fastmath.random — generateme/fastmath 2.2.1

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 - 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. 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.

->seq clj

(->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.

ball-random clj

(ball-random dims)

(ball-random rng dims)

Return random vector from a ball

billow-noise clj

(billow-noise)

(billow-noise cfg__6408__auto__)

Create billow-noise function with optional configuration.

brand clj

Random boolean with default RNG.

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

brandom clj

(brandom rng)

(brandom rng p)

Random boolean with provided RNG

ccdf clj

(ccdf d v)

Complementary cumulative probability.

cdf clj

(cdf d v)

(cdf d v1 v2)

Cumulative probability.

continuous? clj

(continuous? d)

Does distribution support continuous domain?

covariance clj

(covariance d)

Distribution covariance matrix (for multivariate distributions)

default-normal clj

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

default-rng clj

Default RNG - JDK

dimensions clj

(dimensions d)

Distribution dimensionality

discrete-noise clj

(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).

distribution-id clj

(distribution-id d)

Distribution identifier as keyword.

distribution-parameters clj

(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.

distribution? clj

(distribution? distr)

Checks if distr is a distribution object.

distributions-list clj

List of distributions.

drand clj

(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).

drandom clj

(drandom rng)

(drandom rng mx)

(drandom rng mn mx)

Random double number with provided RNG

fbm-noise clj

(fbm-noise)

(fbm-noise cfg__6408__auto__)

Create fbm-noise function with optional configuration.

flip clj

(flip)

(flip p)

Returns 1 with given probability, 0 otherwise

flipb clj

(flipb)

(flipb p)

Returns true with given probability, false otherwise

frand clj

(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).

frandom clj

(frandom rng)

(frandom rng mx)

(frandom rng mn mx)

Random double number with provided RNG

grand clj

(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).

grandom clj

(grandom rng)

(grandom rng stddev)

(grandom rng mean stddev)

Random gaussian double number with provided RNG

icdf clj

(icdf d v)

Inverse cumulative probability

integrate-pdf clj

(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 pdf-func mn mx steps)

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

irand clj

(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).

irandom clj

(irandom rng)

(irandom rng mx)

(irandom rng mn mx)

Random integer number with provided RNG

jittered-sequence-generator clj

(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.

likelihood clj

(likelihood d vs)

Likelihood of samples

log-likelihood clj

(log-likelihood d vs)

Log likelihood of samples

lower-bound clj

(lower-bound d)

Distribution lowest supported value

lpdf clj

(lpdf d v)

Log density

lrand clj

(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).

lrandom clj

(lrandom rng)

(lrandom rng mx)

(lrandom rng mn mx)

Random long number with provided RNG

mean clj

(mean d)

Distribution mean

means clj

(means d)

Distribution means (for multivariate distributions)

noise clj

(noise x)

(noise x y)

(noise x y z)

Improved Perlin Noise.

6 octaves, quintic interpolation.

noise-generators clj

List of possible noise generators as a map of names and functions.

noise-interpolations clj

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

noise-types clj

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

observe clj macro

(observe d vs)

Log likelihood of samples. Alias for log-likelihood.

observe1 clj

(observe1 d v)

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

pdf clj

(pdf d v)

Density

probability clj

(probability d v)

Probability (PMF)

random-noise-cfg clj

(random-noise-cfg)

(random-noise-cfg pre-config)

Create random noise configuration.

Optional map with fixed values.

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)

(randval prob)

(randval v1 v2)

(randval prob v1 v2)

Return value with given probability (default 0.5)

ridgedmulti-noise clj

(ridgedmulti-noise)

(ridgedmulti-noise cfg__6408__auto__)

Create ridgedmulti-noise function with optional configuration.

rng clj multimethod

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

rngs-list clj

List of all possible RNGs.

sample clj

(sample d)

Random sample

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)
• :ball - from an unit ball

Possible dimensions:

• :r2 - 1-15
• :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.

set-seed clj

(set-seed)

(set-seed v)

(set-seed rng v)

Create and return new RNG

set-seed! clj

(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

simplex clj

(simplex x)

(simplex x y)

(simplex x y z)

Simplex noise. 6 octaves.

single-noise clj

(single-noise)

(single-noise cfg__6408__auto__)

Create single-noise function with optional configuration.

source-object clj

(source-object d)

Returns Java or proxy object from backend library (if available)

synced-rng clj

(synced-rng m)

(synced-rng m seed)

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

upper-bound clj

(upper-bound d)

Distribution highest supported value

variance clj

(variance d)

Distribution variance

vnoise clj

(vnoise x)

(vnoise x y)

(vnoise x y z)

Value Noise.

6 octaves, Hermite interpolation (cubic, h01).

warp-noise-fn clj

(warp-noise-fn)

(warp-noise-fn noise)

(warp-noise-fn noise scale)

(warp-noise-fn noise scale depth)

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.