Legendre.h File Reference

Various utility methods for Spectral elements. More...

#include "matrix.h"

Include dependency graph for Legendre.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Functions
bool	Legendre::GL (std::vector< Real > &weights, std::vector< Real > &points, int n)
	Get Gauss-Legendre points and weights in the domain [-1,1]. More...
bool	Legendre::GLL (std::vector< Real > &weights, std::vector< Real > &points, int n)
	Get Gauss-Lobatto-Legendre points and weights in the domain [-1,1]. More...
bool	Legendre::eval (int n, Real x, Real &retval)
	Evaluates the n-th Legendre polynomial. More...
bool	Legendre::derEval (int n, Real x, Real &retval)
	Evaluates the first derivative of the n-th Legendre polynomial. More...
bool	Legendre::basisDerivatives (int n, utl::matrix< Real > &der)
	Evaluates first derivatives of the n one-dimensional Lagrange interpolation polynomials through n GLL-points. More...

Detailed Description

Various utility methods for Spectral elements.

Date

Mar 19 2009

Author

Einar Christensen / SINTEF

Function Documentation

basisDerivatives()

bool Legendre::basisDerivatives	(	int	n,
		utl::matrix< Real > &	der
	)

Evaluates first derivatives of the n one-dimensional Lagrange interpolation polynomials through n GLL-points.

Parameters

[in]	n	Number of GLL points/polynomials
[out]	der	Evaluated values

References Legendre::basisDerivatives(), Legendre::eval(), Legendre::GLL(), Real, and utl::matrix< T >::resize().

Referenced by Legendre::basisDerivatives().

derEval()

bool Legendre::derEval	(	int	n,
		Real	x,
		Real &	retval
	)

Evaluates the first derivative of the n-th Legendre polynomial.

Parameters

[in]	n	Polynomial degree
[in]	x	Evaluation point
[out]	retval	Value of the first derivative at point x

References Legendre::derEval(), and Real.

Referenced by Legendre::derEval(), Legendre::GL(), and Legendre::GLL().

eval()

bool Legendre::eval	(	int	n,
		Real	x,
		Real &	retval
	)

Evaluates the n-th Legendre polynomial.

Parameters

[in]	n	Polynomial degree
[in]	x	Evaluation point
[out]	retval	Polynomial value at point x

References Legendre::eval(), and Real.

Referenced by Legendre::basisDerivatives(), Legendre::eval(), and Legendre::GLL().

GL()

bool Legendre::GL	(	std::vector< Real > &	weights,
		std::vector< Real > &	points,
		int	n
	)

Get Gauss-Legendre points and weights in the domain [-1,1].

Parameters

[out]	weights	Computed Gauss-Legendre weight
[out]	points	Computed Gauss-Legendre points
[in]	n	Number of Gauss points

References Legendre::derEval(), Legendre::GL(), Real, and DenseMatrix::solveEigNon().

Referenced by Legendre::GL(), and Legendre::GLL().

GLL()

bool Legendre::GLL	(	std::vector< Real > &	weights,
		std::vector< Real > &	points,
		int	n
	)

Get Gauss-Lobatto-Legendre points and weights in the domain [-1,1].

Parameters

[out]	weights	Computed Gauss-Legendre weight
[out]	points	Computed Gauss-Legendre points
[in]	n	Number of Gauss points

References Legendre::derEval(), Legendre::eval(), Legendre::GL(), Legendre::GLL(), and Real.

Referenced by Legendre::basisDerivatives(), and Legendre::GLL().