fastmath.random — generateme/fastmath 1.4.0-SNAPSHOT

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 [1,4]. 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 used as into:

• Noise - pure noise value, create with single-noise
• FBM - fractal brownian motion, create with fbm-noise
• Billow - billow noise, billow-noise
• RidgedMulti - ridged multi, ridgedmulti-noise

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. Return is normalized to [0,1] range:

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

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.

billow-noise clj

brand clj

Random boolean with Mersenne Twister RNG.

default-normal clj

Default normal distribution (u=0.0, sigma=1.0).

default-rng clj

Default RNG - JDK

discrete-noise clj macro

(discrete-noise X)

(discrete-noise X Y)

Discrete noise. Parameters:

• X (long)
• Y (long, optional)

Returns double value from [0,1] range

distribution clj 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).

Distributions should be called using DistributionProto and RNGProto.

The rest parameters goes as follows:

Real distributions

• :beta - :alpha (default: 2.0) and :beta (default: 5.0)
• :cauchy - :median (default: 0.0) and :scale (default: 1.0)
• :chi-squared - :degrees-of-freedom (default: 1.0)
• :empirical - :bean-count (default: 1000) and :data as a sequence
• :enumerated-real - :data as a sequence and :probabilities as a optional sequence
• :exponential - :mean (default: 1.0)
• :f - :numerator-degrees-of-freedom (default: 1.0) and :denominator-degrees-of-freedom (default: 1.0)
• :gamma - :shape (default: 2.0) and :scale (default: 2.0)
• :gumbel - :mu (default: 1.0) and :beta (default: 2.0)
• :laplace - :mu (default: 1.0) and :beta (default: 2.0)
• :levy - :mu (default: 0.0) and :c (default: 1.0)
• :logistic - :mu (default: 1.0) and :s (default: 2.0)
• :log-normal - :scale (default: 1.0) and :shape (default: 1.0)
• :nakagami - :mu (default: 1.0) and :omega (default: 1.0)
• :normal - :mu (default: 0.0) and :sd (default: 1.0)
• :pareto - :scale (default: 1.0) and :shape (default: 1.0)
• :t - :degrees-of-freedom (default: 1.0)
• :triangular - :a (default: -1.0), :c (default: 0.0) and :b (default: 1.0)
• :uniform-real - :lower (default: 0.0) and :upper (default: 1.0)
• :weibull - :alpha (default: 2.0) and :beta (default: 1.0)

Integer distributions

• :binomial - :trials (default: 20) and :p (default: 0.5)
• :bernoulli - :p (default: 0.5)
• :enumerated-int - :data and :probabilities as a sequences
• :geometric - :p (default: 0.5)
• :hypergeometric - :population-size (default: 100), :number-of-successes (default: 50) and :sample-size (default: 25)
• :pascal - :r (default: 5) and :p (default: 0.5)
• :poisson - :p (default: 0.5), :epsilon (default: 1.0e-12), :max-iterations (default: 10000000)
• :uniform-int - :lower (default: 0) and :upper (default: Integer/MAX_VALUE)
• :zipf - :number-of-elements (default: 100) and :exponent (default: 3.0)

DistributionProto clj protocol

Get information from distributions.

cdf clj

(cdf d v)

(cdf d v1 v2)

Cumulative probability.

dimensions clj

(dimensions d)

Returns dimensions

icdf clj

(icdf d p)

Inversed cumulative probability

lpdf clj

(lpdf d v)

Log density

pdf clj

(pdf d v)

Density

probability clj

(probability d v)

Probability (PMF)

sample clj

(sample d)

Returns random sample.

source-object clj

(source-object d)

Returns Java object from backend library

distributions-list clj

List of distributions.

drand clj

(drand)

(drand mx)

(drand mn mx)

Random double number with Mersenne Twister RNG.

fbm-noise clj

flip clj

(flip)

(flip p)

Returns 1 with given probability, 0 otherwise

frand clj

Random float number with Mersenne Twister RNG.

grand clj

(grand)

(grand stddev)

(grand mean stddev)

Random gaussian double number with Mersenne Twister RNG.

interpolations clj

List of possible noise interpolations as a map of names and values.

irand clj

(irand)

(irand mx)

(irand mn mx)

Random integer number with Mersenne Twister RNG.

jittered-sequence-generator clj

(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).

See also sequence-generator.

likelihood clj

(likelihood d vs)

Likelihood of samples

log-likelihood clj

(log-likelihood d vs)

Log likelihood of samples

lrand clj

(lrand)

(lrand mx)

(lrand mn mx)

Random long number with Mersenne Twister RNG.

MultivariateDistributionProto clj protocol

Get information from distributions.

covariance clj

(covariance d)

Variance

means clj

(means d)

Mean

noise clj

(noise x)

(noise x y)

(noise x y z)

Create improved Perlin Noise.

6 octaves, quintic interpolation.

noise-types clj

List of possible noise types as a map of names and values.

observe clj

(observe d v)

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

random-noise-cfg clj

(random-noise-cfg)

Create random noise configuration.

random-noise-fn clj

(random-noise-fn)

(random-noise-fn cfg)

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.

randval clj macro

(randval v1 v2)

(randval prob v1 v2)

Retrun value with given probability (default 0.5)

ridgedmulti-noise clj

rng clj multimethod

Create RNG for given name (as keyword) and optional seed. Return object enhanced with RNGProto. See: rngs-list for names.

RNGProto clj protocol

Defines set of random functions for different RNGs or distributions returning primitive values.

->seq clj

(->seq t)

(->seq t n)

Returns sequence of random samples limited to optional n values.

brandom clj

(brandom t)

(brandom t thr)

Boolean random. Returns true or false with equal probability. You can set probability for true setting thr (from [0-1] range).

See brand.

drandom clj

(drandom t)

(drandom t mx)

(drandom t mn mx)

Random double.

For RNGs: 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).

See drand.

For distributions, just returns random double (call without parameters).

frandom clj

(frandom t)

(frandom t mx)

(frandom t mn mx)

Random float.

For RNGs: 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).

See frand.

For distributions, just returns random float (call without parameters).

grandom clj

(grandom t)

(grandom t std)

(grandom t mean std)

Random double from gaussian distribution. 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).

See grand.

irandom clj

(irandom t)

(irandom t mx)

(irandom t mn mx)

Random integer.

For RNGs: 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).

See irand.

For distributions, just returns random integer (call without parameters).

lrandom clj

(lrandom t)

(lrandom t mx)

(lrandom t mn mx)

Random long.

For RNGs: As default returns random long from full long range. When mx is passed, range is set to [0, mx). When mn is passed, range is set to [mn, mx).

See lrand.

For distributions, just returns random long (call without parameters).

set-seed! clj

(set-seed! t v)

Sets seed. Returns RNG or distribution itself.

rngs-list clj

List of all possible RNGs.

sequence-generator clj 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 - 1-4
• :halton - 1-40
• :sobol - 1-1000
• the rest - 1+

See also jittered-sequence-generator.

sequence-generators-list clj

List of random sequence generator. See sequence-generator.

simplex clj

(simplex x)

(simplex x y)

(simplex x y z)

Create Simplex noise. 6 octaves.

single-noise clj

synced-rng clj

(synced-rng m)

(synced-rng m seed)

Create synchronized RNG for given name and optional seed. Wraps rng method.

UnivariateDistributionProto clj protocol

lower-bound clj

(lower-bound d)

Lower value

mean clj

(mean d)

Mean

upper-bound clj

(upper-bound d)

Higher value

variance clj

(variance d)

Variance

vnoise clj

(vnoise x)

(vnoise x y)

(vnoise x y z)

Value Noise.

6 octaves, Hermite interpolation (cubic, h01).