manybody/gauss_tools.hpp File Reference

Tools for Gaussian quadrature and orthogonal polynomials. More...

#include "linalg.hpp"

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Namespaces
namespace	gauss
Functions
void	gauss::computeHermitePolys (dense_vector &x, dense_matrix &P, int N)
	Compute normalized Hermite polynomials: P_n(x) = (1/sqrt[2^n*n!*sqrt(pi)])*H_n(x),.
void	gauss::computeLaguerrePolys (dense_vector &x, dense_matrix &P, int N, double alpha)
	Compute generalized Laguerre polynomials: P^a_n(x).
void	gauss::computeNormalizedLaguerrePolys (dense_vector &x, dense_matrix &P, int N, double alpha)
	Compute normalized generalized Laguerre polynomials.
void	gauss::computeGaussHermite (dense_vector &x, dense_vector &w, long int n)
	Compute Gauss-Hermite quadrature rules using Golub-Welsch algorithm.
void	gauss::computeGaussLaguerre (dense_vector &x, dense_vector &w, long int n)
	Compute Gauss-Laguerre quadrature rules using Golub-Welsch algorithm.
void	gauss::computeGenHalfGaussHermite (dense_vector &x, dense_vector &w, double gam, long int N)
	Compute generalized galf-range Gauss-Hermite quadrature rules.
void	gauss::computeGenHalfHermiteCoeffs (dense_vector &alpha, dense_vector &beta, double gam, int N)
	Compute recursion coefficients of the monic, generalized half-range Hermite polynomials.
void	gauss::computeGenHalfHermiteCoeffsNormalized (dense_vector &a, dense_vector &b, dense_vector &c, double gam, int N)
	Compute coefficients of recursion of normalized generalized half-range Hermite polynomials.
void	gauss::computeNormalizedGenHalfHermitePolys (dense_vector &x, dense_matrix &P, double gam, int N, bool diff)
	Compute normalized generalized half-range Hermite polynomials of order 0..N evaluated at x.

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Detailed Description

Tools for Gaussian quadrature and orthogonal polynomials.

Author:

Simen Kvaal

Date:

6-13-08, update 10-7-2008

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