  Usage

                                                  (drandom (synced-rng :mersenne 1234))
 ;;=> 0.0685985404954157
                                                  view source

                                                  upper-bound

                                                  (upper-bound d)

                                                  Distribution highest supported value

                                                  @@ -860,21 +865,21 @@

                                                  Distribution

                                                  (upper-bound (distribution :gamma))
 ;;=> Infinity
 
-;; Test: ok.
                                                  view source

                                                  variance

                                                  (variance d)

                                                  Distribution variance

                                                  +;; Test: ok.
                                                  view source

                                                  variance

                                                  (variance d)

                                                  Distribution variance

                                                  Examples

                                                  Usage

                                                  (variance (distribution :gamma))
 ;;=> 8.0
 
-;; Test: ok.
                                                  view source

                                                  vnoise

                                                  (vnoise x)(vnoise x y)(vnoise x y z)

                                                  Value Noise.

                                                  +;; Test: ok.
                                                  view source

                                                  vnoise

                                                  (vnoise x)(vnoise x y)(vnoise x y z)

                                                  Value Noise.

                                                  6 octaves, Hermite interpolation (cubic, h01).

                                                  Examples

                                                  Usage

                                                  (vnoise 3.3)
-;;=> 0.7118823098349076
+;;=> 0.3206900454559337
 (vnoise 3.3 1.1)
-;;=> 0.6256694813199928
+;;=> 0.405033127977853
 (vnoise 3.3 0.0 -0.1)
-;;=> 0.7645039402625281

                                                  2d noise

                                                  -
                                                  view source

                                                  warp-noise-fn

                                                  (warp-noise-fn noise scale depth)(warp-noise-fn noise scale)(warp-noise-fn noise)(warp-noise-fn)

                                                  Create warp noise (see Inigo Quilez article).

                                                  +;;=> 0.5235283697595818

                                                  2d noise

                                                  +
                                                  view source

                                                  warp-noise-fn

                                                  (warp-noise-fn noise scale depth)(warp-noise-fn noise scale)(warp-noise-fn noise)(warp-noise-fn)

                                                  Create warp noise (see Inigo Quilez article).

                                                  Parameters:

                                                  • noise function, default: vnoise
                                                    • @@ -885,5 +890,5 @@

                                                    Distribution

                                                  Examples

                                                  Usage

                                                  (let [n (warp-noise-fn simplex 2.0 2.0)]
   [(n 0.0) (n 1.0 0.5) (n 2 2 2)])
-;;=> [0.40514091608287256 0.4384328723070078 0.6539788263760881]

                                                  Default warp (noise=vnoise, scale=4.0, depth=1.0).

                                                  -
                                                  view source
                                                  \ No newline at end of file +;;=> [0.4465743065877865 0.4444313141229481 0.6482438784376463]

                                                  Default warp (noise=vnoise, scale=4.0, depth=1.0).

                                                  +
                                                  view source
                                                  \ No newline at end of file diff --git a/docs/fastmath.signal.html b/docs/fastmath.signal.html index 69c4cb84..1ff22a1b 100644 --- a/docs/fastmath.signal.html +++ b/docs/fastmath.signal.html @@ -1,6 +1,6 @@ -fastmath.signal documentation

                                                  Project

                                                  Namespaces

                                                  Public Vars

                                                  fastmath.signal

                                                  Signal processing (effect) and generation (oscillators).

                                                  +fastmath.signal documentation

                                                  Project

                                                  Namespaces

                                                  Public Vars

                                                  fastmath.signal

                                                  Signal processing (effect) and generation (oscillators).

                                                  Singal is any sequence with double values.

                                                  Signal processing

                                                  To process signal use apply-effects or apply-effects-raw (operates on double-array only) function.

                                                  @@ -172,7 +172,7 @@

                                                  File operations

                                                  (let [lpf (effect :simple-lowpass {:cutoff 10000})
       sgnal (m/seq->double-array [-1.0 1.0 -0.5 0.5 -0.1 0.1 0 0])]
   (apply-effects-raw sgnal lpf))
-;;=> [D@748412d5

                                                  Reset state every two samples

                                                  +;;=> [D@67c1ab90

                                                  Reset state every two samples

                                                  (let [lpf (effect :simple-lowpass {:cutoff 10000})
       sgnal (m/seq->double-array [-1.0 1.0 -0.5 0.5 -0.1 0.1 0 0])]
   (seq (apply-effects-raw sgnal lpf 2)))
@@ -193,9 +193,9 @@ 
                                                  File operations
                                                  
    "After call on sample" result,
    "Extracted sample" (result)})
 ;;=> {"After call on sample"
-;;=>  #object[fastmath.signal.EffectsList 0x70c5de63 "simple-highpass (0.38911967999610275) -> simple-lowpass (0.08629142927556396)"],
+;;=>  #object[fastmath.signal.EffectsList 0x3a82c52a "simple-highpass (0.38911967999610275) -> simple-lowpass (0.08629142927556396)"],
 ;;=>  "Composed effects"
-;;=>  #object[fastmath.signal.EffectsList 0x5b65490d "simple-highpass (0.0) -> simple-lowpass (0.0)"],
+;;=>  #object[fastmath.signal.EffectsList 0x91d6ffa "simple-highpass (0.0) -> simple-lowpass (0.0)"],
 ;;=>  "Extracted sample" 0.08629142927556396}
                                                  view source

                                                  db->linear

                                                  (db->linear x)

                                                  DB to Linear

                                                  Examples

                                                  Usage

                                                  (db->linear 0.5)
@@ -348,7 +348,7 @@ 
                                                  File operations
                                                  
 
                                                  Returns sampled signal as double array.

                                                  Examples

                                                  Usage

                                                  (let [w (oscillator :sin 0.2 0.9 0.2)] (oscillator->signal w 44100 5))
-;;=> [D@7aeb8fc0
                                                  view source

                                                  oscillator-gain

                                                  (oscillator-gain fs gain)

                                                  Examples

                                                  Usage

                                                  +;;=> [D@7cbdfa68
                                                  view source

                                                  oscillator-gain

                                                  (oscillator-gain fs gain)

                                                  Examples

                                                  Usage

                                                  (let [wave-sin (oscillator :sin 1.0 1.0 0.5)
       gained (oscillator-gain wave-sin 0.22)]
   {:original (wave-sin 0.75), :gained (gained 0.75)})
@@ -368,7 +368,7 @@ 
                                                  File operations

                                                  Examples

                                                  Usage

                                                  (let [s (oscillator->signal (oscillator :sin 1 1 0) 11050 5)]
   (save-signal s "signal.raw"))
-;;=> [D@75c3384c
                                                  view source

                                                  savgol-filter

                                                  (savgol-filter)(savgol-filter length)(savgol-filter length order)(savgol-filter length order derivative)

                                                  Creates Savitzky-Golay smoothing filter.

                                                  +;;=> [D@c1fd373
                                                  view source

                                                  savgol-filter

                                                  (savgol-filter)(savgol-filter length)(savgol-filter length order)(savgol-filter length order derivative)

                                                  Creates Savitzky-Golay smoothing filter.

                                                  Arguments:

                                                  • length - length of the kernel (default: 5)
                                                    • diff --git a/docs/fastmath.solver.html b/docs/fastmath.solver.html index 8cb164ed..e0f991b0 100644 --- a/docs/fastmath.solver.html +++ b/docs/fastmath.solver.html @@ -1,6 +1,6 @@ -fastmath.solver documentation

                                                    Project

                                                    Namespaces

                                                    Public Vars

                                                    fastmath.solver

                                                    Categories

                                                      Other vars: find-root

                                                      find-root

                                                      (find-root f lower-bound upper-bound)(find-root f lower-bound upper-bound {:keys [absolute-accuracy relative-accuracy max-iters initial-value solver], :or {max-iters 100, solver :brent}})

                                                      Find zero (root) of a function f in given range lower-bound, upper-bound.

                                                      +fastmath.solver documentation

                                                      Project

                                                      Namespaces

                                                      Public Vars

                                                      fastmath.solver

                                                      Categories

                                                        Other vars: find-root quadratic

                                                        find-root

                                                        (find-root f lower-bound upper-bound)(find-root f lower-bound upper-bound {:keys [absolute-accuracy relative-accuracy max-iters initial-value solver], :or {max-iters 100, solver :brent}})

                                                        Find zero (root) of a function f in given range lower-bound, upper-bound.

                                                        Optional parameters:

                                                        • :absolute-accuracy - default 1.0e-8
                                                          • @@ -9,4 +9,5 @@
                                                        • :initial-value - algorithm starting value
                                                        • :solver - one of: :brent (default), :bisection, :illinois, :muller, :muller2, :pegasus, :regula-falsi, :ridders and :secant.
                                                        -
                                                        view source
                                                        \ No newline at end of file +
                                                        view source

                                                        quadratic

                                                        (quadratic a b c)

                                                        Solution of quadratic formula ax^2+bx+c=0, returns nil when there are no solutions

                                                        +
                                                        view source
                                                        \ No newline at end of file diff --git a/docs/fastmath.stats.bootstrap.html b/docs/fastmath.stats.bootstrap.html index 14aae160..e5b3c7c5 100644 --- a/docs/fastmath.stats.bootstrap.html +++ b/docs/fastmath.stats.bootstrap.html @@ -1,12 +1,12 @@ -fastmath.stats.bootstrap documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.stats.bootstrap

                                                        Bootstrap methods and confidence intervals

                                                        +fastmath.stats.bootstrap documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.stats.bootstrap

                                                        Bootstrap methods and confidence intervals

                                                        Categories

                                                          Other vars: bootstrap bootstrap-stats ci-basic ci-bc ci-bca ci-normal ci-percentile ci-studentized ci-t jackknife jackknife+

                                                          bootstrap

                                                          (bootstrap input)(bootstrap input statistic)(bootstrap input statistic {:keys [rng samples size method antithetic? smoothing dimensions include?], :or {samples 500}, :as params})

                                                          Create set of samples from given data (nonparametric) or model (parametric).

                                                          Input: * sequence of values (any type) or sequence of sequences for multidimensional data * a map containing: * :data - sequence * :model - model for parametric bootstrap (optional) * statistic function which returns statistic value (optional)

                                                          Parameters: * :samples - number of bootstrapped samples (default: 500) * :size - forced size of individual sample (default: same as source) * :method * nil (default) - random * :jackknife for leave-one-out jackknife * :jackknife+ for positive jackknife * any method accepted by fastmath.random/->seq * :rng - random number generator (see: fastmath.random/rng) * :smoothing - smoothing bootstrap: * :kde - kernel density estimation, additional options are: :kernel (default) and :bandwidth (auto) * :gaussian - add random value from N(0,standard error) * :distribution - distribution used to auto generate model (distribution) from data: * :real-discrete-distribution - default * :integer-discrete-distribution - for integer values * :categorical-distribution - for any other type * :dimensions - if set to :multi - multidimensional data and models are created * :antithetic? - antithetic sampling (default: false) * :include? - if set to true (default: false) original dataset is included in samples

                                                          Model can be: * any distribution object * any 0-arity function which returns random sample

                                                          When model is ommited, function creates discrete distribution. When multidimensional data are provided, models should be created for every dimension (as a sequence).

                                                          -
                                                          view source

                                                          bootstrap-stats

                                                          (bootstrap-stats {:keys [data samples], :as input} statistic)

                                                          Calculate bootstrap analysis.

                                                          +
                                                          view source

                                                          bootstrap-stats

                                                          (bootstrap-stats {:keys [data samples], :as input} statistic)

                                                          Calculate bootstrap analysis.

                                                          Arguments:

                                                          • a map containing :data and :samples
                                                            • @@ -20,19 +20,19 @@
                                                          • :bias - difference between mean of ts and t0
                                                          • :mean, :median, :variance, :stddev, :sem - statistics from ts
                                                          -
                                                          view source

                                                          ci-basic

                                                          (ci-basic boot-data)(ci-basic boot-data alpha)(ci-basic {:keys [t0 ts]} alpha estimation-strategy)

                                                          Basic percentile confidence interval

                                                          +
                                                          view source

                                                          ci-basic

                                                          (ci-basic boot-data)(ci-basic boot-data alpha)(ci-basic {:keys [t0 ts]} alpha estimation-strategy)

                                                          Basic percentile confidence interval

                                                          :t0 and :ts are obligatory

                                                          -
                                                          view source

                                                          ci-bc

                                                          (ci-bc boot-data)(ci-bc boot-data alpha)(ci-bc {:keys [t0 ts]} alpha estimation-strategy)

                                                          Bias-corrected confidence interval

                                                          -
                                                          view source

                                                          ci-bca

                                                          (ci-bca boot-data)(ci-bca boot-data alpha)(ci-bca {:keys [t0 ts data statistic]} alpha estimation-strategy)

                                                          Bias-corrected and accelerated confidence interval.

                                                          +
                                                          view source

                                                          ci-bc

                                                          (ci-bc boot-data)(ci-bc boot-data alpha)(ci-bc {:keys [t0 ts]} alpha estimation-strategy)

                                                          Bias-corrected confidence interval

                                                          +
                                                          view source

                                                          ci-bca

                                                          (ci-bca boot-data)(ci-bca boot-data alpha)(ci-bca {:keys [t0 ts data statistic]} alpha estimation-strategy)

                                                          Bias-corrected and accelerated confidence interval.

                                                          There are two ways to calculate acceleration: * jackknife method (when boot-data contains :data and :statistic) * empirical from bootstrap estimations ts otherwise

                                                          -
                                                          view source

                                                          ci-normal

                                                          (ci-normal boot-data)(ci-normal {:keys [t0 ts stddev bias]} alpha)

                                                          Normal (gaussian) bias-corrected confidence interval

                                                          +
                                                          view source

                                                          ci-normal

                                                          (ci-normal boot-data)(ci-normal {:keys [t0 ts stddev bias]} alpha)

                                                          Normal (gaussian) bias-corrected confidence interval

                                                          :t0 and :ts are obligatory

                                                          -
                                                          view source

                                                          ci-percentile

                                                          (ci-percentile boot-data)(ci-percentile boot-data alpha)(ci-percentile {:keys [t0 ts]} alpha estimation-strategy)

                                                          Percentile confidence interval

                                                          +
                                                          view source

                                                          ci-percentile

                                                          (ci-percentile boot-data)(ci-percentile boot-data alpha)(ci-percentile {:keys [t0 ts]} alpha estimation-strategy)

                                                          Percentile confidence interval

                                                          :t0 and :ts are obligatory

                                                          -
                                                          view source

                                                          ci-studentized

                                                          (ci-studentized boot-data)(ci-studentized boot-data alpha)(ci-studentized {:keys [t0 ts data samples]} alpha estimation-strategy)

                                                          Confidence interval from studentized data.

                                                          +
                                                          view source

                                                          ci-studentized

                                                          (ci-studentized boot-data)(ci-studentized boot-data alpha)(ci-studentized {:keys [t0 ts data samples]} alpha estimation-strategy)

                                                          Confidence interval from studentized data.

                                                          :t0, :ts, :data and :samples are obligatory in boot-data

                                                          -
                                                          view source

                                                          ci-t

                                                          (ci-t boot-data)(ci-t {:keys [t0 ts stddev]} alpha)

                                                          Student’s T confidence interval.

                                                          +
                                                          view source

                                                          ci-t

                                                          (ci-t boot-data)(ci-t {:keys [t0 ts stddev]} alpha)

                                                          Student’s T confidence interval.

                                                          :t0 and :ts are obligatory

                                                          -
                                                          view source

                                                          jackknife

                                                          (jackknife vs)

                                                          Generates set of samples using jackknife leave-one-out method

                                                          -
                                                          view source

                                                          jackknife+

                                                          (jackknife+ vs)

                                                          Generates set of samples using jackknife positive method

                                                          -
                                                          view source
                                                          \ No newline at end of file +
                                                          view source

                                                          jackknife

                                                          (jackknife vs)

                                                          Generates set of samples using jackknife leave-one-out method

                                                          +
                                                          view source

                                                          jackknife+

                                                          (jackknife+ vs)

                                                          Generates set of samples using jackknife positive method

                                                          +
                                                          view source
                                                        \ No newline at end of file diff --git a/docs/fastmath.stats.html b/docs/fastmath.stats.html index 9b51b04e..c9d6e6c6 100644 --- a/docs/fastmath.stats.html +++ b/docs/fastmath.stats.html @@ -1,6 +1,6 @@ -fastmath.stats documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.stats

                                                        Statistics functions.

                                                        +fastmath.stats documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.stats

                                                        Statistics functions.

                                                        • Descriptive statistics.
                                                        • Correlation / covariance
                                                          • @@ -51,16 +51,16 @@
                                                          Descriptiv

                                                        Examples

                                                        Usage

                                                        (acf (repeatedly 1000 r/grand) 5)
 ;;=> (1.0
-;;=>  0.02481827283370266
-;;=>  -0.016643111047625267
-;;=>  -0.04387141411591325
-;;=>  -0.0175258579033391
-;;=>  -0.022982146321944872)
+;;=>  0.024818272833702658
+;;=>  -0.016643111047625263
+;;=>  -0.04387141411591324
+;;=>  -0.017525857903339097
+;;=>  -0.02298214632194487)
 (acf (repeatedly 1000 r/grand) [10 20 100 500])
-;;=> (-0.037660639529149706
-;;=>  -0.0340344086980366
-;;=>  -0.010242012560395728
-;;=>  0.004501378382446301)
+;;=> (-0.0376606395291497
+;;=>  -0.034034408698036596
+;;=>  -0.010242012560395726
+;;=>  0.0045013783824463)
 (acf [1 2 3 4 5 4 3 2 1])
 ;;=> (1.0
 ;;=>  0.5396825396825397
@@ -88,8 +88,8 @@ 
                                                        Descriptiv
 ;;=>  :cis (0.653321328180018
 ;;=>        0.8218653739461048
 ;;=>        0.8219599072345126
-;;=>        0.9281841012727746)}
                                                        view source

                                                        ad-test-one-sample

                                                        (ad-test-one-sample xs)(ad-test-one-sample xs distribution-or-ys)(ad-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth], :or {sides :one-sided-greater, kernel :gaussian}})

                                                        Anderson-Darling test

                                                        -
                                                        view source

                                                        adjacent-values

                                                        (adjacent-values vs)(adjacent-values vs estimation-strategy)(adjacent-values vs q1 q3 m)

                                                        Lower and upper adjacent values (LAV and UAV).

                                                        +;;=> 0.9281841012727746)}
                                                        view source

                                                        ad-test-one-sample

                                                        (ad-test-one-sample xs)(ad-test-one-sample xs distribution-or-ys)(ad-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth], :or {sides :one-sided-greater, kernel :gaussian}})

                                                        Anderson-Darling test

                                                        +
                                                        view source

                                                        adjacent-values

                                                        (adjacent-values vs)(adjacent-values vs estimation-strategy)(adjacent-values vs q1 q3 m)

                                                        Lower and upper adjacent values (LAV and UAV).

                                                        Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

                                                        • LAV is smallest value which is greater or equal to the LIF = (- Q1 (* 1.5 IQR)).
                                                          • @@ -178,7 +178,7 @@
                                                          Descriptiv ;;=> :cn 4.0, ;;=> :cp 4.0, ;;=> :dor 0.3333333333333333, -;;=> :f-beta #, +;;=> :f-beta #, ;;=> :f-measure 0.28571428571428575, ;;=> :f1-score 0.28571428571428575, ;;=> :fall-out 0.5, @@ -218,7 +218,7 @@
                                                          Descriptiv ;;=> :total 8.0, ;;=> :tp 1, ;;=> :tpr 0.25, -;;=> :ts 0.16666666666666666}

                                                        Treat 1 as true value.

                                                        +;;=> :ts 0.16666666666666666}

                                                        Treat 1 as true value.

                                                        (binary-measures-all [1 0 1 0 1 0 1 0] [1 0 0 1 0 0 0 1] [1])
 ;;=> {:accuracy 0.375,
 ;;=>  :ba 0.375,
@@ -226,7 +226,7 @@ 
                                                        Descriptiv
 ;;=>  :cn 4.0,
 ;;=>  :cp 4.0,
 ;;=>  :dor 0.3333333333333333,
-;;=>  :f-beta #,
+;;=>  :f-beta #,
 ;;=>  :f-measure 0.28571428571428575,
 ;;=>  :f1-score 0.28571428571428575,
 ;;=>  :fall-out 0.5,
@@ -266,7 +266,7 @@ 
                                                        Descriptiv
 ;;=>  :total 8.0,
 ;;=>  :tp 1,
 ;;=>  :tpr 0.25,
-;;=>  :ts 0.16666666666666666}

                                                        Treat :a and :b as true value.

                                                        +;;=> :ts 0.16666666666666666}

                                                        Treat :a and :b as true value.

                                                        (binary-measures-all [:a :b :c :d :e :f :a :b]
                      [:a :b :a :b :a :f :d :b]
                      {:a true, :b true, :c false})
@@ -276,7 +276,7 @@ 
                                                        Descriptiv
 ;;=>  :cn 4.0,
 ;;=>  :cp 4.0,
 ;;=>  :dor 1.0,
-;;=>  :f-beta #,
+;;=>  :f-beta #,
 ;;=>  :f-measure 0.6,
 ;;=>  :f1-score 0.6,
 ;;=>  :fall-out 0.75,
@@ -316,7 +316,7 @@ 
                                                        Descriptiv
 ;;=>  :total 8.0,
 ;;=>  :tp 3,
 ;;=>  :tpr 0.75,
-;;=>  :ts 0.42857142857142855}

                                                        F-beta is a function. When beta is equal 1.0, you get f1-score.

                                                        +;;=> :ts 0.42857142857142855}

                                                        F-beta is a function. When beta is equal 1.0, you get f1-score.

                                                        (let [fbeta (:f-beta (binary-measures-all
                       [true false true false true false true false]
                       [true false false true false false false true]))]
@@ -325,78 +325,78 @@ 
                                                        Descriptiv
 
                                                        Possible methods are: * :asymptotic (normal aproximation, based on central limit theorem), default * :agresti-coull * :clopper-pearson * :wilson * :prop.test - one sample proportion test * :cloglog * :logit * :probit * :arcsine * :all - apply all methods and return a map of triplets
                                                        
 
                                                        Default alpha is 0.05
                                                        
 
                                                        Returns a triple lower ci, upper ci, p=successes/trials
                                                        
-
                                                        view source

                                                        binomial-ci-methods

                                                        view source

                                                        binomial-test

                                                        (binomial-test xs)(binomial-test xs maybe-params)(binomial-test number-of-successes number-of-trials {:keys [alpha p ci-method sides], :or {alpha 0.05, p 0.5, ci-method :asymptotic, sides :two-sided}})

                                                        Binomial test

                                                        +
                                                        view source

                                                        binomial-ci-methods

                                                        view source

                                                        binomial-test

                                                        (binomial-test xs)(binomial-test xs maybe-params)(binomial-test number-of-successes number-of-trials {:keys [alpha p ci-method sides], :or {alpha 0.05, p 0.5, ci-method :asymptotic, sides :two-sided}})

                                                        Binomial test

                                                        • alpha - significance level (default: 0.05)
                                                        • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
                                                        • ci-method - see binomial-ci-methods
                                                        • p - tested probability
                                                        -
                                                        view source

                                                        bootstrap

                                                        deprecated in Please use fastmath.stats.bootstrap/bootstrap instead

                                                        (bootstrap vs)(bootstrap vs samples)(bootstrap vs samples size)

                                                        Generate set of samples of given size from provided data.

                                                        +
                                                        view source

                                                        bootstrap

                                                        deprecated in Please use fastmath.stats.bootstrap/bootstrap instead

                                                        (bootstrap vs)(bootstrap vs samples)(bootstrap vs samples size)

                                                        Generate set of samples of given size from provided data.

                                                        Default samples is 200, number of size defaults to sample size.

                                                        Examples

                                                        Usage

                                                        (bootstrap [1 2 3 4 1 2 3 1 2 1] 2 20)
 ;;=> ((3.0
 ;;=>   1.0
 ;;=>   2.0
-;;=>   4.0
 ;;=>   1.0
+;;=>   2.0
+;;=>   2.0
 ;;=>   1.0
-;;=>   4.0
 ;;=>   3.0
-;;=>   4.0
+;;=>   1.0
 ;;=>   2.0
 ;;=>   1.0
 ;;=>   1.0
+;;=>   1.0
 ;;=>   3.0
 ;;=>   2.0
-;;=>   1.0
-;;=>   1.0
+;;=>   4.0
 ;;=>   2.0
+;;=>   3.0
+;;=>   3.0
+;;=>   4.0)
+;;=>  (1.0
+;;=>   4.0
 ;;=>   1.0
 ;;=>   1.0
-;;=>   1.0)
-;;=>  (2.0
 ;;=>   2.0
+;;=>   3.0
 ;;=>   1.0
 ;;=>   3.0
+;;=>   3.0
 ;;=>   2.0
 ;;=>   2.0
+;;=>   1.0
 ;;=>   2.0
 ;;=>   1.0
+;;=>   1.0
 ;;=>   3.0
 ;;=>   1.0
 ;;=>   1.0
 ;;=>   4.0
-;;=>   1.0
-;;=>   3.0
-;;=>   2.0
-;;=>   3.0
-;;=>   1.0
-;;=>   3.0
-;;=>   3.0
-;;=>   1.0))
+;;=>   2.0))
 (let [data [1 2 3 4 1 2 3 1 2 1]
       fdata (frequencies data)
       bdata (bootstrap data 5 1000)]
   {:source fdata, :bootstrapped (map frequencies bdata)})
-;;=> {:bootstrapped ({1.0 376, 2.0 325, 3.0 204, 4.0 95}
-;;=>                 {1.0 400, 2.0 312, 3.0 195, 4.0 93}
-;;=>                 {1.0 413, 2.0 305, 3.0 195, 4.0 87}
-;;=>                 {1.0 387, 2.0 312, 3.0 201, 4.0 100}
-;;=>                 {1.0 411, 2.0 301, 3.0 207, 4.0 81}),
+;;=> {:bootstrapped ({1.0 413, 2.0 295, 3.0 203, 4.0 89}
+;;=>                 {1.0 405, 2.0 308, 3.0 197, 4.0 90}
+;;=>                 {1.0 429, 2.0 293, 3.0 188, 4.0 90}
+;;=>                 {1.0 403, 2.0 283, 3.0 204, 4.0 110}
+;;=>                 {1.0 386, 2.0 301, 3.0 207, 4.0 106}),
 ;;=>  :source {1 4, 2 3, 3 2, 4 1}}
                                                        view source

                                                        bootstrap-ci

                                                        deprecated in Please use fastmath.stats.boostrap/ci-basic instead

                                                        (bootstrap-ci vs)(bootstrap-ci vs alpha)(bootstrap-ci vs alpha samples)(bootstrap-ci vs alpha samples stat-fn)

                                                        Bootstrap method to calculate confidence interval.

                                                        Alpha defaults to 0.98, samples to 1000. Last parameter is statistical function used to measure, default: mean.

                                                        Returns ci and statistical function value.

                                                        Examples

                                                        Usage

                                                        (bootstrap-ci [-5 1 1 1 1 2 2 5 11 71])
-;;=> [-5.599999999999998 17.9 9.0]
+;;=> [-6.300000000000001 17.8 9.0]
 (bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.8)
-;;=> [2.5 15.8 9.0]
+;;=> [2.8000000000000007 15.7 9.0]
 (bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.8 100000)
 ;;=> [2.5999999999999996 15.7 9.0]
 (bootstrap-ci [-5 1 1 1 1 2 2 5 11 71] 0.98 1000 median)
-;;=> [-20.698 2.7 1.5]
                                                        view source

                                                        brown-forsythe-test

                                                        (brown-forsythe-test xss)(brown-forsythe-test xss params)
                                                        view source

                                                        chisq-test

                                                        (chisq-test contingency-table-or-xs)(chisq-test contingency-table-or-xs params)
                                                        view source

                                                        ci

                                                        (ci vs)(ci vs alpha)

                                                        T-student based confidence interval for given data. Alpha value defaults to 0.05.

                                                        +;;=> [-20.698 2.7 1.5]
                                                        view source

                                                        brown-forsythe-test

                                                        (brown-forsythe-test xss)(brown-forsythe-test xss params)
                                                        view source

                                                        chisq-test

                                                        (chisq-test contingency-table-or-xs)(chisq-test contingency-table-or-xs params)
                                                        view source

                                                        ci

                                                        (ci vs)(ci vs alpha)

                                                        T-student based confidence interval for given data. Alpha value defaults to 0.05.

                                                        Last value is mean.

                                                        Examples

                                                        Usage

                                                        (ci [-5 1 1 1 1 2 2 5 11 71])
@@ -487,7 +487,7 @@ 
                                                        Descriptiv
 
                                                        (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
       b [:b :f :a :a :b :b :y :z :c :b :b :c :a :a :b :b :c :a :a :b]]
   (cramers-v-corrected a b))
-;;=> 0.3410563654946855
                                                        view source

                                                        cressie-read-test

                                                        (cressie-read-test contingency-table-or-xs)(cressie-read-test contingency-table-or-xs params)
                                                        view source

                                                        demean

                                                        (demean vs)

                                                        Subtract mean from sequence

                                                        +;;=> 0.3410563654946855
                                                        view source

                                                        cressie-read-test

                                                        (cressie-read-test contingency-table-or-xs)(cressie-read-test contingency-table-or-xs params)
                                                        view source

                                                        demean

                                                        (demean vs)

                                                        Subtract mean from sequence

                                                        Examples

                                                        Usage

                                                        (demean [-5 1 1 1 1 2 2 5 11 71])
 ;;=> (-14.0 -8.0 -8.0 -8.0 -8.0 -7.0 -7.0 -4.0 2.0 62.0)
                                                        view source

                                                        epsilon-sq

                                                        (epsilon-sq [group1 group2])(epsilon-sq group1 group2)

                                                        Less biased R2

                                                        @@ -506,11 +506,11 @@
                                                        Descriptiv (estimate-bins vs :rice) ;;=> 20 (estimate-bins vs :doane) -;;=> 16 +;;=> 17 (estimate-bins vs :scott) -;;=> 31 +;;=> 39 (estimate-bins vs :freedman-diaconis) -;;=> 76
                                                        view source

                                                        estimation-strategies-list

                                                        List of estimation strategies for percentile/quantile functions.

                                                        +;;=> 98
                                                        view source

                                                        estimation-strategies-list

                                                        List of estimation strategies for percentile/quantile functions.

                                                        Examples

                                                        List of estimation strategies for percentile

                                                        (sort (keys estimation-strategies-list))
 ;;=> (:legacy :r1 :r2 :r3 :r4 :r5 :r6 :r7 :r8 :r9)
                                                        view source

                                                        eta-sq

                                                        (eta-sq [group1 group2])(eta-sq group1 group2)

                                                        R2, coefficient of determination

                                                        @@ -526,7 +526,7 @@
                                                        Descriptiv
                                                      • alpha - significance level (default: 0.05)
                                                      • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
                                                        • -
                                                        view source

                                                        fligner-killeen-test

                                                        (fligner-killeen-test xss)(fligner-killeen-test xss {:keys [sides], :or {sides :one-sided-greater}})
                                                        view source

                                                        freeman-tukey-test

                                                        (freeman-tukey-test contingency-table-or-xs)(freeman-tukey-test contingency-table-or-xs params)
                                                        view source

                                                        geomean

                                                        (geomean vs)

                                                        Geometric mean for positive values only

                                                        +
                                                        view source

                                                        fligner-killeen-test

                                                        (fligner-killeen-test xss)(fligner-killeen-test xss {:keys [sides], :or {sides :one-sided-greater}})
                                                        view source

                                                        freeman-tukey-test

                                                        (freeman-tukey-test contingency-table-or-xs)(freeman-tukey-test contingency-table-or-xs params)
                                                        view source

                                                        geomean

                                                        (geomean vs)

                                                        Geometric mean for positive values only

                                                        Examples

                                                        Geometric mean

                                                        (geomean [1 2 3 1 1 2 1 11 111])
 ;;=> 2.903203203730772
                                                        view source

                                                        glass-delta

                                                        (glass-delta [group1 group2])(glass-delta group1 group2)

                                                        Glass’s delta effect size for two groups

                                                        @@ -566,20 +566,20 @@
                                                        Descriptiv

                                                        If difference between min and max values is 0, number of bins is set to 1.

                                                        Examples

                                                        3 bins from uniform distribution.

                                                        (histogram (repeatedly 1000 rand) 3)
-;;=> {:bins ([3.6688282750596546E-4 332]
-;;=>         [0.3330912011095961 332]
-;;=>         [0.6658155193916863 336]),
-;;=>  :max 0.9985398376737764,
-;;=>  :min 3.6688282750596546E-4,
+;;=> {:bins ([6.237964863657908E-4 335]
+;;=>         [0.33350733411402445 353]
+;;=>         [0.6663908717416831 312]),
+;;=>  :max 0.9992744093693418,
+;;=>  :min 6.237964863657908E-4,
 ;;=>  :samples 1000,
 ;;=>  :size 3,
-;;=>  :step 0.33272431828209015}

                                                        3 bins from uniform distribution for given range.

                                                        +;;=> :step 0.33288353762765865}

                                                        3 bins from uniform distribution for given range.

                                                        (histogram (repeatedly 10000 rand) 3 [0.1 0.5])
 ;;=> {:bins
-;;=>  ([0.1 1282] [0.23333333333333334 1347] [0.3666666666666667 1275]),
+;;=>  ([0.1 1328] [0.23333333333333334 1355] [0.3666666666666667 1376]),
 ;;=>  :max 0.5,
 ;;=>  :min 0.1,
-;;=>  :samples 3904,
+;;=>  :samples 4059,
 ;;=>  :size 3,
 ;;=>  :step 0.13333333333333333}

                                                        5 bins from normal distribution.

                                                        (histogram (repeatedly 10000 r/grand) 5)
@@ -611,9 +611,9 @@ 
                                                        Descriptiv
 
                                                        (kendall-correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
                      (repeatedly 100000 (partial r/drand -10.0 -5.0)))
 ;;=> 2.81850018500185E-4
                                                        view source

                                                        kruskal-test

                                                        (kruskal-test xss)(kruskal-test xss {:keys [sides], :or {sides :right}})

                                                        Kruskal-Wallis rank sum test.

                                                        -
                                                        view source

                                                        ks-test-one-sample

                                                        (ks-test-one-sample xs)(ks-test-one-sample xs distribution-or-ys)(ks-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth distinct?], :or {sides :two-sided, kernel :gaussian, distinct? true}})

                                                        One sample Kolmogorov-Smirnov test

                                                        -
                                                        view source

                                                        ks-test-two-samples

                                                        (ks-test-two-samples xs ys)(ks-test-two-samples xs ys {:keys [sides distinct?], :or {sides :two-sided, distinct? true}})

                                                        Two samples Kolmogorov-Smirnov test

                                                        -
                                                        view source

                                                        kullback-leibler-divergence

                                                        (kullback-leibler-divergence [vs1 vs2])(kullback-leibler-divergence vs1 vs2)

                                                        Kullback-Leibler divergence of two sequences.

                                                        +
                                                        view source

                                                        ks-test-one-sample

                                                        (ks-test-one-sample xs)(ks-test-one-sample xs distribution-or-ys)(ks-test-one-sample xs distribution-or-ys {:keys [sides kernel bandwidth distinct?], :or {sides :two-sided, kernel :gaussian, distinct? true}})

                                                        One sample Kolmogorov-Smirnov test

                                                        +
                                                        view source

                                                        ks-test-two-samples

                                                        (ks-test-two-samples xs ys)(ks-test-two-samples xs ys {:keys [sides distinct?], :or {sides :two-sided, distinct? true}})

                                                        Two samples Kolmogorov-Smirnov test

                                                        +
                                                        view source

                                                        kullback-leibler-divergence

                                                        (kullback-leibler-divergence [vs1 vs2])(kullback-leibler-divergence vs1 vs2)

                                                        Kullback-Leibler divergence of two sequences.

                                                        Examples

                                                        Kullback-Leibler divergence.

                                                        (kullback-leibler-divergence (repeatedly 100 (fn* [] (r/irand 100)))
                              (repeatedly 100 (fn* [] (r/irand 100))))
@@ -633,7 +633,7 @@ 
                                                        Descriptiv
                                                        view source

                                                        L1

                                                        (L1 [vs1 vs2-or-val])(L1 vs1 vs2-or-val)

                                                        Manhattan distance

                                                        view source

                                                        L2

                                                        (L2 [vs1 vs2-or-val])(L2 vs1 vs2-or-val)

                                                        Euclidean distance

                                                        view source

                                                        L2sq

                                                        (L2sq [vs1 vs2-or-val])(L2sq vs1 vs2-or-val)

                                                        Squared euclidean distance

                                                        -
                                                        view source

                                                        levene-test

                                                        (levene-test xss)(levene-test xss {:keys [sides statistic scorediff], :or {sides :one-sided-greater, statistic mean, scorediff abs}})
                                                        view source

                                                        LInf

                                                        (LInf [vs1 vs2-or-val])(LInf vs1 vs2-or-val)

                                                        Chebyshev distance

                                                        +
                                                        view source

                                                        levene-test

                                                        (levene-test xss)(levene-test xss {:keys [sides statistic scorediff], :or {sides :one-sided-greater, statistic mean, scorediff abs}})
                                                        view source

                                                        LInf

                                                        (LInf [vs1 vs2-or-val])(LInf vs1 vs2-or-val)

                                                        Chebyshev distance

                                                        view source

                                                        mad-extent

                                                        (mad-extent vs)

                                                        -/+ median-absolute-deviation and median

                                                        Examples

                                                        median absolute deviation from median for gaussian distribution

                                                        @@ -665,7 +665,7 @@
                                                        Descriptiv ;;=> 3.0
                                                        view source

                                                        minimum

                                                        (minimum vs)

                                                        Minimum value from sequence.

                                                        Examples

                                                        Minimum value

                                                        (minimum [1 2 3 -1 -1 2 -1 11 111])
-;;=> -1.0
                                                        view source

                                                        minimum-discrimination-information-test

                                                        (minimum-discrimination-information-test contingency-table-or-xs)(minimum-discrimination-information-test contingency-table-or-xs params)
                                                        view source

                                                        mode

                                                        (mode vs method)(mode vs method opts)(mode vs)

                                                        Find the value that appears most often in a dataset vs.

                                                        +;;=> -1.0
                                                        view source

                                                        minimum-discrimination-information-test

                                                        (minimum-discrimination-information-test contingency-table-or-xs)(minimum-discrimination-information-test contingency-table-or-xs params)
                                                        view source

                                                        mode

                                                        (mode vs method)(mode vs method opts)(mode vs)

                                                        Find the value that appears most often in a dataset vs.

                                                        For sample from continuous distribution, three algorithms are possible: * :histogram - calculated from histogram * :kde - calculated from KDE * :pearson - mode = mean-3(median-mean) * :default - discrete mode

                                                        Histogram accepts optional :bins (see histogram). KDE method accepts :kde for kernel name (default :gaussian) and :bandwidth (auto). Pearson can accept :estimation-strategy for median.

                                                        See also modes.

                                                        @@ -707,12 +707,12 @@
                                                        Descriptiv ;;=> 666.2 (moment [3 7 5 9 -8] 0.5 {:absolute? true}) ;;=> 1.8986344545712772
                                                        view source

                                                        mse

                                                        (mse [vs1 vs2-or-val])(mse vs1 vs2-or-val)

                                                        Mean squared error

                                                        -
                                                        view source

                                                        multinomial-likelihood-ratio-test

                                                        (multinomial-likelihood-ratio-test contingency-table-or-xs)(multinomial-likelihood-ratio-test contingency-table-or-xs params)
                                                        view source

                                                        neyman-modified-chisq-test

                                                        (neyman-modified-chisq-test contingency-table-or-xs)(neyman-modified-chisq-test contingency-table-or-xs params)
                                                        view source

                                                        omega-sq

                                                        (omega-sq [group1 group2])(omega-sq group1 group2)

                                                        Adjusted R2

                                                        +
                                                        view source

                                                        multinomial-likelihood-ratio-test

                                                        (multinomial-likelihood-ratio-test contingency-table-or-xs)(multinomial-likelihood-ratio-test contingency-table-or-xs params)
                                                        view source

                                                        neyman-modified-chisq-test

                                                        (neyman-modified-chisq-test contingency-table-or-xs)(neyman-modified-chisq-test contingency-table-or-xs params)
                                                        view source

                                                        omega-sq

                                                        (omega-sq [group1 group2])(omega-sq group1 group2)

                                                        Adjusted R2

                                                        Examples

                                                        Usage

                                                        (let [t [10 10 20 20 20 30 30 30 40 50]
       c [-50 20 30 40 40 50 10 20 30 10]]
   (omega-sq t c))
-;;=> -0.04795737122557726
                                                        view source

                                                        one-way-anova-test

                                                        (one-way-anova-test xss)(one-way-anova-test xss {:keys [sides], :or {sides :one-sided-greater}})
                                                        view source

                                                        outer-fence-extent

                                                        (outer-fence-extent vs)(outer-fence-extent vs estimation-strategy)

                                                        Returns LOF, UOF and median

                                                        +;;=> -0.04795737122557726
                                                        view source

                                                        one-way-anova-test

                                                        (one-way-anova-test xss)(one-way-anova-test xss {:keys [sides], :or {sides :one-sided-greater}})
                                                        view source

                                                        outer-fence-extent

                                                        (outer-fence-extent vs)(outer-fence-extent vs estimation-strategy)

                                                        Returns LOF, UOF and median

                                                        view source

                                                        outliers

                                                        (outliers vs)(outliers vs estimation-strategy)(outliers vs q1 q3)

                                                        Find outliers defined as values outside inner fences.

                                                        Let Q1 is 25-percentile and Q3 is 75-percentile. IQR is (- Q3 Q1).

                                                          @@ -727,23 +727,23 @@
                                                          Descriptiv 
                                                          (count (outliers (repeatedly 3000000 r/grand)))
 ;;=> 20911
                                                        view source

                                                        p-overlap

                                                        (p-overlap [group1 group2])(p-overlap group1 group2)(p-overlap group1 group2 {:keys [kde bandwidth min-iterations steps], :or {kde :gaussian, min-iterations 3, steps 500}})

                                                        Overlapping index, kernel density approximation

                                                        view source

                                                        p-value

                                                        (p-value stat)(p-value distribution stat)(p-value distribution stat sides)

                                                        Calculate p-value for given distribution (default: N(0,1)), stat and sides (one of :two-sided, :one-sided-greater or :one-sided-less/:one-sided).

                                                        -
                                                        view source

                                                        pacf

                                                        (pacf data)(pacf data lags)

                                                        Caluclate pacf (partial autocorrelation function) for given number of lags.

                                                        +
                                                        view source

                                                        pacf

                                                        (pacf data)(pacf data lags)

                                                        Caluclate pacf (partial autocorrelation function) for given number of lags.

                                                        If lags is omitted function returns maximum possible number of lags.

                                                        pacf returns also lag 0 (which is 0.0).

                                                        See also acf, acf-ci, pacf-ci

                                                        Examples

                                                        Usage

                                                        (pacf (repeatedly 1000 r/grand) 10)
 ;;=> (0.0
-;;=>  -0.007493264913704035
-;;=>  0.0395094028897875
-;;=>  -0.02711968252716128
-;;=>  -8.127647576342595E-4
-;;=>  0.02318435307600106
-;;=>  -0.07492493089581811
-;;=>  -0.004158017214958471
+;;=>  -0.007493264913704033
+;;=>  0.03950940288978749
+;;=>  -0.027119682527161276
+;;=>  -8.127647576342593E-4
+;;=>  0.023184353076001057
+;;=>  -0.07492493089581809
+;;=>  -0.00415801721495847
 ;;=>  -0.029857518595778
-;;=>  -0.025366182150073035
-;;=>  0.02293649431732737)
+;;=>  -0.025366182150073028
+;;=>  0.02293649431732736)
 (pacf [1 2 3 4 5 4 3 2 1])
 ;;=> (0.0
 ;;=>  0.5396825396825397
@@ -753,15 +753,15 @@ 
                                                        Descriptiv
 ;;=>  0.17585056996358742
 ;;=>  -0.2652225487589841
 ;;=>  -0.17978918763554708
-;;=>  -0.10771973872263883)
                                                        view source

                                                        pacf-ci

                                                        (pacf-ci data)(pacf-ci data lags)(pacf-ci data lags alpha)

                                                        pacf with added confidence interval data.

                                                        +;;=> -0.10771973872263883)
                                                        view source

                                                        pacf-ci

                                                        (pacf-ci data)(pacf-ci data lags)(pacf-ci data lags alpha)

                                                        pacf with added confidence interval data.

                                                        Examples

                                                        Usage

                                                        (pacf-ci (repeatedly 1000 r/grand) 3)
 ;;=> {:ci 0.06197950323045615,
 ;;=>  :pacf
-;;=>  (0.0 -0.049307948814106516 -0.005276481462760805 -0.03643226574541987)}
+;;=>  (0.0 -0.04930794881410651 -0.005276481462760803 -0.03643226574541986)}
 (pacf-ci [1 2 3 4 5 4 3 2 1] 3)
 ;;=> {:ci 0.653321328180018,
-;;=>  :pacf (0.0 0.5396825396825397 -0.4299857803057234 -0.388084834596935)}
                                                        view source

                                                        pearson-correlation

                                                        (pearson-correlation [vs1 vs2])(pearson-correlation vs1 vs2)

                                                        Pearson’s correlation of two sequences.

                                                        +;;=> :pacf (0.0 0.5396825396825397 -0.4299857803057234 -0.388084834596935)}
                                                        view source

                                                        pearson-correlation

                                                        (pearson-correlation [vs1 vs2])(pearson-correlation vs1 vs2)

                                                        Pearson’s correlation of two sequences.

                                                        Examples

                                                        Pearson’s correlation of uniform and gaussian distribution samples.

                                                        (pearson-correlation (repeatedly 100000 (partial r/grand 1.0 10.0))
                      (repeatedly 100000 (partial r/drand -10.0 -5.0)))
@@ -812,7 +812,7 @@ 
                                                        Descriptiv
 (percentile-bc-extent (repeatedly 100000 r/grand) 10)
 ;;=> [-1.2644568505959903 1.2992608668913583 0.006974183450094526]
 (percentile-bc-extent (repeatedly 100000 r/grand) 30 70)
-;;=> [-0.5390348516759447 0.5110256349062376 7.918286580104579E-4]
                                                        view source

                                                        percentile-bca-extent

                                                        (percentile-bca-extent vs)(percentile-bca-extent vs p)(percentile-bca-extent vs p1 p2)(percentile-bca-extent vs p1 p2 estimation-strategy)(percentile-bca-extent vs p1 p2 accel estimation-strategy)

                                                        Return bias corrected percentile range and mean for bootstrap samples. Also accounts for variance variations throught the accelaration parameter. See https://projecteuclid.org/euclid.ss/1032280214

                                                        +;;=> [-0.5390348516759447 0.5110256349062376 7.918286580104579E-4]
                                                        view source

                                                        percentile-bca-extent

                                                        (percentile-bca-extent vs)(percentile-bca-extent vs p)(percentile-bca-extent vs p1 p2)(percentile-bca-extent vs p1 p2 estimation-strategy)(percentile-bca-extent vs p1 p2 accel estimation-strategy)

                                                        Return bias corrected percentile range and mean for bootstrap samples. Also accounts for variance variations throught the accelaration parameter. See https://projecteuclid.org/euclid.ss/1032280214

                                                        p - calculates extent of bias corrected p and 100-p (default: p=2.5)

                                                        Set estimation-strategy to :r7 to get the same result as in R coxed::bca.

                                                        Examples

                                                        for samples from gaussian distribution

                                                        @@ -821,7 +821,7 @@
                                                        Descriptiv (percentile-bca-extent (repeatedly 100000 r/grand) 10) ;;=> [-1.2666928768037038 1.2838206326649084 0.0011417437187627867] (percentile-bca-extent (repeatedly 100000 r/grand) 30 70) -;;=> [-0.5316035303243614 0.5241767534807082 0.001668106379069707]
                                                        view source

                                                        percentile-extent

                                                        (percentile-extent vs)(percentile-extent vs p)(percentile-extent vs p1 p2)(percentile-extent vs p1 p2 estimation-strategy)

                                                        Return percentile range and median.

                                                        +;;=> [-0.5316035303243614 0.5241767534807082 0.001668106379069707]
                                                        view source

                                                        percentile-extent

                                                        (percentile-extent vs)(percentile-extent vs p)(percentile-extent vs p1 p2)(percentile-extent vs p1 p2 estimation-strategy)

                                                        Return percentile range and median.

                                                        p - calculates extent of p and 100-p (default: p=25)

                                                        Examples

                                                        for samples from gaussian distribution

                                                        (percentile-extent (repeatedly 100000 r/grand))
@@ -851,7 +851,7 @@ 
                                                        Descriptiv
 
                                                        See variance.

                                                        Examples

                                                        Population variance

                                                        (population-variance [1 2 3 -1 -1 2 -1 11 111])
-;;=> 1185.6543209876543
                                                        view source

                                                        power-divergence-test

                                                        (power-divergence-test contingency-table-or-xs)(power-divergence-test contingency-table-or-xs {:keys [lambda ci-sides sides p alpha bootstrap-samples ddof], :or {lambda m/TWO_THIRD, sides :one-sided-greater, ci-sides :two-sided, alpha 0.05, bootstrap-samples 1000, ddof 0}})
                                                        view source

                                                        powmean

                                                        (powmean vs power)

                                                        Generalized power mean

                                                        +;;=> 1185.6543209876543
                                                        view source

                                                        power-divergence-test

                                                        (power-divergence-test contingency-table-or-xs)(power-divergence-test contingency-table-or-xs {:keys [lambda ci-sides sides p alpha bootstrap-samples ddof], :or {lambda m/TWO_THIRD, sides :one-sided-greater, ci-sides :two-sided, alpha 0.05, bootstrap-samples 1000, ddof 0}})
                                                        view source

                                                        powmean

                                                        (powmean vs power)

                                                        Generalized power mean

                                                        Examples

                                                        Power mean

                                                        (powmean [1 2 3 1 1 2 1 11 111] 0.0)
 ;;=> 2.903203203730772
@@ -1011,7 +1011,7 @@ 
                                                        Descriptiv
 
                                                      • sides - one of: :two-sided, :one-sided-less (short: :one-sided) or :one-sided-greater
                                                        • 
 
                                                      • mu - mean (default: 0.0)
                                                        • 
 
-
                                                        view source

                                                        t-test-two-samples

                                                        (t-test-two-samples xs ys)(t-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

                                                        Two samples Student’s t-test

                                                        +
                                                        view source

                                                        t-test-two-samples

                                                        (t-test-two-samples xs ys)(t-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

                                                        Two samples Student’s t-test

                                                        • alpha - significance level (default: 0.05)
                                                        • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
                                                          • @@ -1019,7 +1019,7 @@
                                                          Descriptiv
                                                        • paired? - unpaired or paired test, boolean (default: false)
                                                        • equal-variances? - unequal or equal variances, boolean (default: false)
                                                        -
                                                        view source

                                                        trim

                                                        (trim vs)(trim vs quantile)(trim vs quantile estimation-strategy)(trim vs low high nan)

                                                        Return trimmed data. Trim is done by using quantiles, by default is set to 0.2.

                                                        +
                                                        view source

                                                        trim

                                                        (trim vs)(trim vs quantile)(trim vs quantile estimation-strategy)(trim vs low high nan)

                                                        Return trimmed data. Trim is done by using quantiles, by default is set to 0.2.

                                                        view source

                                                        tschuprows-t

                                                        (tschuprows-t group1 group2)(tschuprows-t contingency-table)

                                                        Tschuprows T effect size for discrete data

                                                        Examples

                                                        Usage

                                                        (let [a [:a :a :b :b :f :a :a :b :b :c :a :a :b :b :c :a :a :b :b :c]
@@ -1077,7 +1077,7 @@ 
                                                        Descriptiv
 ;;=>  :stat 0.5222329678670935,
 ;;=>  :stderr 0.9574271077563381,
 ;;=>  :t 0.5222329678670935,
-;;=>  :test-type :two-sided}
                                                        view source

                                                        ttest-two-samples

                                                        deprecated in Use [[t-test-two-samples]]

                                                        Examples

                                                        Usage

                                                        +;;=> :test-type :two-sided}
                                                        view source

                                                        ttest-two-samples

                                                        deprecated in Use [[t-test-two-samples]]

                                                        Examples

                                                        Usage

                                                        (ttest-two-samples [1 2 3 4 5 6 7 8 9 10]
                    [7 8 9 10 11 12 13 14 15 16 17 18 19 20])
 ;;=> {:alpha 0.05,
@@ -1154,7 +1154,7 @@ 
                                                        Descriptiv
 ;;=>  :stat -3.156496045715208,
 ;;=>  :stderr 31.680698645494967,
 ;;=>  :t -3.156496045715208,
-;;=>  :test-type :two-sided}
                                                        view source

                                                        variance

                                                        (variance vs)(variance vs u)

                                                        Calculate variance of vs.

                                                        +;;=> :test-type :two-sided}
                                                        view source

                                                        variance

                                                        (variance vs)(variance vs u)

                                                        Calculate variance of vs.

                                                        See population-variance.

                                                        Examples

                                                        Variance.

                                                        (variance [1 2 3 -1 -1 2 -1 11 111])
@@ -1178,7 +1178,7 @@ 
                                                        Descriptiv
 
                                                      • sides - one of: :two-sided, :one-sided-less (short: :one-sided) or :one-sided-greater
                                                        • 
 
                                                      • mu - mean (default: 0.0)
                                                        • 
 
-
                                                        view source

                                                        z-test-two-samples

                                                        (z-test-two-samples xs ys)(z-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

                                                        Two samples z-test

                                                        +
                                                        view source

                                                        z-test-two-samples

                                                        (z-test-two-samples xs ys)(z-test-two-samples xs ys {:keys [paired? equal-variances?], :or {paired? false, equal-variances? false}, :as params})

                                                        Two samples z-test

                                                        • alpha - significance level (default: 0.05)
                                                        • sides - one of: :two-sided (default), :one-sided-less (short: :one-sided) or :one-sided-greater
                                                          • @@ -1186,4 +1186,4 @@
                                                          Descriptiv
                                                        • paired? - unpaired or paired test, boolean (default: false)
                                                        • equal-variances? - unequal or equal variances, boolean (default: false)
                                                        -
                                                        view source
                                                        \ No newline at end of file +
                                                        view source
                                                        \ No newline at end of file diff --git a/docs/fastmath.transform.html b/docs/fastmath.transform.html index c644c691..0c48adb9 100644 --- a/docs/fastmath.transform.html +++ b/docs/fastmath.transform.html @@ -1,6 +1,6 @@ -fastmath.transform documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.transform

                                                        Transforms.

                                                        +fastmath.transform documentation

                                                        Project

                                                        Namespaces

                                                        Public Vars

                                                        fastmath.transform

                                                        Transforms.

                                                        See transformer and TransformProto for details.

                                                        Wavelet

                                                        Based on JWave library.

                                                        @@ -116,7 +116,7 @@

                                                        Fourier

                                                        Examples

                                                        Usage

                                                        (transformer :packet :discrete-mayer)
-;;=> jwave.transforms.WaveletPacketTransform@5de80493
                                                        view source

                                                        wavelets-list

                                                        List of all possible wavelets.

                                                        +;;=> jwave.transforms.WaveletPacketTransform@7b42883
                                                        view source

                                                        wavelets-list

                                                        List of all possible wavelets.

                                                        Examples

                                                        List of wavelets

                                                        (sort wavelets-list)
 ;;=> (:battle-23
diff --git a/docs/fastmath.vector.html b/docs/fastmath.vector.html
index fe30142f..80fdd0fc 100644
--- a/docs/fastmath.vector.html
+++ b/docs/fastmath.vector.html
@@ -1,6 +1,6 @@
 
-fastmath.vector documentation
                                                        Project
                                                        Namespaces
                                                        Public Vars
                                                        fastmath.vector
                                                        Mathematical vector operations.
                                                        
+fastmath.vector documentation
                                                        Project
                                                        Namespaces
                                                        Public Vars
                                                        fastmath.vector
                                                        Mathematical vector operations.
                                                        
 
                                                        Types
                                                        
 
                                                          
 
                                                        • Fixed size (custom types):
@@ -41,29 +41,30 @@ 
                                                          Types
                                                          
 
                                                        • IReduce and IReduceInit
                                                          • 
 
                                                        
 
                                                        That means that vectors can be destructured, treated as sequence or called as a function. See vec2 for examples.
                                                        
-
                                                        Categories
                                                          Other vars: ->ArrayVec ->Vec2 ->Vec3 ->Vec4 abs acos acosh acot acoth acsc add aligned? angle-between applyf approx array->vec2 array->vec3 array->vec4 array-vec as-vec asec asech asin asinh atan atanh average average-vectors axis-rotate base-from cbrt ceil clamp cos cosh cot coth cross csc csch degrees dhash-code dist dist-abs dist-ang dist-canberra dist-cheb dist-discrete dist-emd dist-sq distances div dot econstrain ediv einterpolate emn emult emx exp expm1 faceforward floor fmap frac from-polar generate-vec2 generate-vec3 generate-vec4 heading interpolate is-near-zero? is-zero? jinc limit ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmeanexp logmxp1 logsoftmax logsumexp mag magsq make-vector maxdim mindim mn mult mx nonzero-count normalize permute perpendicular project radians reciprocal relative-angle-between rint rotate round safe-sqrt sec sech seq->vec2 seq->vec3 seq->vec4 set-mag sfrac sgn shift sigmoid signum sim-cos sin sinc sinh softmax sq sqrt sub sum tan tanh to-polar to-vec transform triple-product trunc vec->RealVector vec->Vec vec2 vec3 vec4 xlogx zero-count
                                                          view source

                                                          acos

                                                          (acos vector)

                                                          Apply acos to vector elements.

                                                          Examples

                                                          Usage

                                                          (acos (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.0471975511965976 ##NaN ##NaN 1.5707963267948966]
                                                          view source

                                                          acosh

                                                          (acosh vector)

                                                          Apply acosh to vector elements.

                                                          +;;=> [1.0471975511965976 ##NaN ##NaN 1.5707963267948966]
                                                          view source

                                                          acosh

                                                          (acosh vector)

                                                          Apply acosh to vector elements.

                                                          Examples

                                                          Usage

                                                          (acosh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [##NaN ##NaN 1.37285914424258 ##NaN]
                                                          view source

                                                          acot

                                                          (acot vector)

                                                          Apply acot to vector elements.

                                                          +;;=> [##NaN ##NaN 1.37285914424258 ##NaN]
                                                          view source

                                                          acot

                                                          (acot vector)

                                                          Apply acot to vector elements.

                                                          Examples

                                                          Usage

                                                          (acot (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
 ;;=> [1.1071487177940904 2.5535900500422257 0.44441920990109884
-;;=>  1.5707963267948966]
                                                          view source

                                                          acoth

                                                          (acoth vector)

                                                          Apply acoth to vector elements.

                                                          +;;=> 1.5707963267948966]
                                                          view source

                                                          acoth

                                                          (acoth vector)

                                                          Apply acoth to vector elements.

                                                          Examples

                                                          Usage

                                                          (acoth (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [##NaN -0.8047189562170501 0.5180459658433878 ##NaN]
                                                          view source

                                                          acsc

                                                          (acsc vector)

                                                          Apply acsc to vector elements.

                                                          +;;=> [##NaN -0.8047189562170501 0.5180459658433878 ##NaN]
                                                          view source

                                                          acsc

                                                          (acsc vector)

                                                          Apply acsc to vector elements.

                                                          Examples

                                                          Usage

                                                          (acsc (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [##NaN -0.7297276562269663 0.49631736212546657 ##NaN]
                                                          view source

                                                          add

                                                          (add v)(add v1 v2)

                                                          Sum of two vectors.

                                                          +;;=> [##NaN -0.7297276562269663 0.49631736212546657 ##NaN]
                                                          view source

                                                          acsch

                                                          (acsch vector)

                                                          Apply acsch to vector elements.

                                                          +
                                                          view source

                                                          add

                                                          (add v)(add v1 v2)

                                                          Sum of two vectors.

                                                          Examples

                                                          Usage

                                                          (add (vec2 1 2) (vec2 -1 -2))
-;;=> [0.0 0.0]
                                                          view source

                                                          aligned?

                                                          (aligned? v1 v2 tol)(aligned? v1 v2)

                                                          Are vectors aligned (have the same direction)?

                                                          +;;=> [0.0 0.0]
                                                          view source

                                                          aligned?

                                                          (aligned? v1 v2 tol)(aligned? v1 v2)

                                                          Are vectors aligned (have the same direction)?

                                                          Examples

                                                          Usage

                                                          (aligned? (vec2 1.0 1.0) (vec2 2.0 2.000001))
 ;;=> true
@@ -72,31 +73,31 @@ 
                                                          Types
                                                          
 (aligned? (vec2 1.0 1.0) (vec2 2.0 2.00001) 0.001)
 ;;=> true
 
-;; Test: ok.
                                                          view source

                                                          angle-between

                                                          (angle-between v1 v2)

                                                          Angle between two vectors

                                                          +;; Test: ok.
                                                          view source

                                                          angle-between

                                                          (angle-between v1 v2)

                                                          Angle between two vectors

                                                          See also relative-angle-between.

                                                          Examples

                                                          Usage

                                                          (m/degrees (angle-between (vec3 1.0 0.0 0.0) (vec3 0.0 1.0 0.0)))
 ;;=> 90.0
 (m/degrees (angle-between (vec (repeatedly 50 rand))
                           (vec (repeatedly 50 rand))))
-;;=> 47.112737511777
                                                          view source

                                                          applyf

                                                          deprecated in v1.3.0

                                                          Same as fmap. Deprecated.

                                                          +;;=> 39.57994267909173
                                                          view source

                                                          applyf

                                                          deprecated in v1.3.0

                                                          Same as fmap. Deprecated.

                                                          Examples

                                                          Usage

                                                          (applyf [5 3] (fn [v] (m/sin v)))
-;;=> [-0.9589242746631386 0.1411200080598671]
                                                          view source

                                                          approx

                                                          (approx v)(approx v d)

                                                          Round to 2 (or d) decimal places

                                                          +;;=> [-0.9589242746631386 0.1411200080598671]
                                                          view source

                                                          approx

                                                          (approx v)(approx v d)

                                                          Round to 2 (or d) decimal places

                                                          Examples

                                                          Usage

                                                          (approx (vec2 (m/sin -1) (m/cos 1)))
 ;;=> [-0.84 0.54]
 (approx (vec2 (m/sin -1) (m/cos 1)) 6)
-;;=> [-0.841471 0.540302]
                                                          view source

                                                          array->vec2

                                                          (array->vec2 arr)

                                                          Doubles array to Vec2

                                                          +;;=> [-0.841471 0.540302]
                                                          view source

                                                          array->vec2

                                                          (array->vec2 arr)

                                                          Doubles array to Vec2

                                                          Examples

                                                          Usage

                                                          (array->vec2 (double-array [11 22 33 44 55]))
-;;=> [11.0 22.0]
                                                          view source

                                                          array->vec3

                                                          (array->vec3 arr)

                                                          Doubles array to Vec3

                                                          +;;=> [11.0 22.0]
                                                          view source

                                                          array->vec3

                                                          (array->vec3 arr)

                                                          Doubles array to Vec3

                                                          Examples

                                                          Usage

                                                          (array->vec3 (double-array [11 22 33 44 55]))
-;;=> [11.0 22.0 33.0]
                                                          view source

                                                          array->vec4

                                                          (array->vec4 arr)

                                                          Doubles array to Vec4

                                                          +;;=> [11.0 22.0 33.0]
                                                          view source

                                                          array->vec4

                                                          (array->vec4 arr)

                                                          Doubles array to Vec4

                                                          Examples

                                                          Usage

                                                          (array->vec4 (double-array [11 22 33 44 55]))
-;;=> [11.0 22.0 33.0 44.0]
                                                          view source

                                                          array-vec

                                                          (array-vec xs)

                                                          Make ArrayVec type based on provided sequence xs.

                                                          +;;=> [11.0 22.0 33.0 44.0]
                                                          view source

                                                          array-vec

                                                          (array-vec xs)

                                                          Make ArrayVec type based on provided sequence xs.

                                                          Examples

                                                          Usage

                                                          (array-vec [1 2 3 4 5 6 7])
 ;;=> [1.0 2.0 3.0 4.0 5.0 6.0 7.0]
@@ -109,7 +110,7 @@ 
                                                          Types
                                                          
 (count (array-vec (range 0.1 1.0 0.05)))
 ;;=> 18
 (seq (array-vec [1 2]))
-;;=> (1.0 2.0)
                                                          view source

                                                          as-vec

                                                          (as-vec v)(as-vec v xs)

                                                          Create vector from sequence as given type. If there is no sequence fill with 0.0.

                                                          +;;=> (1.0 2.0)
                                                          view source

                                                          as-vec

                                                          (as-vec v)(as-vec v xs)

                                                          Create vector from sequence as given type. If there is no sequence fill with 0.0.

                                                          Examples

                                                          Create vectors

                                                          (as-vec [1 2 3])
 ;;=> [0.0 0.0 0.0]
@@ -118,31 +119,31 @@ 
                                                          Types
                                                          
 (as-vec (vec3 1 2 3) (repeat -10))
 ;;=> [-10.0 -10.0 -10.0]
 (type (as-vec (array-vec [1 1 11 2 3]) (repeat -10)))
-;;=> class fastmath.vector.ArrayVec
                                                          view source

                                                          asec

                                                          (asec vector)

                                                          Apply asec to vector elements.

                                                          +;;=> class fastmath.vector.ArrayVec
                                                          view source

                                                          asec

                                                          (asec vector)

                                                          Apply asec to vector elements.

                                                          Examples

                                                          Usage

                                                          (asec (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [##NaN 2.300523983021863 1.07447896466943 ##NaN]
                                                          view source

                                                          asech

                                                          (asech vector)

                                                          Apply asech to vector elements.

                                                          +;;=> [##NaN 2.300523983021863 1.07447896466943 ##NaN]
                                                          view source

                                                          asech

                                                          (asech vector)

                                                          Apply asech to vector elements.

                                                          Examples

                                                          Usage

                                                          (asech (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.3169578969248166 ##NaN ##NaN ##Inf]
                                                          view source

                                                          asin

                                                          (asin vector)

                                                          Apply asin to vector elements.

                                                          +;;=> [1.3169578969248166 ##NaN ##NaN ##Inf]
                                                          view source

                                                          asin

                                                          (asin vector)

                                                          Apply asin to vector elements.

                                                          Examples

                                                          Usage

                                                          (asin (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5235987755982989 ##NaN ##NaN 0.0]
                                                          view source

                                                          asinh

                                                          (asinh vector)

                                                          Apply asinh to vector elements.

                                                          +;;=> [0.5235987755982989 ##NaN ##NaN 0.0]
                                                          view source

                                                          asinh

                                                          (asinh vector)

                                                          Apply asinh to vector elements.

                                                          Examples

                                                          Usage

                                                          (asinh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.48121182505960347 -1.1947632172871094 1.4874828366412711 0.0]
                                                          view source

                                                          atan

                                                          (atan vector)

                                                          Apply atan to vector elements.

                                                          +;;=> [0.48121182505960347 -1.1947632172871094 1.4874828366412711 0.0]
                                                          view source

                                                          atan

                                                          (atan vector)

                                                          Apply atan to vector elements.

                                                          Examples

                                                          Usage

                                                          (atan (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.4636476090008061 -0.9827937232473292 1.1263771168937977 0.0]
                                                          view source

                                                          atanh

                                                          (atanh vector)

                                                          Apply atanh to vector elements.

                                                          +;;=> [0.4636476090008061 -0.9827937232473292 1.1263771168937977 0.0]
                                                          view source

                                                          atanh

                                                          (atanh vector)

                                                          Apply atanh to vector elements.

                                                          Examples

                                                          Usage

                                                          (atanh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5493061443340548 ##NaN ##NaN 0.0]
                                                          view source

                                                          average

                                                          (average v)(average v weights)

                                                          Mean or weighted average of the vector

                                                          -
                                                          view source

                                                          average-vectors

                                                          (average-vectors init vs)(average-vectors vs)

                                                          Average / centroid of vectors. Input: initial vector (optional), list of vectors

                                                          +;;=> [0.5493061443340548 ##NaN ##NaN 0.0]
                                                          view source

                                                          average

                                                          (average v)(average v weights)

                                                          Mean or weighted average of the vector

                                                          +
                                                          view source

                                                          average-vectors

                                                          (average-vectors init vs)(average-vectors vs)

                                                          Average / centroid of vectors. Input: initial vector (optional), list of vectors

                                                          Examples

                                                          Usage

                                                          (average-vectors [[1 2] [0 1] [3 4] [1 2] [4 -1]])
 ;;=> [1.8 1.6]
 (average-vectors (vec2 0 0) [(vec2 1 1) (vec2 1 1) (vec2 1 1)])
-;;=> [0.75 0.75]
                                                          view source

                                                          axis-rotate

                                                          (axis-rotate v angle axis)(axis-rotate v angle axis pivot)

                                                          Rotate vector. Only for Vec3 types

                                                          +;;=> [0.75 0.75]
                                                          view source

                                                          axis-rotate

                                                          (axis-rotate v angle axis)(axis-rotate v angle axis pivot)

                                                          Rotate vector. Only for Vec3 types

                                                          Examples

                                                          Usage

                                                          (axis-rotate (vec3 1.0 0.0 0.0) m/HALF_PI (vec3 0.0 1.0 0.0))
 ;;=> [6.12323399538461E-17 0.0 -1.0]
@@ -150,110 +151,111 @@ 
                                                          Types
                                                          
              m/HALF_PI
              (vec3 0.0 1.0 0.0)
              (vec3 1.0 1.0 1.0))
-;;=> [0.0 0.0 0.9999999999999999]
                                                          view source

                                                          base-from

                                                          (base-from v)

                                                          List of perpendicular vectors (basis). Works only for Vec2 and Vec3 types.

                                                          +;;=> [0.0 0.0 0.9999999999999999]
                                                          view source

                                                          base-from

                                                          (base-from v)

                                                          List of perpendicular vectors (basis). Works only for Vec2 and Vec3 types.

                                                          Examples

                                                          Usage

                                                          (base-from (vec3 0.1 1.0 -1.0))
 ;;=> [[0.1 1.0 -1.0] [0.0 -0.7071067811865475 -0.7071067811865475]
 ;;=>  [-1.414213562373095 0.07071067811865475 -0.07071067811865475]]
 (base-from (vec2 1.0 0.0))
-;;=> [[1.0 0.0] [-0.0 1.0]]
                                                          view source

                                                          cbrt

                                                          (cbrt vector)

                                                          Apply cbrt to vector elements.

                                                          +;;=> [[1.0 0.0] [-0.0 1.0]]
                                                          view source

                                                          cb

                                                          (cb vector)

                                                          Apply cb to vector elements.

                                                          +
                                                          view source

                                                          cbrt

                                                          (cbrt vector)

                                                          Apply cbrt to vector elements.

                                                          Examples

                                                          Usage

                                                          (cbrt (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.7937005259840997 -1.1447142425533319 1.2805791649874945 0.0]
                                                          view source

                                                          ceil

                                                          (ceil vector)

                                                          Apply ceil to vector elements.

                                                          +;;=> [0.7937005259840997 -1.1447142425533319 1.2805791649874945 0.0]
                                                          view source

                                                          ceil

                                                          (ceil vector)

                                                          Apply ceil to vector elements.

                                                          Examples

                                                          Usage

                                                          (ceil (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.0 -1.0 3.0 0.0]
                                                          view source

                                                          clamp

                                                          (clamp v mn mx)(clamp v)

                                                          Clamp elements.

                                                          +;;=> [1.0 -1.0 3.0 0.0]
                                                          view source

                                                          clamp

                                                          (clamp v mn mx)(clamp v)

                                                          Clamp elements.

                                                          Examples

                                                          Clamp

                                                          (clamp [-1 -2 -3 1 2 3])
 ;;=> [0.0 0.0 0.0 1.0 2.0 3.0]
 (clamp [-1 -2 -3 1 2 3] -2.5 2.5)
-;;=> [-1.0 -2.0 -2.5 1.0 2.0 2.5]
                                                          view source

                                                          cos

                                                          (cos vector)

                                                          Apply cos to vector elements.

                                                          +;;=> [-1.0 -2.0 -2.5 1.0 2.0 2.5]
                                                          view source

                                                          cos

                                                          (cos vector)

                                                          Apply cos to vector elements.

                                                          Examples

                                                          Usage

                                                          (cos (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.8775825618903728 0.07073720166770284 -0.5048461045998573 1.0]
                                                          view source

                                                          cosh

                                                          (cosh vector)

                                                          Apply cosh to vector elements.

                                                          +;;=> [0.8775825618903728 0.07073720166770284 -0.5048461045998573 1.0]
                                                          view source

                                                          cosh

                                                          (cosh vector)

                                                          Apply cosh to vector elements.

                                                          Examples

                                                          Usage

                                                          (cosh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.1276259652063807 2.3524096152432477 4.1443131704103155 1.0]
                                                          view source

                                                          cot

                                                          (cot vector)

                                                          Apply cot to vector elements.

                                                          +;;=> [1.1276259652063807 2.3524096152432477 4.1443131704103155 1.0]
                                                          view source

                                                          cot

                                                          (cot vector)

                                                          Apply cot to vector elements.

                                                          Examples

                                                          Usage

                                                          (cot (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.8304877217124518 -0.0709148443026525 -0.5848478064594647
-;;=>  1.6331239354134602E16]
                                                          view source

                                                          coth

                                                          (coth vector)

                                                          Apply coth to vector elements.

                                                          +;;=> [1.830487721712452 -0.07091484430265245 -0.5848478064594645 ##Inf]
                                                          view source

                                                          coth

                                                          (coth vector)

                                                          Apply coth to vector elements.

                                                          Examples

                                                          Usage

                                                          (coth (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [2.163953413738653 -1.104791392982512 1.0304477349900076 ##Inf]
                                                          view source

                                                          cross

                                                          (cross v1 v2)

                                                          Cross product

                                                          +;;=> [2.163953413738653 -1.104791392982512 1.0304477349900076 ##Inf]
                                                          view source

                                                          cross

                                                          (cross v1 v2)

                                                          Cross product

                                                          Examples

                                                          Usage

                                                          (cross (vec3 1 2 3) (vec3 4 3 2))
 ;;=> [-5.0 10.0 -5.0]
 (cross (vec2 1 2) (vec2 -1 2))
-;;=> 4.0
                                                          view source

                                                          csc

                                                          (csc vector)

                                                          Apply csc to vector elements.

                                                          +;;=> 4.0
                                                          view source

                                                          csc

                                                          (csc vector)

                                                          Apply csc to vector elements.

                                                          Examples

                                                          Usage

                                                          (csc (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [2.0858296429334886 -1.0025113042467249 1.1584675035237058 ##Inf]
                                                          view source

                                                          csch

                                                          (csch vector)

                                                          Apply csch to vector elements.

                                                          +;;=> [2.0858296429334886 -1.0025113042467249 1.1584675035237058 ##Inf]
                                                          view source

                                                          csch

                                                          (csch vector)

                                                          Apply csch to vector elements.

                                                          Examples

                                                          Usage

                                                          (csch (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
 ;;=> [1.9190347513349437 -0.46964244059522453 0.24864137738123349 ##Inf]

                                                          Usage

                                                          (csch (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.9190347513349437 -0.46964244059522453 0.24864137738123349 ##Inf]
                                                          view source

                                                          degrees

                                                          (degrees vector)

                                                          Apply degrees to vector elements.

                                                          +;;=> [1.9190347513349437 -0.46964244059522453 0.24864137738123349 ##Inf]
                                                          view source

                                                          degrees

                                                          (degrees vector)

                                                          Apply degrees to vector elements.

                                                          Examples

                                                          Usage

                                                          (degrees (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [28.64788975654116 -85.94366926962348 120.32113697747289 0.0]
                                                          view source

                                                          dhash-code

                                                          (dhash-code state a)(dhash-code a)

                                                          double hashcode

                                                          -
                                                          view source

                                                          dist

                                                          (dist v1 v2)

                                                          Euclidean distance between vectors

                                                          +;;=> [28.64788975654116 -85.94366926962348 120.32113697747289 0.0]
                                                          view source

                                                          delta-eq

                                                          (delta-eq v1 v2 tol)(delta-eq v1 v2)

                                                          Equality with given toleance

                                                          +
                                                          view source

                                                          dhash-code

                                                          (dhash-code state a)(dhash-code a)

                                                          double hashcode

                                                          +
                                                          view source

                                                          dist

                                                          (dist v1 v2)

                                                          Euclidean distance between vectors

                                                          Examples

                                                          Usage

                                                          (dist (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 8.246211251235321
 (dist [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 5.477225575051661
                                                          view source

                                                          dist-abs

                                                          (dist-abs v1 v2)

                                                          Manhattan distance between vectors

                                                          +;;=> 5.477225575051661
                                                          view source

                                                          dist-abs

                                                          (dist-abs v1 v2)

                                                          Manhattan distance between vectors

                                                          Examples

                                                          Usage

                                                          (dist-abs (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 14.0
 (dist-abs [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 10.0
                                                          view source

                                                          dist-ang

                                                          (dist-ang v1 v2)

                                                          Angular distance

                                                          +;;=> 10.0
                                                          view source

                                                          dist-ang

                                                          (dist-ang v1 v2)

                                                          Angular distance

                                                          Examples

                                                          Usage

                                                          (dist-ang (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 0.7996068408289091
 (dist-ang [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 0.09160164480902667
                                                          view source

                                                          dist-canberra

                                                          (dist-canberra v1 v2)

                                                          Canberra distance

                                                          +;;=> 0.09160164480902667
                                                          view source

                                                          dist-canberra

                                                          (dist-canberra v1 v2)

                                                          Canberra distance

                                                          Examples

                                                          Usage

                                                          (dist-canberra (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 3.0
 (dist-canberra [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 1.4563492063492063
                                                          view source

                                                          dist-cheb

                                                          (dist-cheb v1 v2)

                                                          Chebyshev distance between 2d vectors

                                                          +;;=> 1.4563492063492063
                                                          view source

                                                          dist-cheb

                                                          (dist-cheb v1 v2)

                                                          Chebyshev distance between 2d vectors

                                                          Examples

                                                          Usage

                                                          (dist-cheb (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 6.0
 (dist-cheb [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 4.0
                                                          view source

                                                          dist-discrete

                                                          (dist-discrete v1 v2)

                                                          Discrete distance between 2d vectors

                                                          +;;=> 4.0
                                                          view source

                                                          dist-discrete

                                                          (dist-discrete v1 v2)

                                                          Discrete distance between 2d vectors

                                                          Examples

                                                          Usage

                                                          (dist-discrete (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 3.0
 (dist-discrete [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 4.0
                                                          view source

                                                          dist-emd

                                                          (dist-emd v1 v2)

                                                          Earth Mover’s Distance

                                                          +;;=> 4.0
                                                          view source

                                                          dist-emd

                                                          (dist-emd v1 v2)

                                                          Earth Mover’s Distance

                                                          Examples

                                                          Usage

                                                          (dist-emd (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 4.0
 (dist-emd [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 10.0
                                                          view source

                                                          dist-sq

                                                          (dist-sq v1 v2)

                                                          Squared Euclidean distance between vectors

                                                          +;;=> 10.0
                                                          view source

                                                          dist-sq

                                                          (dist-sq v1 v2)

                                                          Squared Euclidean distance between vectors

                                                          Examples

                                                          Usage

                                                          (dist-sq (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> 68.0
 (dist-sq [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 30.0
                                                          view source

                                                          distances

                                                          Examples

                                                          List of distances

                                                          +;;=> 30.0
                                                          view source

                                                          distances

                                                          Examples

                                                          List of distances

                                                          (sort (keys distances))
-;;=> (:abs :angular :canberra :cheb :discrete :emd :euclid :euclid-sq)
                                                          view source

                                                          div

                                                          (div v1 v)(div v1)

                                                          Vector division or reciprocal.

                                                          +;;=> (:abs :angular :canberra :cheb :discrete :emd :euclid :euclid-sq)
                                                          view source

                                                          div

                                                          (div v1 v)(div v1)

                                                          Vector division or reciprocal.

                                                          Examples

                                                          Usage

                                                          (div [5 4 3 5] 4.0)
 ;;=> [1.25 1.0 0.75 1.25]

                                                          Applied to vector is reciprocal

                                                          (div [1 2 4 -5])
-;;=> [1.0 0.5 0.25 -0.2]
                                                          view source

                                                          dot

                                                          (dot v1 v2)

                                                          Dot product of two vectors.

                                                          +;;=> [1.0 0.5 0.25 -0.2]
                                                          view source

                                                          dot

                                                          (dot v1 v2)

                                                          Dot product of two vectors.

                                                          Examples

                                                          Usage

                                                          (dot (vec4 1 0 0 0) (vec4 -1 0 -1 0))
-;;=> -1.0
                                                          view source

                                                          econstrain

                                                          (econstrain v mn mx)

                                                          Element-wise constrain

                                                          +;;=> -1.0
                                                          view source

                                                          econstrain

                                                          (econstrain v mn mx)

                                                          Element-wise constrain

                                                          Examples

                                                          Usage

                                                          (econstrain (vec3 2 0 -2) -1 1)
-;;=> [1.0 0.0 -1.0]
                                                          view source

                                                          ediv

                                                          (ediv v1 v2)

                                                          Element-wise division of two vectors.

                                                          +;;=> [1.0 0.0 -1.0]
                                                          view source

                                                          ediv

                                                          (ediv v1 v2)

                                                          Element-wise division of two vectors.

                                                          Examples

                                                          Usage

                                                          (ediv (vec2 1 3) (vec2 2 4))
-;;=> [0.5 0.75]
                                                          view source

                                                          einterpolate

                                                          (einterpolate v1 v2 v)(einterpolate v1 v2 v f)

                                                          Interpolate vector selement-wise, optionally set interpolation fn (default: lerp)

                                                          +;;=> [0.5 0.75]
                                                          view source

                                                          einterpolate

                                                          (einterpolate v1 v2 v)(einterpolate v1 v2 v f)

                                                          Interpolate vector selement-wise, optionally set interpolation fn (default: lerp)

                                                          Examples

                                                          Usage

                                                          (einterpolate (vec2 -1 -1) (vec2 1 1) (vec2 0.25 0.75))
 ;;=> [-0.5 0.5]
@@ -261,57 +263,57 @@ 
                                                          Types
                                                          
               (vec2 1 1)
               (vec2 0.25 0.75)
               m/smooth-interpolation)
-;;=> [-0.6875 0.6875]
                                                          view source

                                                          emn

                                                          (emn v1 v2)

                                                          Element-wise min from two vectors.

                                                          +;;=> [-0.6875 0.6875]
                                                          view source

                                                          emn

                                                          (emn v1 v2)

                                                          Element-wise min from two vectors.

                                                          Examples

                                                          Usage

                                                          (emn [-1 2] [1 -2])
-;;=> [-1.0 -2.0]
                                                          view source

                                                          emult

                                                          (emult v1 v2)

                                                          Element-wise vector multiplication (Hadamard product).

                                                          +;;=> [-1.0 -2.0]
                                                          view source

                                                          emult

                                                          (emult v1 v2)

                                                          Element-wise vector multiplication (Hadamard product).

                                                          Examples

                                                          Usage

                                                          (emult (vec3 1 2 3) (vec3 9 9 9))
-;;=> [9.0 18.0 27.0]
                                                          view source

                                                          emx

                                                          (emx v1 v2)

                                                          Element-wise max from two vectors.

                                                          +;;=> [9.0 18.0 27.0]
                                                          view source

                                                          emx

                                                          (emx v1 v2)

                                                          Element-wise max from two vectors.

                                                          Examples

                                                          Usage

                                                          (emx [-1 2] [1 -2])
-;;=> [1.0 2.0]
                                                          view source

                                                          exp

                                                          (exp vector)

                                                          Apply exp to vector elements.

                                                          +;;=> [1.0 2.0]
                                                          view source

                                                          exp

                                                          (exp vector)

                                                          Apply exp to vector elements.

                                                          Examples

                                                          Usage

                                                          (exp (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.6487212707001282 0.22313016014842985 8.16616991256765 1.0]
                                                          view source

                                                          expm1

                                                          (expm1 vector)

                                                          Apply expm1 to vector elements.

                                                          +;;=> [1.6487212707001282 0.22313016014842985 8.16616991256765 1.0]
                                                          view source

                                                          expm1

                                                          (expm1 vector)

                                                          Apply expm1 to vector elements.

                                                          Examples

                                                          Usage

                                                          (expm1 (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.6487212707001282 -0.7768698398515701 7.16616991256765 0.0]
                                                          view source

                                                          faceforward

                                                          (faceforward n v)

                                                          Flip normal n to match the same direction as v.

                                                          +;;=> [0.6487212707001282 -0.7768698398515701 7.16616991256765 0.0]
                                                          view source

                                                          faceforward

                                                          (faceforward n v)

                                                          Flip normal n to match the same direction as v.

                                                          Examples

                                                          Usage

                                                          (faceforward (vec2 1.0 1.0) (vec2 -1.0 -3.0))
 ;;=> [-1.0 -1.0]
 (faceforward (vec2 1.0 1.0) (vec2 1.0 0.0))
-;;=> [1.0 1.0]
                                                          view source

                                                          floor

                                                          (floor vector)

                                                          Apply floor to vector elements.

                                                          +;;=> [1.0 1.0]
                                                          view source

                                                          floor

                                                          (floor vector)

                                                          Apply floor to vector elements.

                                                          Examples

                                                          Usage

                                                          (floor (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.0 -2.0 2.0 0.0]
                                                          view source

                                                          fmap

                                                          (fmap v f)

                                                          Apply function to all vector values (like map but returns the same type).

                                                          +;;=> [0.0 -2.0 2.0 0.0]
                                                          view source

                                                          fmap

                                                          (fmap v f)

                                                          Apply function to all vector values (like map but returns the same type).

                                                          Examples

                                                          Usage

                                                          (fmap [5 3] (fn [v] (m/sin v)))
-;;=> [-0.9589242746631386 0.1411200080598671]
                                                          view source

                                                          frac

                                                          (frac vector)

                                                          Apply frac to vector elements.

                                                          +;;=> [-0.9589242746631386 0.1411200080598671]
                                                          view source

                                                          frac

                                                          (frac vector)

                                                          Apply frac to vector elements.

                                                          Examples

                                                          Usage

                                                          (frac (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5 0.5 0.10000000000000009 0.0]
                                                          view source

                                                          from-polar

                                                          (from-polar v)

                                                          From polar coordinates (2d, 3d only)

                                                          +;;=> [0.5 0.5 0.10000000000000009 0.0]
                                                          view source

                                                          from-polar

                                                          (from-polar v)

                                                          From polar coordinates (2d, 3d only)

                                                          Examples

                                                          Usage

                                                          (from-polar (vec2 1.0 (m/radians 90)))
 ;;=> [6.12323399538461E-17 1.0]
 (from-polar (vec3 1.0 (m/radians 90) (m/radians 45)))
-;;=> [0.7071067811865476 0.7071067811865475 6.12323399538461E-17]
                                                          view source

                                                          generate-vec2

                                                          (generate-vec2 f1 f2)(generate-vec2 f)

                                                          Generate Vec2 with fn(s)

                                                          +;;=> [0.7071067811865476 0.7071067811865475 6.12323399538461E-17]
                                                          view source

                                                          generate-vec2

                                                          (generate-vec2 f1 f2)(generate-vec2 f)

                                                          Generate Vec2 with fn(s)

                                                          Examples

                                                          Usage

                                                          (generate-vec2 (constantly 2))
 ;;=> [2.0 2.0]
 (generate-vec2 rand (constantly 1))
-;;=> [0.07256179097106774 1.0]
                                                          view source

                                                          generate-vec3

                                                          (generate-vec3 f1 f2 f3)(generate-vec3 f)

                                                          Generate Vec3 with fn(s)

                                                          +;;=> [0.47270573541960936 1.0]
                                                          view source

                                                          generate-vec3

                                                          (generate-vec3 f1 f2 f3)(generate-vec3 f)

                                                          Generate Vec3 with fn(s)

                                                          Examples

                                                          Usage

                                                          (generate-vec3 rand)
-;;=> [0.19411383068751242 0.5803200562037911 0.11123856448070413]
+;;=> [0.43355112657170225 0.7996146342199197 0.8638598435744879]
 (generate-vec3 rand (constantly 1) (constantly 2))
-;;=> [0.7239251956474805 1.0 2.0]
                                                          view source

                                                          generate-vec4

                                                          (generate-vec4 f1 f2 f3 f4)(generate-vec4 f)

                                                          Generate Vec4 with fn(s)

                                                          +;;=> [0.3323612928213867 1.0 2.0]
                                                          view source

                                                          generate-vec4

                                                          (generate-vec4 f1 f2 f3 f4)(generate-vec4 f)

                                                          Generate Vec4 with fn(s)

                                                          Examples

                                                          Usage

                                                          (generate-vec4 rand)
-;;=> [0.11832876704046924 0.8431673524156665 0.21740956001841527
-;;=>  0.5263302053065584]
+;;=> [0.18535306751065117 0.8663829122320332 0.40138340601374456
+;;=>  0.021421674191622775]
 (generate-vec4 rand rand (constantly 1) (constantly 2))
-;;=> [0.26170753019905457 0.6905634281232684 1.0 2.0]
                                                          view source

                                                          heading

                                                          (heading v)

                                                          Angle between vector and unit vector [1,0,...]

                                                          +;;=> [0.704209581038395 0.5095570085568898 1.0 2.0]
                                                          view source

                                                          heading

                                                          (heading v)

                                                          Angle between vector and unit vector [1,0,...]

                                                          Examples

                                                          Usage

                                                          (m/degrees (heading (vec2 1.0 1.0)))
 ;;=> 45.0
@@ -322,12 +324,12 @@ 
                                                          Types
                                                          
 (heading [1 2 3 4 5 6 7 8 9])
 ;;=> 1.5115267439240436
 (heading (array-vec [1 2 3 4 5 6 7 8 9]))
-;;=> 1.5115267439240436
                                                          view source

                                                          interpolate

                                                          (interpolate v1 v2 t)(interpolate v1 v2 t f)

                                                          Interpolate vectors, optionally set interpolation fn (default: lerp)

                                                          +;;=> 1.5115267439240436
                                                          view source

                                                          interpolate

                                                          (interpolate v1 v2 t)(interpolate v1 v2 t f)

                                                          Interpolate vectors, optionally set interpolation fn (default: lerp)

                                                          Examples

                                                          Usage

                                                          (interpolate (vec2 -1 -1) (vec2 1 1) 0.25)
 ;;=> [-0.5 -0.5]
 (interpolate (vec2 -1 -1) (vec2 1 1) 0.25 m/smooth-interpolation)
-;;=> [-0.6875 -0.6875]
                                                          view source

                                                          is-near-zero?

                                                          (is-near-zero? v)(is-near-zero? v tol)

                                                          Is vector almost zero? (all absolute values of elements are less than tol tolerance or 1.0e-6)

                                                          +;;=> [-0.6875 -0.6875]
                                                          view source

                                                          is-near-zero?

                                                          (is-near-zero? v)(is-near-zero? v tol)

                                                          Is vector almost zero? (all absolute values of elements are less than tol tolerance or 1.0e-6)

                                                          Examples

                                                          Usage

                                                          (is-near-zero? [0 1.0E-7])
 ;;=> true
@@ -336,50 +338,51 @@ 
                                                          Types
                                                          
 (is-near-zero? [0 1.0E-6] 1.0E-4)
 ;;=> true
 
-;; Test: ok.
                                                          view source

                                                          is-zero?

                                                          (is-zero? v)

                                                          Is vector zero?

                                                          +;; Test: ok.
                                                          view source

                                                          is-zero?

                                                          (is-zero? v)

                                                          Is vector zero?

                                                          Examples

                                                          Usage

                                                          (is-zero? [0 1.0E-7])
 ;;=> false
 (is-zero? [0 0.0])
-;;=> true
                                                          view source

                                                          jinc

                                                          (jinc vector)

                                                          Apply jinc to vector elements.

                                                          -
                                                          view source

                                                          limit

                                                          (limit v len)

                                                          Limit length of the vector by given value

                                                          +;;=> true
                                                          view source

                                                          jinc

                                                          (jinc vector)

                                                          Apply jinc to vector elements.

                                                          +
                                                          view source

                                                          lerp

                                                          (lerp v1 v2 t)

                                                          Linear interpolation of vectors

                                                          +
                                                          view source

                                                          limit

                                                          (limit v len)

                                                          Limit length of the vector by given value

                                                          Examples

                                                          Usage

                                                          (limit (vec3 1.0 1.0 1.0) 1.0)
 ;;=> [0.5773502691896258 0.5773502691896258 0.5773502691896258]
 (limit (vec3 1.0 1.0 1.0) 2.0)
-;;=> [1.0 1.0 1.0]
                                                          view source

                                                          ln

                                                          (ln vector)

                                                          Apply ln to vector elements.

                                                          +;;=> [1.0 1.0 1.0]
                                                          view source

                                                          ln

                                                          (ln vector)

                                                          Apply ln to vector elements.

                                                          Examples

                                                          Usage

                                                          (ln (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [-0.6931471805599453 ##NaN 0.7419373447293773 ##-Inf]
                                                          view source

                                                          log

                                                          (log vector)

                                                          Apply log to vector elements.

                                                          +;;=> [-0.6931471805599453 ##NaN 0.7419373447293773 ##-Inf]
                                                          view source

                                                          log

                                                          (log vector)

                                                          Apply log to vector elements.

                                                          Examples

                                                          Usage

                                                          (log (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [-0.6931471805599453 ##NaN 0.7419373447293773 ##-Inf]
                                                          view source

                                                          log10

                                                          (log10 vector)

                                                          Apply log10 to vector elements.

                                                          +;;=> [-0.6931471805599453 ##NaN 0.7419373447293773 ##-Inf]
                                                          view source

                                                          log10

                                                          (log10 vector)

                                                          Apply log10 to vector elements.

                                                          Examples

                                                          Usage

                                                          (log10 (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [-0.3010299956639812 ##NaN 0.3222192947339193 ##-Inf]
                                                          view source

                                                          log1mexp

                                                          (log1mexp vector)

                                                          Apply log1mexp to vector elements.

                                                          -
                                                          view source

                                                          log1p

                                                          (log1p vector)

                                                          Apply log1p to vector elements.

                                                          +;;=> [-0.3010299956639812 ##NaN 0.3222192947339193 ##-Inf]
                                                          view source

                                                          log1mexp

                                                          (log1mexp vector)

                                                          Apply log1mexp to vector elements.

                                                          +
                                                          view source

                                                          log1p

                                                          (log1p vector)

                                                          Apply log1p to vector elements.

                                                          Examples

                                                          Usage

                                                          (log1p (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.4054651081081644 ##NaN 1.1314021114911006 0.0]
                                                          view source

                                                          log1pexp

                                                          (log1pexp vector)

                                                          Apply log1pexp to vector elements.

                                                          -
                                                          view source

                                                          log1pmx

                                                          (log1pmx vector)

                                                          Apply log1pmx to vector elements.

                                                          -
                                                          view source

                                                          log1psq

                                                          (log1psq vector)

                                                          Apply log1psq to vector elements.

                                                          -
                                                          view source

                                                          log2

                                                          (log2 vector)

                                                          Apply log2 to vector elements.

                                                          +;;=> [0.4054651081081644 ##NaN 1.1314021114911006 0.0]
                                                          view source

                                                          log1pexp

                                                          (log1pexp vector)

                                                          Apply log1pexp to vector elements.

                                                          +
                                                          view source

                                                          log1pmx

                                                          (log1pmx vector)

                                                          Apply log1pmx to vector elements.

                                                          +
                                                          view source

                                                          log1psq

                                                          (log1psq vector)

                                                          Apply log1psq to vector elements.

                                                          +
                                                          view source

                                                          log2

                                                          (log2 vector)

                                                          Apply log2 to vector elements.

                                                          Examples

                                                          Usage

                                                          (log2 (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [-1.0 ##NaN 1.070389327891398 ##-Inf]
                                                          view source

                                                          logexpm1

                                                          (logexpm1 vector)

                                                          Apply logexpm1 to vector elements.

                                                          -
                                                          view source

                                                          logit

                                                          (logit vector)

                                                          Apply logit to vector elements.

                                                          -
                                                          view source

                                                          logmeanexp

                                                          (logmeanexp v)
                                                          view source

                                                          logmxp1

                                                          (logmxp1 vector)

                                                          Apply logmxp1 to vector elements.

                                                          -
                                                          view source

                                                          logsoftmax

                                                          (logsoftmax v)
                                                          view source

                                                          logsumexp

                                                          (logsumexp v)
                                                          view source

                                                          mag

                                                          (mag v)

                                                          Length of the vector.

                                                          +;;=> [-1.0 ##NaN 1.070389327891398 ##-Inf]
                                                          view source

                                                          logexpm1

                                                          (logexpm1 vector)

                                                          Apply logexpm1 to vector elements.

                                                          +
                                                          view source

                                                          logit

                                                          (logit vector)

                                                          Apply logit to vector elements.

                                                          +
                                                          view source

                                                          logmeanexp

                                                          (logmeanexp v)
                                                          view source

                                                          logmxp1

                                                          (logmxp1 vector)

                                                          Apply logmxp1 to vector elements.

                                                          +
                                                          view source

                                                          logsoftmax

                                                          (logsoftmax v)
                                                          view source

                                                          logsumexp

                                                          (logsumexp v)
                                                          view source

                                                          mag

                                                          (mag v)

                                                          Length of the vector.

                                                          Examples

                                                          Length of the vector

                                                          (mag (vec2 1 1))
 ;;=> 1.4142135623730951
 
-;; Test: ok.
                                                          view source

                                                          magsq

                                                          (magsq v)

                                                          Length of the vector squared.

                                                          +;; Test: ok.
                                                          view source

                                                          magsq

                                                          (magsq v)

                                                          Length of the vector squared.

                                                          Examples

                                                          Length of the vector, squared

                                                          (magsq [1 2 1 2])
 ;;=> 10.0
 
-;; Test: ok.
                                                          view source

                                                          make-vector

                                                          (make-vector dims xs)(make-vector dims)

                                                          Returns fixed size vector for given number of dimensions.

                                                          +;; Test: ok.
                                                          view source

                                                          make-vector

                                                          (make-vector dims xs)(make-vector dims)

                                                          Returns fixed size vector for given number of dimensions.

                                                          Proper type is used.

                                                          Examples

                                                          Usage

                                                          (make-vector 2)
@@ -399,51 +402,52 @@ 
                                                          Types
                                                          
 (make-vector 6 (cycle [1 2 3]))
 ;;=> [1.0 2.0 3.0 1.0 2.0 3.0]
 (type (make-vector 6))
-;;=> class fastmath.vector.ArrayVec
                                                          view source

                                                          maxdim

                                                          (maxdim v)

                                                          Index of maximum value.

                                                          +;;=> class fastmath.vector.ArrayVec
                                                          view source

                                                          maxdim

                                                          (maxdim v)

                                                          Index of maximum value.

                                                          Examples

                                                          Usage

                                                          (let [v (vec (repeatedly 100 (fn [] (- (int (rand-int 200)) 100))))
       mdim (maxdim v)]
   [mdim (v mdim)])
-;;=> [60 99]
+;;=> [80 99]
 (maxdim (vec3 1 2 3))
-;;=> 2
                                                          view source

                                                          mindim

                                                          (mindim v)

                                                          Index of minimum value.

                                                          +;;=> 2
                                                          view source

                                                          mindim

                                                          (mindim v)

                                                          Index of minimum value.

                                                          Examples

                                                          Usage

                                                          (let [v (vec (repeatedly 100 (fn [] (- (int (rand-int 200)) 100))))
       mdim (mindim v)]
   [mdim (v mdim)])
-;;=> [11 -99]
+;;=> [93 -100]
 (mindim (vec3 1 2 3))
-;;=> 0
                                                          view source

                                                          mn

                                                          (mn v)

                                                          Minimum value of vector elements

                                                          +;;=> 0
                                                          view source

                                                          mn

                                                          (mn v)

                                                          Minimum value of vector elements

                                                          Examples

                                                          Usage

                                                          (mn (vec4 -1 -2 3 4))
-;;=> -2.0
                                                          view source

                                                          mult

                                                          (mult v x)

                                                          Multiply vector by number x.

                                                          +;;=> -2.0
                                                          view source

                                                          mult

                                                          (mult v x)

                                                          Multiply vector by number x.

                                                          Examples

                                                          Usage

                                                          (mult (vec4 5 4 3 5) 4.0)
-;;=> [20.0 16.0 12.0 20.0]
                                                          view source

                                                          mx

                                                          (mx v)

                                                          Maximum value of vector elements

                                                          +;;=> [20.0 16.0 12.0 20.0]
                                                          view source

                                                          mx

                                                          (mx v)

                                                          Maximum value of vector elements

                                                          Examples

                                                          Usage

                                                          (mx (vec4 -1 -2 3 4))
-;;=> 4.0
                                                          view source

                                                          nonzero-count

                                                          (nonzero-count v)

                                                          Count non zero velues in vector

                                                          +;;=> 4.0
                                                          view source

                                                          nonzero-count

                                                          (nonzero-count v)

                                                          Count non zero velues in vector

                                                          Examples

                                                          Usage

                                                          (nonzero-count [1 2 3 -1 0 2 0 0])
-;;=> 5
                                                          view source

                                                          normalize

                                                          (normalize v)

                                                          Normalize vector (set length = 1.0)

                                                          +;;=> 5
                                                          view source

                                                          normalize

                                                          (normalize v)

                                                          Normalize vector (set length = 1.0)

                                                          Examples

                                                          Usage

                                                          (normalize (vec2 1.0 -1.0))
-;;=> [0.7071067811865475 -0.7071067811865475]
                                                          view source

                                                          permute

                                                          (permute v idxs)

                                                          Permute vector elements with given indices.

                                                          +;;=> [0.7071067811865475 -0.7071067811865475]
                                                          view source

                                                          permute

                                                          (permute v idxs)

                                                          Permute vector elements with given indices.

                                                          Examples

                                                          Usage

                                                          (permute (vec4 1 2 3 4) (vec4 0 3 2 1))
-;;=> [1.0 4.0 3.0 2.0]
                                                          view source

                                                          perpendicular

                                                          (perpendicular v)(perpendicular v1 v2)

                                                          Perpendicular vector. Only for Vec2 and Vec3 types.

                                                          +;;=> [1.0 4.0 3.0 2.0]
                                                          view source

                                                          perpendicular

                                                          (perpendicular v)(perpendicular v1 v2)

                                                          Perpendicular vector. Only for Vec2 and Vec3 types.

                                                          Examples

                                                          Usage

                                                          (perpendicular (vec2 -4 0))
 ;;=> [-0.0 -1.0]
 (perpendicular (vec3 1.0 0.0 0.0) (vec3 0.0 -1.0 0.0))
-;;=> [0.0 0.0 -1.0]
                                                          view source

                                                          project

                                                          (project v1 v2)

                                                          Project v1 onto v2

                                                          -
                                                          view source

                                                          radians

                                                          (radians vector)

                                                          Apply radians to vector elements.

                                                          +;;=> [0.0 0.0 -1.0]
                                                          view source

                                                          prod

                                                          (prod v)

                                                          Product of elements

                                                          +
                                                          view source

                                                          project

                                                          (project v1 v2)

                                                          Project v1 onto v2

                                                          +
                                                          view source

                                                          radians

                                                          (radians vector)

                                                          Apply radians to vector elements.

                                                          Examples

                                                          Usage

                                                          (radians (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.008726646259971648 -0.026179938779914945 0.03665191429188092 0.0]
                                                          view source

                                                          reciprocal

                                                          (reciprocal v)

                                                          Reciprocal of elements.

                                                          +;;=> [0.008726646259971648 -0.026179938779914945 0.03665191429188092 0.0]
                                                          view source

                                                          reciprocal

                                                          (reciprocal v)

                                                          Reciprocal of elements.

                                                          Examples

                                                          Usage

                                                          (reciprocal (vec3 1 2 5))
-;;=> [1.0 0.5 0.2]
                                                          view source

                                                          relative-angle-between

                                                          (relative-angle-between v1 v2)

                                                          Angle between two vectors relative to each other.

                                                          +;;=> [1.0 0.5 0.2]
                                                          view source

                                                          relative-angle-between

                                                          (relative-angle-between v1 v2)

                                                          Angle between two vectors relative to each other.

                                                          See also angle-between.

                                                          Examples

                                                          Usage

                                                          (m/degrees (relative-angle-between (vec3 1.0 0.0 0.0)
@@ -451,92 +455,92 @@ 
                                                          Types
                                                          
 ;;=> 90.0
 (m/degrees (relative-angle-between (vec (repeatedly 50 rand))
                                    (vec (repeatedly 50 rand))))
-;;=> 12.97021749559487
                                                          view source

                                                          rint

                                                          (rint vector)

                                                          Apply rint to vector elements.

                                                          +;;=> 7.038199609205948
                                                          view source

                                                          rint

                                                          (rint vector)

                                                          Apply rint to vector elements.

                                                          Examples

                                                          Usage

                                                          (rint (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.0 -2.0 2.0 0.0]
                                                          view source

                                                          rotate

                                                          (rotate v angle)(rotate v angle-x angle-y angle-z)

                                                          Rotate vector. Only for Vec2 and Vec3 types.

                                                          +;;=> [0.0 -2.0 2.0 0.0]
                                                          view source

                                                          rotate

                                                          (rotate v angle)(rotate v angle-x angle-y angle-z)

                                                          Rotate vector. Only for Vec2 and Vec3 types.

                                                          Examples

                                                          Usage

                                                          (rotate (vec2 1 2) (m/radians 90))
 ;;=> [-2.0 1.0000000000000002]
 (rotate (vec3 1 2 3) (m/radians 90) 0 0)
-;;=> [1.0 -3.0 2.0]
                                                          view source

                                                          round

                                                          (round vector)

                                                          Apply round to vector elements.

                                                          +;;=> [1.0 -3.0 2.0]
                                                          view source

                                                          round

                                                          (round vector)

                                                          Apply round to vector elements.

                                                          Examples

                                                          Usage

                                                          (round (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.0 -1.0 2.0 0.0]
                                                          view source

                                                          safe-sqrt

                                                          (safe-sqrt vector)

                                                          Apply safe-sqrt to vector elements.

                                                          +;;=> [1.0 -1.0 2.0 0.0]
                                                          view source

                                                          safe-sqrt

                                                          (safe-sqrt vector)

                                                          Apply safe-sqrt to vector elements.

                                                          Examples

                                                          Usage

                                                          (safe-sqrt (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.7071067811865476 0.0 1.449137674618944 0.0]
                                                          view source

                                                          sec

                                                          (sec vector)

                                                          Apply sec to vector elements.

                                                          +;;=> [0.7071067811865476 0.0 1.449137674618944 0.0]
                                                          view source

                                                          sec

                                                          (sec vector)

                                                          Apply sec to vector elements.

                                                          Examples

                                                          Usage

                                                          (sec (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.139493927324549 14.136832902969918 -1.9808016559672244 1.0]
                                                          view source

                                                          sech

                                                          (sech vector)

                                                          Apply sech to vector elements.

                                                          +;;=> [1.139493927324549 14.136832902969918 -1.9808016559672244 1.0]
                                                          view source

                                                          sech

                                                          (sech vector)

                                                          Apply sech to vector elements.

                                                          Examples

                                                          Usage

                                                          (sech (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.886818883970074 0.4250960349422804 0.2412945062018547 1.0]
                                                          view source

                                                          seq->vec2

                                                          (seq->vec2 xs)

                                                          Any seq to Vec2

                                                          +;;=> [0.886818883970074 0.4250960349422804 0.2412945062018547 1.0]
                                                          view source

                                                          seq->vec2

                                                          (seq->vec2 xs)

                                                          Any seq to Vec2

                                                          Examples

                                                          Usage

                                                          (seq->vec2 [11 22 33 44 55])
-;;=> [11.0 22.0]
                                                          view source

                                                          seq->vec3

                                                          (seq->vec3 xs)

                                                          Any seq to Vec3

                                                          +;;=> [11.0 22.0]
                                                          view source

                                                          seq->vec3

                                                          (seq->vec3 xs)

                                                          Any seq to Vec3

                                                          Examples

                                                          Usage

                                                          (seq->vec3 (lazy-seq (quote (1 2))))
-;;=> [1.0 2.0 0.0]
                                                          view source

                                                          seq->vec4

                                                          (seq->vec4 xs)

                                                          Any seq to Vec4

                                                          +;;=> [1.0 2.0 0.0]
                                                          view source

                                                          seq->vec4

                                                          (seq->vec4 xs)

                                                          Any seq to Vec4

                                                          Examples

                                                          Usage

                                                          (seq->vec4 (double-array [11 22 33 44 55]))
-;;=> [11.0 22.0 33.0 44.0]
                                                          view source

                                                          set-mag

                                                          (set-mag v len)

                                                          Set length of the vector

                                                          +;;=> [11.0 22.0 33.0 44.0]
                                                          view source

                                                          set-mag

                                                          (set-mag v len)

                                                          Set length of the vector

                                                          Examples

                                                          Usage

                                                          (set-mag (vec2 0.22 0.22) (m/sqrt 2.0))
 ;;=> [1.0000000000000002 1.0000000000000002]
 (set-mag (vec2 1.0 1.0) 0.0)
-;;=> [0.0 0.0]
                                                          view source

                                                          sfrac

                                                          (sfrac vector)

                                                          Apply sfrac to vector elements.

                                                          +;;=> [0.0 0.0]
                                                          view source

                                                          sfrac

                                                          (sfrac vector)

                                                          Apply sfrac to vector elements.

                                                          Examples

                                                          Usage

                                                          (sfrac (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5 -0.5 0.10000000000000009 0.0]
                                                          view source

                                                          sgn

                                                          (sgn vector)

                                                          Apply sgn to vector elements.

                                                          +;;=> [0.5 -0.5 0.10000000000000009 0.0]
                                                          view source

                                                          sgn

                                                          (sgn vector)

                                                          Apply sgn to vector elements.

                                                          Examples

                                                          Usage

                                                          (sgn (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.0 -1.0 1.0 1.0]
                                                          view source

                                                          shift

                                                          (shift v)(shift v x)

                                                          Add value to every vector element.

                                                          -
                                                          view source

                                                          sigmoid

                                                          (sigmoid vector)

                                                          Apply sigmoid to vector elements.

                                                          +;;=> [1.0 -1.0 1.0 1.0]
                                                          view source

                                                          shift

                                                          (shift v)(shift v x)

                                                          Add value to every vector element.

                                                          +
                                                          view source

                                                          sigmoid

                                                          (sigmoid vector)

                                                          Apply sigmoid to vector elements.

                                                          Examples

                                                          Usage

                                                          (sigmoid (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.6224593312018546 0.18242552380635632 0.8909031788043871 0.5]
                                                          view source

                                                          signum

                                                          (signum vector)

                                                          Apply signum to vector elements.

                                                          +;;=> [0.6224593312018546 0.18242552380635632 0.8909031788043871 0.5]
                                                          view source

                                                          signum

                                                          (signum vector)

                                                          Apply signum to vector elements.

                                                          Examples

                                                          Usage

                                                          (signum (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [1.0 -1.0 1.0 0.0]
                                                          view source

                                                          sim-cos

                                                          (sim-cos v1 v2)

                                                          Cosine similarity

                                                          +;;=> [1.0 -1.0 1.0 0.0]
                                                          view source

                                                          sim-cos

                                                          (sim-cos v1 v2)

                                                          Cosine similarity

                                                          Examples

                                                          Usage

                                                          (sim-cos (vec4 1.0 2.0 -1.0 -2.0) (vec4 1.0 -2.0 3.0 4.0))
 ;;=> -0.808290376865476
 (sim-cos [9 8 7 6 5 4 3 2 1] [9 8 7 6 5 5 5 5 5])
-;;=> 0.9588777312999299
                                                          view source

                                                          sin

                                                          (sin vector)

                                                          Apply sin to vector elements.

                                                          +;;=> 0.9588777312999299
                                                          view source

                                                          sin

                                                          (sin vector)

                                                          Apply sin to vector elements.

                                                          Examples

                                                          Usage

                                                          (sin (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.47942553860420295 -0.9974949866040544 0.8632093666488738 0.0]
                                                          view source

                                                          sinc

                                                          (sinc vector)

                                                          Apply sinc to vector elements.

                                                          +;;=> [0.47942553860420295 -0.9974949866040544 0.8632093666488738 0.0]
                                                          view source

                                                          sinc

                                                          (sinc vector)

                                                          Apply sinc to vector elements.

                                                          Examples

                                                          Usage

                                                          (sinc (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.6366197723675814 -0.2122065907891938 0.04683960205159357 1.0]
                                                          view source

                                                          sinh

                                                          (sinh vector)

                                                          Apply sinh to vector elements.

                                                          +;;=> [0.6366197723675814 -0.2122065907891938 0.04683960205159357 1.0]
                                                          view source

                                                          sinh

                                                          (sinh vector)

                                                          Apply sinh to vector elements.

                                                          Examples

                                                          Usage

                                                          (sinh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5210953054937474 -2.1292794550948178 4.021856742157334 0.0]
                                                          view source

                                                          softmax

                                                          (softmax v)
                                                          view source

                                                          sq

                                                          (sq vector)

                                                          Apply sq to vector elements.

                                                          +;;=> [0.5210953054937474 -2.1292794550948178 4.021856742157334 0.0]
                                                          view source

                                                          softmax

                                                          (softmax v)
                                                          view source

                                                          sq

                                                          (sq vector)

                                                          Apply sq to vector elements.

                                                          Examples

                                                          Usage

                                                          (sq (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.25 2.25 4.41 0.0]
                                                          view source

                                                          sqrt

                                                          (sqrt vector)

                                                          Apply sqrt to vector elements.

                                                          +;;=> [0.25 2.25 4.41 0.0]
                                                          view source

                                                          sqrt

                                                          (sqrt vector)

                                                          Apply sqrt to vector elements.

                                                          Examples

                                                          Usage

                                                          (sqrt (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.7071067811865476 ##NaN 1.449137674618944 0.0]
                                                          view source

                                                          sub

                                                          (sub v)(sub v1 v2)

                                                          Subtraction of two vectors.

                                                          +;;=> [0.7071067811865476 ##NaN 1.449137674618944 0.0]
                                                          view source

                                                          sub

                                                          (sub v)(sub v1 v2)

                                                          Subtraction of two vectors.

                                                          Examples

                                                          Usage

                                                          (sub (vec2 1 2) (vec2 -1 -2))
-;;=> [2.0 4.0]
                                                          view source

                                                          sum

                                                          (sum v)

                                                          Sum of elements

                                                          +;;=> [2.0 4.0]
                                                          view source

                                                          sum

                                                          (sum v)

                                                          Sum of elements

                                                          Examples

                                                          Usage

                                                          (sum (vec (range 1000)))
-;;=> 499500.0
                                                          view source

                                                          tan

                                                          (tan vector)

                                                          Apply tan to vector elements.

                                                          +;;=> 499500.0
                                                          view source

                                                          tan

                                                          (tan vector)

                                                          Apply tan to vector elements.

                                                          Examples

                                                          Usage

                                                          (tan (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.5463024898437905 -14.101419947171719 -1.7098465429045075 0.0]
                                                          view source

                                                          tanh

                                                          (tanh vector)

                                                          Apply tanh to vector elements.

                                                          +;;=> [0.5463024898437905 -14.101419947171719 -1.7098465429045075 0.0]
                                                          view source

                                                          tanh

                                                          (tanh vector)

                                                          Apply tanh to vector elements.

                                                          Examples

                                                          Usage

                                                          (tanh (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.46211715726000974 -0.9051482536448664 0.9704519366134539 0.0]
                                                          view source

                                                          to-polar

                                                          (to-polar v)

                                                          To polar coordinates (2d, 3d only), first element is length, the rest angle.

                                                          +;;=> [0.46211715726000974 -0.9051482536448664 0.9704519366134539 0.0]
                                                          view source

                                                          to-polar

                                                          (to-polar v)

                                                          To polar coordinates (2d, 3d only), first element is length, the rest angle.

                                                          Examples

                                                          Usage

                                                          (to-polar (vec2 1.0 1.0))
 ;;=> [1.4142135623730951 0.7853981633974483]
 (to-polar (vec3 1.0 0.0 1.0))
-;;=> [1.4142135623730951 0.7853981633974483 0.0]
                                                          view source

                                                          to-vec

                                                          deprecated in v1.5.0

                                                          Same as vec->Vec. Deprecated.

                                                          -
                                                          view source

                                                          transform

                                                          (transform v o vx vy)(transform v o vx vy vz)

                                                          Transform vector; map point to coordinate system defined by origin, vx and vy (as bases), Only for Vec2 and Vec3 types.

                                                          +;;=> [1.4142135623730951 0.7853981633974483 0.0]
                                                          view source

                                                          to-vec

                                                          deprecated in v1.5.0

                                                          Same as vec->Vec. Deprecated.

                                                          +
                                                          view source

                                                          transform

                                                          (transform v o vx vy)(transform v o vx vy vz)

                                                          Transform vector; map point to coordinate system defined by origin, vx and vy (as bases), Only for Vec2 and Vec3 types.

                                                          Examples

                                                          Usage

                                                          (transform (vec2 1 1) (vec2 -1 -1) (vec2 1.0 0.0) (vec2 0.0 1.0))
 ;;=> [0.0 0.0]
@@ -545,12 +549,12 @@ 
                                                          Types
                                                          
            (vec3 1.0 0.0 1.0)
            (vec3 0.0 1.0 0.0)
            (vec3 0.0 1.0 1.0))
-;;=> [0.0 1.0 2.0]
                                                          view source

                                                          triple-product

                                                          (triple-product a b c)

                                                          a o (b x c)

                                                          -
                                                          view source

                                                          trunc

                                                          (trunc vector)

                                                          Apply trunc to vector elements.

                                                          +;;=> [0.0 1.0 2.0]
                                                          view source

                                                          triple-product

                                                          (triple-product a b c)

                                                          a o (b x c)

                                                          +
                                                          view source

                                                          trunc

                                                          (trunc vector)

                                                          Apply trunc to vector elements.

                                                          Examples

                                                          Usage

                                                          (trunc (fastmath.vector/vec4 0.5 -1.5 2.1 0.0))
-;;=> [0.0 -1.0 2.0 0.0]
                                                          view source

                                                          vec->RealVector

                                                          (vec->RealVector v)

                                                          Convert to Apache Commons Math RealVector

                                                          -
                                                          view source

                                                          vec->Vec

                                                          (vec->Vec v)

                                                          Convert to Clojure primitive vector Vec.

                                                          +;;=> [0.0 -1.0 2.0 0.0]
                                                          view source

                                                          vec->RealVector

                                                          (vec->RealVector v)

                                                          Convert to Apache Commons Math RealVector

                                                          +
                                                          view source

                                                          vec->Vec

                                                          (vec->Vec v)

                                                          Convert to Clojure primitive vector Vec.

                                                          Examples

                                                          Check types

                                                          (type (vec->Vec [1 2 3]))
 ;;=> class clojure.core.Vec
@@ -561,7 +565,7 @@ 
                                                          Types
                                                          
 (type (vec->Vec (vec4 1 2 3 4)))
 ;;=> class clojure.core.Vec
 (type (vec->Vec (array-vec 1)))
-;;=> class clojure.core.Vec
                                                          view source

                                                          vec2

                                                          (vec2 x y)(vec2)

                                                          Make 2d vector.

                                                          +;;=> class clojure.core.Vec
                                                          view source

                                                          vec2

                                                          (vec2 x y)(vec2)

                                                          Make 2d vector.

                                                          Examples

                                                          Usage

                                                          (vec2 0.5 -0.5)
 ;;=> [0.5 -0.5]
@@ -571,7 +575,7 @@ 
                                                          Types
                                                          
 ;;=> 6.5

                                                          As function

                                                          [((vec2 11 22) 0) ((vec2 11 22) 1)]
 ;;=> [11.0 22.0]

                                                          As sequence

                                                          -
                                                          (map (fn* [p1__34355#] (* 2.0 p1__34355#)) (vec2 1 2))
+
                                                          (map (fn* [p1__34447#] (* 2.0 p1__34447#)) (vec2 1 2))
 ;;=> (2.0 4.0)
 (reduce clojure.core/+ (vec2 6 4))
 ;;=> 10.0
@@ -588,14 +592,14 @@ 
                                                          Types
                                                          
 (filter clojure.core/neg? (vec2 -1 2))
 ;;=> (-1.0)

                                                          Count

                                                          (count (vec2 4 3))
-;;=> 2
                                                          view source

                                                          vec3

                                                          (vec3 x y z)(vec3 v z)(vec3)

                                                          Make Vec2 vector

                                                          +;;=> 2
                                                          view source

                                                          vec3

                                                          (vec3 x y z)(vec3 v z)(vec3)

                                                          Make Vec2 vector

                                                          Examples

                                                          Usage

                                                          (vec3)
 ;;=> [0.0 0.0 0.0]
 (vec3 0.5 -0.5 1.0)
 ;;=> [0.5 -0.5 1.0]
 (let [v (vec2 1 2)] (vec3 v -1.0))
-;;=> [1.0 2.0 -1.0]
                                                          view source

                                                          vec4

                                                          (vec4 x y z w)(vec4 v w)(vec4 v z w)(vec4)

                                                          Make Vec4 vector

                                                          +;;=> [1.0 2.0 -1.0]
                                                          view source

                                                          vec4

                                                          (vec4 x y z w)(vec4 v w)(vec4 v z w)(vec4)

                                                          Make Vec4 vector

                                                          Examples

                                                          Usage

                                                          (vec4)
 ;;=> [0.0 0.0 0.0 0.0]
@@ -604,8 +608,8 @@ 
                                                          Types
                                                          
 (let [v (vec2 1 2)] (vec4 v -1.0 0.1))
 ;;=> [1.0 2.0 -1.0 0.1]
 (let [v (vec3 0 1 2)] (vec4 v 0.1))
-;;=> [0.0 1.0 2.0 0.1]
                                                          view source

                                                          xlogx

                                                          (xlogx vector)

                                                          Apply xlogx to vector elements.

                                                          -
                                                          view source

                                                          zero-count

                                                          (zero-count v)

                                                          Count zeros in vector

                                                          +;;=> [0.0 1.0 2.0 0.1]
                                                          view source

                                                          xlogx

                                                          (xlogx vector)

                                                          Apply xlogx to vector elements.

                                                          +
                                                          view source

                                                          zero-count

                                                          (zero-count v)

                                                          Count zeros in vector

                                                          Examples

                                                          Usage

                                                          (zero-count [1 2 3 -1 0 2 0 0])
-;;=> 3
                                                          view source
                                                          \ No newline at end of file +;;=> 3
                                                          view source
                                                          \ No newline at end of file diff --git a/docs/index.html b/docs/index.html index f6312bfa..da243e64 100644 --- a/docs/index.html +++ b/docs/index.html @@ -1,9 +1,9 @@ -Fastmath 2.2.1-SNAPSHOT

                                                          Project

                                                          Namespaces

                                                          Fastmath 2.2.1-SNAPSHOT

                                                          Released under the MIT Licence

                                                          Fast and primitive math library.

                                                          Installation

                                                          To install, add the following dependency to your project or build file:

                                                          [generateme/fastmath "2.2.1-SNAPSHOT"]

                                                          Namespaces

                                                          fastmath.clustering

                                                          Clustering.

                                                          +Fastmath 2.2.2-SNAPSHOT

                                                          Project

                                                          Namespaces

                                                          Fastmath 2.2.2-SNAPSHOT

                                                          Released under the MIT Licence

                                                          Fast and primitive math library.

                                                          Installation

                                                          To install, add the following dependency to your project or build file:

                                                          [generateme/fastmath "2.2.2-SNAPSHOT"]

                                                          Namespaces

                                                          fastmath.clustering

                                                          Clustering.

                                                          Categories

                                                            Other vars: ->ClusteringResult clarans clustering-methods-list dbscan denclue deterministic-annealing g-means k-means lloyd map->ClusteringResult mec predict regroup spectral x-means

                                                            fastmath.complex

                                                            Complex numbers functions.

                                                            -

                                                            Categories

                                                              Other vars: -I I I- ONE TWO ZERO abs acos acosech acosh acoth acsch add arg asech asin asinh atan atanh complex conjugate cos cosh coth csc csch div exp flip im log mult mult-I mult-I- neg pow re reciprocal scale sec sech sin sinh sq sqrt sqrt1z sub tan tanh

                                                              fastmath.core

                                                              Collection of fast math functions and plethora of constants known from other math libraries.

                                                              -

                                                              Categories

                                                                Other vars: * + - / < << <= == > >= >> >>> Ci I0 Si abs acos acosh acot acoth acovercos acoversin acrd acsc acsch aexcsc aexsec ahacovercos ahacoversin ahavercos ahaversin approx approx-eq approx= asec asech asin asinh atan atan2 atanh avercos aversin bessel-j between-? between? bit-and bit-and-not bit-clear bit-flip bit-not bit-or bit-set bit-shift-left bit-shift-right bit-test bit-xor bits->double bool-and bool-not bool-or bool-xor cb cbrt ceil cexpexp cloglog cnorm co-intervals combinations constrain copy-sign cos cos-interpolation cosh cot coth covercos coversin crd csc csch cut dec degrees delta-eq delta= difference-of-products digamma dist double-array->seq double-bits double-double-array->seq double-high-bits double-low-bits eq erf erfc evalpoly even? excsc exp expm1 exsec factorial factorial20 fast* fast+ fast- fast-identity fast-max fast-min floor fma fpow frac gamma gcd group-by-intervals hacovercos hacoversin havercos haversin haversine haversine-dist high-2-exp high-exp hypot hypot-sqrt iabs inc inf? inv-erf inv-erfc inv-gamma-1pm1 invalid-double? itrunc jinc lcm lerp ln log log-I0 log-beta log-combinations log-factorial log-gamma log-gamma-1p log10 log1mexp log1p log1pexp log1pmx log1psq log2 log2mexp logaddexp logb logcosh logexpm1 logistic logit logmxp1 logsubexp logsumexp low-2-exp low-exp make-norm makepoly max mevalpoly min minkowski mlerp mnorm mod muladd nan? neg-inf? neg? negmuladd next-double norm not-neg? not-pos? not== odd? one? order pos-inf? pos? pow pow2 pow3 prev-double qceil qcos qdist qexp qfloor qlog qpow qround qsin qsqrt quad-interpolation quot radians rank rank1 regularized-beta regularized-gamma-p regularized-gamma-q rem remainder rint round round-even round-up-pow2 rqsqrt safe-sqrt sample sec sech seq->double-array seq->double-double-array sfrac sgn sigmoid signum sin sinc sinh slice-range smooth-interpolation smoothstep sq sqrt sum-of-products tan tanh trigamma trunc unsigned-bit-shift-right unuse-primitive-operators use-primitive-operators valid-double? vercos versin wrap xexpx xexpy xlog1py xlogx xlogy zero?

                                                                fastmath.curves

                                                                Collection of parametric curves

                                                                +

                                                                Categories

                                                                  Other vars: -I I I- ONE TWO ZERO abs acos acosh acot acoth acsc acsch add arg asec asech asin asinh atan atanh complex conjugate cos cosh cot coth csc csch csgn delta-eq div exp flip im imaginary? inf? log logb mult mult-I mult-I- nan? neg norm pow re real? reciprocal scale sec sech sin sinh sq sqrt sqrt1z sub tan tanh zero?

                                                                  fastmath.core

                                                                  Collection of fast math functions and plethora of constants known from other math libraries.

                                                                  +

                                                                  Categories

                                                                    Other vars: * + - / < << <= == > >= >> >>> Ci I0 Si abs acos acosh acot acoth acovercos acoversin acrd acsc acsch aexcsc aexsec ahacovercos ahacoversin ahavercos ahaversin approx approx-eq approx= asec asech asin asinh atan atan2 atanh avercos aversin bessel-j between-? between? bit-and bit-and-not bit-clear bit-flip bit-not bit-or bit-set bit-shift-left bit-shift-right bit-test bit-xor bits->double bool-and bool-not bool-or bool-xor cb cbrt ceil cexpexp cloglog cnorm co-intervals combinations constrain copy-sign cos cos-interpolation cosh cot coth covercos coversin crd csc csch cut dec degrees delta-eq delta= difference-of-products digamma dist double-array->seq double-bits double-double-array->seq double-exponent double-high-bits double-low-bits double-significand eq erf erfc evalpoly even? excsc exp expm1 exsec factorial factorial20 fast* fast+ fast- fast-identity fast-max fast-min floor fma fpow frac gamma gcd group-by-intervals hacovercos hacoversin havercos haversin haversine haversine-dist high-2-exp high-exp hypot hypot-sqrt iabs inc inf? inv-erf inv-erfc inv-gamma-1pm1 invalid-double? itrunc jinc lcm lerp ln log log-I0 log-beta log-combinations log-factorial log-gamma log-gamma-1p log10 log1mexp log1p log1pexp log1pmx log1psq log2 log2int log2mexp logaddexp logb logcosh logexpm1 logistic logit logmxp1 logsubexp logsumexp low-2-exp low-exp make-norm makepoly max mevalpoly min minkowski mlerp mnorm mod muladd nan? neg-inf? neg? negative-zero? negmuladd next-double norm not-neg? not-pos? not== odd? one? order pos-inf? pos? pow pow2 pow3 prev-double qceil qcos qdist qexp qfloor qlog qpow qround qsin qsqrt quad-interpolation quot radians rank rank1 regularized-beta regularized-gamma-p regularized-gamma-q rem remainder rint round round-even round-up-pow2 rqsqrt safe-sqrt sample sec sech seq->double-array seq->double-double-array sfrac sgn sigmoid signum sin sinc sinh slice-range smooth-interpolation smoothstep sq sqrt sum-of-products tan tanh trigamma trunc ulp unsigned-bit-shift-right unuse-primitive-operators use-primitive-operators valid-double? vercos versin wrap xexpx xexpy xlog1py xlogx xlogy zero?

                                                                    fastmath.curves

                                                                    Collection of parametric curves

                                                                    Categories

                                                                      Other vars: add curve curves-list mult parametrization

                                                                      fastmath.distance

                                                                      Distance objects.

                                                                      Categories

                                                                        Other vars: angular canberra chebyshev correlation cosine discrete earth-movers euclidean euclidean-sq jensen-shannon make-mahalanobis make-minkowski manhattan

                                                                        fastmath.easings

                                                                        Easing functions.

                                                                        Categories

                                                                          Other vars: back-in back-in-out back-out bounce-in bounce-in-out bounce-out circle-in circle-in-out circle-out cubic-in cubic-in-out cubic-out easings-list elastic-in elastic-in-out elastic-out exp-in exp-in-out exp-out in-out linear out poly-in poly-in-out poly-out quad-in quad-in-out quad-out reflect sin-in sin-in-out sin-out

                                                                          fastmath.efloat

                                                                          (re)Implementation of EFloat/Interval from pbrt-v3/pbrt-v4.

                                                                          @@ -13,12 +13,12 @@

                                                                          Categories

                                                                            Other vars: cell->anchor cell->mid cell-names coords->anchor coords->cell coords->mid corners flat-hex-corners grid grid-type pointy-hex-corners

                                                                            fastmath.interpolation

                                                                            1d, 2d interpolation functions.

                                                                            Categories

                                                                              Other vars: akima-spline b-spline b-spline-interp bicubic bicubic-smile bilinear cubic-2d cubic-spline divided-difference interpolators-1d-list interpolators-2d-list kriging-spline linear linear-smile loess microsphere-2d-projection microsphere-projection monotone neville piecewise-bicubic polynomial rbf shepard spline step step-after step-before

                                                                              fastmath.kernel

                                                                              Various kernel functions.

                                                                              Categories

                                                                                Other vars: approx cauchy-density-kernel cosine-density-kernel cpd->pd epanechnikov-density-kernel exp fields gaussian-density-kernel kernel kernel->rbf kernel-density kernel-density-ci kernel-density-list kernels-list laplace-density-kernel logistic-density-kernel mult quartic-density-kernel rbf rbf->kernel rbf-list scale sigmoid-density-kernel silverman-density-kernel smile-mercer smile-rbf triangular-density-kernel tricube-density-kernel triweight-density-kernel uniform-density-kernel wadd wigner-density-kernel

                                                                                fastmath.matrix

                                                                                Fixed size (2x2, 3x3, 4x4) matrix types.

                                                                                -

                                                                                Categories

                                                                                  Other vars: ->Mat2x2 ->Mat3x3 ->Mat4x4 acos acosh acot acoth acsc add adds asec asech asin asinh atan atanh cbrt ceil col cols cols->mat2x2 cols->mat3x3 cols->mat4x4 cos cosh cot coth csc csch degrees det diag diagonal emulm exp expm1 eye floor fmap frac inverse jinc ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmxp1 mat->RealMatrix mat->array2d mat2x2 mat3x3 mat4x4 mulm mulmt muls mulv ncol negate nrow outer radians rint round row rows rows->mat2x2 rows->mat3x3 rows->mat4x4 safe-sqrt sec sech sfrac sgn sigmoid signum sin sinc sinh solve sq sqrt sub symmetric? tan tanh tmulm tmulmt trace transpose trunc vtmul xlogx zero

                                                                                  fastmath.optimization

                                                                                  Optimization.

                                                                                  -

                                                                                  Categories

                                                                                    Other vars: bayesian-optimization maximize maximizer minimize minimizer scan-and-maximize scan-and-minimize

                                                                                    fastmath.optimization.bo

                                                                                    Categories

                                                                                      Other vars: args args-cont categorical-drop categorical-keep continuous-append continuous-append-key continuous-restrict continuous-restrict-key example-data initialize-bo prepare-args target utility-function

                                                                                      fastmath.optimization.lbfgsb

                                                                                      Categories

                                                                                        Other vars: ->lbfgsb grad-function

                                                                                        fastmath.protocols

                                                                                        Set of protocols for fastmath.

                                                                                        -

                                                                                        Categories

                                                                                          Other vars: ->seq abs add approx as-vec axis-rotate base-from brandom cdf cell->anchor cell->mid continuous? coords->cell coords->mid corners covariance cross dimensions distribution-id distribution-parameters distribution? dot drandom econstrain einterpolate emn emult emx fmap forward-1d forward-2d frandom from-polar grandom grid-type heading icdf interpolate irandom is-near-zero? is-zero? lower-bound lpdf lrandom mag magsq maxdim mean means mindim mn mult mx pdf permute perpendicular probability reciprocal reverse-1d reverse-2d rotate sample set-seed set-seed! shift source-object sub sum to-acm-vec to-polar to-vec transform upper-bound variance

                                                                                          fastmath.protocols.matrix

                                                                                          Categories

                                                                                            Other vars: add adds cols column det diag emulm fmap inverse mulm muls mulv ncol nrow row rows sub symmetric? to-acm-mat to-array2d trace transpose vtmul

                                                                                            fastmath.random

                                                                                            Various random and noise functions.

                                                                                            -

                                                                                            Categories

                                                                                              Other vars: ->seq ball-random billow-noise brand brandom ccdf cdf continuous? covariance default-normal default-rng dimensions discrete-noise distribution distribution-id distribution-parameters distribution? distributions-list drand drandom fbm-noise flip flipb frand frandom grand grandom icdf integrate-pdf irand irandom jittered-sequence-generator likelihood log-likelihood lower-bound lpdf lrand lrandom mean means noise noise-generators noise-interpolations noise-types observe observe1 pdf probability random-noise-cfg random-noise-fn randval ridgedmulti-noise rng rngs-list sample sequence-generator sequence-generators-list set-seed set-seed! simplex single-noise source-object synced-rng upper-bound variance vnoise warp-noise-fn

                                                                                              fastmath.signal

                                                                                              Signal processing (effect) and generation (oscillators).

                                                                                              -

                                                                                              Categories

                                                                                                Other vars: ->BiquadConf ->EffectsList ->SampleAndState ->StateBassTreble ->StateBiquad ->StateDecimator ->StateDivider ->StateEcho ->StateFm ->StateMdaThruZero ->StateVcf303 apply-effects apply-effects-raw compose-effects db->linear effect effect-node effects-list kernel-smoothing-filter linear->db load-signal moving-average-filter oscillator oscillator->signal oscillator-gain oscillators oscillators-sum reset-effects save-signal savgol-filter signal->oscillator single-pass

                                                                                                fastmath.solver

                                                                                                Categories

                                                                                                  Other vars: find-root

                                                                                                  fastmath.stats

                                                                                                  Statistics functions.

                                                                                                  +

                                                                                                  Categories

                                                                                                    Other vars: ->Mat2x2 ->Mat3x3 ->Mat4x4 acos acosh acot acoth acsc acsch add adds asec asech asin asinh atan atanh cb cbrt ceil cholesky col cols cols->mat2x2 cols->mat3x3 cols->mat4x4 cos cosh cot coth csc csch degrees det diag diagonal emulm exp expm1 eye floor fmap frac inverse jinc ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmxp1 mat->RealMatrix mat->array mat->array2d mat->float-array mat->float-array2d mat2x2 mat3x3 mat4x4 mulm mulmt muls mulv ncol negate nrow outer radians rint round row rows rows->mat2x2 rows->mat3x3 rows->mat4x4 safe-sqrt sec sech sfrac sgn sigmoid signum sin sinc sinh solve sq sqrt sub symmetric? tan tanh tmulm tmulmt trace transpose trunc vtmul xlogx zero

                                                                                                    fastmath.optimization

                                                                                                    Optimization.

                                                                                                    +

                                                                                                    Categories

                                                                                                      Other vars: bayesian-optimization linear-optimization maximize maximizer minimize minimizer scan-and-maximize scan-and-minimize

                                                                                                      fastmath.optimization.bo

                                                                                                      Categories

                                                                                                        Other vars: args args-cont categorical-drop categorical-keep continuous-append continuous-append-key continuous-restrict continuous-restrict-key example-data initialize-bo prepare-args target utility-function

                                                                                                        fastmath.optimization.lbfgsb

                                                                                                        Categories

                                                                                                          Other vars: ->lbfgsb grad-function

                                                                                                          fastmath.protocols

                                                                                                          Set of protocols for fastmath.

                                                                                                          +

                                                                                                          Categories

                                                                                                            Other vars: ->seq abs add approx as-vec axis-rotate base-from brandom cdf cell->anchor cell->mid continuous? coords->cell coords->mid corners covariance cross dimensions distribution-id distribution-parameters distribution? dot drandom econstrain einterpolate emn emult emx fmap forward-1d forward-2d frandom from-polar grandom grid-type heading icdf interpolate irandom is-near-zero? is-zero? lower-bound lpdf lrandom mag magsq maxdim mean means mindim mn mult mx pdf permute perpendicular probability prod reciprocal reverse-1d reverse-2d rotate sample set-seed set-seed! shift source-object sub sum to-acm-vec to-polar to-vec transform upper-bound variance

                                                                                                            fastmath.protocols.matrix

                                                                                                            Categories

                                                                                                              Other vars: add adds cholesky cols column det diag emulm fmap inverse mulm muls mulv ncol nrow row rows sub symmetric? to-double-array to-double-array2d to-float-array to-float-array2d trace transpose vtmul

                                                                                                              fastmath.quaternion

                                                                                                              Categories

                                                                                                                Other vars: -I -J -K I J K ONE ZERO acos acosh acot acoth acsc acsch add arg asec asech asin asinh atan atanh complex->quaternion conjugate cos cosh cot coth csc csch delta-eq div exp from-euler im-i im-j im-k imaginary? inf? log logb mult nan? neg norm normalize pow qsgn quaternion re real? reciprocal rotate rotation-quaternion scalar scale sec sech sin sinh slerp sq sqrt sub tan tanh to-euler vector zero?

                                                                                                                fastmath.random

                                                                                                                Various random and noise functions.

                                                                                                                +

                                                                                                                Categories

                                                                                                                  Other vars: ->seq ball-random billow-noise brand brandom ccdf cdf continuous? covariance default-normal default-rng dimensions discrete-noise distribution distribution-id distribution-parameters distribution? distributions-list drand drandom fbm-noise flip flip-rng flipb flipb-rng frand frandom grand grandom icdf integrate-pdf irand irandom jittered-sequence-generator likelihood log-likelihood lower-bound lpdf lrand lrandom mean means noise noise-generators noise-interpolations noise-types observe observe1 pdf probability random-noise-cfg random-noise-fn randval randval-rng ridgedmulti-noise rng rngs-list roll-a-dice roll-a-dice-rng sample sequence-generator sequence-generators-list set-seed set-seed! simplex single-noise source-object synced-rng upper-bound variance vnoise warp-noise-fn

                                                                                                                  fastmath.signal

                                                                                                                  Signal processing (effect) and generation (oscillators).

                                                                                                                  +

                                                                                                                  Categories

                                                                                                                    Other vars: ->BiquadConf ->EffectsList ->SampleAndState ->StateBassTreble ->StateBiquad ->StateDecimator ->StateDivider ->StateEcho ->StateFm ->StateMdaThruZero ->StateVcf303 apply-effects apply-effects-raw compose-effects db->linear effect effect-node effects-list kernel-smoothing-filter linear->db load-signal moving-average-filter oscillator oscillator->signal oscillator-gain oscillators oscillators-sum reset-effects save-signal savgol-filter signal->oscillator single-pass

                                                                                                                    fastmath.solver

                                                                                                                    Categories

                                                                                                                      Other vars: find-root quadratic

                                                                                                                      fastmath.stats

                                                                                                                      Statistics functions.

                                                                                                                      Categories

                                                                                                                        Other vars: ->confusion-matrix L0 L1 L2 L2sq LInf acf acf-ci ad-test-one-sample adjacent-values ameasure binary-measures binary-measures-all binomial-ci binomial-ci-methods binomial-test bootstrap bootstrap-ci brown-forsythe-test chisq-test ci cliffs-delta coefficient-matrix cohens-d cohens-d-corrected cohens-f cohens-f2 cohens-kappa cohens-q cohens-u2 cohens-u3 cohens-w contingency-2x2-measures contingency-2x2-measures-all contingency-table contingency-table->marginals correlation correlation-matrix count= covariance covariance-matrix cramers-c cramers-v cramers-v-corrected cressie-read-test demean epsilon-sq estimate-bins estimation-strategies-list eta-sq extent f-test fligner-killeen-test freeman-tukey-test geomean glass-delta harmean hedges-g hedges-g* hedges-g-corrected histogram hpdi-extent inner-fence-extent iqr jensen-shannon-divergence kendall-correlation kruskal-test ks-test-one-sample ks-test-two-samples kullback-leibler-divergence kurtosis levene-test mad mad-extent mae mape maximum mcc me mean mean-absolute-deviation means-ratio means-ratio-corrected median median-3 median-absolute-deviation minimum minimum-discrimination-information-test mode modes moment mse multinomial-likelihood-ratio-test neyman-modified-chisq-test omega-sq one-way-anova-test outer-fence-extent outliers p-overlap p-value pacf pacf-ci pearson-correlation pearson-r percentile percentile-bc-extent percentile-bca-extent percentile-extent percentiles pi pi-extent pooled-stddev pooled-variance population-stddev population-variance power-divergence-test powmean psnr quantile quantile-extent quantiles r2 r2-determination rank-epsilon-sq rank-eta-sq rescale rmse robust-standardize rows->contingency-table rss second-moment sem sem-extent skewness span spearman-correlation standardize stats-map stddev stddev-extent sum t-test-one-sample t-test-two-samples trim tschuprows-t ttest-one-sample ttest-two-samples variance variation weighted-kappa winsor wmean wmedian wmw-odds wquantile wquantiles z-test-one-sample z-test-two-samples

                                                                                                                        fastmath.stats.bootstrap

                                                                                                                        Bootstrap methods and confidence intervals

                                                                                                                        Categories

                                                                                                                          Other vars: bootstrap bootstrap-stats ci-basic ci-bc ci-bca ci-normal ci-percentile ci-studentized ci-t jackknife jackknife+

                                                                                                                          fastmath.transform

                                                                                                                          Transforms.

                                                                                                                          Categories

                                                                                                                            Other vars: compress denoise forward-1d forward-2d reverse-1d reverse-2d transformer wavelets-list

                                                                                                                            fastmath.vector

                                                                                                                            Mathematical vector operations.

                                                                                                                            -

                                                                                                                            Categories

                                                                                                                              Other vars: ->ArrayVec ->Vec2 ->Vec3 ->Vec4 abs acos acosh acot acoth acsc add aligned? angle-between applyf approx array->vec2 array->vec3 array->vec4 array-vec as-vec asec asech asin asinh atan atanh average average-vectors axis-rotate base-from cbrt ceil clamp cos cosh cot coth cross csc csch degrees dhash-code dist dist-abs dist-ang dist-canberra dist-cheb dist-discrete dist-emd dist-sq distances div dot econstrain ediv einterpolate emn emult emx exp expm1 faceforward floor fmap frac from-polar generate-vec2 generate-vec3 generate-vec4 heading interpolate is-near-zero? is-zero? jinc limit ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmeanexp logmxp1 logsoftmax logsumexp mag magsq make-vector maxdim mindim mn mult mx nonzero-count normalize permute perpendicular project radians reciprocal relative-angle-between rint rotate round safe-sqrt sec sech seq->vec2 seq->vec3 seq->vec4 set-mag sfrac sgn shift sigmoid signum sim-cos sin sinc sinh softmax sq sqrt sub sum tan tanh to-polar to-vec transform triple-product trunc vec->RealVector vec->Vec vec2 vec3 vec4 xlogx zero-count

                                                                                                                              \ No newline at end of file +

                                                                                                                              Categories

                                                                                                                                Other vars: ->ArrayVec ->Vec2 ->Vec3 ->Vec4 abs acos acosh acot acoth acsc acsch add aligned? angle-between applyf approx array->vec2 array->vec3 array->vec4 array-vec as-vec asec asech asin asinh atan atanh average average-vectors axis-rotate base-from cb cbrt ceil clamp cos cosh cot coth cross csc csch degrees delta-eq dhash-code dist dist-abs dist-ang dist-canberra dist-cheb dist-discrete dist-emd dist-sq distances div dot econstrain ediv einterpolate emn emult emx exp expm1 faceforward floor fmap frac from-polar generate-vec2 generate-vec3 generate-vec4 heading interpolate is-near-zero? is-zero? jinc lerp limit ln log log10 log1mexp log1p log1pexp log1pmx log1psq log2 logexpm1 logit logmeanexp logmxp1 logsoftmax logsumexp mag magsq make-vector maxdim mindim mn mult mx nonzero-count normalize permute perpendicular prod project radians reciprocal relative-angle-between rint rotate round safe-sqrt sec sech seq->vec2 seq->vec3 seq->vec4 set-mag sfrac sgn shift sigmoid signum sim-cos sin sinc sinh softmax sq sqrt sub sum tan tanh to-polar to-vec transform triple-product trunc vec->RealVector vec->Vec vec2 vec3 vec4 xlogx zero-count

                                                                                                                                \ No newline at end of file diff --git a/src/fastmath/optimization.clj b/src/fastmath/optimization.clj index d3e63e5f..a2797db1 100644 --- a/src/fastmath/optimization.clj +++ b/src/fastmath/optimization.clj @@ -10,7 +10,9 @@ * Multidirectional simplex * CMAES * Gradient + * L-BFGS-B * Bayesian Optimization (see below) + * Linear optimization All optimizers require bounds. @@ -57,7 +59,9 @@ ## Bayesian Optimization - Bayesian optimizer can be used for optimizing expensive to evaluate black box functions. Refer this [article](http://krasserm.github.io/2018/03/21/bayesian-optimization/) or this [article](https://nextjournal.com/a/LKqpdDdxiggRyHhqDG5FH?token=Ss1Qq3MzHWN8ZyEt9UC1ZZ)" + Bayesian optimizer can be used for optimizing expensive to evaluate black box functions. Refer this [article](http://krasserm.github.io/2018/03/21/bayesian-optimization/) or this [article](https://nextjournal.com/a/LKqpdDdxiggRyHhqDG5FH?token=Ss1Qq3MzHWN8ZyEt9UC1ZZ) + + ## Linear optimization " (:require [fastmath.core :as m] [fastmath.random :as r] [fastmath.vector :as v] @@ -67,6 +71,8 @@ (:import [org.apache.commons.math3.optim.nonlinear.scalar GoalType ObjectiveFunction ObjectiveFunctionGradient] [org.apache.commons.math3.optim.univariate SearchInterval BrentOptimizer UnivariateObjectiveFunction UnivariatePointValuePair] [org.apache.commons.math3.optim BaseOptimizer OptimizationData MaxEval MaxIter SimpleBounds SimpleValueChecker InitialGuess PointValuePair] + [org.apache.commons.math3.optim.linear LinearObjectiveFunction LinearConstraint + Relationship LinearConstraintSet SimplexSolver NonNegativeConstraint PivotSelectionRule] [org.apache.commons.math3.analysis UnivariateFunction MultivariateFunction MultivariateVectorFunction] [org.apache.commons.math3.optim.nonlinear.scalar MultivariateFunctionMappingAdapter] [org.apache.commons.math3.optim.nonlinear.scalar.noderiv BOBYQAOptimizer PowellOptimizer NelderMeadSimplex SimplexOptimizer MultiDirectionalSimplex CMAESOptimizer CMAESOptimizer$PopulationSize CMAESOptimizer$Sigma] @@ -235,15 +241,16 @@ (wrap-multivariate-function f))) (defn- parse-result - [^MultivariateFunctionMappingAdapter mfma res] - (condp instance? res - UnivariatePointValuePair (let [^UnivariatePointValuePair res res] - [(list (.getPoint res)) (.getValue res)]) - PointValuePair (let [^PointValuePair res res] - [(seq (if mfma - (.unboundedToBounded mfma (.getPointRef res)) - (.getPointRef res))) (.getValue res)]) - res)) + ([res] (parse-result nil res)) + ([^MultivariateFunctionMappingAdapter mfma res] + (condp instance? res + UnivariatePointValuePair (let [^UnivariatePointValuePair res res] + [(list (.getPoint res)) (.getValue res)]) + PointValuePair (let [^PointValuePair res res] + [(seq (if mfma + (.unboundedToBounded mfma (.getPointRef res)) + (.getPointRef res))) (.getValue res)]) + res))) (defn- find-dimensions ^long [bounds] @@ -309,6 +316,14 @@ :iterations (.-k obj) :gradient (seq (.m_grad obj))})))))) +(defn- maybe-stats? + [stats? ^BaseOptimizer optimizer res] + (if-not stats? + res + {:result res + :evaluations (.getEvaluations optimizer) + :iterations (.getIterations optimizer)})) + (defn- optimizer [method f {:keys [max-evals max-iters goal bounds stats? population-size bounded? gradient-h] :or {gradient-h 0.0001} @@ -357,15 +372,11 @@ (fn local-optimizer ([] (local-optimizer nil)) - ([init] (let [res (->> (conj base-opt-data (wrap-initial method bounds init mfma)) - (into-array OptimizationData) - (.optimize optimizer) - (parse-result mfma))] - (if-not stats? - res - {:result res - :evaluations (.getEvaluations optimizer) - :iterations (.getIterations optimizer)})))))))) + ([init] (->> (conj base-opt-data (wrap-initial method bounds init mfma)) + (into-array OptimizationData) + (.optimize optimizer) + (parse-result mfma) + (maybe-stats? stats? optimizer)))))))) (defn minimizer "Create optimizer which minimizes function. @@ -374,7 +385,7 @@ [method f config] (optimizer method f (assoc config :goal :minimize))) (defn maximizer - "Create optimizer which maximizer function. + "Create optimizer which maximizes function. Returns function which performs optimization for optionally given initial point." [method f config] (optimizer method f (assoc config :goal :maximize))) @@ -557,7 +568,77 @@ :xs xs :ys ys})))) -;; root finding methods +;; linear optimization + +(defn- constraint-relations + ^Relationship [relation] + (cond + (#{:>= '>= :geq} relation) Relationship/GEQ + (#{:<= '<= :leq} relation) Relationship/LEQ + :else Relationship/EQ)) + +(defn- build-constraint + ^LinearConstraint [[left relation right]] + (let [relationship (constraint-relations relation)] + (if (number? right) + (LinearConstraint. (m/seq->double-array left) relationship (double right)) + (LinearConstraint. (m/seq->double-array (butlast left)) + (double (last left)) + relationship + (m/seq->double-array (butlast right)) + (double (last right)))))) + +(defn linear-optimization + "Solves a linear problem. + + Target is defined as a vector of coefficients and constant as the last value: + `[a1 a2 a3 ... c]` means `f(x1,x2,x3) = a1*x1 + a2*x2 + a3*x3 + ... + c` + + Constraints are defined as a sequence of one of the following triplets: + + * `[a1 a2 a3 ...] R n` - which means `a1*x1+a2*x2+a3*x3+... R n` + * `[a1 a2 a3 ... ca] R [b1 b2 b3 ... cb] - which means `a1*x1+a2*x2+a3*x3+...+ca R b1*x1+b2*x2+b3*x3+...+cb` + where `R` is a relationship and can be one of `<=`, `>=` or `=` as symbol or keyword. Also `:leq`, `:geq` and `:eq` are valid. + + Function returns pair of optimal point and function value. If `stat?` option is set to true, returns also information about number of iterations. + + Possible options: + + * `:goal` - `:minimize` (default) or `:maximize` + * `:rule` - pivot selection rule, `:dantzig` (default) or `:bland` + * `:max-iter` - maximum number of iterations, maximum integer by default + * `:non-negative?` - allow non-negative variables only, default: `false` + * `:epsilon` - convergence value, default: `1.0e-6`: + * `:max-ulps` - floating point comparisons, default: `10` ulp + * `:cut-off` - pivot elements smaller than cut-off are treated as zero, default: `1.0e-10` + + ```clojure + (linear-optimization [-1 4 0] [[-3 1] :<= 6 + [-1 -2] :>= -4 + [0 1] :>= -3]) + ;; => [(9.999999999999995 -3.0) -21.999999999999993] + ```" + ([target constraints] (linear-optimization target constraints {})) + ([target constraints {:keys [goal ^double epsilon ^int max-ulps ^double cut-off + rule non-negative? ^int max-iter stats?] + :or {goal :minimize epsilon 1.0e-6 max-ulps 10 cut-off 1.0e-10 + rule :dantzig non-negative? false max-iter Integer/MAX_VALUE}}] + (let [goal (if (= goal :minimize) GoalType/MINIMIZE GoalType/MAXIMIZE) + rule (if (= rule :dantzig) PivotSelectionRule/DANTZIG PivotSelectionRule/BLAND) + max-iter (MaxIter. max-iter) + non-negative? (NonNegativeConstraint. non-negative?) + target (LinearObjectiveFunction. (m/seq->double-array (butlast target)) + (double (last target))) + constraints (->> constraints + (partition 3) + ^java.util.Collection (map build-constraint) + (LinearConstraintSet.)) + ^BaseOptimizer solver (SimplexSolver. epsilon max-ulps cut-off)] + (->> [goal rule max-iter non-negative? target constraints] + (into-array OptimizationData) + (.optimize solver) + (parse-result nil) + (maybe-stats? stats? solver))))) #_(let [f (fn [^double x ^double y] (inc (- (- (* x x)) (m/sq (dec y))))) diff --git a/test/fastmath/optimization_test.clj b/test/fastmath/optimization_test.clj new file mode 100644 index 00000000..94695700 --- /dev/null +++ b/test/fastmath/optimization_test.clj @@ -0,0 +1,28 @@ +(ns fastmath.optimization-test + (:require [fastmath.optimization :as sut] + [clojure.test :as t] + [fastmath.vector :as v] + [fastmath.core :as m])) + +(t/deftest linear-programming + (t/are [res target constrains opts] (let [[p v] res + [rp rv] (sut/linear-optimization target constrains opts)] + (and (v/delta-eq (vec rp) p) + (m/delta-eq v rv))) + ;; scipy + [[10 -3] -22] [-1 4 0] [[-3 1] :<= 6 + [-1 -2] :>= -4 + [0 1] :>= -3] nil + + ;; http://people.brunel.ac.uk/~mastjjb/jeb/or/morelp.html + [[45.0 6.25] 1.25] [1 1 -50] [[50 24] :leq 2400 + [30 33] :leq 2100 + [1 0] :geq 45 + [0 1] :geq 5] {:goal :maximize} + + ;; transportation problem https://dewwool.com/linear-programming-examples/ + [[0.0 0.0 10.0 30.0 20.0 20.0] 290.0] [5 4 6 3 2 5 0] '[[1 1 1 0 0 0] <= 50 + [0 0 0 1 1 1] <= 70 + [1 0 0 1 0 0] >= 30 + [0 1 0 0 1 0] >= 20 + [0 0 1 0 0 1] >= 30] {:non-negative? true}))