basis Namespace Reference

Functions
void	jacobip (double alpha, double beta, unsigned int N, double *x, double *p, unsigned int np)
void	gradjacobip (double alpha, double beta, int N, double *x, double *dp, unsigned int np)
void	jacobiglq (double alpha, double beta, int N, double *x, double *w)
void	jacobigq (double alpha, double beta, int N, double *x, double *w)
void	lagrange (const double *x0, int N, int at, const double *x, double *px, int m)
	computes the Lagrange polynomials evalueated at x coords. More...

Detailed Description

Author

Milinda Fernando School of Computing, University of Utah. Contains implementation of Jacobi polynomials, and Jacobi Gauss-Lobatto quadrature. reference: Mangll implementation.

Function Documentation

gradjacobip()

void basis::gradjacobip	(	double	alpha,
		double	beta,
		int	N,
		double *	x,
		double *	dp,
		unsigned int	np
	)

Evaluate the derivative of the N'th order Jacobi Polynomial of type (alpha, beta ) > -1.

This is C reimplemetation of the function in JacobiP from Nodal Discontinuous Galerkin Methods by Jan S. Hesthaven and Tim Warburton.

Parameters

[in]	alpha	Jacobi polynomial parameter
[in]	beta	Jacobi polynomial parameter
[in]	N	Order of the polynomial
[in]	np	size of x and p.
[in]	x	Row vector of locations to evaluate the polynomial.
[out]	dp	Row vector of the evaluated derivative of the N'th order polynomial

Note

The matrix P is assumed to have the correct size of (1, len(x)). Also then polynomials are normalized to be orthonormal.

jacobiglq()

void basis::jacobiglq	(	double	alpha,
		double	beta,
		int	N,
		double *	x,
		double *	w
	)

Compute the N'th order Gauss Lobatto quadrature points and weights.

Where (alpha, beta ) > -1 and (alpha + beta <> -1).

Parameters

[in]	alpha	Jacobi polynomial parameter
[in]	beta	Jacobi polynomial parameter
[in]	N	Order of the polynomial
[out]	x	Row vector of Gauss Lobatto node locations
[out]	w	Row vector of Gauss Lobatto weights

Note

The matrices x and w are assumed to have the correct size of (1, N+1). Also the node location will be between [-1,1].

jacobigq()

void basis::jacobigq	(	double	alpha,
		double	beta,
		int	N,
		double *	x,
		double *	w
	)

Compute the N'th order Gauss quadrature points and weights.

Where (alpha, beta ) > -1.

This is C reimplemetation of the function in JacobiGQ from Nodal Discontinuous Galerkin Methods by Jan S. Hesthaven and Tim Warburton.

Parameters

[in]	alpha	Jacobi polynomial parameter
[in]	beta	Jacobi polynomial parameter
[in]	N	Order of the polynomial
[out]	x	Row vector of Gauss node locations
[out]	w	Row vector of Gauss weights

Note

The matrices x and w are assumed to have the correct size of (1, N+1). Also the node locaiton will be between [-1,1].

jacobip()

void basis::jacobip	(	double	alpha,
		double	beta,
		unsigned int	N,
		double *	x,
		double *	p,
		unsigned int	np
	)

Evaluate N'th order Jacobi Polynomial of type (alpha, beta ) > -1.

Also (alpha + beta <> -1).

This is C reimplemetation of the function in JacobiP from Nodal Discontinuous Galerkin Methods by Jan S. Hesthaven and Tim Warburton.

Parameters

[in]	alpha	Jacobi polynomial parameter
[in]	beta	Jacobi polynomial parameter
[in]	N	Order of the polynomial
[in]	np	size of x and p.
[in]	x	Row vector of locations to evaluate the polynomial.
[out]	p	Row vector of the evaluated N'th order polynomial

Note

The matrix P is assumed to have the correct size of (1, len(x)). Also then polynomials are normalized to be orthonormal.

lagrange()

void basis::lagrange	(	const double *	x0,
		int	N,
		int	at,
		const double *	x,
		double *	px,
		int	m
	)

computes the Lagrange polynomials evalueated at x coords.

Parameters

x0	nodal locations. N+1 points.
N	order of the Lagrange polynomial
x	points which Lagrange evaluated at.
px	P(x)
m	size of x points, (i.e. similar to px)