FST_semi_memo.c File Reference

Routines to perform convolutions on the 2-sphere using a combination of seminaive and naive algorithms. More...

#include "s2kit/FST_semi_memo.h"
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <fftw3.h>
#include "s2kit/cospml.h"
#include "s2kit/naive.h"
#include "s2kit/seminaive.h"
#include "s2kit/weights.h"
#include "s2kit/chebyshev_nodes.h"
#include "s2kit/util.h"

Go to the source code of this file.

Functions
void	FSTSemiMemo (double *rdata, double *idata, double *rcoeffs, double *icoeffs, const int bw, double **seminaive_naive_table, double *workspace, DataFormat data_format, const int cutoff, fftw_plan *DCT_plan, fftw_plan *FFT_plan, double *weights)
	Computes spherical harmonic transform using the seminaive and naive algorithms. More...
void	InvFSTSemiMemo (double *rcoeffs, double *icoeffs, double *rdata, double *idata, const int bw, double **transpose_seminaive_naive_table, double *workspace, DataFormat data_format, const int cutoff, fftw_plan *inv_DCT_plan, fftw_plan *inv_FFT_plan)
	Computes inverse spherical harmonic transform. More...
void	FZTSemiMemo (double *rdata, double *idata, double *rres, double *ires, const int bw, double *cos_pml_table, double *workspace, const DataFormat data_format, fftw_plan *DCT_plan, double *weights)
	Computes zonal harmonic transform using seminaive algorithm. More...
void	ConvOn2SphereSemiMemo (double *rdata, double *idata, double *rfilter, double *ifilter, double *rres, double *ires, const int bw, double *workspace)
	Convolves two functions defined on the 2-sphere. More...

Detailed Description

Routines to perform convolutions on the 2-sphere using a combination of seminaive and naive algorithms.

Assumes that all precomputed data is already in memory (e.g. tables are generated).
For descriptions on calling these functions, see the documentation preceding each function.

Definition in file FST_semi_memo.c.

Function Documentation

ConvOn2SphereSemiMemo()

void ConvOn2SphereSemiMemo	(	double *	rdata,
		double *	idata,
		double *	rfilter,
		double *	ifilter,
		double *	rres,
		double *	ires,
		const int	bw,
		double *	workspace
	)

Convolves two functions defined on the 2-sphere.

Uses seminaive algorithms for spherical harmonic transforms.

Note

See an example of use in test_conv_semi_memo.c

Conv2Sphere requires memory for spharmonic tables, local workspace and workspace for FSTSemiMemo() (reuses in InvFSTSemiMemo()):

legendre_size = Reduced_Naive_TableSize(bw, cutoff) + Reduced_SpharmonicTableSize(bw,cutoff)
2*legendre_size + (8*(bw*bw)+10*bw) + (4*(bw*bw)+2*bw) = 2*legendre_size + (12*(bw*bw)+12*bw)

Parameters

rdata	array of length 4*bw*bw of the real part of sampled function
idata	array of length 4*bw*bw of the imaginary part of sampled function
rfilter	array of length 4*bw*bw of the real part of sampled filter function
ifilter	array of length 4*bw*bw of the imaginary part of sampled filter function
rres	array of length 4*bw*bw which will contain the real part of result function
ires	array of length 4*bw*bw which will contain the imaginary part of result function
bw	bandwidth of problem
workspace	space for computations of size (2*legendre_size)+(12*(bw*bw)+12*bw)

Note

We assume that data is real.

This function will do seminaive algorithm for all orders.

If you want to do multiple convolutions, you can freely reuse once allocated workspace and generated spharmonic Pml tables. Same for FSTSemiMemo(), FZTSemiMemo() and InvFSTSemiMemo() functions.

Definition at line 439 of file FST_semi_memo.c.

FSTSemiMemo()

void FSTSemiMemo	(	double *	rdata,
		double *	idata,
		double *	rcoeffs,
		double *	icoeffs,
		const int	bw,
		double **	seminaive_naive_table,
		double *	workspace,
		DataFormat	data_format,
		const int	cutoff,
		fftw_plan *	DCT_plan,
		fftw_plan *	FFT_plan,
		double *	weights
	)

Computes spherical harmonic transform using the seminaive and naive algorithms.

Output ordering of coeffs (in rcoeffs and icoeffs) f(m,l) is:

f(0,0) f(0,1) f(0,2) ... f(0,bw-1)
       f(1,1) f(1,2) ... f(1,bw-1)
       etc.
           f(bw-2,bw-2), f(bw-2,bw-1)
                         f(bw-1,bw-1)
                         f(-(bw-1),bw-1)
        f(-(bw-2),bw-2), f(-(bw-2),bw-1)
       etc.
             f(-2,2) ... f(-2,bw-1)
     f(-1,1) f(-1,2) ... f(-1,bw-1)

This only requires an array of size bw*bw. If zero-padding is used to make the indexing nice, then you need a an (2bw-1)*bw array, but that is not done here. Because of the amount of space necessary for doing large transforms, it is important not to use any more than necessary.

Note

See an example of use in test_s2_semi_memo.c and test_s2_semi_memo_fwd.c

Parameters

rdata	array of length 4*bw*bw of the real part of the function samples
idata	array of length 4*bw*bw of the imaginary part of the function samples
rcoeffs	array of length bw*bw which will contain the real part of harmonic coefficients in a linearized form
icoeffs	array of length bw*bw which will contain the imaginary part of harmonic coefficients in a linearized form
bw	bandwidth of problem
seminaive_naive_table	pre-generated spharmonic Pml table
workspace	space for computations of size (8*bw^2)+(7*bw)
data_format	determines the format of the computed data
cutoff	determines order to switch from seminaive to naive algorithm
DCT_plan	plan for DLT which is used as argument for call DLTSemi()
FFT_plan	plan for FFT
weights	array which is used as argument for call DLTSemi() and DLTNaive()

Note

seminaive_naive_table should be generated by Spharmonic_Pml_Table(). This table can be re-used in the inverse transform and, for example, in series of convolutions.

See more info about DCT_plan and weights in DLTSemi().

Definition at line 68 of file FST_semi_memo.c.

FZTSemiMemo()

void FZTSemiMemo	(	double *	rdata,
		double *	idata,
		double *	rres,
		double *	ires,
		const int	bw,
		double *	cos_pml_table,
		double *	workspace,
		const DataFormat	data_format,
		fftw_plan *	DCT_plan,
		double *	weights
	)

Computes zonal harmonic transform using seminaive algorithm.

This transform is used in convolutions. Only computes spherical harmonics for m=0.

Parameters

rdata	array of length 4*bw*bw of the real part of the data samples
idata	array of length 4*bw*bw of the imaginary part of the data samples
rres	array of length bw which will contain the real part of harmonic coefficients
ires	array of length bw which will contain the imaginary part of harmonic coefficients
bw	bandwidth of problem
cos_pml_table	pre-generated table of Legendre coefficients of P(0,l) functions
workspace	space for computations of size 12*bw
data_format	determines the format of the computed data
DCT_plan	plan for DLT which is used as argument for call DLTSemi()
weights	array which is used as argument for call DLTSemi()

Note

cos_pml_table should be generated by GenerateCosPmlTable() with m = 0.

See more info about DCT_plan and weights in DLTSemi().

Definition at line 374 of file FST_semi_memo.c.

InvFSTSemiMemo()

void InvFSTSemiMemo	(	double *	rcoeffs,
		double *	icoeffs,
		double *	rdata,
		double *	idata,
		const int	bw,
		double **	transpose_seminaive_naive_table,
		double *	workspace,
		DataFormat	data_format,
		const int	cutoff,
		fftw_plan *	inv_DCT_plan,
		fftw_plan *	inv_FFT_plan
	)

Computes inverse spherical harmonic transform.

Note

See an example of use in test_s2_semi_memo.c and test_s2_semi_memo_inv.c

Parameters

rcoeffs	array of length bw*bw of the real part of harmonic coefficients
icoeffs	array of length bw*bw of the imaginary part of harmonic coefficients
rdata	array of length 4*bw*bw which will contain the real part of transformed result
idata	array of length 4*bw*bw which will contain the imaginary part of transformed result
bw	bandwidth of problem
transpose_seminaive_naive_table	pre-generated transposed spharmonic Pml table
workspace	space for computations of size (8*bw^2)+(10*bw)
data_format	determines the format of the computed data
cutoff	determines order to switch from seminaive to naive algorithm
inv_DCT_plan	plan for inverse DLT which is used as argument for call InvDLTSemi()
inv_FFT_plan	plan for inverse FFT

Note

The real and imaginary part of harmonic coefficients should be stored in rcoeffs and icoeffs before passing to this function in the same order as it was mentioned in FSTSemiMemo().

transpose_seminaive_naive_table should be generated by Transpose_Spharmonic_Pml_Table().

See more info about inv_DCT_plan in InvDLTSemi().

Definition at line 228 of file FST_semi_memo.c.