probability.cpp File Reference

Probability and random number generation- related tools. More...

#include <math.h>
#include <iostream>
#include <float.h>
#include <limits.h>
#include "Array1D.h"
#include "Array2D.h"
#include "probability.h"
#include "rosenblatt.h"
#include "combin.h"
#include "arraytools.h"
#include "gen_defs.h"
#include "minmax.h"

Functions
double	erff (const double x)
	An implementation of error function using incomplete gamma function.
double	inverf (double y0)
	Inverse error function, input scaled to [-1,1].
double	invnormcdf (double y)
	Inverse of the CDF of the normal random variable, uses inverf.
double	normcdf (double y)
	Normal random variable CDF.
double	normcdfc (double y)
	Complementary function for normcdf.
void	generate_uniform (double *rvar, int ns, int nd, int zSeed)
	Generates a vector of i.i.d. uniform(0,1) random variable samples of size ns*nd, given integer seed.
void	generate_uniform (Array2D< double > &rvar, int zSeed)
	Generates a matrix of i.i.d. uniform(0,1) random variable samples, given integer seed.
void	generate_uniform (double *rvar, int ns, int nd, dsfmt_t *rnstate)
	Generates a vector of i.i.d. uniform(0,1) random variable samples of size ns*nd, given pointer to the state of current random number generator.
void	generate_uniform (Array2D< double > &rvar, dsfmt_t *rnstate)
	Generates a matrix of i.i.d. uniform(0,1) random variable samples, given pointer to the state of current random number generator.
void	generate_uniform_lhs (double *rvar, int nsample, int ndim, int zSeed)
	Generates a vector of i.i.d. uniform(0,1) random variable LHS samples of size ns*nd, given integer seed.
void	generate_uniform_lhs (Array2D< double > &rvar, int zSeed)
	Generates a matrix of i.i.d. uniform(0,1) random variable LHS samples, given integer seed.
void	generate_uniform_lhs (double *rvar, int nsample, int ndim, dsfmt_t *rnstate)
	Generates a vector of i.i.d. uniform(0,1) random variable LHS samples of size ns*nd, given pointer to the state of current random number generator.
void	generate_uniform_lhs (Array2D< double > &rvar, dsfmt_t *rnstate)
	Generates a matrix of i.i.d. uniform(0,1) random variable LHS samples, given pointer to the state of current random number generator.
void	generate_normal (Array2D< double > &rvar, int zSeed)
	Generates a matrix of i.i.d. normal(0,1) random variable samples.
void	generate_normal_lhs (Array2D< double > &rvar, int zSeed)
	Generates a matrix of i.i.d. normal(0,1) random variable LHS samples.
double	get_median (const Array1D< double > &data)
	Returns the median of a data array.
double	get_mean (const Array1D< double > &data)
	Returns the mean of a 1D data array.
double	get_mean (const Array2D< double > &data)
	Returns the mean of a 2D data array.
double	get_std (const Array1D< double > &data)
	Returns the std of a data array.
double	get_var (const Array1D< double > &data)
	Returns the std of a data array.
double	getMean_Variance (Array2D< double > &data_c, Array1D< double > &w, Array1D< double > &mean)
	Vector-mean and weighted variance.
void	getMean (Array2D< double > &data_c, Array1D< double > &mean)
	Vector mean, column by column.
void	getMean (Array2D< double > &matrix, Array1D< double > &mean, char *RC)
	Vector mean, either column by column for RC="C" or row by row for RC="R".
void	rperm (int n, int *a, dsfmt_t *rnstate)
	Random permutation of 0..n-1.
void	getPdf_figtree (Array2D< double > &source, Array2D< double > &target, Array1D< double > &sig, Array1D< double > &density, Array1D< double > &weight)
	KDE estimation of a PDF.
void	getPdf_cl (Array2D< double > &data, Array2D< double > &points, Array1D< double > &dens, int ncl, double sfac)
	Compute the PDF of data at the given points using given number of clusters (if ncl=0, then find the optimal cluster number) and a scale factor for the optimal bandwidth.
double	covariance (Array1D< double > &x1, Array1D< double > &x2, Array1D< double > &param, string covtype)
	Compute a few standard covariance functions C(x_1,x_2)
void	ihsU (Array2D< double > &rndnos, const int dfac, dsfmt_t *rnstate)
void	ihsU (const int ndim, const int ns, double *rndnos, const int dfac, dsfmt_t *rnstate)
void	ihsP (const int ndim, const int ns, int *x, const int dupl, dsfmt_t *rnstate)
void	distCorr (const Array2D< double > &spl, Array2D< double > &dCor)
	Compute distance correlation factors given a set of samples (no. of rows in spl) from a collection of random variables (no. of columns in spl). dCor(i,j), with i>j stores the distance correlation values between random variables i and j.

Detailed Description

Probability and random number generation- related tools.

Function Documentation

covariance()

double covariance	(	Array1D< double > &	x1,
		Array1D< double > &	x2,
		Array1D< double > &	param,
		string	covtype )

Compute a few standard covariance functions C(x_1,x_2)

distCorr()

void distCorr	(	const Array2D< double > &	spl,
		Array2D< double > &	dCor )

Compute distance correlation factors given a set of samples (no. of rows in spl) from a collection of random variables (no. of columns in spl). dCor(i,j), with i>j stores the distance correlation values between random variables i and j.

erff()

double erff

(

const double

x

)

An implementation of error function using incomplete gamma function.

generate_normal()

void generate_normal	(	Array2D< double > &	rvar,
		int	zSeed )

Generates a matrix of i.i.d. normal(0,1) random variable samples.

generate_normal_lhs()

void generate_normal_lhs	(	Array2D< double > &	rvar,
		int	zSeed )

Generates a matrix of i.i.d. normal(0,1) random variable LHS samples.

Todo

LHS generation is far from optimal, it is quite slow

generate_uniform() [1/4]

void generate_uniform	(	Array2D< double > &	rvar,
		dsfmt_t *	rnstate )

Generates a matrix of i.i.d. uniform(0,1) random variable samples, given pointer to the state of current random number generator.

generate_uniform() [2/4]

void generate_uniform	(	Array2D< double > &	rvar,
		int	zSeed )

Generates a matrix of i.i.d. uniform(0,1) random variable samples, given integer seed.

generate_uniform() [3/4]

void generate_uniform	(	double *	rvar,
		int	ns,
		int	nd,
		dsfmt_t *	rnstate )

Generates a vector of i.i.d. uniform(0,1) random variable samples of size ns*nd, given pointer to the state of current random number generator.

generate_uniform() [4/4]

void generate_uniform	(	double *	rvar,
		int	ns,
		int	nd,
		int	zSeed )

Generates a vector of i.i.d. uniform(0,1) random variable samples of size ns*nd, given integer seed.

generate_uniform_lhs() [1/4]

void generate_uniform_lhs	(	Array2D< double > &	rvar,
		dsfmt_t *	rnstate )

Generates a matrix of i.i.d. uniform(0,1) random variable LHS samples, given pointer to the state of current random number generator.

generate_uniform_lhs() [2/4]

void generate_uniform_lhs	(	Array2D< double > &	rvar,
		int	zSeed )

Generates a matrix of i.i.d. uniform(0,1) random variable LHS samples, given integer seed.

generate_uniform_lhs() [3/4]

void generate_uniform_lhs	(	double *	rvar,
		int	nsample,
		int	ndim,
		dsfmt_t *	rnstate )

Generates a vector of i.i.d. uniform(0,1) random variable LHS samples of size ns*nd, given pointer to the state of current random number generator.

generate_uniform_lhs() [4/4]

void generate_uniform_lhs	(	double *	rvar,
		int	nsample,
		int	ndim,
		int	zSeed )

Generates a vector of i.i.d. uniform(0,1) random variable LHS samples of size ns*nd, given integer seed.

get_mean() [1/2]

double get_mean

(

const Array1D< double > &

data

)

Returns the mean of a 1D data array.

get_mean() [2/2]

double get_mean

(

const Array2D< double > &

data

)

Returns the mean of a 2D data array.

get_median()

double get_median

(

const Array1D< double > &

data

)

Returns the median of a data array.

get_std()

double get_std

(

const Array1D< double > &

data

)

Returns the std of a data array.

get_var()

double get_var

(

const Array1D< double > &

data

)

Returns the std of a data array.

getMean() [1/2]

void getMean	(	Array2D< double > &	data_c,
		Array1D< double > &	mean )

Vector mean, column by column.

getMean() [2/2]

void getMean	(	Array2D< double > &	matrix,
		Array1D< double > &	mean,
		char *	RC )

Vector mean, either column by column for RC="C" or row by row for RC="R".

getMean_Variance()

double getMean_Variance	(	Array2D< double > &	data_c,
		Array1D< double > &	w,
		Array1D< double > &	mean )

Vector-mean and weighted variance.

getPdf_cl()

void getPdf_cl	(	Array2D< double > &	data,
		Array2D< double > &	points,
		Array1D< double > &	dens,
		int	ncl,
		double	sfac )

Compute the PDF of data at the given points using given number of clusters (if ncl=0, then find the optimal cluster number) and a scale factor for the optimal bandwidth.

getPdf_figtree()

void getPdf_figtree	(	Array2D< double > &	source,
		Array2D< double > &	target,
		Array1D< double > &	sig,
		Array1D< double > &	density,
		Array1D< double > &	weight )

KDE estimation of a PDF.

ihsP()

void ihsP	(	const int	ndim,
		const int	ns,
		int *	x,
		const int	dupl,
		dsfmt_t *	rnstate )

ihsU() [1/2]

void ihsU	(	Array2D< double > &	rndnos,
		const int	dfac,
		dsfmt_t *	rnstate )

ihsU() [2/2]

void ihsU	(	const int	ndim,
		const int	ns,
		double *	rndnos,
		const int	dfac,
		dsfmt_t *	rnstate )

inverf()

double inverf

(

double

y0

)

Inverse error function, input scaled to [-1,1].

Note

Cephes Math Library Release 2.8: June, 2000. Copyright 1984, 1987, 1988, 1992, 2000 by Stephen L. Moshier

invnormcdf()

double invnormcdf

(

double

y

)

Inverse of the CDF of the normal random variable, uses inverf.

normcdf()

double normcdf

(

double

y

)

Normal random variable CDF.

normcdfc()

double normcdfc

(

double

y

)

Complementary function for normcdf.

rperm()

void rperm	(	int	n,
		int *	a,
		dsfmt_t *	rnstate )

Random permutation of 0..n-1.