mk_gnode_gweight.c File Reference

Construct the Gaussian nodes and weights. More...

#include "libftsh.h"

Defines
#define	ENTEREXIT   0
#define	LNOF2   0.693147180559945309417232121458
Functions
void	mk_gnode_gweight (REAL *gnode, REAL *gweight, REAL epsilon, int numpts)
void	mk_cosi_gnode (REAL *gnode, REAL epsilon, int numpts)
void	cosi_gnode_to_gweight (REAL *gweight, REAL *gnode, int numpts)

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Detailed Description

Construct the Gaussian nodes and weights.

Summary:

• mk_gnode_gweight drives the construction.
• mk_cosi_gnode constructs the nodes.
• cosi_gnode_to_gweight constructs the weights from the nodes.

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Function Documentation

void cosi_gnode_to_gweight	(	REAL *	gweight,
		REAL *	gnode,
		int	numpts
	)

This routine computes the gaussian weights that go with a set of gaussian nodes.

The nodes input here are \(\cos^{-1}(\text{the usual nodes} )\).

INPUTS:

• gweight -- the array in which to put the gaussian weights. Memory must already be allocated.
• gnode -- the gausian nodes, theta values between 0 and PI This is \(\cos^{-1}(\text{the usual nodes} )\).
• numpts -- the order of the weights we compute this is the length of gnode and gweight.

OUTPUTS: numpts values of gweight are filled in

NOTES:

• We use the Christoffel function method, mainly because we can avoid derivatives.
• Do I use normalized Pmn?

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void mk_gnode_gweight	(	REAL *	gnode,
		REAL *	gweight,
		REAL	epsilon,
		int	numpts
	)

This routine constructs the gaussian nodes and weights.

We make cosine inverse of the ordinary gaussian nodes.

INPUTS:

• gnode -- the array of length numpts in which to put the gaussian nodes. Memory must already be allocated.
• gweight -- the array in which to put the gaussian weights. Memory must already be allocated.
• epsilon -- the precision to which to compute the gaussian nodes.
• numpts -- the order of the nodes and weights we compute this is the length of gnode and gweight.

OUTPUTS:

• gnode -- the numpts gaussian node values are written on gnode We make cosine inverse of the ordinary gaussian nodes.
• gweight -- numpts values of gweight are filled in

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