gq.h File Reference

Header for quadrature generation utilities. More...

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Functions
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	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.
void	gchb (const int kind, const int n, double *x, double *w)
	Computes abscissas and weights for Chebyshev quadrature rules.

Detailed Description

Header for quadrature generation utilities.

Function Documentation

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.

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