Utilitary function dealing with random numbers. More...

#include <Bpp/Numeric/Random/RandomTools.h>

Public Member Functions
	RandomTools ()

virtual	~RandomTools ()

Static Public Member Functions
static void	setSeed (std::mt19937::result_type seed)
	Set the default generator seed. More...

static double	giveRandomNumberBetweenZeroAndEntry (double entry)
	Get a double random value (between 0 and specified range). More...

static bool	flipCoin (double prob=0.5)
	Get a boolean random value. More...

template<class intType >
static intType	giveIntRandomNumberBetweenZeroAndEntry (intType entry)
	Get an integer random value (between 0 and specified range). More...

static double	randGaussian (double mean, double variance)

static double	randGamma (double alpha)

static double	randGamma (double alpha, double beta)

static double	randBeta (double alpha, double beta)

static double	randExponential (double mean)

template<class T >
static T	pickOne (std::vector< T > &v, bool replace=false)
	Pick (and extract) one element randomly in a vector and return it. More...

template<class T >
static T	pickOne (const std::vector< T > &v)
	Pick one element randomly in a vector and return it. More...

template<class T >
static void	getSample (const std::vector< T > &vin, std::vector< T > &vout, bool replace=false)
	Sample a vector. More...

template<class T >
static T	pickOne (std::vector< T > &v, std::vector< double > &w, bool replace=false)
	Pick one element in a vector, with associated probability weights. More...

template<class T >
static T	pickOne (const std::vector< T > &v, const std::vector< double > &w)
	Pick one element in a vector, with associated probability weights. More...

static size_t	pickFromCumSum (const std::vector< double > &w)
	Pick one index from a cumsum vector of probabilities. More...

template<class T >
static void	getSample (const std::vector< T > &vin, const std::vector< double > &w, std::vector< T > &vout, bool replace=false)
	Sample a vector, with associated probability weights. More...

static std::vector< size_t >	randMultinomial (size_t n, const std::vector< double > &probs)
	Get a random state from a set of probabilities/scores. More...

Probability functions.
Adapted from Yang's PAML package.
static double	qNorm (double prob)
	Normal quantile function. More...

static double	qNorm (double prob, double mu, double sigma)
	Normal quantile function. More...

static double	lnGamma (double alpha)
	Computes $ln\left(\Gamma\left(\alpha\right)\right)$ given $\alpha$ . More...

static double	incompleteGamma (double x, double alpha, double ln_gamma_alpha)
	Returns the incomplete gamma ratio I(x,alpha). More...

static double	qChisq (double prob, double v)
	$\chi^2$ quantile function. More...

static double	pChisq (double x, double v)
	$\chi^2$ cumulative probability function. More...

static double	qGamma (double prob, double alpha, double beta)
	The Gamma quantile function. More...

static double	pGamma (double x, double alpha, double beta)
	$\Gamma$ cumulative probability function. More...

Other probability functions.
Adapted from C routines for R programming langague Copyright (C) 1995, 1996 Robert Gentleman and Ross Ihaka Copyright (C) 1998 Ross Ihaka Copyright (C) 2000-2002 The R Development Core Team Copyright (C) 2003 The R Foundation
static double	pNorm (double z)
	Normal cumulative function. More...

static double	pNorm (double z, double mu, double sigma)

static double	lnBeta (double alpha, double beta)
	Computes $ln\left(Beta\left(\alpha,\beta\right)\right)$ given $\alpha$ and $b\eta$ . More...

static double	incompleteBeta (double x, double alpha, double beta)
	Returns the regularized incomplete beta function $I_x(\alpha,\beta) = pbeta(x,\alpha,\beta$ . More...

static double	pBeta (double x, double alpha, double beta)

static double	qBeta (double prob, double alpha, double beta)
	The Beta quantile function. More...

Static Public Attributes
static std::random_device	RANDOM_DEVICE

static std::mt19937	DEFAULT_GENERATOR

Static Private Member Functions
static double	incompletebetafe (double a, double b, double x, double big, double biginv)
	functions for the computation of incompleteBeta More...

static double	incompletebetafe2 (double a, double b, double x, double big, double biginv)

static double	incompletebetaps (double a, double b, double x, double maxgam)

static double	DblGammaGreaterThanOne (double dblAlpha)

static double	DblGammaLessThanOne (double dblAlpha)

Detailed Description

Utilitary function dealing with random numbers.

This class is adapted from Pupko's SEMPHY library. It also borrow some code from Yang's PAML package.

Most of these function are provided for convenience, directly using the "random" library might prove more efficient.

Definition at line 34 of file RandomTools.h.

Constructor & Destructor Documentation

◆ RandomTools()

bpp::RandomTools::RandomTools ( )

inline

Definition at line 37 of file RandomTools.h.

◆ ~RandomTools()

virtual bpp::RandomTools::~RandomTools ( )

inlinevirtual

Definition at line 38 of file RandomTools.h.

References incompletebetafe(), incompletebetafe2(), and incompletebetaps().

Member Function Documentation

◆ DblGammaGreaterThanOne()

double RandomTools::DblGammaGreaterThanOne ( double dblAlpha )

staticprivate

Definition at line 43 of file RandomTools.cpp.

References giveRandomNumberBetweenZeroAndEntry().

Referenced by pBeta().

◆ DblGammaLessThanOne()

double RandomTools::DblGammaLessThanOne ( double dblAlpha )

staticprivate

Definition at line 87 of file RandomTools.cpp.

Referenced by pBeta().

◆ flipCoin()

static bool bpp::RandomTools::flipCoin ( double prob = 0.5 )

inlinestatic

Get a boolean random value.

Parameters

prob	Probability of getting 'true'.

Definition at line 89 of file RandomTools.h.

◆ getSample() [1/2]

template<class T >

static void bpp::RandomTools::getSample	(	const std::vector< T > &	vin,
		std::vector< T > &	vout,
		bool	replace = `false`
	)

inlinestatic

Sample a vector.

The sample is a new vector of the specified size. If the size of the sample is identical to the original vector, the result is a shuffle of the original vector.

Parameters

vin	The vector to sample.
vout	[out] The output vector to fill, with the appropriate size.
replace	Should sampling be with replacement?

Returns: A vector which is a sample of v.

Exceptions

IndexOutOfBoundException	if the sample size exceeds the original size when sampling without replacement.
EmptyVectorException	if the vector is empty.

Author: Sylvain Gaillard

Definition at line 227 of file RandomTools.h.

References DEFAULT_GENERATOR, and pickOne().

◆ getSample() [2/2]

template<class T >

static void bpp::RandomTools::getSample	(	const std::vector< T > &	vin,
		const std::vector< double > &	w,
		std::vector< T > &	vout,
		bool	replace = `false`
	)

inlinestatic

Sample a vector, with associated probability weights.

The sample is a new vector of the specified size. If the size of the sample is identical to the original vector, the result is a shuffle of the original vector.

It has to be noted that in case of sampling without replacement, the effect of the weighting scheme will be weaker as the sample size becomes close to the population size. In case the two are equal (pure permutations), the weigths have no effect at all.

Parameters

vin	[in] The vector to sample.
w	[in] The vector of weights.
vout	[out] The output vector to fill, with the appropriate size already set.
replace	Should sampling be with replacement?

Returns: A vector which is a sample of v.

Exceptions

IndexOutOfBoundException	if the sample size exceeds the original size when sampling without replacement.
EmptyVectorException	if the vector is empty.

Warning: : For large sampling with replacement, the function is not efficient, as it recomputes the some of weights for each element picked.

Author: Julien Dutheil

Definition at line 383 of file RandomTools.h.

References pickOne(), qNorm(), and randMultinomial().

◆ giveIntRandomNumberBetweenZeroAndEntry()

template<class intType >

static intType bpp::RandomTools::giveIntRandomNumberBetweenZeroAndEntry ( intType entry )

inlinestatic

Get an integer random value (between 0 and specified range).

Note : the number you get is between 0 and entry not including entry !

Parameters

entry Max number to reach.

Definition at line 103 of file RandomTools.h.

◆ giveRandomNumberBetweenZeroAndEntry()

static double bpp::RandomTools::giveRandomNumberBetweenZeroAndEntry ( double entry )

inlinestatic

Get a double random value (between 0 and specified range).

Parameters

entry Max number to reach.

Definition at line 78 of file RandomTools.h.

Referenced by DblGammaGreaterThanOne(), pickFromCumSum(), pickOne(), bpp::AbstractDiscreteDistribution::rand(), bpp::UniformDiscreteDistribution::randC(), randMultinomial(), bpp::ContingencyTableGenerator::rcont2(), and bpp::AbstractHmmTransitionMatrix::sample().

◆ incompleteBeta()

double RandomTools::incompleteBeta	(	double	x,
		double	alpha,
		double	beta
	)

static

Returns the regularized incomplete beta function $I_x(\alpha,\beta) = pbeta(x,\alpha,\beta$ .

alpha and beta are the parameters of the function.

Adapted From Cephes Math Library Release 2.8: June, 2000 Copyright by Stephen L. Moshier Under GPL License

Parameters

x	the upper limit of the integration.
alpha,beta	the shape parameters.

Definition at line 549 of file RandomTools.cpp.

References bpp::NumConstants::VERY_BIG(), and bpp::NumConstants::VERY_TINY().

Referenced by pBeta(), and pGamma().

◆ incompletebetafe()

double RandomTools::incompletebetafe	(	double	a,
		double	b,
		double	x,
		double	big,
		double	biginv
	)

staticprivate

functions for the computation of incompleteBeta

Definition at line 660 of file RandomTools.cpp.

References bpp::NumConstants::VERY_TINY().

Referenced by ~RandomTools().

◆ incompletebetafe2()

double RandomTools::incompletebetafe2	(	double	a,
		double	b,
		double	x,
		double	big,
		double	biginv
	)

staticprivate

Definition at line 771 of file RandomTools.cpp.

References bpp::NumConstants::VERY_TINY().

Referenced by ~RandomTools().

◆ incompletebetaps()

double RandomTools::incompletebetaps	(	double	a,
		double	b,
		double	x,
		double	maxgam
	)

staticprivate

Definition at line 887 of file RandomTools.cpp.

References bpp::NumConstants::VERY_BIG(), and bpp::NumConstants::VERY_TINY().

Referenced by ~RandomTools().

◆ incompleteGamma()

double RandomTools::incompleteGamma	(	double	x,
		double	alpha,
		double	ln_gamma_alpha
	)

static

Returns the incomplete gamma ratio I(x,alpha).

X is the upper limit of the integration and alpha is the shape parameter. returns (-1) if in error ln_gamma_alpha = ln(Gamma(alpha)), is almost redundant. (1) series expansion if (alpha>x || x<=1) (2) continued fraction otherwise RATNEST FORTRAN by Bhattacharjee GP (1970) The incomplete gamma integral. Applied Statistics, 19: 285-287 (AS32)

Parameters

x	the upper limit of the integration.
alpha	the shape parameter.
ln_gamma_alpha	ln(Gamma(alpha)).

Definition at line 143 of file RandomTools.cpp.

Referenced by lnGamma(), and pGamma().

◆ lnBeta()

double RandomTools::lnBeta	(	double	alpha,
		double	beta
	)

static

Computes $ln\left(Beta\left(\alpha,\beta\right)\right)$ given $\alpha$ and $b\eta$ .

Returns ln(beta(alpha,beta)) for alpha>0 and beta>0.

Parameters

alpha,beta Alpha and Beta parameters.

Returns: $ln\left(Beta\left(\alpha,\beta\right)\right)$

Definition at line 405 of file RandomTools.cpp.

Referenced by bpp::BetaDiscreteDistribution::BetaDiscreteDistribution(), bpp::BetaDiscreteDistribution::fireParameterChanged(), and pGamma().

◆ lnGamma()

static double bpp::RandomTools::lnGamma ( double alpha )

inlinestatic

Computes $ln\left(\Gamma\left(\alpha\right)\right)$ given $\alpha$ .

Parameters

alpha Alpha parameter.

Returns: $ln\left(\Gamma\left(\alpha\right)\right)$

Definition at line 472 of file RandomTools.h.

References incompleteGamma(), and qChisq().

Referenced by bpp::GammaDiscreteDistribution::fireParameterChanged(), bpp::GammaDiscreteDistribution::GammaDiscreteDistribution(), and pGamma().

◆ pBeta()

static double bpp::RandomTools::pBeta	(	double	x,
		double	alpha,
		double	beta
	)

inlinestatic

Definition at line 615 of file RandomTools.h.

References DblGammaGreaterThanOne(), DblGammaLessThanOne(), incompleteBeta(), and qBeta().

Referenced by bpp::BetaDiscreteDistribution::Expectation(), and bpp::BetaDiscreteDistribution::pProb().

◆ pChisq()

static double bpp::RandomTools::pChisq	(	double	x,
		double	v
	)

inlinestatic

$\chi^2$ cumulative probability function.

Parameters

x	The quantile for which the probability should be computed.
v	number of degree of freedom.

Returns: The corresponding probability of the quantile.

Definition at line 516 of file RandomTools.h.

References pGamma().

Referenced by bpp::ContingencyTableTest::ContingencyTableTest().

◆ pGamma()

static double bpp::RandomTools::pGamma	(	double	x,
		double	alpha,
		double	beta
	)

inlinestatic

$\Gamma$ cumulative probability function.

Parameters

x	The quantile for which the probability should be computed.
alpha	Alpha parameter.
beta	Beta parameter.

Returns: The corresponding probability of the quantile.

Exceptions

Exception If alpha or beta is invalid (<0).

Definition at line 545 of file RandomTools.h.

References incompleteBeta(), incompleteGamma(), lnBeta(), lnGamma(), and pNorm().

Referenced by bpp::GammaDiscreteDistribution::Expectation(), pChisq(), and bpp::GammaDiscreteDistribution::pProb().

◆ pickFromCumSum()

static size_t bpp::RandomTools::pickFromCumSum ( const std::vector< double > & w )

inlinestatic

Pick one index from a cumsum vector of probabilities.

Last probability of the vector is assumed to be one.

Parameters

w	The vector of cumsumed weights.

Returns: An index from the vector.

Exceptions

EmptyVectorException if the vector is empty.

Author: Laurent Guéguen

Definition at line 345 of file RandomTools.h.

References giveRandomNumberBetweenZeroAndEntry().

◆ pickOne() [1/4]

template<class T >

static T bpp::RandomTools::pickOne	(	std::vector< T > &	v,
		bool	replace = `false`
	)

inlinestatic

Pick (and extract) one element randomly in a vector and return it.

Parameters

v	The vector of elements.
replace	If set to yes, then elements are allowed to be picked more than once, and therefore can be re-"placed" in the final sample (default: false, in which case the vector will lost one element).

Returns: One element of the vector.

Exceptions

EmptyVectorException if the vector is empty.

Author: Sylvain Gaillard

Definition at line 175 of file RandomTools.h.

Referenced by getSample().

◆ pickOne() [2/4]

template<class T >

static T bpp::RandomTools::pickOne ( const std::vector< T > & v )

inlinestatic

Pick one element randomly in a vector and return it.

Parameters

v	The vector of elements.

Returns: One element of the vector.

Exceptions

EmptyVectorException if the vector is empty.

Author: Sylvain Gaillard

Definition at line 201 of file RandomTools.h.

◆ pickOne() [3/4]

template<class T >

static T bpp::RandomTools::pickOne	(	std::vector< T > &	v,
		std::vector< double > &	w,
		bool	replace = `false`
	)

inlinestatic

Pick one element in a vector, with associated probability weights.

Pick one element randomly in a vector and return it. If you choose to make the picking without replacement the element is removed from the vector, and so is the corresponding weight.

Parameters

v	The vector of elements.
w	The vector of weight associated to the v elements.
replace	Should pick with replacement? (default: false)

Returns: One element of the vector.

Exceptions

EmptyVectorException if the vector is empty.

Author: Julien Dutheil

Definition at line 266 of file RandomTools.h.

References bpp::VectorTools::cumSum(), and giveRandomNumberBetweenZeroAndEntry().

◆ pickOne() [4/4]

template<class T >

static T bpp::RandomTools::pickOne	(	const std::vector< T > &	v,
		const std::vector< double > &	w
	)

inlinestatic

Pick one element in a vector, with associated probability weights.

Pick one element randomly in a vector and return it, with no change in the original vector.

Parameters

v	The vector of elements.
w	The vector of weight associated to the v elements.

Returns: One element of the vector.

Exceptions

EmptyVectorException if the vector is empty.

Author: Julien Dutheil

Definition at line 312 of file RandomTools.h.

References bpp::VectorTools::cumSum(), and giveRandomNumberBetweenZeroAndEntry().

◆ pNorm() [1/2]

double RandomTools::pNorm ( double z )

static

Normal cumulative function.

Returns Prob{x<=z} where x ~ N(0,1)

Parameters

z	the value.

Returns: The corresponding probability.

Definition at line 276 of file RandomTools.cpp.

Referenced by bpp::GaussianDiscreteDistribution::Expectation(), pGamma(), pNorm(), and bpp::GaussianDiscreteDistribution::pProb().

◆ pNorm() [2/2]

double RandomTools::pNorm	(	double	z,
		double	mu,
		double	sigma
	)

static

Definition at line 270 of file RandomTools.cpp.

References pNorm().

◆ qBeta()

double RandomTools::qBeta	(	double	prob,
		double	alpha,
		double	beta
	)

static

The Beta quantile function.

Code adapted from Ziheng Yang's PAML. Original comment from the PAML package: Cran, G. W., K. J. Martin and G. E. Thomas (1977). Remark AS R19 and Algorithm AS 109, Applied Statistics, 26(1), 111-114. Remark AS R83 (v.39, 309-310) and correction (v.40(1) p.236).

My own implementation of the algorithm did not bracket the variable well. This version is Adpated from the pbeta and qbeta routines from "R : A Computer Language for Statistical Data Analysis". It fails for extreme values of p and q as well, although it seems better than my previous version. Ziheng Yang, May 2001

Parameters

prob	The probability.
alpha	Alpha parameter.
beta	Beta parameter.

Returns: The quantile corresponding to prob.

Definition at line 416 of file RandomTools.cpp.

Referenced by pBeta(), bpp::BetaDiscreteDistribution::qProb(), and randBeta().

◆ qChisq()

double RandomTools::qChisq	(	double	prob,
		double	v
	)

static

$\chi^2$ quantile function.

returns z so that Prob{x<z}=prob where x is Chi2 distributed with df=v returns -1 if in error. 0.000002<prob<0.999998 RATNEST FORTRAN by Best DJ & Roberts DE (1975) The percentage points of the Chi2 distribution. Applied Statistics 24: 385-388. (AS91) Converted into C by Ziheng Yang, Oct. 1993.

Parameters

prob	The probability.
v	number of degree of freedom.

Returns: The quantile corresponding to prob.

Definition at line 210 of file RandomTools.cpp.

Referenced by lnGamma(), and qGamma().

◆ qGamma()

static double bpp::RandomTools::qGamma	(	double	prob,
		double	alpha,
		double	beta
	)

inlinestatic

The Gamma quantile function.

Parameters

prob	The probability.
alpha	Alpha parameter.
beta	Beta parameter.

Returns: The quantile corresponding to prob.

Definition at line 530 of file RandomTools.h.

References qChisq().

Referenced by bpp::GammaDiscreteDistribution::qProb().

◆ qNorm() [1/2]

double RandomTools::qNorm ( double prob )

static

Normal quantile function.

Returns z so that Prob{x<z}=prob where x ~ N(0,1) and (1e-12)<prob<1-(1e-12) returns (-9999) if in error Odeh RE & Evans JO (1974) The percentage points of the normal distribution. Applied Statistics 22: 96-97 (AS70)

Newer methods: Wichura MJ (1988) Algorithm AS 241: the percentage points of the normal distribution. 37: 477-484. Beasley JD & Springer SG (1977). Algorithm AS 111: the percentage points of the normal distribution. 26: 118-121.

Parameters

prob	The probability.

Returns: The quantile corresponding to prob.

Definition at line 122 of file RandomTools.cpp.

Referenced by getSample(), qNorm(), and bpp::GaussianDiscreteDistribution::qProb().

◆ qNorm() [2/2]

double RandomTools::qNorm	(	double	prob,
		double	mu,
		double	sigma
	)

static

Normal quantile function.

Returns z so that Prob{x<z}=prob where x ~ N(mu,sigma^2) and (1e-12)<prob<1-(1e-12) returns (-9999) if in error Odeh RE & Evans JO (1974) The percentage points of the normal distribution. Applied Statistics 22: 96-97 (AS70)

Newer methods: Wichura MJ (1988) Algorithm AS 241: the percentage points of the normal distribution. 37: 477-484. Beasley JD & Springer SG (1977). Algorithm AS 111: the percentage points of the normal distribution. 26: 118-121.

Parameters

prob	The probability.
mu	The mean of the distribution
sigma	The standard deviation of the distribution

Returns: The quantile corresponding to prob.

Definition at line 138 of file RandomTools.cpp.

References qNorm().

◆ randBeta()

double RandomTools::randBeta	(	double	alpha,
		double	beta
	)

static

Returns: A random number drawn from a beta distribution.

Parameters

alpha	The alpha parameter.
beta	The beta parameter.

Definition at line 410 of file RandomTools.cpp.

References qBeta().

Referenced by bpp::BetaDiscreteDistribution::randC(), and randGamma().

◆ randExponential()

static double bpp::RandomTools::randExponential ( double mean )

inlinestatic

Returns: A random number drawn from an exponential distribution.

Parameters

mean	The mean of the distribution.

Definition at line 154 of file RandomTools.h.

Referenced by bpp::ExponentialDiscreteDistribution::randC(), and bpp::TruncatedExponentialDiscreteDistribution::randC().

◆ randGamma() [1/2]

static double bpp::RandomTools::randGamma ( double alpha )

inlinestatic

Returns: A random number drawn from a gamma distribution with unit scale (beta=1).

Parameters

alpha The alpha parameter.

Definition at line 126 of file RandomTools.h.

Referenced by bpp::GammaDiscreteDistribution::randC().

◆ randGamma() [2/2]

static double bpp::RandomTools::randGamma	(	double	alpha,
		double	beta
	)

inlinestatic

Returns: A random number drawn from a gamma distribution.

Parameters

alpha	The alpha parameter.
beta	The beta parameter.

Definition at line 137 of file RandomTools.h.

References randBeta().

◆ randGaussian()

static double bpp::RandomTools::randGaussian	(	double	mean,
		double	variance
	)

inlinestatic

Returns: A random number drawn from a normal distribution.

Parameters

mean	The mean of the law.
variance	The variance of the law.

Definition at line 116 of file RandomTools.h.

Referenced by bpp::GaussianDiscreteDistribution::randC().

◆ randMultinomial()

std::vector< size_t > RandomTools::randMultinomial	(	size_t	n,
		const std::vector< double > &	probs
	)

static

Get a random state from a set of probabilities/scores.

The input probabilities are scaled so that they sum to one. If 'x' probabilities are provided as input, the output vector will contain values between 0 and 'x-1'.

Parameters

n	The sample size.
probs	The set of intput probabilities.

Returns: A vector of int values corresponding to the output states. States are supposed to be in the same order as the input probabilities, the first state being '0'.

Definition at line 13 of file RandomTools.cpp.

References giveRandomNumberBetweenZeroAndEntry(), and bpp::VectorTools::sum().

Referenced by getSample().

◆ setSeed()

static void bpp::RandomTools::setSeed ( std::mt19937::result_type seed )

inlinestatic

Set the default generator seed.

Parameters

seed New seed.

Definition at line 68 of file RandomTools.h.

Referenced by bpp::BppApplication::BppApplication().

Member Data Documentation

◆ DEFAULT_GENERATOR

std::mt19937 RandomTools::DEFAULT_GENERATOR

static

Definition at line 61 of file RandomTools.h.

Referenced by getSample().

◆ RANDOM_DEVICE

std::random_device RandomTools::RANDOM_DEVICE

static

Definition at line 60 of file RandomTools.h.

The documentation for this class was generated from the following files:

Bpp/Numeric/Random/RandomTools.h
Bpp/Numeric/Random/RandomTools.cpp

Public Member Functions

Static Public Member Functions

Static Public Attributes

Static Private Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ RandomTools()

◆ ~RandomTools()

Member Function Documentation

◆ DblGammaGreaterThanOne()

◆ DblGammaLessThanOne()

◆ flipCoin()

◆ getSample() [1/2]

◆ getSample() [2/2]

◆ giveIntRandomNumberBetweenZeroAndEntry()

◆ giveRandomNumberBetweenZeroAndEntry()

◆ incompleteBeta()

◆ incompletebetafe()

◆ incompletebetafe2()

◆ incompletebetaps()

◆ incompleteGamma()

◆ lnBeta()

◆ lnGamma()

◆ pBeta()

◆ pChisq()

◆ pGamma()

◆ pickFromCumSum()

◆ pickOne() [1/4]

◆ pickOne() [2/4]

◆ pickOne() [3/4]

◆ pickOne() [4/4]

◆ pNorm() [1/2]

◆ pNorm() [2/2]

◆ qBeta()

◆ qChisq()

◆ qGamma()

◆ qNorm() [1/2]

◆ qNorm() [2/2]

◆ randBeta()

◆ randExponential()

◆ randGamma() [1/2]

◆ randGamma() [2/2]

◆ randGaussian()

◆ randMultinomial()

◆ setSeed()

Member Data Documentation

◆ DEFAULT_GENERATOR

◆ RANDOM_DEVICE