gl Namespace Reference

Gauss-Legendre interfaces and implementations. More...

Classes
struct	GLNode
	Container for weight and nodes. More...

Functions
double	GLQuad (size_t n, double(*f)(double, void *), void *data, double a, double b)
gl::GLNode	GL (size_t l, size_t k)
gl::GLNode	GLS (size_t n, size_t k)
double	besseljzero (int k)
double	besselj1squared (int k)

Variables
const double *	weights [_GL_LUT_TABLE_SIZE]
	Weight used for Gauss-Legendre integration. More...
const double *	abcissas [_GL_LUT_TABLE_SIZE]
	Abcissae or coordinates used for Gauss-Legendre integration. More...

Detailed Description

Gauss-Legendre interfaces and implementations.

Function Documentation

besselj1squared()

double besselj1squared

(

int

k

)

This function computes the square of BesselJ(1, BesselZero(0,k))

Parameters

k

Returns

besseljzero()

double besseljzero

(

int

k

)

This function computes the k'th zero of the BesselJ(0,x)

Parameters

k

Returns

GL()

gl::GLNode GL	(	size_t	l,
		size_t	k
	)

Purpose:

GL computes the kth GL pair of an n-point rule. It uses look-up tables for the n < 101.

Licensing:

This code is distributed under the BSD license.

Modified:

22 December 2015

Author:

Ignace Bogaert

Reference:

Ignace Bogaert, Iteration-free computation of Gauss-Legendre quadrature nodes and weights, SIAM Journal on Scientific Computing, Volume 36, Number 3, 2014, pages A1008-1026.

The only function that needs to be public

Parameters

l	The number of points in the given rule
k	The index of the point to be returned

Returns

The location and weight of the point

GLQuad()

double GLQuad	(	size_t	n,
		double(*)(double, void *)	f,
		void *	data,
		double	a,
		double	b
	)

Gauss-Legendre quadrature using an n-point rule.

Parameters

n	Quadrature order
f	Integrand
data	Pointer to user-defined data which will be passed to f every time it is called (as second parameter).
a	Lower integration limit
b	Upper integration limit

Returns

GLS()

gl::GLNode GLS	(	size_t	n,
		size_t	k
	)

GLS computes the kth GL pair of an n-point rule using the formula rather than look-up tables.

Reference:

Ignace Bogaert, Iteration-free computation of Gauss-Legendre quadrature nodes and weights, SIAM Journal on Scientific Computing, Volume 36, Number 3, 2014, pages A1008-1026.

Parameters

n	The number of points in the given rule
k	The index of the point to be returned

Returns

Variable Documentation

abcissas

const double* abcissas[_GL_LUT_TABLE_SIZE]

extern

Abcissae or coordinates used for Gauss-Legendre integration.

weights

const double* weights[_GL_LUT_TABLE_SIZE]

extern

Weight used for Gauss-Legendre integration.

Referenced by CalcFastFourAny(), CalcFastFourAny2(), and CalcFourFast().