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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.

Currently supported RNGs:

  • :jdk - default java.util.Random
  • :mersenne - MersenneTwister
  • :isaac - ISAAC
  • :well512a, :well1024a, :well19937a, :well19937c, :well44497a, :well44497b - several WELL variants

To create your RNG use rng multimethod. Pass RNG name and (optional) seed. Returned RNG is equipped with RNGProto protocol with methods: irandom, lrandom, frandom drandom, grandom, brandom which return random primitive value with given RNG.

(let [rng (rng :isaac 1337)]
  (irandom rng))

For conveniency default RNG (:jdk) with following functions are created: irand, lrand, frand, drand, grand, brand.

Each prefix denotes returned type:

  • i - int
  • l - long
  • f - float
  • d - double
  • g - gaussian (double)
  • b - boolean

Check individual function for parameters description.

Random Vector Sequences

Couple of functions to generate sequences of numbers or vectors.

To create generator call sequence-generator with generator name and vector size. Following generators are available:

  • :halton - Halton low-discrepancy sequence; range 0,1
  • :sobol - Sobol low-discrepancy sequence; range 0,1
  • :r2 - R2 low-discrepancy sequence; range 0,1, more…
  • :sphere - uniformly random distributed on unit sphere
  • :ball - uniformly random distributed from unit ball
  • :gaussian - gaussian distributed (mean=0, stddev=1)
  • :default - uniformly random; range:0,1

:halton, :sobol and :r2 can be also randomly jittered according to this article. Call jittered-sequence-generator.

After creation you get lazy sequence

Noise

List of continuous noise functions (1d, 2d and 3d):

  • :value - value noise
  • :gradient - gradient noise (improved Ken Perlin version)
  • :simplex - simplex noise

First two (:value and :gradient) can use 4 different interpolation types: :none, :linear, :hermite (cubic) and :quintic.

All can be combined in following variants:

Noise creation requires detailed configuration which is simple map of following keys:

  • :seed - seed as integer
  • :noise-type - type of noise: :value, :gradient (default), :simplex
  • :interpolation - type of interpolation (for value and gradient): :none, :linear, :hermite (default) or :quintic
  • :octaves - number of octaves for combined noise (like FBM), default: 6
  • :lacunarity - scaling factor for combined noise, default: 2.00
  • :gain - amplitude scaling factor for combined noise, default: 0.5
  • :normalize? - should be normalized to [0,1] range (true, default) or to [-1,1] range (false)

For usage convenience 3 ready to use functions are prepared. Returning value from [0,1] range:

  • noise - Perlin Noise (gradient noise, 6 octaves, quintic interpolation)
  • vnoise - Value Noise (as in Processing, 6 octaves, hermite interpolation)
  • simplex - Simplex Noise (6 octaves)

For random noise generation you can use random-noise-cfg and random-noise-fn. Both can be feed with configuration. Additional configuration:

  • :generator can be set to one of the noise variants, defaults to :fbm
  • :warp-scale - 0.0 - do not warp, >0.0 warp
  • :warp-depth - depth for warp (default 1.0, if warp-scale is positive)

Discrete Noise

discrete-noise is a 1d or 2d hash function for given integers. Returns double from [0,1] range.

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 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)
;;=> (4.1687630473847435
;;=>  0.11489652782773863
;;=>  3.5038148440291073
;;=>  3.6810345721073534
;;=>  1.6948726884788454)
(->seq (distribution :gamma) 5 :stratified)
;;=> (1.600601368607516
;;=>  2.7030326250022294
;;=>  3.9802593653442395
;;=>  5.874946153835131
;;=>  13.600897944977005)
(->seq default-rng 5 :systematic)
;;=> (0.009986363810732058
;;=>  0.2099863638107321
;;=>  0.4099863638107321
;;=>  0.6099863638107321
;;=>  0.8099863638107321)
    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__22233__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.

    Returns true or false with equal probability. You can set p probability for true

    Examples

    Usage

    (brand)
;;=> true
(brand 0.1)
;;=> false

    Count number of true values with probability 0.15

    (count (filter true? (repeatedly 100000 (fn* [] (brand 0.15)))))
;;=> 15085
    view source

    brandom

    (brandom rng)(brandom rng p)

    Random boolean with provided RNG

    Examples

    boolean

    (rngproto-snippet brandom ...)
;;=> 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?

    Examples

    Usage

    (continuous? (distribution :gamma))
;;=> true
(continuous? (distribution :pascal))
;;=> false

;; 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).

    Examples

    Usage

    (sample default-normal)
;;=> 1.3545645038826972
(set-seed! default-normal 1234)
;;=> org.apache.commons.math3.distribution.NormalDistribution@4f0ac32c
(sample default-normal)
;;=> 0.14115907833078006
(irandom default-normal)
;;=> 0
(mean default-normal)
;;=> 0.0
(variance default-normal)
;;=> 1.0
    view source

    default-rng

    Default RNG - JDK

    Examples

    Usage

    (set-seed! default-rng 111)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@75f84e75
(irandom default-rng)
;;=> -1196652709
(set-seed! default-rng 999)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@75f84e75
(irandom default-rng)
;;=> -1242822577
(set-seed! default-rng 111)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@75f84e75
(irandom default-rng)
;;=> -1196652709
    view source

    dimensions

    (dimensions d)

    Distribution dimensionality

    Examples

    Usage

    (dimensions (distribution :gamma))
;;=> 1
(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:

    • X (long)
    • Y (long, optional)

    Returns double value from 0,1 range

    Examples

    Example calls

    (discrete-noise 123 444)
;;=> 0.8660251823561383
(discrete-noise 123 444)
;;=> 0.8660251823561383
(discrete-noise 123 445)
;;=> 0.4702831345937602
(discrete-noise 123)
;;=> 0.28831296287864117

    Draw noise for 0-180 range.

    view source

    distribution

    multimethod

    Create distribution object.

    • First parameter is distribution as a :key.
    • Second parameter is a map with configuration.

    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@5e2a0361
(distribution :beta {:alpha 1.0, :beta 1.0})
;;=> org.apache.commons.math3.distribution.BetaDistribution@10fa8f92

    All parameters

    (into (sorted-map)
      (map (fn* [p1__36077#]
             (vector p1__36077#
                     (sort (distribution-parameters (distribution
                                                     p1__36077#)))))
           (keys (methods distribution))))
;;=> {:anderson-darling ({:n 1.0}),
;;=>  :bb (:bd :mu :sigma),
;;=>  :bernoulli (:p :trials),
;;=>  :beta (:alpha :beta),
;;=>  :binomial (:p :trials),
;;=>  :categorical-distribution (:data :probabilities),
;;=>  :cauchy (:median :scale),
;;=>  :chi ({:nu 1.0}),
;;=>  :chi-squared (:degrees-of-freedom),
;;=>  :chi-squared-noncentral ({:lambda 1.0, :nu 1.0}),
;;=>  :continuous-distribution (:bandwidth :data :kde :steps),
;;=>  :cramer-von-mises ({:n 1.0}),
;;=>  :dirichlet (:alpha),
;;=>  :empirical (:bin-count :data),
;;=>  :enumerated-int (:data :probabilities),
;;=>  :enumerated-real (:data :probabilities),
;;=>  :erlang ({:k 1, :lambda 1}),
;;=>  :exgaus (:mu :nu :sigma),
;;=>  :exponential (:mean),
;;=>  :f (:denominator-degrees-of-freedom :numerator-degrees-of-freedom),
;;=>  :fatigue-life ({:beta 1.0, :gamma 1.0, :mu 0.0}),
;;=>  :fishers-noncentral-hypergeometric (:n :nf :ns :omega),
;;=>  :folded-normal ({:mu 0.0, :sigma 1.0}),
;;=>  :frechet ({:alpha 1.0, :beta 1.0, :delta 0.0}),
;;=>  :gamma (:scale :shape),
;;=>  :geometric (:p),
;;=>  :gumbel (:beta :mu),
;;=>  :half-cauchy (:scale),
;;=>  :half-normal (:sigma),
;;=>  :hyperbolic-secant ({:mu 0.0, :sigma 1.0}),
;;=>  :hypergeometric (:number-of-successes :population-size :sample-size),
;;=>  :hypoexponential (:lambdas),
;;=>  :hypoexponential-equal ({:h 1.0, :k 1.0, :n 1.0}),
;;=>  :integer-discrete-distribution (:data :probabilities),
;;=>  :inverse-gamma ({:alpha 2.0, :beta 1.0}),
;;=>  :inverse-gaussian ({:lambda 1.0, :mu 1.0}),
;;=>  :johnson-sb ({:delta 1.0, :gamma 0.0, :lambda 1.0, :xi 0.0}),
;;=>  :johnson-sl ({:delta 1.0, :gamma 0.0, :lambda 1.0, :xi 0.0}),
;;=>  :johnson-su ({:delta 1.0, :gamma 0.0, :lambda 1.0, :xi 0.0}),
;;=>  :kde (:bandwidth :data :kde :steps),
;;=>  :kolmogorov (),
;;=>  :kolmogorov-smirnov ({:n 1.0}),
;;=>  :kolmogorov-smirnov+ ({:n 1.0}),
;;=>  :laplace (:beta :mu),
;;=>  :levy (:c :mu),
;;=>  :log-logistic ({:alpha 3.0, :beta 1.0}),
;;=>  :log-normal (:scale :shape),
;;=>  :logarithmic (:theta),
;;=>  :logistic (:mu :s),
;;=>  :mixture (:distrs :weights),
;;=>  :multi-normal (:covariances :means),
;;=>  :multinomial (:n :ps),
;;=>  :nakagami (:mu :omega),
;;=>  :nbi (:mu :sigma),
;;=>  :negative-binomial (:p :r),
;;=>  :normal (:mu :sd),
;;=>  :normal-inverse-gaussian
;;=>  ({:alpha 1.0, :beta 0.0, :delta 1.0, :mu 0.0}),
;;=>  :pareto (:scale :shape),
;;=>  :pascal (:p :r),
;;=>  :pearson-6 ({:alpha1 1.0, :alpha2 1.0, :beta 1.0}),
;;=>  :poisson (:p),
;;=>  :power ({:a 0.0, :b 1.0, :c 2.0}),
;;=>  :rayleigh ({:a 0.0, :beta 1.0}),
;;=>  :real-discrete-distribution (:data :probabilities),
;;=>  :reciprocal-sqrt (:a),
;;=>  :t (:degrees-of-freedom),
;;=>  :triangular (:a :b :c),
;;=>  :truncated (:distr :left :right),
;;=>  :uniform-int (:lower :upper),
;;=>  :uniform-real (:lower :upper),
;;=>  :watson-g ({:n 2.0}),
;;=>  :watson-u ({:n 2.0}),
;;=>  :weibull (:alpha :beta),
;;=>  :zabb (:bd :mu :nu :sigma),
;;=>  :zabi (:bd :mu :sigma),
;;=>  :zaga (:lower-tail? :mu :nu :sigma),
;;=>  :zanbi (:mu :nu :sigma),
;;=>  :zibb (:bd :mu :nu :sigma),
;;=>  :zibi (:bd :mu :sigma),
;;=>  :zinbi (:mu :nu :sigma),
;;=>  :zip (:mu :sigma),
;;=>  :zip2 (:mu :sigma),
;;=>  :zipf (:exponent :number-of-elements)}

    PDFs of anderson-darling

    CDFs of anderson-darling

    ICDFs of anderson-darling

    PDFs of bb

    CDFs of bb

    ICDFs of bb

    PDFs of bernoulli

    CDFs of bernoulli

    ICDFs of bernoulli

    PDFs of beta

    CDFs of beta

    ICDFs of beta

    PDFs of binomial

    CDFs of binomial

    ICDFs of binomial

    PDFs of cauchy

    CDFs of cauchy

    ICDFs of cauchy

    PDFs of chi

    CDFs of chi

    ICDFs of chi

    PDFs of chi-squared

    CDFs of chi-squared

    ICDFs of chi-squared

    PDFs of chi-squared-noncentral

    CDFs of chi-squared-noncentral

    ICDFs of chi-squared-noncentral

    PDFs of continuous-distribution

    CDFs of continuous-distribution

    ICDFs of continuous-distribution

    PDFs of empirical

    CDFs of empirical

    ICDFs of empirical

    PDFs of enumerated-int

    CDFs of enumerated-int

    ICDFs of enumerated-int

    PDFs of enumerated-real

    CDFs of enumerated-real

    ICDFs of enumerated-real

    PDFs of erlang

    CDFs of erlang

    ICDFs of erlang

    PDFs of exgaus

    CDFs of exgaus

    ICDFs of exgaus

    PDFs of exponential

    CDFs of exponential

    ICDFs of exponential

    PDFs of f

    CDFs of f

    ICDFs of f

    PDFs of fatigue-life

    CDFs of fatigue-life

    ICDFs of fatigue-life

    PDFs of fishers-noncentral-hypergeometric

    CDFs of fishers-noncentral-hypergeometric

    ICDFs of fishers-noncentral-hypergeometric

    PDFs of folded-normal

    CDFs of folded-normal

    ICDFs of folded-normal

    PDFs of frechet

    CDFs of frechet

    ICDFs of frechet

    PDFs of gamma

    CDFs of gamma

    ICDFs of gamma

    PDFs of geometric

    CDFs of geometric

    ICDFs of geometric

    PDFs of gumbel

    CDFs of gumbel

    ICDFs of gumbel

    PDFs of half-cauchy

    CDFs of half-cauchy

    ICDFs of half-cauchy

    PDFs of half-normal

    CDFs of half-normal

    ICDFs of half-normal

    PDFs of hyperbolic-secant

    CDFs of hyperbolic-secant

    ICDFs of hyperbolic-secant

    PDFs of hypergeometric

    CDFs of hypergeometric

    ICDFs of hypergeometric

    PDFs of hypoexponential

    CDFs of hypoexponential

    ICDFs of hypoexponential

    PDFs of hypoexponential-equal

    CDFs of hypoexponential-equal

    ICDFs of hypoexponential-equal

    PDFs of integer-discrete-distribution

    CDFs of integer-discrete-distribution

    ICDFs of integer-discrete-distribution

    PDFs of inverse-gamma

    CDFs of inverse-gamma

    ICDFs of inverse-gamma

    PDFs of inverse-gaussian

    CDFs of inverse-gaussian

    ICDFs of inverse-gaussian

    PDFs of johnson-sb

    CDFs of johnson-sb

    ICDFs of johnson-sb

    PDFs of johnson-sl

    CDFs of johnson-sl

    ICDFs of johnson-sl

    PDFs of johnson-su

    CDFs of johnson-su

    ICDFs of johnson-su

    PDFs of kolmogorov

    CDFs of kolmogorov

    ICDFs of kolmogorov

    PDFs of kolmogorov-smirnov

    CDFs of kolmogorov-smirnov

    ICDFs of kolmogorov-smirnov

    PDFs of kolmogorov-smirnov+

    CDFs of kolmogorov-smirnov+

    ICDFs of kolmogorov-smirnov+

    PDFs of laplace

    CDFs of laplace

    ICDFs of laplace

    PDFs of levy

    CDFs of levy

    ICDFs of levy

    PDFs of log-logistic

    CDFs of log-logistic

    ICDFs of log-logistic

    PDFs of log-normal

    CDFs of log-normal

    ICDFs of log-normal

    PDFs of logistic

    CDFs of logistic

    ICDFs of logistic

    PDFs of mixture

    CDFs of mixture

    ICDFs of mixture

    PDFs of multinomial

    CDFs of multinomial

    ICDFs of multinomial

    PDFs of nakagami

    CDFs of nakagami

    ICDFs of nakagami

    PDFs of nbi

    CDFs of nbi

    ICDFs of nbi

    PDFs of negative-binomial

    CDFs of negative-binomial

    ICDFs of negative-binomial

    PDFs of normal

    CDFs of normal

    ICDFs of normal

    PDFs of pareto

    CDFs of pareto

    ICDFs of pareto

    PDFs of pascal

    CDFs of pascal

    ICDFs of pascal

    PDFs of pearson-6

    CDFs of pearson-6

    ICDFs of pearson-6

    PDFs of poisson

    CDFs of poisson

    ICDFs of poisson

    PDFs of power

    CDFs of power

    ICDFs of power

    PDFs of rayleigh

    CDFs of rayleigh

    ICDFs of rayleigh

    PDFs of real-discrete-distribution

    CDFs of real-discrete-distribution

    ICDFs of real-discrete-distribution

    PDFs of reciprocal-sqrt

    CDFs of reciprocal-sqrt

    ICDFs of reciprocal-sqrt

    PDFs of t

    CDFs of t

    ICDFs of t

    PDFs of triangular

    CDFs of triangular

    ICDFs of triangular

    PDFs of truncated

    CDFs of truncated

    ICDFs of truncated

    PDFs of uniform-int

    CDFs of uniform-int

    ICDFs of uniform-int

    PDFs of uniform-real

    CDFs of uniform-real

    ICDFs of uniform-real

    PDFs of watson-g

    CDFs of watson-g

    ICDFs of watson-g

    PDFs of watson-u

    CDFs of watson-u

    ICDFs of watson-u

    PDFs of weibull

    CDFs of weibull

    ICDFs of weibull

    PDFs of zabb

    CDFs of zabb

    ICDFs of zabb

    PDFs of zabi

    CDFs of zabi

    ICDFs of zabi

    PDFs of zaga

    CDFs of zaga

    ICDFs of zaga

    PDFs of zanbi

    CDFs of zanbi

    ICDFs of zanbi

    PDFs of zibb

    CDFs of zibb

    ICDFs of zibb

    PDFs of zibi

    CDFs of zibi

    ICDFs of zibi

    PDFs of zinbi

    CDFs of zinbi

    ICDFs of zinbi

    PDFs of zip

    CDFs of zip

    ICDFs of zip

    PDFs of zip2

    CDFs of zip2

    ICDFs of zip2

    PDFs of zipf

    CDFs of zipf

    ICDFs of zipf

    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.

    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.

    When all? is true, technical parameters are included, ie: :rng and :inverser-cumm-accuracy.

    Examples

    Usage

    (distribution-parameters (distribution :gamma))
;;=> [:scale :shape]
(distribution-parameters (distribution :gamma) true)
;;=> [:rng :shape :scale :inverse-cumm-accuracy]
(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.

    Examples

    Number and list of distributions

    distributions-list
;;=> #{:anderson-darling :bb :bernoulli :beta :binomial
;;=>   :categorical-distribution :cauchy :chi :chi-squared
;;=>   :chi-squared-noncentral :continuous-distribution :cramer-von-mises
;;=>   :dirichlet :empirical :enumerated-int :enumerated-real :erlang :exgaus
;;=>   :exponential :f :fatigue-life :fishers-noncentral-hypergeometric
;;=>   :folded-normal :frechet :gamma :geometric :gumbel :half-cauchy
;;=>   :half-normal :hyperbolic-secant :hypergeometric :hypoexponential
;;=>   :hypoexponential-equal :integer-discrete-distribution :inverse-gamma
;;=>   :inverse-gaussian :johnson-sb :johnson-sl :johnson-su :kde :kolmogorov
;;=>   :kolmogorov-smirnov :kolmogorov-smirnov+ :laplace :levy :log-logistic
;;=>   :log-normal :logarithmic :logistic :mixture :multi-normal :multinomial
;;=>   :nakagami :nbi :negative-binomial :normal :normal-inverse-gaussian
;;=>   :pareto :pascal :pearson-6 :poisson :power :rayleigh
;;=>   :real-discrete-distribution :reciprocal-sqrt :t :triangular :truncated
;;=>   :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.

    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)
;;=> 0.6178882774976912
(drand 10)
;;=> 3.234654167181481
(drand 10 20)
;;=> 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 ...)
;;=> 0.12887351924500923

    Double random value from distribution

    (drandom (distribution :gamma))
;;=> 4.477314503655649
    view source

    fbm-noise

    (fbm-noise)(fbm-noise cfg__22233__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))
;;=> 0.3596888698390143

    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

    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

    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)
;;=> 0.93785393
(frand 10)
;;=> 9.578358
(frand 10 20)
;;=> 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 ...)
;;=> 0.28929412

    Float random value from distribution (sample cast to float)

    (frandom (distribution :gamma))
;;=> 6.0880103
    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)
;;=> -1.5236953146011685
(grand 10)
;;=> 7.944277491488467
(grand 10 20)
;;=> 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 ...)
;;=> -1.2620959490529822
    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

    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.

    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)
;;=> 403368085
(irand 10)
;;=> 7
(irand 10 20)
;;=> 16
    view source

    irandom

    (irandom rng)(irandom rng mx)(irandom rng mn mx)

    Random integer number with provided RNG

    Examples

    integer

    (rngproto-snippet irandom ...)
;;=> -870209046

    Integer random value from distribution (sample cast to int)

    (irandom (distribution :gamma))
;;=> 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.

    Examples

    Usage

    (let [gen1 (jittered-sequence-generator :r2 2 0.5)
      gen2 (jittered-sequence-generator :r2 2 0.5)]
  [(first gen1) (first gen2)])
;;=> [[0.3349098031447362 0.3632196608626955]
;;=>  [0.46362255181031453 0.23019358923493558]]

    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

    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

    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

    Examples

    Usage

    (lower-bound (distribution :gamma))
;;=> 0.0

;; 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.

    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)
;;=> -6983603299110100805
(lrand 10)
;;=> 1
(lrand 10 20)
;;=> 19
    view source

    lrandom

    (lrandom rng)(lrandom rng mx)(lrandom rng mn mx)

    Random long number with provided RNG

    Examples

    long

    (rngproto-snippet lrandom ...)
;;=> -2549412008922664795

    Long random value from distribution (sample cast to long)

    (lrandom (distribution :gamma))
;;=> 2
    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)

    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.

    6 octaves, quintic interpolation.

    Examples

    Usage

    (noise 3.3)
;;=> 0.5733724444444446
(noise 3.3 1.1)
;;=> 0.5240146679060318
(noise 3.3 0.0 -0.1)
;;=> 0.598906850336508

    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.

    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.

    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.

    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.

    Examples

    Usage

    (observe1 (distribution :gamma) 10)
;;=> -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)

    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.

    Optional map with fixed values.

    Examples

    Random configuration

    (random-noise-cfg)
;;=> {:gain 0.5470770409714059,
;;=>  :generator :ridgemulti,
;;=>  :interpolation :linear,
;;=>  :lacunarity 2.276291258543873,
;;=>  :noise-type :gradient,
;;=>  :normalize? true,
;;=>  :octaves 6,
;;=>  :seed -1748984410,
;;=>  :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.

    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__22251@597a247
(random-noise-fn (random-noise-cfg))
;;=> fastmath.random$fbm_noise$fn__22247@494f5bd

    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)

    Examples

    Usage

    (randval :val-one :val-two)
;;=> :val-one
(randval 0.001 :low-probability :high-probability)
;;=> :high-probability

    Check probability of nil (should return value around 1000).

    (count (filter nil?
               (repeatedly 1000000 (fn* [] (randval 0.001 nil 101)))))
;;=> 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__22233__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))
;;=> 0.6151828850470207

    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@6b009752
(rng :isaac 1234)
;;=> org.apache.commons.math3.random.ISAACRandom@7d5b7023

    Usage

    (irandom (rng :mersenne 999) 15 25)
;;=> 24
    view source

    rngs-list

    List of all possible RNGs.

    Examples

    Contains

    (sort rngs-list)
;;=> (:isaac :jdk :mersenne
;;=>         :well1024a :well19937a
;;=>         :well19937c :well44497a
;;=>         :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))
;;=> 3.8220900629270256
    view source

    sequence-generator

    multimethod

    Create Sequence generator. See sequence-generators-list for names.

    Values:

    • :r2, :halton, :sobol, :default/:uniform - range [0-1] for each dimension
    • :gaussian - from N(0,1) distribution
    • :sphere - from surface of unit sphere (ie. euclidean distance from origin equals 1.0)
    • :ball - from an unit ball

    Possible dimensions:

    • :r2 - 1-15
    • :halton - 1-40
    • :sobol - 1-1000
    • the rest - 1+

    See also jittered-sequence-generator.

    Examples

    Usage (2d)

    (let [gen (sequence-generator :halton 2)] (take 5 gen))
;;=> ([0.0 0.0]
;;=>  [0.5 0.6666666666666666]
;;=>  [0.25 0.3333333333333333]
;;=>  [0.75 0.2222222222222222]
;;=>  [0.125 0.8888888888888888])

    Usage (1d)

    (let [gen (sequence-generator :sobol 1)] (take 5 gen))
;;=> (0.0 0.5 0.75 0.25 0.375)

    Usage (10d)

    (second (sequence-generator :halton 10))
;;=> [0.5 0.6666666666666666 0.6000000000000001 0.42857142857142855
;;=>  0.7272727272727273 0.8461538461538463 0.7058823529411764
;;=>  0.7368421052631579 0.30434782608695654 0.6206896551724138]

    Usage, R2 sequence

    (take 5 (sequence-generator :r2 3))
;;=> ([0.3191725133961645 0.17104360670378926 0.0497004779019703]
;;=>  [0.13834502679232896 0.8420872134075785 0.5994009558039406]
;;=>  [0.9575175401884934 0.5131308201113678 0.1491014337059109]
;;=>  [0.7766900535846579 0.18417442681515706 0.6988019116078812]
;;=>  [0.5958625669808224 0.8552180335189463 0.24850238950985148])

    R2 plot (500 samples)

    Halton plot (500 samples)

    Sobol plot (500 samples)

    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.

    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.

    If rng is :smile calls smile.math.MathEx/setSeed().

    Without rng sets both :smile and default-rng

    Examples

    Set seed for the RNG object

    (let [rng (rng :isaac)]
  (set-seed! rng 1234)
  (irandom rng 10 15))
;;=> 10

;; Test: ok.

    Set seed for the distribution object

    (let [d (distribution :enumerated-int {:data [1 1 1 2 3]})]
  (set-seed! d 1234)
  (irandom d))
;;=> 2

;; Test: ok.

    Set seed to SMILE (global) RNG

    (set-seed! :smile 1234)
;;=> nil

    Set seed to both SMILE and fastmath default RNGs

    (set-seed! 1234)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@75f84e75

    Set to random seed both default RNGs

    (set-seed!)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@75f84e75
    view source

    simplex

    (simplex x)(simplex x y)(simplex x y z)

    Simplex noise. 6 octaves.

    Examples

    Usage

    (simplex 3.3)
;;=> 0.5333568931885713
(simplex 3.3 1.1)
;;=> 0.5337502464278872
(simplex 3.3 0.0 -0.1)
;;=> 0.39681219935985423

    2d noise

    view source

    single-noise

    (single-noise)(single-noise cfg__22233__auto__)

    Create single-noise function with optional configuration.

    Examples

    Usage

    (let [n (single-noise {:interpolation :linear})] (n 0.5 1.1 -1.3))
;;=> 0.5405

    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@4f0ac32c
    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

    Examples

    Usage

    (upper-bound (distribution :gamma))
;;=> Infinity

;; 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.

    6 octaves, Hermite interpolation (cubic, h01).

    Examples

    Usage

    (vnoise 3.3)
;;=> 0.3685741220739981
(vnoise 3.3 1.1)
;;=> 0.32606184202712973
(vnoise 3.3 0.0 -0.1)
;;=> 0.4377780763909749

    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
    • scale factor, default: 4.0
    • depth (1 or 2), default 1

    Normalization of warp noise depends on normalization of noise function.

    Examples

    Usage

    (let [n (warp-noise-fn simplex 2.0 2.0)]
  [(n 0.0) (n 1.0 0.5) (n 2 2 2)])
;;=> [0.40098715790712897 0.46270697250804094 0.6131643768058173]

    Default warp (noise=vnoise, scale=4.0, depth=1.0).

    view source