NAME
PDL::GSL::Randist - Comprehensive Perl Data Language (PDL) binding to the GNU Scientific Library (GSL) Random Distribution (randist) functions.
SYNOPSIS
use PDL;
use PDL::GSL::RNG;
use PDL::GSL::Randist qw/:binomial :gaussian :multinomial/;
my $rng = PDL::GSL::RNG->new('taus');
$rng->set_seed(time);
### PDF/CDF
# pdf's are named "ran_DISTNAME_pdf" and cdf are called "cdf_DISTNAME_P" and
# "cdf_DISTNAME_Q". (Note: P + Q = 1)
# evaluate pdf/cdf at various x's
my $x_continuous = zeroes(21)->xlinvals(-1, 1); # -1 to -1 by .1
my $x_discrete = long 1 .. 10;
print ran_gaussian_pdf($x_continuous, .5);
print cdf_gaussian_P($x_continuous, .5);
print ran_binomial_pdf($x_discrete, .5, 20);
print cdf_binomial_P($x_discrete, .5, 20);
### Inverse CDF
my $P = zeroes(9)->xlinvals(.1, .9);
print cdf_gaussian_Pinv($P, .5);
# should give us back $x_continuous
print cdf_gaussian_Pinv(cdf_gaussian_P($x_continuous, .5), .5);
### Samplers
# sampling functions are called ran_DISTNAME. The first argument is always a
# PDL::GSL::RNG object. The following arguments are parameters specific to
# that dist. (n, p for binomial, sigma for gaussian, mu for exponential, etc.
# See the PDL::GSL::Randist pod).
#
# There are three ways to specify the output.
# 1) Pass nothing in the last parameter, in which case it'll return a scalar PDL.
print ran_binomial($rng, pdl(.5), long(100)); # n = 100, p = .5
print ran_gaussian($rng, pdl(3)); # sigma = 3.0
# 2) Pass an output-PDL to be filled with results:
my $counts = zeroes long, 10;
my $values = zeroes double, 10;
# draw 10 samples,put them in the outpdl
ran_binomial($rng, pdl(.5), long(100), $counts);
ran_gaussian($rng, pdl(3), $values);
# 3) Pass dimensions
# draw 10 samples, return as 1-D pdl.
print ran_binomial($rng, pdl(.5), long(100), 10);
print ran_gaussian($rng, pdl(3), 10);
# draw 100 samples, return as 10x10 pdl
print ran_binomial($rng, pdl(.5), long(100), 10, 10);
print ran_gaussian($rng, pdl(3), 10, 10);
# Multivariate dists like Multinomial are slighly different because the first
# dimensions are implicit:
# sample a single n=10 draw from a multinomial dist with p = [.1, .2, # .3, .4]
# return as a dim(4) PDL.
print ran_multinomial($rng, 10, pdl(.1, .2, .3, .4));
# draw 15 multinomial with p=[.1,.2,.3,.4] and return as 4 x 15
print ran_multinomial($rng, 10, pdl(.1, .2, .3, .4), 15);EXPORT
Nothing is exported by default. :all exports everything. :gaussian exports all gaussian functions, :binomial all binomial functions, etc. Tag names are in parentheses below.
NOTES
Function Naming Convention
Samplers are named "ran_RANDIST()" (eg. "ran_gaussian()"), probability density/mass functions are named "ran_RANDIST_pdf()" (eg. "ran_gaussian_pdf()"), cumulative distribution function are named "cdf_RANDIST_P()" and "cdf_RANDIST_Q()" (eg. "cdf_gaussian_P()" and "cdf_gaussian_Q()"), inverse cumulative distribution functions (quantiles) are named "cdf_RANDIST_Pinv()" and "cdf_RANDIST_Qinv()" (eg. "cdf_gaussian_Pinv()" and "cdf_gaussian_Qinv()").
The _Q CDF functions are complementary CDF functions: cdf_RANDIST_P + cdf_RANDIST_Q = 1. Both exist because it is often more accurate numerically to calculate the complementary CDF directly instead of calculating 1 - CDF.
A particular distribution may not have all 4 types of functions. (Discrete distributions don't have inverse CDF's, Levy distributions don't have pdf's, etc.).
Arguments
All of the univariate distributions functions have arguments identical (even in order) to their underlying C functions. For the multivariate functions, see their individual sections below.
Threading
Unless otherwise noted, PDL threading works on all variables expect the PDL::GSL::RNG argument for samplers.
More Documentation
Most of the documentation is automatically generated. For more details, see the The GSL Randist manual page.
Location Parameters
None of the functions provided by this module contain a 'location' parameter. For example, the gaussian functions only have a sigma argument, and not a mean. I thought about adding the location parameters to the appropriate randists, but this would be contrary to the goal of module to create a straight binding to GSL's Randist. Instead, I plan to make an alternative interface to the functions (possibly modelled after R) which includes such conveniences.
Bad Values
All the non-sampler functions should handle PDL's BAD values appropriately.
Floating point and integer PDL's
If you pass a floating point PDL to a function where an integer PDL is expected, it will be cast automatically to a integer, as in C, by truncation. (ADD MORE ON THIS.)
FUNCTIONS
Bernoulli Distribution (:bernoulli)
ran_bernoulli_pdf
Signature: (int val() ; double p() ; double [o] out())ran_bernoulli
Signature: (PDL::GSL::RNG rng(); double p() ; int [o] out())Usage:
my $single_draw = ran_bernoulli($rng, $p);
my $multi_draws = ran_bernoulli($rng, $p, [ ... output pdl dims ...] );
my $outpdl_draw = ran_bernoulli($rng, $p, $outpdl);Beta Distribution (:beta)
ran_beta_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_beta_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_beta_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_beta_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_beta_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_beta
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_beta($rng, $a, $b);
my $multi_draws = ran_beta($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_beta($rng, $a, $b, $outpdl);Binomial Distribution (:binomial)
ran_binomial_pdf
Signature: (int val() ; double p() ; int n() ; double [o] out())cdf_binomial_P
Signature: (int val() ; double p() ; int n() ; double [o] out())cdf_binomial_Q
Signature: (int val() ; double p() ; int n() ; double [o] out())ran_binomial
Signature: (PDL::GSL::RNG rng(); double p() ; int n() ; int [o] out())Usage:
my $single_draw = ran_binomial($rng, $p, $n);
my $multi_draws = ran_binomial($rng, $p, $n, [ ... output pdl dims ...] );
my $outpdl_draw = ran_binomial($rng, $p, $n, $outpdl);Cauchy Distribution (:cauchy)
ran_cauchy_pdf
Signature: (double val() ; double scale() ; double [o] out())cdf_cauchy_P
Signature: (double val() ; double scale() ; double [o] out())cdf_cauchy_Q
Signature: (double val() ; double scale() ; double [o] out())cdf_cauchy_Pinv
Signature: (double val() ; double scale() ; double [o] out())cdf_cauchy_Qinv
Signature: (double val() ; double scale() ; double [o] out())ran_cauchy
Signature: (PDL::GSL::RNG rng(); double scale() ; double [o] out())Usage:
my $single_draw = ran_cauchy($rng, $scale);
my $multi_draws = ran_cauchy($rng, $scale, [ ... output pdl dims ...] );
my $outpdl_draw = ran_cauchy($rng, $scale, $outpdl);Chi-squared Distribution (:chisq)
ran_chisq_pdf
Signature: (double val() ; double nu() ; double [o] out())cdf_chisq_P
Signature: (double val() ; double nu() ; double [o] out())cdf_chisq_Q
Signature: (double val() ; double nu() ; double [o] out())cdf_chisq_Pinv
Signature: (double val() ; double nu() ; double [o] out())cdf_chisq_Qinv
Signature: (double val() ; double nu() ; double [o] out())ran_chisq
Signature: (PDL::GSL::RNG rng(); double nu() ; double [o] out())Usage:
my $single_draw = ran_chisq($rng, $nu);
my $multi_draws = ran_chisq($rng, $nu, [ ... output pdl dims ...] );
my $outpdl_draw = ran_chisq($rng, $nu, $outpdl);Exponential Distribution (:exponential)
ran_exponential_pdf
Signature: (double val() ; double mu() ; double [o] out())cdf_exponential_P
Signature: (double val() ; double mu() ; double [o] out())cdf_exponential_Q
Signature: (double val() ; double mu() ; double [o] out())cdf_exponential_Pinv
Signature: (double val() ; double mu() ; double [o] out())cdf_exponential_Qinv
Signature: (double val() ; double mu() ; double [o] out())ran_exponential
Signature: (PDL::GSL::RNG rng(); double mu() ; double [o] out())Usage:
my $single_draw = ran_exponential($rng, $mu);
my $multi_draws = ran_exponential($rng, $mu, [ ... output pdl dims ...] );
my $outpdl_draw = ran_exponential($rng, $mu, $outpdl);The Exponential Power Distribution (:exppow)
ran_exppow_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_exppow_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_exppow_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_exppow
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_exppow($rng, $a, $b);
my $multi_draws = ran_exppow($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_exppow($rng, $a, $b, $outpdl);F-distribution (:fdist)
ran_fdist_pdf
Signature: (double val() ; double nu1() ; double nu2() ; double [o] out())cdf_fdist_P
Signature: (double val() ; double nu1() ; double nu2() ; double [o] out())cdf_fdist_Q
Signature: (double val() ; double nu1() ; double nu2() ; double [o] out())cdf_fdist_Pinv
Signature: (double val() ; double nu1() ; double nu2() ; double [o] out())cdf_fdist_Qinv
Signature: (double val() ; double nu1() ; double nu2() ; double [o] out())ran_fdist
Signature: (PDL::GSL::RNG rng(); double nu1() ; double nu2() ; double [o] out())Usage:
my $single_draw = ran_fdist($rng, $nu1, $nu2);
my $multi_draws = ran_fdist($rng, $nu1, $nu2, [ ... output pdl dims ...] );
my $outpdl_draw = ran_fdist($rng, $nu1, $nu2, $outpdl);Flat (Uniform) Distribution (:flat)
ran_flat_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_flat_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_flat_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_flat_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_flat_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_flat
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_flat($rng, $a, $b);
my $multi_draws = ran_flat($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_flat($rng, $a, $b, $outpdl);Gamma Distribution (:gamma)
ran_gamma_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gamma_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gamma_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gamma_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gamma_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_gamma
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_gamma($rng, $a, $b);
my $multi_draws = ran_gamma($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gamma($rng, $a, $b, $outpdl);Gaussian Distribution (:gaussian)
ran_gaussian_pdf
Signature: (double val() ; double sigma() ; double [o] out())cdf_gaussian_P
Signature: (double val() ; double sigma() ; double [o] out())cdf_gaussian_Q
Signature: (double val() ; double sigma() ; double [o] out())cdf_gaussian_Pinv
Signature: (double val() ; double sigma() ; double [o] out())cdf_gaussian_Qinv
Signature: (double val() ; double sigma() ; double [o] out())ran_gaussian
Signature: (PDL::GSL::RNG rng(); double sigma() ; double [o] out())Usage:
my $single_draw = ran_gaussian($rng, $sigma);
my $multi_draws = ran_gaussian($rng, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gaussian($rng, $sigma, $outpdl);Gaussian Tail Distribution (:gaussian_tail)
ran_gaussian_tail_pdf
Signature: (double val() ; double a() ; double sigma() ; double [o] out())ran_gaussian_tail
Signature: (PDL::GSL::RNG rng(); double a() ; double sigma() ; double [o] out())Usage:
my $single_draw = ran_gaussian_tail($rng, $a, $sigma);
my $multi_draws = ran_gaussian_tail($rng, $a, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gaussian_tail($rng, $a, $sigma, $outpdl);Geometric Distribution (:geometric)
ran_geometric_pdf
Signature: (int val() ; double p() ; double [o] out())cdf_geometric_P
Signature: (int val() ; double p() ; double [o] out())cdf_geometric_Q
Signature: (int val() ; double p() ; double [o] out())ran_geometric
Signature: (PDL::GSL::RNG rng(); double p() ; int [o] out())Usage:
my $single_draw = ran_geometric($rng, $p);
my $multi_draws = ran_geometric($rng, $p, [ ... output pdl dims ...] );
my $outpdl_draw = ran_geometric($rng, $p, $outpdl);Type-1 Gumbel Distribution (:gumbel1)
ran_gumbel1_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel1_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel1_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel1_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel1_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_gumbel1
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_gumbel1($rng, $a, $b);
my $multi_draws = ran_gumbel1($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gumbel1($rng, $a, $b, $outpdl);The Type-2 Gumbel Distribution (:gumbel2)
ran_gumbel2_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel2_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel2_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel2_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_gumbel2_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_gumbel2
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_gumbel2($rng, $a, $b);
my $multi_draws = ran_gumbel2($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gumbel2($rng, $a, $b, $outpdl);Hypergeometric Distribution (:hypergeometric)
ran_hypergeometric_pdf
Signature: (int val() ; int n1() ; int n2() ; int t() ; double [o] out())cdf_hypergeometric_P
Signature: (int val() ; int n1() ; int n2() ; int t() ; double [o] out())cdf_hypergeometric_Q
Signature: (int val() ; int n1() ; int n2() ; int t() ; double [o] out())ran_hypergeometric
Signature: (PDL::GSL::RNG rng(); int n1() ; int n2() ; int t() ; int [o] out())Usage:
my $single_draw = ran_hypergeometric($rng, $n1, $n2, $t);
my $multi_draws = ran_hypergeometric($rng, $n1, $n2, $t, [ ... output pdl dims ...] );
my $outpdl_draw = ran_hypergeometric($rng, $n1, $n2, $t, $outpdl);Landau Distribution (:landau)
ran_landau_pdf
Signature: (double val() ; double [o] out())ran_landau
Signature: (PDL::GSL::RNG rng(); double [o] out())Usage:
my $single_draw = ran_landau($rng, );
my $multi_draws = ran_landau($rng, , [ ... output pdl dims ...] );
my $outpdl_draw = ran_landau($rng, , $outpdl);The Laplace Distribution (:laplace)
ran_laplace_pdf
Signature: (double val() ; double a() ; double [o] out())cdf_laplace_P
Signature: (double val() ; double a() ; double [o] out())cdf_laplace_Q
Signature: (double val() ; double a() ; double [o] out())cdf_laplace_Pinv
Signature: (double val() ; double a() ; double [o] out())cdf_laplace_Qinv
Signature: (double val() ; double a() ; double [o] out())ran_laplace
Signature: (PDL::GSL::RNG rng(); double a() ; double [o] out())Usage:
my $single_draw = ran_laplace($rng, $a);
my $multi_draws = ran_laplace($rng, $a, [ ... output pdl dims ...] );
my $outpdl_draw = ran_laplace($rng, $a, $outpdl);Levy alpha-Stable Distributions (:levy)
ran_levy
Signature: (PDL::GSL::RNG rng(); double scale() ; double stability() ; double [o] out())Usage:
my $single_draw = ran_levy($rng, $scale, $stability);
my $multi_draws = ran_levy($rng, $scale, $stability, [ ... output pdl dims ...] );
my $outpdl_draw = ran_levy($rng, $scale, $stability, $outpdl);Levy skew alpha-Stable Distribution (:levy_skew)
ran_levy_skew
Signature: (PDL::GSL::RNG rng(); double scale() ; double stability() ; double skewness() ; double [o] out())Usage:
my $single_draw = ran_levy_skew($rng, $scale, $stability, $skewness);
my $multi_draws = ran_levy_skew($rng, $scale, $stability, $skewness, [ ... output pdl dims ...] );
my $outpdl_draw = ran_levy_skew($rng, $scale, $stability, $skewness, $outpdl);Logarithmic Distribution (:logarithmic)
ran_logarithmic_pdf
Signature: (int val() ; double p() ; double [o] out())ran_logarithmic
Signature: (PDL::GSL::RNG rng(); double p() ; int [o] out())Usage:
my $single_draw = ran_logarithmic($rng, $p);
my $multi_draws = ran_logarithmic($rng, $p, [ ... output pdl dims ...] );
my $outpdl_draw = ran_logarithmic($rng, $p, $outpdl);Logistic Distribution (:logistic)
ran_logistic_pdf
Signature: (double val() ; double a() ; double [o] out())cdf_logistic_P
Signature: (double val() ; double a() ; double [o] out())cdf_logistic_Q
Signature: (double val() ; double a() ; double [o] out())cdf_logistic_Pinv
Signature: (double val() ; double a() ; double [o] out())cdf_logistic_Qinv
Signature: (double val() ; double a() ; double [o] out())ran_logistic
Signature: (PDL::GSL::RNG rng(); double a() ; double [o] out())Usage:
my $single_draw = ran_logistic($rng, $a);
my $multi_draws = ran_logistic($rng, $a, [ ... output pdl dims ...] );
my $outpdl_draw = ran_logistic($rng, $a, $outpdl);Lognormal Distribution (:lognormal)
ran_lognormal_pdf
Signature: (double val() ; double zeta() ; double sigma() ; double [o] out())cdf_lognormal_P
Signature: (double val() ; double zeta() ; double sigma() ; double [o] out())cdf_lognormal_Q
Signature: (double val() ; double zeta() ; double sigma() ; double [o] out())cdf_lognormal_Pinv
Signature: (double val() ; double zeta() ; double sigma() ; double [o] out())cdf_lognormal_Qinv
Signature: (double val() ; double zeta() ; double sigma() ; double [o] out())ran_lognormal
Signature: (PDL::GSL::RNG rng(); double zeta() ; double sigma() ; double [o] out())Usage:
my $single_draw = ran_lognormal($rng, $zeta, $sigma);
my $multi_draws = ran_lognormal($rng, $zeta, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_lognormal($rng, $zeta, $sigma, $outpdl);Negative Binomial Distribution (:negative_binomial)
ran_negative_binomial_pdf
Signature: (int val() ; double p() ; double n() ; double [o] out())cdf_negative_binomial_P
Signature: (int val() ; double p() ; double n() ; double [o] out())cdf_negative_binomial_Q
Signature: (int val() ; double p() ; double n() ; double [o] out())ran_negative_binomial
Signature: (PDL::GSL::RNG rng(); double p() ; double n() ; int [o] out())Usage:
my $single_draw = ran_negative_binomial($rng, $p, $n);
my $multi_draws = ran_negative_binomial($rng, $p, $n, [ ... output pdl dims ...] );
my $outpdl_draw = ran_negative_binomial($rng, $p, $n, $outpdl);Pareto Distribution (:pareto)
ran_pareto_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_pareto_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_pareto_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_pareto_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_pareto_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_pareto
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_pareto($rng, $a, $b);
my $multi_draws = ran_pareto($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_pareto($rng, $a, $b, $outpdl);Pascal Distribution (:pascal)
ran_pascal_pdf
Signature: (int val() ; double p() ; int n() ; double [o] out())cdf_pascal_P
Signature: (int val() ; double p() ; int n() ; double [o] out())cdf_pascal_Q
Signature: (int val() ; double p() ; int n() ; double [o] out())ran_pascal
Signature: (PDL::GSL::RNG rng(); double p() ; int n() ; int [o] out())Usage:
my $single_draw = ran_pascal($rng, $p, $n);
my $multi_draws = ran_pascal($rng, $p, $n, [ ... output pdl dims ...] );
my $outpdl_draw = ran_pascal($rng, $p, $n, $outpdl);Poisson Distribution (:poisson)
ran_poisson_pdf
Signature: (int val() ; double mu() ; double [o] out())cdf_poisson_P
Signature: (int val() ; double mu() ; double [o] out())cdf_poisson_Q
Signature: (int val() ; double mu() ; double [o] out())ran_poisson
Signature: (PDL::GSL::RNG rng(); double mu() ; int [o] out())Usage:
my $single_draw = ran_poisson($rng, $mu);
my $multi_draws = ran_poisson($rng, $mu, [ ... output pdl dims ...] );
my $outpdl_draw = ran_poisson($rng, $mu, $outpdl);Rayleigh Distribution (:rayleigh)
ran_rayleigh_pdf
Signature: (double val() ; double sigma() ; double [o] out())cdf_rayleigh_P
Signature: (double val() ; double sigma() ; double [o] out())cdf_rayleigh_Q
Signature: (double val() ; double sigma() ; double [o] out())cdf_rayleigh_Pinv
Signature: (double val() ; double sigma() ; double [o] out())cdf_rayleigh_Qinv
Signature: (double val() ; double sigma() ; double [o] out())ran_rayleigh
Signature: (PDL::GSL::RNG rng(); double sigma() ; double [o] out())Usage:
my $single_draw = ran_rayleigh($rng, $sigma);
my $multi_draws = ran_rayleigh($rng, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_rayleigh($rng, $sigma, $outpdl);Rayleigh Tail Distribution (:rayleigh_tail)
ran_rayleigh_tail_pdf
Signature: (double val() ; double a() ; double sigma() ; double [o] out())ran_rayleigh_tail
Signature: (PDL::GSL::RNG rng(); double a() ; double sigma() ; double [o] out())Usage:
my $single_draw = ran_rayleigh_tail($rng, $a, $sigma);
my $multi_draws = ran_rayleigh_tail($rng, $a, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_rayleigh_tail($rng, $a, $sigma, $outpdl);t-distribution (:tdist)
ran_tdist_pdf
Signature: (double val() ; double nu() ; double [o] out())cdf_tdist_P
Signature: (double val() ; double nu() ; double [o] out())cdf_tdist_Q
Signature: (double val() ; double nu() ; double [o] out())cdf_tdist_Pinv
Signature: (double val() ; double nu() ; double [o] out())cdf_tdist_Qinv
Signature: (double val() ; double nu() ; double [o] out())ran_tdist
Signature: (PDL::GSL::RNG rng(); double nu() ; double [o] out())Usage:
my $single_draw = ran_tdist($rng, $nu);
my $multi_draws = ran_tdist($rng, $nu, [ ... output pdl dims ...] );
my $outpdl_draw = ran_tdist($rng, $nu, $outpdl);Weibull Distribution (:weibull)
ran_weibull_pdf
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_weibull_P
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_weibull_Q
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_weibull_Pinv
Signature: (double val() ; double a() ; double b() ; double [o] out())cdf_weibull_Qinv
Signature: (double val() ; double a() ; double b() ; double [o] out())ran_weibull
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_weibull($rng, $a, $b);
my $multi_draws = ran_weibull($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_weibull($rng, $a, $b, $outpdl);Alternate Gaussian Samplers (:gaussian)
ran_gaussian_ratio_method
Signature: (PDL::GSL::RNG rng(); double sigma() ; double [o] out())Usage:
my $single_draw = ran_gaussian_ratio_method($rng, $sigma);
my $multi_draws = ran_gaussian_ratio_method($rng, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gaussian_ratio_method($rng, $sigma, $outpdl);ran_gaussian_ziggurat
Signature: (PDL::GSL::RNG rng(); double sigma() ; double [o] out())Usage:
my $single_draw = ran_gaussian_ziggurat($rng, $sigma);
my $multi_draws = ran_gaussian_ziggurat($rng, $sigma, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gaussian_ziggurat($rng, $sigma, $outpdl);Alternate Gamma Samplers (:gamma)
ran_gamma_knuth
Signature: (PDL::GSL::RNG rng(); double a() ; double b() ; double [o] out())Usage:
my $single_draw = ran_gamma_knuth($rng, $a, $b);
my $multi_draws = ran_gamma_knuth($rng, $a, $b, [ ... output pdl dims ...] );
my $outpdl_draw = ran_gamma_knuth($rng, $a, $b, $outpdl);Multinomial Distribution (:multinomial)
ran_multinomial
Draws $numdraws samples from a multinomial distribution with probabilities $p, returns counts in a pdl with the same (first) dimensions as $p.
Signature: (PDL::GSL::RNG rng(); int numdraws(); double p(n); int [o] counts(n))Usage:
ran_multinomial($rng, $numdraws, $p, $outpdl); # $outpdl's first dimensions must be ($p->dims())
my $single_draw = ran_multinomial($rng, $numdraws, $p);
my $multi_draws = ran_multinomial($rng, $numdraws, $p, @dims); # returns pdl with dimensions ($p->dims(), @dims)ran_multinomial_pdf
Signature: (double p(n); int counts(n); double [o] probability())Note the slightly strange order of arguments.
ran_multinomial_lnpdf
Signature: (double p(n); int counts(n); double [o] probability())Note the slightly strange order of arguments.
Dirichlet Distribution (:dirichlet)
ran_dirichlet
Signature: (PDL::GSL::RNG rng(); double alpha(n); double [o] theta(n))Usage:
ran_dirichlet($rng, $alpha, $outpdl); # $outpdl's first dimensions must be ($alpha->dims())
my $single_draw = ran_dirichlet($rng, $alpha);
my $multi_draws = ran_dirichlet($rng, $alpha, @dims); # returns pdl with dimensions ($alpha->dims(), @dims)ran_dirichlet_pdf
Signature: (double theta(n); double alpha(n); double [o] probability())Note: the argument order is swapped compared to C so that theta comes first.
ran_dirichlet_pdf processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
ran_dirichlet_lnpdf
Signature: (double theta(n); double alpha(n); double [o] probability())Note: the argument order is swapped compared to C so that theta comes first.
ran_dirichlet_lnpdf processes bad values. It will set the bad-value flag of all output piddles if the flag is set for any of the input piddles.
Bivariate Gaussian Distribution (:bivariate_gaussian)
ran_bivariate_gaussian
Signature: (PDL::GSL::RNG rng(); double sigma(n=2); double rho(); double [o] out(n=2))Usage:
ran_bivariate_gaussian($rng, pdl($sigma_x, $sigma_y), $rho, $dim); # returns pdl dim(2, $dim);
my $xy = ran_bivariate_gaussian($rng, pdl($sigma_x, $sigma_y), $rho); # returns pdl dim(2)
my $xy_vec = ran_bivariate_gaussian($rng, pdl($sigma_x, $sigma_y), $rho, $dim); # returns pdl dim(2, $dim);ran_bivariate_gaussian_pdf
Signature: (double xy(n=2); double sigma(n=2); double rho(); double [o] prob())Spherical Vector Distribution (:spherical)
ran_dir_2d
Signature: (PDL::GSL::RNG rng(); double [o] vector(n=2))ran_dir_2d_trig_method
Signature: (PDL::GSL::RNG rng(); double [o] vector(n=2))ran_dir_3d
Signature: (PDL::GSL::RNG rng(); double [o] vector(n=3))
Signature: (PDL::GSL::RNG rng(); int size(); double [o] vector(n))Sampling (:sample)
ran_choose
Sample count items from src without replacement, put them (in order) into out(). ran_choose is not threadable (src must be one dimensional). count must be <= n.
Signature: (PDL::GSL::RNG rng(); src(n); count(); out())ran_sample
Sample count items from src with replacement, put them (in order) into out(). ran_sample is not threadable (src must be one dimensional).
Signature: (PDL::GSL::RNG rng(); src(n); count(); out())Shuffling (:shuffle)
ran_shuffle
Return a new piddle with shuffled elements from src. src must be one-dimensional.
Signature: (PDL::GSL::RNG rng(); src(n))BUGS
The discrete distribution has no binding yet. Probably a whole lot more.