gq.cpp File Reference

Utilities to generate quadrature rules. More...

#include "stdio.h"
#include "stdlib.h"
#include <iostream>
#include <cmath>
#include "Array1D.h"
#include "Array2D.h"
#include "deplapack.h"
#include "gq.h"
#include "combin.h"

Macros
#define	DPI   3.14159265358979323846

Functions
double	lpol_gq (int n, double x)
double	hpol_gq (int n, double x)
double	hpol_phys_gq (int n, double x)
double	jpol_gq (int n, double a, double b, double x)
double	jpolp_gq (int n, double a, double b, double x)
double	lgpol_gq (int n, double a, double x)
double	fact_gq (int n)
void	gq (const int kind, const double a, const double b, Array1D< double > &x, Array1D< double > &w)
	Computes abscissas and weights for several quadrature rules.
void	gq (const int kind, const int n, const double a, const double b, double *x, double *w)
	Computes abscissas and weights for several quadrature rules.
void	gchb (const int kind, const int n, double *x, double *w)
	Computes abscissas and weights for Chebyshev quadrature rules.
void	gq_gen (Array1D< double > &a, Array1D< double > &b, const double amu0, Array1D< double > &x, Array1D< double > &w)
	Computes abscissas and weights for a generic orthogonal polynomial recursion using the Golub-Welsch algorithm.
void	vandermonde_gq (Array1D< double > &x, Array1D< double > &w, Array1D< double > &q)
	Computes abscissas and weights for Newton-Cotes rules through the solution of a Vandermonde matrix. This function was tested as an internal function only, called by the quadrature class.

Detailed Description

Utilities to generate quadrature rules.

Macro Definition Documentation

DPI

#define DPI   3.14159265358979323846

Function Documentation

fact_gq()

double fact_gq

(

int

n

)

gchb()

void gchb	(	const int	kind,
		const int	n,
		double *	x,
		double *	w )

Computes abscissas and weights for Chebyshev quadrature rules.

Parameters

kind	: defines quadrature type (1) Gauss-Chebyshev 1st kind (2) Gauss-Chebyshev 2nd kind
n	: quadrature order
x	: on return it holds quadrature abscissas.
w	: on return it holds quadrature weights.

gq() [1/2]

void gq	(	const int	kind,
		const double	a,
		const double	b,
		Array1D< double > &	x,
		Array1D< double > &	w )

Computes abscissas and weights for several quadrature rules.

Parameters

kind	: defines quadrature type (1) Gauss-Legendre, (2) Gauss-Chebyshev 1st kind (3) Gauss-Chebyshev 2nd kind, (4) Gauss-Hermite, (5) Gauss-Jacobi (6) Gauss-Laguerre
a	: optional parameter needed by Gauss-Jacobi and Gauss-Laguerre rules
b	: optional parameter needed by Gauss-Jacobi rule
x	: on return it holds quadrature abscissas. Its initial size determines the quadrature order
w	: on return it holds quadrature weights.

gq() [2/2]

void gq	(	const int	kind,
		const int	n,
		const double	a,
		const double	b,
		double *	x,
		double *	w )

Computes abscissas and weights for several quadrature rules.

Parameters

kind	: defines quadrature type (1) Gauss-Legendre, (2) Gauss-Chebyshev 1st kind (3) Gauss-Chebyshev 2nd kind, (4) Gauss-Hermite, (5) Gauss-Jacobi (6) Gauss-Laguerre
n	: quadrature order
a	: optional parameter needed by Gauss-Jacobi and Gauss-Laguerre rules
b	: optional parameter needed by Gauss-Jacobi rule
x	: on return it holds quadrature abscissas.
w	: on return it holds quadrature weights.

gq_gen()

void gq_gen	(	Array1D< double > &	a,
		Array1D< double > &	b,
		const double	amu0,
		Array1D< double > &	x,
		Array1D< double > &	w )

Computes abscissas and weights for a generic orthogonal polynomial recursion using the Golub-Welsch algorithm.

Parameters

a	: array of parameters for the orthogonal polynomial recursion. Its initial size determines the quadrature order
b	: array of parameters for the orthogonal polynomial recursion
amu0	: parameter for custom scaling of quadrature weights
x	: on return it holds quadrature abscissas
w	: on return it holds quadrature weights.

hpol_gq()

double hpol_gq	(	int	n,
		double	x )

hpol_phys_gq()

double hpol_phys_gq	(	int	n,
		double	x )

jpol_gq()

double jpol_gq	(	int	n,
		double	a,
		double	b,
		double	x )

jpolp_gq()

double jpolp_gq	(	int	n,
		double	a,
		double	b,
		double	x )

lgpol_gq()

double lgpol_gq	(	int	n,
		double	a,
		double	x )

lpol_gq()

double lpol_gq	(	int	n,
		double	x )

vandermonde_gq()

void vandermonde_gq	(	Array1D< double > &	x,
		Array1D< double > &	w,
		Array1D< double > &	q )

Computes abscissas and weights for Newton-Cotes rules through the solution of a Vandermonde matrix. This function was tested as an internal function only, called by the quadrature class.

Parameters

x	: holds quadrature abscissas
w	: on return it holds quadrature weights.
q	: array of parameters needed to setup the Vandermonde matrix