random sampling

0.0.0

Functions to generate random samples with various distributions

Table of Contents

About Random-Sampling

This library provides additional functions used in statistics or random generation. It provides a variety of distribution functions to provide a biased random number generation and generators for random numbers on 3D volumes.

How To

This library relies on random-state for uniform random number generation. As such, you can pick from a variety of underlying sources of randomness to drive the other algorithms in this library. For multivariate distributions such as over volumes, it relies on the 3d-math library for vector and matrix representation.

To generate samples, simply invoke one of the various functions exposed by this library. To influence the underlying random source, set or bind the org.shirakumo.random-state:*generator*.

Sampling for the following volume types is available:

box
convex-mesh
cylinder
disc
half-sphere
normal
pill
sphere
triangle

The following distribution functions are available:

bernoulli
beta
binomial
-binomial
cauchy
chi-squared
exponential
fdist
flat
gamma
gaussian-tail
gaussian
geometric
gumbel-1
gumbel-2
laplace
levy-skew
levy
logarithmic
logistic
lognormal
pareto
poisson
rayleigh-tail
rayleigh
tdist
weibull

Most distributions also have their probility density function available. You can retrieve it via the pdf function. Every distribution function also has a random-state:generator of the same name defined. Those generators rely on an underlying generator source to draw randomness from, and will then turn that into a random float biased according to the distribution.

System Information

Version: 0.0.0

Dependencies:

Author: Yukari Hafner

License: zlib

Homepage: https://Shinmera.github.io/random-sampling/

Bug Tracker: https://github.com/Shinmera/random-sampling/issues

Sources: https://github.com/Shinmera/random-sampling.git

Definition Index

ORG.SHIRAKUMO.RANDOM-SAMPLING

No documentation provided.

EXTERNAL STRUCTURE
-BINOMIAL
Source
No documentation provided.
EXTERNAL STRUCTURE
BERNOULLI
Source
No documentation provided.
EXTERNAL STRUCTURE
BETA
Source
No documentation provided.
EXTERNAL STRUCTURE
BINOMIAL
Source
No documentation provided.
EXTERNAL STRUCTURE
CAUCHY
Source
No documentation provided.
EXTERNAL STRUCTURE
CHI-SQUARED
Source
No documentation provided.

EXTERNAL STRUCTURE

DISTRIBUTION

Supertype for all distribution generators.

A distribution generator is a random-state generator that uses an
underlying source generator to obtain random samples, and then biases
them according to the represented distribution.

To control the source, pass the :SOURCE initarg or bind
RANDOM-STATE:*GENERATOR* around the constructor. The resulting
generator will only output SINGLE-FLOAT samples.

See RANDOM-STATE:GENERATOR
See RANDOM-STATE:*GENERATOR*

EXTERNAL STRUCTURE
EXPONENTIAL
Source
No documentation provided.
EXTERNAL STRUCTURE
FDIST
Source
No documentation provided.
EXTERNAL STRUCTURE
FLAT
Source
No documentation provided.
EXTERNAL STRUCTURE
GAMMA
Source
No documentation provided.
EXTERNAL STRUCTURE
GAUSSIAN
Source
No documentation provided.
EXTERNAL STRUCTURE
GAUSSIAN-TAIL
Source
No documentation provided.
EXTERNAL STRUCTURE
GEOMETRIC
Source
No documentation provided.
EXTERNAL STRUCTURE
GUMBEL-1
Source
No documentation provided.
EXTERNAL STRUCTURE
GUMBEL-2
Source
No documentation provided.
EXTERNAL STRUCTURE
LAPLACE
Source
No documentation provided.
EXTERNAL STRUCTURE
LEVY
Source
No documentation provided.
EXTERNAL STRUCTURE
LEVY-SKEW
Source
No documentation provided.
EXTERNAL STRUCTURE
LOGARITHMIC
Source
No documentation provided.
EXTERNAL STRUCTURE
LOGISTIC
Source
No documentation provided.
EXTERNAL STRUCTURE
LOGNORMAL
Source
No documentation provided.
EXTERNAL STRUCTURE
PARETO
Source
No documentation provided.
EXTERNAL STRUCTURE
POISSON
Source
No documentation provided.
EXTERNAL STRUCTURE
RAYLEIGH
Source
No documentation provided.
EXTERNAL STRUCTURE
RAYLEIGH-TAIL
Source
No documentation provided.
EXTERNAL STRUCTURE
TDIST
Source
No documentation provided.
EXTERNAL STRUCTURE
WEIBULL
Source
No documentation provided.

EXTERNAL FUNCTION

-BINOMIAL

P
N
&OPTIONAL
RESULT0
&REST

Draws a sample from the negative binomial distribution.

See BINOMIAL
See -BINOMIAL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

-BINOMIAL-PDF

X
P
N
&REST

Computes the probability density of the given sample X under the -binomial distribution.

See PDF
See -BINOMIAL

EXTERNAL FUNCTION

BERNOULLI

P
&OPTIONAL
RESULT0
&REST

Draws a sample from the Bernoulli distribution.

See BERNOULLI-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

BERNOULLI-PDF

X
P
&REST

Computes the probability density of the given sample X under the Bernoulli distribution.

See PDF
See BERNOULLI

EXTERNAL FUNCTION

BETA

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the beta distribution.

See BETA-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

BETA-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the beta distribution.

See PDF
See BETA

EXTERNAL FUNCTION

BINOMIAL

P
N
&OPTIONAL
RESULT0
&REST

Draws a sample from the binomial distribution.

See -BINOMIAL
See BINOMIAL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

BINOMIAL-PDF

X
P
N
&REST

Computes the probability density of the given sample X under the binomial distribution.

See PDF
See BINOMIAL

EXTERNAL FUNCTION

BOX

BSIZE
&OPTIONAL
RESULT0
&REST

Samples a uniform box.

BSIZE should be the half-size of the box in each direction, with the
box being centered at 0,0,0.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

CAUCHY

A
&OPTIONAL
RESULT0
&REST

Draws a sample from the Cauchy distribution.

See CAUCHY-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

CAUCHY-PDF

X
A
&REST

Computes the probability density of the given sample X under the Cauchy distribution.

See PDF
See CAUCHY

EXTERNAL FUNCTION

CHI-SQUARED

NU
&OPTIONAL
RESULT0
&REST

Draws a sample from the chi-squared distribution.

See CHI-SQUARED-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

CHI-SQUARED-PDF

X
NU
&REST

Computes the probability density of the given sample X under the chi-squared distribution.

See PDF
See CHI-SQUARED

EXTERNAL FUNCTION

CONVEX-MESH

VERTICES
FACES
&OPTIONAL
RESULT0
&REST

Samples a uniform convex mesh.

VERTICES must be a (SIMPLE-ARRAY SINGLE-FLOAT (*)) that contains the
packed representation of the vertex coordinates.
FACES must be a (SIMPLE-ARRAY (UNSIGNED-BYTE 16) (*)) that contains
the packed indices of the vertices that compose the faces. The
vertices of each face must occur in counter-clockwise order.
Both arrays must have a length that is a multiple of 3.

The consequences are undefined if the mesh described by VERTICES and
FACES is not convex and manifold.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

CYLINDER

RADIUS
HEIGHT
&OPTIONAL
NORMAL
RESULT0
&REST

Samples a uniform cylinder.

HEIGHT is the half-height of the cylinder with the cylinder's center
always at 0,0,0.
NORMAL may be a normalised vector pointing in the UP direction of the
cylinder.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

DISC

&OPTIONAL
RADIUS
NORMAL
RESULT0
&REST

Samples a uniform disc.

NORMAL may be a normalised vector pointing in the UP direction of the
disc's plane.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

EXPONENTIAL

MU
&OPTIONAL
RESULT0
&REST

Draws a sample from the exponential distribution.

See EXPONENTIAL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

EXPONENTIAL-PDF

X
MU
&REST

Computes the probability density of the given sample X under the exponential distribution.

See PDF
See EXPONENTIAL

EXTERNAL FUNCTION

FDIST

NU-1
NU-2
&OPTIONAL
RESULT0
&REST

Draws a sample from the F distribution.

See FDIST-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

FDIST-PDF

X
NU-1
NU-2
&REST

Computes the probability density of the given sample X under the F distribution.

See PDF
See FDIST

EXTERNAL FUNCTION

FLAT

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the flat distribution.

See FLAT-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

FLAT-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the flat distribution.

See PDF
See FLAT

EXTERNAL FUNCTION

GAMMA

A
&OPTIONAL
B
RESULT0
&REST

Draws a sample from the gamma distribution.

See GAMMA-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GAMMA-PDF

X
A
&OPTIONAL
B
&REST

Computes the probability density of the given sample X under the gamma distribution.

See PDF
See GAMMA

EXTERNAL FUNCTION

GAUSSIAN

&OPTIONAL
SIGMA
RESULT0
&REST

Draws a sample from the Gaussian distribution.

See GAUSSIAN-TAIL
See GAUSSIAN-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GAUSSIAN-PDF

X
&OPTIONAL
SIGMA
&REST

Computes the probability density of the given sample X under the Gaussian distribution.

See PDF
See GAUSSIAN

EXTERNAL FUNCTION

GAUSSIAN-TAIL

A
&OPTIONAL
SIGMA
RESULT0
&REST

Draws a sample from the Gaussian-tail distribution.

See GAUSSIAN
See GAUSSIAN-TAIL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GAUSSIAN-TAIL-PDF

X
A
&OPTIONAL
SIGMA
&REST

Computes the probability density of the given sample X under the Gaussian-tail distribution.

See PDF
See GAUSSIAN-TAIL

EXTERNAL FUNCTION

GEOMETRIC

P
&OPTIONAL
RESULT0
&REST

Draws a sample from the geometric distribution.

See GEOMETRIC-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GEOMETRIC-PDF

X
P
&REST

Computes the probability density of the given sample X under the geometric distribution.

See PDF
See GEOMETRIC

EXTERNAL FUNCTION

GUMBEL-1

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the Gumbel-1 distribution.

See GUMBEL-1-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GUMBEL-1-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the Gumbel-1 distribution.

See PDF
See GUMBEL-1

EXTERNAL FUNCTION

GUMBEL-2

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the Gumbel-2 distribution.

See GUMBEL-2-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

GUMBEL-2-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the Gumbel-2 distribution.

See PDF
See GUMBEL-2

EXTERNAL FUNCTION

HALF-SPHERE

&OPTIONAL
NORMAL
RADIUS
RESULT0
&REST

Samples a uniform half-sphere.

RADIUS may either be a real of the radius, or a VEC3 to generate an
ellipsoid. NORMAL may be a normalised vector pointing in the UP
direction of the half-sphere.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

LAPLACE

A
&OPTIONAL
RESULT0
&REST

Draws a sample from the Laplace distribution.

See LAPLACE-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

LAPLACE-PDF

X
A
&REST

Computes the probability density of the given sample X under the Laplace distribution.

See PDF
See LAPLACE

EXTERNAL FUNCTION

LEVY

C
ALPHA
&OPTIONAL
RESULT0
&REST

Draws a sample from the Levy distribution.

See LEVY-SKEW
See MAP-SAMPLES

EXTERNAL FUNCTION

LEVY-SKEW

C
ALPHA
BETA
&OPTIONAL
RESULT0
&REST

Draws a sample from the Levy-skew distribution.

See LEVY
See MAP-SAMPLES

EXTERNAL FUNCTION

LOGARITHMIC

P
&OPTIONAL
RESULT0
&REST

Draws a sample from the logarithmic distribution.

See LOGARITHMIC-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

LOGARITHMIC-PDF

X
P
&REST

Computes the probability density of the given sample X under the logarithmic distribution.

See PDF
See LOGARITHMIC

EXTERNAL FUNCTION

LOGISTIC

A
&OPTIONAL
RESULT0
&REST

Draws a sample from the logistic distribution.

See LOGISTIC-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

LOGISTIC-PDF

X
A
&REST

Computes the probability density of the given sample X under the logistic distribution.

See PDF
See LOGISTIC

EXTERNAL FUNCTION

LOGNORMAL

ZETA
SIGMA
&OPTIONAL
RESULT0
&REST

Draws a sample from the lognormal distribution.

See LOGNORMAL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

LOGNORMAL-PDF

X
ZETA
SIGMA
&REST

Computes the probability density of the given sample X under the lognormal distribution.

See PDF
See LOGNORMAL

EXTERNAL FUNCTION

MAP-SAMPLES

RESULT
SAMPLE-1
&REST

Gathers samples into RESULT, drawing them from SAMPLE-1.

RESULT may be one of the following:

  NULL      --- A single single-float is sampled and returned
  INTEGER   --- An array of result size is sampled and returned
  SEQUENCE  --- Each element of the sequence is set to a fresh sample

SAMPLE-1 must be a function of zero arguments and must return the
freshly drawn sample as a single-float.

This function is implicitly used by every distribution sampling
function. The optional RESULT argument of those functions corresponds
to the above.

EXTERNAL FUNCTION

MAP-VOLUME-SAMPLES

RESULT
SAMPLE-1
&REST

Gathers samples into RESULT, drawing them from SAMPLE-1.

RESULT may be one of the following:

  NULL      --- A fresh VEC3 is sampled and returned
  VEC3      --- The result is sampled and returned
  INTEGER   --- An array of result size is sampled and returned
  SEQUENCE  --- Each element of result is sampled and result is
                returned. Each element of result must be a VEC3

SAMPLE-1 must be a function of one argument, a VEC3, and must return
said VEC3 after performing its sampling operation to fill the vector's
elements.

This function is implicitly used by every volume sampling
function. The optional RESULT argument of those functions corresponds
to the above.

EXTERNAL FUNCTION

NORMAL

&OPTIONAL
RADIUS
RESULT0
&REST

Samples a uniform normal vector.

This is equivalent to sampling the surface of a sphere.

RADIUS may either be a real of the radius, or a VEC3 to generate an
ellipsoid.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

PARETO

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the Pareto distribution.

See PARETO-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

PARETO-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the Pareto distribution.

See PDF
See PARETO

EXTERNAL FUNCTION

PDF

DISTRIBUTION
&OPTIONAL
ERRORP
&REST

Returns the probability density function for the given distribution.

The distribution must be given as a name. If no PDF exists, and errorp
is true, an error is signalled.

Every PDF takes the same arguments as its corresponding distribution
function, plus an additional first argument, which is the sample for
which to evaluate the PDF.

EXTERNAL FUNCTION

PILL

RADIUS
HEIGHT
&OPTIONAL
NORMAL
RESULT0
&REST

Samples a uniform pill.

A pill is a cylinder with its caps being spheres.

HEIGHT is the half-height of the pill cylinder with the pill's center
always at 0,0,0. If the height is zero, this is equivalent to a
sphere.
NORMAL may be a normalised vector pointing in the UP direction of the
cylinder.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

POISSON

MU
&OPTIONAL
RESULT0
&REST

Draws a sample from the Poisson distribution.

See POISSON-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

POISSON-PDF

X
MU
&REST

Computes the probability density of the given sample X under the Poisson distribution.

See PDF
See POISSON

EXTERNAL FUNCTION

RAYLEIGH

SIGMA
&OPTIONAL
RESULT0
&REST

Draws a sample from the Rayleigh distribution.

See RAYLEIGH-TAIL
See RAYLEIGH-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

RAYLEIGH-PDF

X
SIGMA
&REST

Computes the probability density of the given sample X under the Rayleigh distribution.

See PDF
See RAYLEIGH

EXTERNAL FUNCTION

RAYLEIGH-TAIL

A
SIGMA
&OPTIONAL
RESULT0
&REST

Draws a sample from the Rayleigh-tail distribution.

See RAYLEIGH
See RAYLEIGH-TAIL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

RAYLEIGH-TAIL-PDF

X
A
SIGMA
&REST

Computes the probability density of the given sample X under the Rayleigh-tail distribution.

See PDF
See RAYLEIGH-TAIL

EXTERNAL FUNCTION

REJECTION-SAMPLE

GENERATOR
PREDICATE
&OPTIONAL
RESULT0
&REST

Perform rejection sampling using GENERATOR to draw samples and PREDICATE to determine whether to keep the sample.

GENERATOR must be a function of one argument, the VEC3 to sample.
PREDICATE must be a function of one argument, the VEC3 to examine, and
must return true if the sample is suitable.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

SPHERE

&OPTIONAL
RADIUS
RESULT0
&REST

Samples a uniform sphere.

RADIUS may either be a real of the radius, or a VEC3 to generate an
ellipsoid.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

SURFACE-NORMAL

&OPTIONAL
NORMAL
THETA
RESULT0
&REST

Samples a normal vector on a surface.

This is equivalent to sampling the surface of a half-sphere

NORMAL may be a normalised vector pointing in the UP direction of the
half-sphere. THETA may be the angle to which the sample is constrained
along the NORMAL.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

TDIST

NU
&OPTIONAL
RESULT0
&REST

Draws a sample from the T distribution.

See TDIST-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

TDIST-PDF

X
NU
&REST

Computes the probability density of the given sample X under the T distribution.

See PDF
See TDIST

EXTERNAL FUNCTION

TRIANGLE

P0
P1
P2
&OPTIONAL
RESULT0
&REST

Samples a uniform triangle.

P0, P1, P2 designate the corners of the triangle.

See MAP-VOLUME-SAMPLES

EXTERNAL FUNCTION

WEIBULL

A
B
&OPTIONAL
RESULT0
&REST

Draws a sample from the Weibull distribution.

See WEIBULL-PDF
See MAP-SAMPLES

EXTERNAL FUNCTION

WEIBULL-PDF

X
A
B
&REST

Computes the probability density of the given sample X under the Weibull distribution.

See PDF
See WEIBULL