#include "geoslib_d.h"
#include "geoslib_old_f.h"
#include "geoslib_define.h"
#include "Matrix/MatrixRectangular.hpp"
#include "Basic/MathFunc.hpp"
#include "Basic/Law.hpp"
#include "Basic/WarningMacro.hpp"
#include <math.h>
#include <boost/math/special_functions/legendre.hpp>
#include <boost/math/special_functions/spherical_harmonic.hpp>
#include <Geometry/GeometryHelper.hpp>

Classes
struct	Reg_Coor

Macros
#define	COORD(i, ip) (coord[3 * (ip) + (i)])

#define	RCOORD(i, ip) (R_coor->coor[3 * (ip) + (i)])

#define	w ((double *)&equiv_99)

#define	x ((double *)&equiv_100)

#define	X 0.525731112119133696

#define	Z 0.850650808352039932

Functions
void	mvndst (int n, double lower, double upper, int infin, double correl, int maxpts, double abseps, double releps, double error, double value, int *inform)

void	mvndst4 (double lower, double upper, double correl, int maxpts, double abseps, double releps, double error, double value, int inform)

void	mvndst2n (double lower, double upper, double means, double correl, int maxpts, double abseps, double releps, double error, double value, int *inform)

int	mvndst_infin (double low, double sup)

int	bessel_j (double x, double alpha, int nb, double *b)

int	bessel_k (double x, double alpha, int nb, double *bk)

double	loggamma (double parameter)

double	ut_legendre (int flag_norm, int n, double v)

double	ut_flegendre (int flag_norm, int n, int k0, double theta)

double	golden_search (double(func_evaluate)(double test, void user_data), void user_data, double tolstop, double a0, double c0, double test_loc, double *niter)

int	ut_chebychev_count (double(func)(double, double, int, double ), Cheb_Elem cheb_elem, double x, int nblin, double blin)

int	ut_chebychev_coeffs (double(func)(double, double, int, double ), Cheb_Elem cheb_elem, int nblin, double blin)

void	ut_vandercorput (int n, int flag_sym, int flag_rot, int ntri_arg, double *coor_arg)

void	st_subdivide (double v1[3], double v2[3], double v3[3], int depth, Reg_Coor *R_coor)

int	ut_icosphere (int n, int flag_rot, int ntri_arg, double *coor_arg)

void	ut_log_factorial (int nbpoly, double *factor)

double	ut_factorial (int k)

DISABLE_WARNING_POP MatrixRectangular *	vanDerCorput (int n, int nd)

MatrixRectangular	fillLegendreMatrix (const VectorDouble &r, int legendreOrder)

Macro Definition Documentation

◆ COORD

#define COORD	(	i,
		ip
	)	(coord[3 * (ip) + (i)])

◆ RCOORD

#define RCOORD	(	i,
		ip
	)	(R_coor->coor[3 * (ip) + (i)])

◆ w

#define w ((double *)&equiv_99)

◆ x

#define x ((double *)&equiv_100)

◆ X

#define X 0.525731112119133696

◆ Z

#define Z 0.850650808352039932

Function Documentation

◆ bessel_j()

int bessel_j	(	double	x,
		double	alpha,
		int	nb,
		double *	b
	)

This routine calculates Bessel functions J SUB(NB+ALPHA) (X) for non-negative argument X, and non-negative order NB+ALPHA.

Returns: Error return code : NCALC; NCALC < -1: An argument is out of range.; 1 < NCALC < NB: Not all requested function values could be; calculated accurately. BY(I) contains correct function values

Parameters

[in]	x	Working precision non-negative real argument for which J's are to be calculated.
[in]	alpha	Working precision fractional part of order for which J's are to be calculated. 0 <= ALPHA < 1.0.
[in]	nb	Integer number of functions to be calculated, NB > 0 The first function calculated is of order ALPHA, and the last is of order (NB - 1 + ALPHA).
[out]	b	Working precision output vector of length NB. If the routine terminates normally (NCALC=NB), the vector by[] contains the functions Y(ALPHA,X), ... ,Y(NB-1+ALPHA,X),

Remarks: This program is based on a program written by David J. Sookne (2); that computes values of the Bessel functions J or I of real; argument and integer order. Modifications include the; restriction of the computation to the J Bessel function of; non-negative real argument, the extension of the computation to; arbitrary positive order, and the elimination of most underflow.; References: "A Note on Backward Recurrence Algorithms," Olver, F.; W. J., and Sookne, D. J., Math. Comp. 26, 1972, pp 941-947.; "Bessel Functions of Real Argument and Integer Order," Sookne, D.; J., NBS Jour. of Res. B. 77B, 1973, pp 125-132.

◆ bessel_k()

int bessel_k	(	double	x,
		double	alpha,
		int	nb,
		double *	bk
	)

This routine calculates modified Bessel functions of the second kind, K SUB(N+ALPHA) (X), for non-negative argument X and non-negative order N+ALPHA

Returns: Error return code : NCALC NCALC < -1: An argument is out of; range. 0 < NCALC < NB: Not all requested function values could be; calculated accurately. BK(I) contains correct function values; for I <= NCALC, and contains the ratios; K(ALPHA+I-1,X)/K(ALPHA+I-2,X) for the rest of the array.

Parameters

[in]	x	Working precision non-negative real argument for which K's are to calculated. If K's are to be calculated, X must not be greater than XMAX.
[in]	alpha	Working precision fractional part of order for which K's are to be calculated. 0 <= ALPHA <1.0.
[in]	nb	Integer number of functions to be calculated, NB > 0. The first function calculated is of order ALPHA, and the last is of order (NB - 1 + ALPHA).
[out]	bk	Working precision output vector of length NB. If the routine terminates normally (NCALC=NB), the vector BK contains the functions : K(ALPHA,X), ... , K(NB-1+ALPHA,X),

Remarks: This program is based on a program written by J. B. Campbell (2); that computes values of the Bessel functions K of real argument; and real order. References: "On Temme's Algorithm for the \remark Modified Bessel Functions of the Third Kind," Campbell, J. B.,; TOMS 6(4), Dec. 1980, pp. 581-586. "A FORTRAN IV Subroutine for; the Modified Bessel Functions of the Third Kind of Real Order and; Real Argument," Campbell, J. B., Report NRC/ERB-925, National; Research Council, Canada.

◆ fillLegendreMatrix()

MatrixRectangular fillLegendreMatrix	(	const VectorDouble &	r,
		int	legendreOrder
	)

◆ golden_search()

double golden_search	(	double()(double test, void user_data)	func_evaluate,
		void *	user_data,
		double	tolstop,
		double	a0,
		double	c0,
		double *	test_loc,
		double *	niter
	)

Golden Search algorithm

Returns: The estimated value

Parameters

[in]	func_evaluate	Evaluating function
[in]	user_data	User Data
[in]	tolstop	Tolerance parameter
[in]	a0	Initial value for lower bound of interval
[in]	c0	Initial value for upper bound of interval
[out]	test_loc	Final value of the evaluating function
[out]	niter	Number of iterations

◆ loggamma()

double loggamma ( double parameter )

Calculation of the logarithm of the gamma function

Returns: Logarithm of the gamma function

Parameters

[in] parameter raw value

◆ mvndst()

void mvndst	(	int	n,
		double *	lower,
		double *	upper,
		int *	infin,
		double *	correl,
		int	maxpts,
		double	abseps,
		double	releps,
		double *	error,
		double *	value,
		int *	inform
	)

Multivariate Normal Probability

Parameters

[in]	n	Number of variables
[in]	lower	Array of lower integration limits
[in]	upper	Array of upper integration limits
[in]	infin	Array of integration limit flags <0 for ]-Infinity; +Infinity[ =0 for ]-Infinity; upper] =1 for [lower; +Infinity[ =2 for [lower; upper]
[in]	correl	Array of correlation coefficients
[in]	maxpts	Maximum number of function values allowed
[in]	abseps	Absolute error tolerance
[in]	releps	Relative error tolerance
[out]	error	Estimated absolute error with 90% confidence level
[out]	value	Estimated value for the integral
[out]	inform	Returned code

Remarks: The array correl must be entered as the non-diagonal upper part; of the correlation matrix, entered by line; This subroutine uses an algorithm given in the paper:; "Numerical Computation of Multivariate Normal Probabilities", in; J. of Computational and Graphical Stat., 1(1992), pp. 141-149, by; Alan Genz; Department of Mathematics; Washington State University; Pullman, WA 99164-3113; Email : AlanG.nosp@m.enz@.nosp@m.wsu.e.nosp@m.du

◆ mvndst2n()

void mvndst2n	(	double *	lower,
		double *	upper,
		double *	means,
		double *	correl,
		int	maxpts,
		double	abseps,
		double	releps,
		double *	error,
		double *	value,
		int *	inform
	)

Calculate the multigaussian integral (non-normalized)

Parameters

[in]	lower	Array of lower bounds (Dimension: nvar)
[in]	upper	Array of upper bounds (Dimension: nvar)
[in]	means	Array of means (Dimension: 2)
[in]	correl	Correlation matrix (Dimension: 2*2)
[in]	maxpts	Maximum number of function values allowed
[in]	abseps	Absolute error tolerance
[in]	releps	Relative error tolerance
[out]	error	Estimated absolute error with 90% confidence level
[out]	value	Estimated value for the integral
[out]	inform	Returned code

◆ mvndst4()

void mvndst4	(	double *	lower,
		double *	upper,
		double *	correl,
		int	maxpts,
		double	abseps,
		double	releps,
		double *	error,
		double *	value,
		int *	inform
	)

Calculate the quadri-variable gaussian integral

Parameters

[in]	lower	Array of lower bounds
[in]	upper	Array of upper bounds
[in]	correl	Correlation matrix (Dimension: 4*4)
[in]	maxpts	Maximum number of function values allowed
[in]	abseps	Absolute error tolerance
[in]	releps	Relative error tolerance
[out]	error	Estimated absolute error with 90% confidence level
[out]	value	Estimated value for the integral
[out]	inform	Returned code

◆ mvndst_infin()

int mvndst_infin	(	double	low,
		double	sup
	)

Set the flags for the bound of numerical integration

Returns: Flag for the bound

Parameters

[in]	low	Lower integration bound
[in]	sup	Upper integration bound

◆ st_subdivide()

void st_subdivide	(	double	v1[3],
		double	v2[3],
		double	v3[3],
		int	depth,
		Reg_Coor *	R_coor
	)

◆ ut_chebychev_coeffs()

int ut_chebychev_coeffs	(	double()(double, double, int, double )	func,
		Cheb_Elem *	cheb_elem,
		int	nblin,
		double *	blin
	)

Calculates the coefficients of the Chebychev polynomial which is an approximation of a given function

Returns: Error return code

Parameters

[in]	func	Function to be approximated
[in]	cheb_elem	Cheb_Elem structure
[in]	nblin	Number of terms in the polynomial expansion
[in]	blin	Array of coefficients for polynomial expansion

◆ ut_chebychev_count()

int ut_chebychev_count	(	double()(double, double, int, double )	func,
		Cheb_Elem *	cheb_elem,
		double	x,
		int	nblin,
		double *	blin
	)

Evaluate the number of coefficients necessary to evaluate a function (at a sample location) at a given approximation

Returns: Minimum number of necessary coefficients

Parameters

[in]	func	Function to be approximated
[in]	cheb_elem	Cheb_Elem structure
[in]	x	Sampling value
[in]	nblin	Number of terms in the polynomial expansion
[in]	blin	Array of coefficients for polynomial expansion

◆ ut_factorial()

double ut_factorial ( int k )

Calculates the factorial coefficient

Returns: Returned value

Parameters

[in] k Value

◆ ut_flegendre()

double ut_flegendre	(	int	flag_norm,
		int	n,
		int	k0,
		double	theta
	)

Returns the Spherical Legendre normalized function

Parameters

[in]	flag_norm	1 for normalized and 0 otherwise
[in]	n	Degree
[in]	k0	Order (ABS(k0) <= n)
[in]	theta	Theta angle in radian

◆ ut_icosphere()

int ut_icosphere	(	int	n,
		int	flag_rot,
		int *	ntri_arg,
		double **	coor_arg
	)

Generate regular Icosahedron discretization

Returns: Error return code

Parameters

[in]	n	Number of discretization steps
[in]	flag_rot	Perform a random rotation
[out]	ntri_arg	Number of points
[out]	coor_arg	Array of point coordinates (Dimension: 3*ntri)

Remarks: As random number are used in this function, a specific seed; is fixed here

◆ ut_legendre()

double ut_legendre	(	int	flag_norm,
		int	n,
		double	v
	)

Returns the Associated Legendre Function

Parameters

[in]	flag_norm	1 for normalized and 0 otherwise
[in]	n	Degree
[in]	v	Value

◆ ut_log_factorial()

void ut_log_factorial	(	int	nbpoly,
		double *	factor
	)

Calculates the nbpoly log-factorial coefficients

Parameters

[in]	nbpoly	Number of terms
[out]	factor	logarithm of factorials

◆ ut_vandercorput()

void ut_vandercorput	(	int	n,
		int	flag_sym,
		int	flag_rot,
		int *	ntri_arg,
		double **	coor_arg
	)

Generate a Van Der Corput list of points in R^3

Parameters

[in]	n	Number of points
[in]	flag_sym	Duplicate the samples by symmetry
[in]	flag_rot	Perform a random rotation
[out]	ntri_arg	Number of points
[out]	coor_arg	Array of point coordinates (Dimension: 3*ntri)

◆ vanDerCorput()

DISABLE_WARNING_POP MatrixRectangular* vanDerCorput	(	int	n,
		int	nd
	)

Function to compute the vector Van der Corput sequence or the Halton sequence

Parameters

n	The number of values to be computed
nd	The dimension of output sequence

Returns: A matrix of dimensions [n,nd] with the sequence values (between 0 and 1)

Note: The dimension nd should be lower or equal to 50.

Classes

Macros

Functions

Macro Definition Documentation

◆ COORD

◆ RCOORD

◆ w

◆ x

◆ X

◆ Z

Function Documentation

◆ bessel_j()

◆ bessel_k()

◆ fillLegendreMatrix()

◆ golden_search()

◆ loggamma()

◆ mvndst()

◆ mvndst2n()

◆ mvndst4()

◆ mvndst_infin()

◆ st_subdivide()

◆ ut_chebychev_coeffs()

◆ ut_chebychev_count()

◆ ut_factorial()

◆ ut_flegendre()

◆ ut_icosphere()

◆ ut_legendre()

◆ ut_log_factorial()

◆ ut_vandercorput()

◆ vanDerCorput()