direct1_tofile.c File Reference

Precompute and save data for direct1 spherical harmonic transform. More...

#include "libftsh.h"

Defines
#define	ENTEREXIT   0
Functions
void	direct1_tofile (int numpts, int band_limit, REAL *node, REAL *weight, FILE *fp)
void	init_direct1 (Pm_Direct_d **out, int halfpts, int band_limit, REAL *node)
void	dump_direct1 (int numpts, int band_limit, REAL *node, REAL *weight, Pm_Direct_d *pmn_matrix, FILE *fp)

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Detailed Description

Precompute and save data for direct1 spherical harmonic transform.

Summary:

• direct1_tofile drives the initialization and saving.
• init_direct1 does the actual initialization.
• dump_direct1 does the actual saving.

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Function Documentation

void direct1_tofile	(	int	numpts,
		int	band_limit,
		REAL *	node,
		REAL *	weight,
		FILE *	fp
	)

This routine initializes the direct transform for spherical harmonics (version 1) and dumps it to a file.

INPUTS:

• numpts -- the number of points on the full interval. Must be divisible by 2.
• band_limit -- the bound on the degree of the expansion. In \(P^m_n\) notation this bounds n.
• node -- an array of length numpts with the nodes, usually Arcsin of the usual gaussian nodes.
• weight -- an array of length numpts with the quadrature weights

OUTPUTS: fp - the objects created are written onto the file pointed to by fp, in binary format. The file must be opened before calling this routine.

NOTES:

• node and weight are input so the user can select.

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void dump_direct1	(	int	numpts,
		int	band_limit,
		REAL *	node,
		REAL *	weight,
		Pm_Direct_d *	pmn_matrix,
		FILE *	fp
	)

This routine dumps the initialization constructed by init_direct1 and general parameters for the direct transform for spherical harmonics, dense version.

INPUTS:

• numpts -- the number of points on the full interval.
• band_limit -- the bound on the degree of the expansion. In \(P^m_n\) notation this bounds n.
• node -- an array of length numpts with the nodes, usually Arcsin of the usual gaussian nodes.
• weights -- an array of length numpts with the quadrature weights
• pmn_matrix -- an array of band_limit (==order_limit) Pm_Direct_d structures, each representing the matrix for one m.

OUTPUTS: fp -- the objects above are written into the file pointed to by fp, in binary format. The file must be opened before calling this routine.

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void init_direct1	(	Pm_Direct_d **	out,
		int	halfpts,
		int	band_limit,
		REAL *	node
	)

This routine initializes for the transform for spherical harmonics, direct version 1. This version simple precomputes the Pm matrices and stores them in dense matrix format.

INPUTS:

• halfpts -- half the number of points on the full interval. This implies the full number of points is even, and we also assume the nodes are symmetric. Currrently halfpts must also be even for our trig transforms to work.
• band_limit -- the bound on the degree of the expansion. In \(P^m_n\) notation this bounds n. For gaussian nodes this must be < 2*halfpts and for other nodes it should be even smaller. We confirn band_limit < 2*halfpts but leave the rest to the user.
• node -- an array with the nodes, usually Arcsin of the usual gaussian nodes. We use halfpts of these, representing half of the interval.

OUTPUTS: out -- memory is allocated for band_limit (==order_limit) Pm_Direct_d structures, each representing the matrix for one m. Various bits of memory are allocated for these, and values filled in.

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