cospml.c File Reference

Source code for generating cosine transforms of Pml and Gml functions. More...

#include "s2kit/cospml.h"
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <fftw3.h>
#include "s2kit/chebyshev_nodes.h"
#include "s2kit/pml.h"
#include "s2kit/pmm.h"
#include "util/l2_norms.h"
#include "util/vector_funcs.h"

Go to the source code of this file.

Functions
int	TableSize (const int m, const int bw)
	Computes the number of non-zero entries of coeffs in a table for seminaive transform. More...
int	Spharmonic_TableSize (const int bw)
	Returns the amount of space needed for an entire spharmonic table. More...
int	Reduced_SpharmonicTableSize (const int bw, const int m)
int	TableOffset (int m, int l)
void	GenerateCosPmlTable (const int bw, const int m, double *tablespace, double *workspace)
int	RowSize (const int m, const int l)
int	Transpose_RowSize (const int row, const int m, const int bw)
void	TransposeCosPmlTable (const int bw, const int m, double *cos_pml_table, double *result)
double **	Spharmonic_Pml_Table (const int bw, double *resultspace, double *workspace)
double **	Transpose_Spharmonic_Pml_Table (double **spharmonic_pml_table, const int bw, double *resultspace)
int	Reduced_Naive_TableSize (const int bw, const int m)
double **	SemiNaive_Naive_Pml_Table (const int bw, const int m, double *resultspace, double *workspace)
double **	Transpose_SemiNaive_Naive_Pml_Table (double **seminaive_naive_pml_table, const int bw, const int m, double *resultspace, double *workspace)

Variables
const int	BW_LIMIT = 512
	Limit for bw is used in functions which calculate table size. More...

Detailed Description

Source code for generating cosine transforms of Pml and Gml functions.

Contains functions for generating tables of cosine transforms of Pml and Gml and utility functions for table management.

Definition in file cospml.c.

Function Documentation

GenerateCosPmlTable()

void GenerateCosPmlTable	(	const int	bw,
		const int	m,
		double *	tablespace,
		double *	workspace
	)

Definition at line 161 of file cospml.c.

Reduced_Naive_TableSize()

int Reduced_Naive_TableSize	(	const int	bw,
		const int	m
	)

Definition at line 434 of file cospml.c.

Reduced_SpharmonicTableSize()

int Reduced_SpharmonicTableSize	(	const int	bw,
		const int	m
	)

Definition at line 107 of file cospml.c.

RowSize()

int RowSize	(	const int	m,
		const int	l
	)

Definition at line 250 of file cospml.c.

SemiNaive_Naive_Pml_Table()

double** SemiNaive_Naive_Pml_Table	(	const int	bw,
		const int	m,
		double *	resultspace,
		double *	workspace
	)

Definition at line 451 of file cospml.c.

Spharmonic_Pml_Table()

double** Spharmonic_Pml_Table	(	const int	bw,
		double *	resultspace,
		double *	workspace
	)

Definition at line 387 of file cospml.c.

Spharmonic_TableSize()

int Spharmonic_TableSize

(

const int

bw

)

Returns the amount of space needed for an entire spharmonic table.

Returns an integer value for the amount of space necessary to fill out an entire spharmonic table. Note that in TableSize() formula, you need to sum this formula over m as m ranges from 0 to (bw-1). The critical closed form that you need is that:

\sum_{k=0}^n = \frac{(n(n+1)(2n+1)}{6}

You also need to account for integer division. From this you should derive an upper bound on the amount of space.

Some notes - because of integer division, you need to account for a fudge factor - this is the additional " + bw" at the end. This guarantees that you will always have slightly more space than you need, which is clearly better than underestimating! Also, if bw > 512, the closed form fails because of the bw*bw*bw term (at least on Sun Sparcstations) so the loop computation is used instead.

Note

Size of transposed table is exactly the same, obviously.

Definition at line 85 of file cospml.c.

TableOffset()

int TableOffset	(	int	m,
		int	l
	)

Definition at line 123 of file cospml.c.

TableSize()

int TableSize	(	const int	m,
		const int	bw
	)

Computes the number of non-zero entries of coeffs in a table for seminaive transform.

Computes the number of non-zero entries in a table containing cosine series coefficients of all the P(m,l) or G(m,l) functions necessary for computing the seminaive legendre transform for a given bandwidth bw and order m.

Parameters

m	order
bw	bandwidth

Note

Assumes the table is generated by GenerateCosPmlTable().

Definition at line 39 of file cospml.c.

Transpose_RowSize()

int Transpose_RowSize	(	const int	row,
		const int	m,
		const int	bw
	)

Definition at line 270 of file cospml.c.

Transpose_SemiNaive_Naive_Pml_Table()

double** Transpose_SemiNaive_Naive_Pml_Table	(	double **	seminaive_naive_pml_table,
		const int	bw,
		const int	m,
		double *	resultspace,
		double *	workspace
	)

Definition at line 490 of file cospml.c.

Transpose_Spharmonic_Pml_Table()

double** Transpose_Spharmonic_Pml_Table	(	double **	spharmonic_pml_table,
		const int	bw,
		double *	resultspace
	)

Definition at line 415 of file cospml.c.

TransposeCosPmlTable()

void TransposeCosPmlTable	(	const int	bw,
		const int	m,
		double *	cos_pml_table,
		double *	result
	)

Definition at line 301 of file cospml.c.

Variable Documentation

BW_LIMIT

const int BW_LIMIT = 512

Limit for bw is used in functions which calculate table size.

Definition at line 25 of file cospml.c.