FST_semi_fly.c File Reference

Routines to perform spherical harmonic transforms and convolutions on the 2-sphere using a combination of semi-naive and naive algorithms. More...

#include "s2kit/FST_semi_fly.h"
#include <math.h>
#include <stdlib.h>
#include <string.h>
#include <fftw3.h>
#include "s2kit/cospml.h"
#include "s2kit/pml.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	FSTSemiFly (double *rdata, double *idata, double *rcoeffs, double *icoeffs, const int bw, 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	InvFSTSemiFly (double *rcoeffs, double *icoeffs, double *rdata, double *idata, const int bw, 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	FZTSemiFly (double *rdata, double *idata, double *rres, double *ires, const int bw, double *workspace, DataFormat data_format, fftw_plan *DCT_plan, double *weights)
	Computes zonal harmonic transform using seminaive algorithm. More...
void	ConvOn2SphereSemiFly (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 spherical harmonic transforms and convolutions on the 2-sphere using a combination of semi-naive and naive algorithms.

Just like FST_semi_memo.c, except that these routines compute associated Legendre functions on the fly.
For descriptions on calling these functions, see the documentation preceding each function.

Definition in file FST_semi_fly.c.

Function Documentation

ConvOn2SphereSemiFly()

void ConvOn2SphereSemiFly	(	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_fly.c

Memory requirements for Conv2Sphere:

4*bw^2 + 2*bw + 10*bw^2 + 24*bw = 14*bw^2 + 26*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 (14*bw*bw)+(26*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. Same for FSTSemiFly(), FZTSemiFly() and InvFSTSemiFly() functions.

Definition at line 454 of file FST_semi_fly.c.

FSTSemiFly()

void FSTSemiFly	(	double *	rdata,
		double *	idata,
		double *	rcoeffs,
		double *	icoeffs,
		const int	bw,
		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_fly.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
workspace	space for computations of size (10*bw*bw)+(21*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

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

Definition at line 67 of file FST_semi_fly.c.

FZTSemiFly()

void FZTSemiFly	(	double *	rdata,
		double *	idata,
		double *	rres,
		double *	ires,
		const int	bw,
		double *	workspace,
		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
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

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

Definition at line 390 of file FST_semi_fly.c.

InvFSTSemiFly()

void InvFSTSemiFly	(	double *	rcoeffs,
		double *	icoeffs,
		double *	rdata,
		double *	idata,
		const int	bw,
		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_fly.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
workspace	space for computations of size (10*bw*bw)+(24*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 FSTSemiFly().

See more info about inv_DCT_plan in InvDLTSemi().

Definition at line 235 of file FST_semi_fly.c.