#include "Basic/Law.hpp"
#include "Basic/Utilities.hpp"
#include "Basic/MathFunc.hpp"
#include "Basic/VectorHelper.hpp"
#include <math.h>
#include <random>

Functions
void	law_set_old_style (bool style)

int	law_get_random_seed (void)

void	law_set_random_seed (int seed)

double	law_uniform (double mini, double maxi)

int	law_int_uniform (int mini, int maxi)

double	law_gaussian (double mean, double sigma)

double	law_exponential (double lambda)

double	law_gamma (double alpha, double beta)

double	law_stable_standard_abgd (double alpha)

double	law_stable_standard_agd (double alpha, double beta)

double	law_stable_standard_a1gd (double beta)

double	law_stable_a (double alpha, double beta, double gamma, double delta)

double	law_stable_a1 (double beta, double gamma, double delta)

double	law_stable (double alpha, double beta, double gamma, double delta)

double	law_beta1 (double parameter1, double parameter2)

double	law_beta2 (double parameter1, double parameter2)

double	law_df_gaussian (double value)

double	law_dnorm (double value, double mean, double std)

double	law_cdf_gaussian (double value)

double	law_invcdf_gaussian (double value)

double	law_gaussian_between_bounds (double binf, double bsup)

double	law_df_bigaussian (VectorDouble &vect, VectorDouble &mean, MatrixSquareSymmetric &correl)

double	law_df_quadgaussian (VectorDouble &vect, MatrixSquareSymmetric &correl)

double	law_df_multigaussian (VectorDouble &vect, MatrixSquareSymmetric &correl)

VectorDouble	law_df_poisson_vec (VectorInt is, double parameter)

double	law_df_poisson (int i, double parameter)

int	law_poisson (double parameter)

VectorInt	law_random_path (int nech)

int	law_binomial (int n, double p)

VectorDouble	law_exp_sample (const double tabin, int mode, int nvar, int nechin, int nechout, int niter, int nconst, double consts, int seed, double percent)

int	sampleInteger (int mini, int maxi)

Variables
static int	Random_factor = 105

static int	Random_congruent = 20000159

static int	Random_value = 43241421

static bool	Random_Old_Style = true

std::mt19937	Random_gen

Function Documentation

◆ law_beta1()

double law_beta1	(	double	parameter1,
		double	parameter2
	)

Generate random numbers according to a beta distribution (first kind)

Returns: Beta random value (first kind)

Parameters

[in]	parameter1	first parameter of the beta distribution
[in]	parameter2	first parameter of the beta distribution

◆ law_beta2()

double law_beta2	(	double	parameter1,
		double	parameter2
	)

Generate random numbers according to a beta distribution (second kind)

Returns: Beta random value (second kind)

Parameters

[in]	parameter1	first parameter of the beta distribution
[in]	parameter2	first parameter of the beta distribution

◆ law_binomial()

int law_binomial	(	int	n,
		double	p
	)

Generates a binomial value

Returns: The binomial value

Parameters

[in]	n	Number of trials
[in]	p	Event probability

◆ law_cdf_gaussian()

double law_cdf_gaussian ( double value )

Cumulated density function of a gaussian distribution

Returns: Gaussian cumulated density function

Parameters

[in] value raw value

Remarks: Handbook P932 (26.2.17) precision <7.5 E-08

◆ law_df_bigaussian()

double law_df_bigaussian	(	VectorDouble &	vect,
		VectorDouble &	mean,
		MatrixSquareSymmetric &	correl
	)

Density function of a bigaussian distribution

Returns: Gaussian density function

Parameters

[in]	vect	Array of values (Dimension = 2)
[in]	mean	Array of means (Dimension = 2)
[in]	correl	Correlation matrix (Dimension: 2*2)

◆ law_df_gaussian()

double law_df_gaussian ( double value )

Density function of a gaussian distribution

Returns: Gaussian density function

Parameters

[in] value raw value

◆ law_df_multigaussian()

double law_df_multigaussian	(	VectorDouble &	vect,
		MatrixSquareSymmetric &	correl
	)

Density function of a multigaussian distribution

Returns: Gaussian density function

Parameters

[in]	vect	Array of values (Dimension = nvar)
[in]	correl	Correlation matrix (Dimension: nvar*nvar)

◆ law_df_poisson()

double law_df_poisson	(	int	i,
		double	parameter
	)

◆ law_df_poisson_vec()

VectorDouble law_df_poisson_vec	(	VectorInt	is,
		double	parameter
	)

◆ law_df_quadgaussian()

double law_df_quadgaussian	(	VectorDouble &	vect,
		MatrixSquareSymmetric &	correl
	)

Density function of a quadrigaussian distribution

Returns: Gaussian density function

Parameters

[in]	vect	Array of values (Dimension = nvar)
[in]	correl	Correlation matrix (Dimension: nvar*nvar)

◆ law_dnorm()

double law_dnorm	(	double	value,
		double	mean,
		double	std
	)

Density function of a (non-normalized) gaussian distribution

Returns: Gaussian density function

Parameters

[in]	value	Raw value
[in]	mean	Mean value
[in]	std	Standard deviation

◆ law_exp_sample()

VectorDouble law_exp_sample	(	const double *	tabin,
		int	mode,
		int	nvar,
		int	nechin,
		int	nechout,
		int	niter,
		int	nconst,
		double *	consts,
		int	seed,
		double	percent
	)

Sample a multivariate empirical distribution

Returns: Address to the newly created array

Parameters

[in]	tabin	Input array
[in]	mode	Describes the way 'tabin' and 'tabout' are filled 1: by column; 2: by row
[in]	nvar	Number of variables (input and output)
[in]	nechin	Number of samples in the input array
[in]	nechout	Number of created samples
[in]	niter	Maximum number of iterations
[in]	nconst	Number of constraints
[in]	consts	Array of constraints (optional) (Dimension: nconst * (nvar+1)) This array is entered by line
[in]	seed	Value for the seed generator
[in]	percent	Dimension of the convolution kernel expressed as a percentage of the dispersion st. dev. Should be between 0 and 100

Remarks: The input array must be isotopic (otherwise, an error is issued); The resulting VectorDouble if dimensionned to nvar * nechout; Consider nvar1 = nvar + 1; Sample temp[1:nvar1] is authorized for Constraint 'iconst' if:; Sum_ivar1^{1:nvar1) consts[iconst,ivar1) * temp[ivar1] > 0

◆ law_exponential()

double law_exponential ( double lambda )

Generate random numbers according to exponential distribution

Returns: Exponential random value

Parameters

[in] lambda Parameter of exponential distribution

◆ law_gamma()

double law_gamma	(	double	alpha,
		double	beta
	)

Generate random numbers according to a gamma distribution

Returns: Gamma random value

Parameters

[in]	alpha	parameter of the gamma distribution
[in]	beta	Second parameter of the Gamma distribution

◆ law_gaussian()

double law_gaussian	(	double	mean,
		double	sigma
	)

Generate random numbers according to a gaussian distribution

Returns: Gaussian random value

Parameters

[in]	mean	Mean of the Normal Distribution
[in]	sigma	Standard deviation of the Normal Distribution

◆ law_gaussian_between_bounds()

double law_gaussian_between_bounds	(	double	binf,
		double	bsup
	)

Generates a gaussian value which lies in an interval

Returns: The gaussian value

Parameters

[in]	binf	lower bound of the interval
[in]	bsup	upper bound of the interval

◆ law_get_random_seed()

int law_get_random_seed ( void )

read the seed for the random number generator

Returns: The current value of the seed (integer)

◆ law_int_uniform()

int law_int_uniform	(	int	mini,
		int	maxi
	)

Draw an integer random number according to a uniform distribution

Returns: Integer Uniform random value within an interval

Parameters

[in]	mini	minimum value
[in]	maxi	maximum value

◆ law_invcdf_gaussian()

double law_invcdf_gaussian ( double value )

Inverse cumulated density function of a gaussian distribution

Returns: Inverse of gaussian cumulated density function

Parameters

[in] value cumulative density

◆ law_poisson()

int law_poisson ( double parameter )

Generate random number according to a poisson distribution

Returns: Poisson random value

Parameters

[in] parameter parameter of the Poisson distribution

Remarks: Method Ahrens-Dieter (1973)

◆ law_random_path()

VectorInt law_random_path ( int nech )

Define a random path

Parameters

[in] nech : Number of samples

◆ law_set_old_style()

void law_set_old_style ( bool style )

Set the type of Usage for Random Number Generation

Parameters

style true for using Old Style; false for using New Style

◆ law_set_random_seed()

void law_set_random_seed ( int seed )

Sets the seed for the random number generator

Parameters

[in] seed the new value given to the seed

◆ law_stable()

double law_stable	(	double	alpha,
		double	beta,
		double	gamma,
		double	delta
	)

Generate random numbers according to a stable distribution

Returns: Stable value with unit parameters

Parameters

[in]	alpha	value of the alpha parameter
[in]	beta	value of the beta parameter
[in]	gamma	value of the gamma parameter
[in]	delta	value of the delta parameter

◆ law_stable_a()

double law_stable_a	(	double	alpha,
		double	beta,
		double	gamma,
		double	delta
	)

Generate random numbers according to a stable distribution (alpha != 1)

Returns: Stable value with unit parameters

Parameters

[in]	alpha	value of the alpha parameter
[in]	beta	value of the beta parameter
[in]	gamma	value of the gamma parameter
[in]	delta	value of the delta parameter

◆ law_stable_a1()

double law_stable_a1	(	double	beta,
		double	gamma,
		double	delta
	)

Generate random numbers according to a stable distribution (alpha=1)

Returns: Stable value with unit parameters

Parameters

[in]	beta	value of the beta parameter
[in]	gamma	value of the gamma parameter
[in]	delta	value of the delta parameter

◆ law_stable_standard_a1gd()

double law_stable_standard_a1gd ( double beta )

Generate random numbers according to a standard stable distribution (alpha=1)

Returns: Stable value with standard parameters (alpha=gamma=1,delta=0)

Parameters

[in] beta value of the beta parameter

◆ law_stable_standard_abgd()

double law_stable_standard_abgd ( double alpha )

Generate random numbers according to a standard stable distribution

Returns: Stable value with std. parameters (beta=gamma=1,delta=0,alpha!=1)

Parameters

[in] alpha value of the alpha parameter

◆ law_stable_standard_agd()

double law_stable_standard_agd	(	double	alpha,
		double	beta
	)

Generate random numbers according to a standard stable distribution

Returns: Stable value with standard parameters (gamma=1,delta=0,alpha!=1)

Parameters

[in]	alpha	value of the alpha parameter
[in]	beta	value of the beta parameter

◆ law_uniform()

double law_uniform	(	double	mini,
		double	maxi
	)

Draw a random number according to a uniform distribution

Returns: Uniform random value within an interval

Parameters

[in]	mini	minimum value
[in]	maxi	maximum value

◆ sampleInteger()

int sampleInteger	(	int	mini,
		int	maxi
	)

Returns an integer sampled uniformly wihtin the interval [mini, maxi]

Parameters

mini	Lower bound (included)
maxi	Upper bound (included)

Variable Documentation

◆ Random_congruent

int Random_congruent = 20000159

static

◆ Random_factor

int Random_factor = 105

static

◆ Random_gen

std::mt19937 Random_gen

◆ Random_Old_Style

bool Random_Old_Style = true

static

◆ Random_value

int Random_value = 43241421

static

Functions

Variables

Function Documentation

◆ law_beta1()

◆ law_beta2()

◆ law_binomial()

◆ law_cdf_gaussian()

◆ law_df_bigaussian()

◆ law_df_gaussian()

◆ law_df_multigaussian()

◆ law_df_poisson()

◆ law_df_poisson_vec()

◆ law_df_quadgaussian()

◆ law_dnorm()

◆ law_exp_sample()

◆ law_exponential()

◆ law_gamma()

◆ law_gaussian()

◆ law_gaussian_between_bounds()

◆ law_get_random_seed()

◆ law_int_uniform()

◆ law_invcdf_gaussian()

◆ law_poisson()

◆ law_random_path()

◆ law_set_old_style()

◆ law_set_random_seed()

◆ law_stable()

◆ law_stable_a()

◆ law_stable_a1()

◆ law_stable_standard_a1gd()

◆ law_stable_standard_abgd()

◆ law_stable_standard_agd()

◆ law_uniform()

◆ sampleInteger()

Variable Documentation

◆ Random_congruent

◆ Random_factor

◆ Random_gen

◆ Random_Old_Style

◆ Random_value