gaussher.cpp File Reference

(Last Changed on August 27, 2014 for git-revision dbdbfae70442067ef6b20da218e016c0f8de90b9.)

This file has routines used for Gauss-Hermite Quadrature and Gauss-Legendre Quadrature. More...

#include <fvar.hpp>

Go to the source code of this file.

Functions
void	gauss_hermite (const dvector &_t, const dvector &_wts)
	Gauss-Hermite quadature. More...
void	gauss_legendre (double a, double b, const dvector &_t, const dvector &_wts)
	Gauss-Legendre quadature. More...
void	gauss_legendre (const dvector &_x, const dvector &_w)
	Gauss-Legendre quadature. More...
void	imtqlx (const dvector &_d, const dvector &_e, const dvector &_z)
	Diagonalizes a symmetric tridiagonal matrix. More...
void	normalized_gauss_hermite (const dvector &_x, const dvector &_w)
	Gauss-Hermite quadature. More...
double	sign (const double x)
	The sign of a number. More...

Detailed Description

This file has routines used for Gauss-Hermite Quadrature and Gauss-Legendre Quadrature.

Definition in file gaussher.cpp.

Function Documentation

void gauss_hermite	(	const dvector &	_t,
		const dvector &	_wts
	)

Gauss-Hermite quadature.

Computes a Gauss-Hermite quadrature formula with simple knots.

Parameters

_t	array of abscissa
_wts	array of corresponding wights

Definition at line 36 of file gaussher.cpp.

Referenced by normalized_gauss_hermite().

void gauss_legendre	(	double	a,
		double	b,
		const dvector &	_t,
		const dvector &	_wts
	)

Gauss-Legendre quadature.

computes knots and weights of a Gauss-Legendre quadrature formula.

Parameters

a	Left endpoint of interval
b	Right endpoint of interval
_t	array of abscissa
_wts	array of corresponding wights

Definition at line 148 of file gaussher.cpp.

Referenced by gauss_legendre().

void gauss_legendre	(	const dvector &	_x,
		const dvector &	_w
	)

Gauss-Legendre quadature.

Parameters

_x	array of abscissa
_w	array of corresponding wights

Definition at line 331 of file gaussher.cpp.

void imtqlx	(	const dvector &	_d,
		const dvector &	_e,
		const dvector &	_z
	)

Diagonalizes a symmetric tridiagonal matrix.

Parameters

_d	diagonal entries
_e	the subdiagonals
_z	a vector

Definition at line 359 of file gaussher.cpp.

Referenced by gauss_hermite(), and gauss_legendre().

void normalized_gauss_hermite	(	const dvector &	_x,
		const dvector &	_w
	)

Gauss-Hermite quadature.

this is normlaized so that standard normal density integrates to 1

Parameters

_x	array of abscissa
_w	array of corresponding wights

Definition at line 343 of file gaussher.cpp.

Referenced by gauss_hermite_stuff::gauss_hermite_stuff().

double sign

(

const double

x

)

The sign of a number.

Parameters

x

Double

Definition at line 25 of file gaussher.cpp.

Referenced by csolve(), imtqlx(), itoa(), function_minimizer::likeprof_routine(), and solve().