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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.

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
  • :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: jittered-sequence-generator

->seq

(->seq rng)(->seq rng n)

Returns lazy sequence of random samples (can be limited to optional n values).

Examples

Sequence of random values from distribution

(->seq (distribution :gamma) 5)
;;=> (3.5656586756068793
;;=>  4.183711137226517
;;=>  4.867611475289719
;;=>  2.8127240034882934
;;=>  3.6049999735181344)
view source

billow-noise

(billow-noise)(billow-noise cfg__14990__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)))))
;;=> 14969
view source

brandom

(brandom rng)(brandom rng p)

Random boolean with provided RNG

Examples

boolean

(rngproto-snippet brandom ...)
;;=> true
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)
;;=> -0.3805445381799295
(set-seed! default-normal 1234)
;;=> org.apache.commons.math3.distribution.NormalDistribution@6f74e852
(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@10732713
(irandom default-rng)
;;=> -1641157356
(set-seed! default-rng 999)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@10732713
(irandom default-rng)
;;=> -421961713
(set-seed! default-rng 111)
;;=> org.apache.commons.math3.random.JDKRandomGenerator@10732713
(irandom default-rng)
;;=> -1641157356
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@2c257485
(distribution :beta {:alpha 1.0, :beta 1.0})
;;=> org.apache.commons.math3.distribution.BetaDistribution@8891aa8

All parameters

(into (sorted-map)
      (map (fn* [p1__22237#]
             (vector p1__22237#
                     (sort (distribution-parameters (distribution
                                                     p1__22237#)))))
           (keys (methods distribution))))
;;=> {:anderson-darling (:n),
;;=>  :bernoulli (:p :trials),
;;=>  :beta (:alpha :beta),
;;=>  :binomial (:p :trials),
;;=>  :categorical-distribution (:data :probabilities),
;;=>  :cauchy (:median :scale),
;;=>  :chi (:nu),
;;=>  :chi-squared (:degrees-of-freedom),
;;=>  :chi-squared-noncentral (:lambda :nu),
;;=>  :continuous-distribution (:bin-count :data :h :kernel :probabilities),
;;=>  :cramer-von-mises (:n),
;;=>  :dirichlet (:alpha),
;;=>  :empirical (:bin-count :data),
;;=>  :enumerated-int (:data :probabilities),
;;=>  :enumerated-real (:data :probabilities),
;;=>  :erlang (:k :lambda),
;;=>  :exponential (:mean),
;;=>  :f (:denominator-degrees-of-freedom :numerator-degrees-of-freedom),
;;=>  :fatigue-life (:beta :gamma :mu),
;;=>  :folded-normal (:mu :sigma),
;;=>  :frechet (:alpha :beta :delta),
;;=>  :gamma (:scale :shape),
;;=>  :geometric (:p),
;;=>  :gumbel (:beta :mu),
;;=>  :half-cauchy (:scale),
;;=>  :hyperbolic-secant (:mu :sigma),
;;=>  :hypergeometric (:number-of-successes :population-size :sample-size),
;;=>  :hypoexponential (:lambdas),
;;=>  :hypoexponential-equal (:h :k :n),
;;=>  :integer-discrete-distribution (:data :probabilities),
;;=>  :inverse-gamma (:alpha :beta),
;;=>  :inverse-gaussian (:lambda :mu),
;;=>  :johnson-sb (:delta :gamma :lambda :xi),
;;=>  :johnson-sl (:delta :gamma :lambda :xi),
;;=>  :johnson-su (:delta :gamma :lambda :xi),
;;=>  :kolmogorov-smirnov (:n),
;;=>  :kolmogorov-smirnov+ (:n),
;;=>  :laplace (:beta :mu),
;;=>  :levy (:c :mu),
;;=>  :log-logistic (:alpha :beta),
;;=>  :log-normal (:scale :shape),
;;=>  :logarithmic (:theta),
;;=>  :logistic (:mu :s),
;;=>  :multi-normal (:covariances :means),
;;=>  :nakagami (:mu :omega),
;;=>  :negative-binomial (:p :r),
;;=>  :normal (:mu :sd),
;;=>  :normal-inverse-gaussian (:alpha :beta :delta :mu),
;;=>  :pareto (:scale :shape),
;;=>  :pascal (:p :r),
;;=>  :pearson-6 (:alpha1 :alpha2 :beta),
;;=>  :poisson (:epsilon :max-iterations :p),
;;=>  :power (:a :b :c),
;;=>  :rayleigh (:a :beta),
;;=>  :real-discrete-distribution (:data :probabilities),
;;=>  :reciprocal-sqrt (:a),
;;=>  :t (:degrees-of-freedom),
;;=>  :triangular (:a :b :c),
;;=>  :uniform-int (:lower :upper),
;;=>  :uniform-real (:lower :upper),
;;=>  :watson-g (:n),
;;=>  :watson-u (:n),
;;=>  :weibull (:alpha :beta),
;;=>  :zipf (:exponent :number-of-elements)}

PDFs of anderson-darling

CDFs of anderson-darling

ICDFs of anderson-darling

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 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 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 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-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 nakagami

CDFs of nakagami

ICDFs of nakagami

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 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 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

distributions-list

List of distributions.

Examples

Number and list of distributions

distributions-list
;;=> #{:anderson-darling :bernoulli :beta :binomial :categorical-distribution
;;=>   :cauchy :chi :chi-squared :chi-squared-noncentral
;;=>   :continuous-distribution :cramer-von-mises :dirichlet :empirical
;;=>   :enumerated-int :enumerated-real :erlang :exponential :f :fatigue-life
;;=>   :folded-normal :frechet :gamma :geometric :gumbel :half-cauchy
;;=>   :hyperbolic-secant :hypergeometric :hypoexponential
;;=>   :hypoexponential-equal :integer-discrete-distribution :inverse-gamma
;;=>   :inverse-gaussian :johnson-sb :johnson-sl :johnson-su
;;=>   :kolmogorov-smirnov :kolmogorov-smirnov+ :laplace :levy :log-logistic
;;=>   :log-normal :logarithmic :logistic :multi-normal :nakagami
;;=>   :negative-binomial :normal :normal-inverse-gaussian :pareto :pascal
;;=>   :pearson-6 :poisson :power :rayleigh :real-discrete-distribution
;;=>   :reciprocal-sqrt :t :triangular :uniform-int :uniform-real :watson-g
;;=>   :watson-u :weibull :zipf}
(count distributions-list)
;;=> 64
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)
;;=> 0.38178681319155416
(drand 10)
;;=> 6.592415290746953
(drand 10 20)
;;=> 12.544011338963232
view source

drandom

(drandom rng)(drandom rng mx)(drandom rng mn mx)

Random double number with provided RNG

Examples

double

(rngproto-snippet drandom ...)
;;=> 0.6451540636325555

Double random value from distribution

(drandom (distribution :gamma))
;;=> 1.3987098491779502
view source

fbm-noise

(fbm-noise)(fbm-noise cfg__14990__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))
;;=> 0.5565531220960567

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 0 0 0 0 0 0 0 0 0)
view source

flipb

(flipb p)(flipb)

Returns true with given probability, false otherwise

Examples

Usage

(flipb)
;;=> true
(flipb 0.2)
;;=> true
(repeatedly 10 (fn* [] (flipb 0.1)))
;;=> (false false false false false true true false false false)
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)
;;=> 0.288085013628006
(frand 10)
;;=> 6.10488748550415
(frand 10 20)
;;=> 18.232948303222656
view source

frandom

(frandom rng)(frandom rng mx)(frandom rng mn mx)

Random double number with provided RNG

Examples

float

(rngproto-snippet frandom ...)
;;=> 0.8122085332870483

Float random value from distribution (sample cast to float)

(frandom (distribution :gamma))
;;=> 3.709850311279297
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)
;;=> 0.11619737635740301
(grand 10)
;;=> 1.1210684816151368
(grand 10 20)
;;=> 17.305779775324304
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 ...)
;;=> -0.5076621677752612
view source

icdf

(icdf d v)

Inverse cumulative probability

Examples

Usage

(icdf (distribution :gamma) 0.5)
;;=> 3.3566939800333233
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)
;;=> 1034032361
(irand 10)
;;=> 9
(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 ...)
;;=> 154677565

Integer random value from distribution (sample cast to int)

(irandom (distribution :gamma))
;;=> 3
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)])
;;=> [[0.4613760402754695 0.07709416278300169]
;;=>  [0.4119796194930869 0.28702226482504817]]

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)
;;=> 3047173689416362927
(lrand 10)
;;=> 2
(lrand 10 20)
;;=> 14
view source

lrandom

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

Random long number with provided RNG

Examples

long

(rngproto-snippet lrandom ...)
;;=> -7006375016781005293

Long random value from distribution (sample cast to long)

(lrandom (distribution :gamma))
;;=> 0
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)
;;=> 0.3792675555555556
(noise 3.3 1.1)
;;=> 0.5979212982044446
(noise 3.3 0.0 -0.1)
;;=> 0.5611104175542858

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
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observe1

(observe1 d v)

Log of probability/density of the value. Alias for lpdf.

Examples

Usage

(observe1 (distribution :gamma) 10)
;;=> -4.083709268125845
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pdf

(pdf d v)

Density

Examples

Usage

(pdf (distribution :gamma) 1)
;;=> 0.15163266492815838
(pdf (distribution :pascal) 1)
;;=> 0.078125
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probability

(probability d v)

Probability (PMF)

Examples

Usage

(probability (distribution :gamma) 1)
;;=> 0.15163266492815838
(probability (distribution :pascal) 1)
;;=> 0.078125
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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 0.618855368328213,
;;=>  :generator :single,
;;=>  :interpolation :none,
;;=>  :lacunarity 1.599940053984084,
;;=>  :noise-type :gradient,
;;=>  :normalize? true,
;;=>  :octaves 3,
;;=>  :seed -1844158816,
;;=>  :warp-depth 2,
;;=>  :warp-scale 0.0}
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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$single_noise$fn__15000@4ada5f90
(random-noise-fn (random-noise-cfg))
;;=> fastmath.random$ridgedmulti_noise$fn__15012@3e4bca9

One

Two

Three

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randval

macro

(randval v1 v2)(randval prob v1 v2)(randval prob)(randval)

Retrun 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)))))
;;=> 965
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ridgedmulti-noise

(ridgedmulti-noise)(ridgedmulti-noise cfg__14990__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))
;;=> 0.7702044687581495

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@6a6ce193
(rng :isaac 1234)
;;=> org.apache.commons.math3.random.ISAACRandom@4c4b1983

Usage

(irandom (rng :mersenne 999) 15 25)
;;=> 17
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rngs-list

List of all possible RNGs.

Examples

Contains

(sort rngs-list)
;;=> (:isaac :jdk :mersenne
;;=>         :well1024a :well19937a
;;=>         :well19937c :well44497a
;;=>         :well44497b :well512a)
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sample

(sample d)

Random sample

Examples

Random value from distribution

(sample (distribution :gamma))
;;=> 2.2970553541786
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
  • :gaussian - from N(0,1) distribution
  • :sphere - from surface of unit sphere (ie. euclidean distance from origin equals 1.0)

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)
;;=> (:default :gaussian :halton :r2 :sobol :sphere)
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set-seed!

(set-seed! rng v)

Sets seed. Returns 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.
view source

simplex

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

Simplex noise. 6 octaves.

Examples

Usage

(simplex 3.3)
;;=> 0.6560218691923807
(simplex 3.3 1.1)
;;=> 0.3940602659610949
(simplex 3.3 0.0 -0.1)
;;=> 0.656340461166634

2d noise

view source

single-noise

(single-noise)(single-noise cfg__14990__auto__)

Create single noise function with optional configuration.

Examples

Usage

(let [n (single-noise {:interpolation :linear})] (n 0.5 1.1 -1.3))
;;=> 0.3275

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@6f74e852
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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))
;;=> 0.1915194466361949
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)
;;=> 0.5459827831802206
(vnoise 3.3 1.1)
;;=> 0.6047808080658774
(vnoise 3.3 0.0 -0.1)
;;=> 0.34661294144531285

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)])
;;=> [0.28698139304052883 0.3188025978522241 0.45982809810709013]

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

view source