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fftw++.h
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fftw++.h
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/* Fast Fourier transform C++ header class for the FFTW3 Library
Copyright (C) 2004-2024
John C. Bowman, University of Alberta
Malcolm Roberts, University of Strasbourg
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
#ifndef __fftwpp_h__
#define __fftwpp_h__ 1
#define __FFTWPP_H_VERSION__ 3.03
#include <cstdlib>
#include <fstream>
#include <iostream>
#include <fftw3.h>
#include <cerrno>
#include <map>
#include <typeinfo>
#include <climits>
#include "seconds.h"
#include "parallel.h"
#ifndef __Complex_h__
#include <complex>
typedef std::complex<double> Complex;
#endif
#include "statistics.h"
#include "align.h"
namespace fftwpp {
// Return the memory alignment used by FFTW.
// Use of this function requires applying patches/fftw-3.3.8-alignment.patch
// to the FFTW source, recompiling, and reinstalling the FFW library.
extern "C" size_t fftw_alignment();
class fftw;
extern "C" fftw_plan Planner(fftw *F, Complex *in, Complex *out);
void loadWisdom();
void saveWisdom();
extern std::string wisdomName;
extern const char *inout;
class ThreadBase
{
public:
size_t threads;
size_t innerthreads;
ThreadBase();
ThreadBase(size_t threads) : threads(threads) {}
void Threads(size_t nthreads) {threads=nthreads;}
size_t Threads() {return threads;}
size_t Innerthreads() {return innerthreads;}
void multithread(size_t n) {
if(n >= threads) {
innerthreads=1;
} else {
innerthreads=threads;
threads=1;
}
}
};
inline size_t realsize(size_t n, bool inplace)
{
return inplace ? 2*(n/2+1) : n;
}
inline size_t Inplace(Complex *in, Complex *out=NULL)
{
return !out || in == out;
}
inline size_t Inplace(Complex *in, double *out)
{
return Inplace(in,(Complex *) out);
}
inline size_t Inplace(double *in, Complex *out)
{
return Inplace((Complex *) in,out);
}
class Doubles {
public:
size_t rsize,csize;
Doubles(size_t nx, size_t M,
size_t istride, size_t ostride,
size_t idist, size_t odist, bool inplace) {
rsize=(realsize(nx,inplace)-2)*istride+(M-1)*idist+2;
csize=2*(nx/2*ostride+(M-1)*odist+1);
if(inplace)
rsize=csize=std::max(rsize,csize);
}
};
// Base clase for fft routines
//
class fftw : public ThreadBase {
protected:
size_t doubles; // number of double precision values in output
int sign;
size_t threads;
double norm;
fftw_plan plan;
bool inplace;
size_t Dist(size_t n, size_t stride, size_t dist) {
return dist ? dist : ((stride == 1) ? n : 1);
}
static const double twopi;
public:
static size_t effort;
static size_t maxthreads;
static fftw_plan (*planner)(fftw *f, Complex *in, Complex *out);
static bool wiser;
virtual size_t Threads() {return threads;}
static const char *oddshift;
// In-place shift of Fourier origin to (nx/2,0) for even nx.
static void Shift(Complex *data, size_t nx, size_t ny,
size_t threads) {
size_t nyp=ny/2+1;
size_t stop=nx*nyp;
if(nx % 2 == 0) {
size_t inc=2*nyp;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=nyp; i < stop; i += inc) {
Complex *p=data+i;
for(size_t j=0; j < nyp; j++) p[j]=-p[j];
}
} else {
std::cerr << oddshift << std::endl;
exit(1);
}
}
// Out-of-place shift of Fourier origin to (nx/2,0) for even nx.
static void Shift(double *data, size_t nx, size_t ny,
size_t threads) {
if(nx % 2 == 0) {
size_t stop=nx*ny;
size_t inc=2*ny;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=ny; i < stop; i += inc) {
double *p=data+i;
for(size_t j=0; j < ny; j++) p[j]=-p[j];
}
} else {
std::cerr << oddshift << std::endl;
exit(1);
}
}
// In-place shift of Fourier origin to (nx/2,ny/2,0) for even nx and ny.
static void Shift(Complex *data, size_t nx, size_t ny,
size_t nz, size_t threads) {
size_t nzp=nz/2+1;
size_t nyzp=ny*nzp;
if(nx % 2 == 0 && ny % 2 == 0) {
size_t pinc=2*nzp;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=0; i < nx; i++) {
Complex *pstart=data+i*nyzp;
Complex *pstop=pstart+nyzp;
for(Complex *p=pstart+(1-(i % 2))*nzp; p < pstop; p += pinc) {
for(size_t k=0; k < nzp; k++) p[k]=-p[k];
}
}
} else {
std::cerr << oddshift << " or odd ny" << std::endl;
exit(1);
}
}
// Out-of-place shift of Fourier origin to (nx/2,ny/2,0) for even nx and ny.
static void Shift(double *data, size_t nx, size_t ny,
size_t nz, size_t threads) {
size_t nyz=ny*nz;
if(nx % 2 == 0 && ny % 2 == 0) {
size_t pinc=2*nz;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=0; i < nx; i++) {
double *pstart=data+i*nyz;
double *pstop=pstart+nyz;
for(double *p=pstart+(1-(i % 2))*nz; p < pstop; p += pinc) {
for(size_t k=0; k < nz; k++) p[k]=-p[k];
}
}
} else {
std::cerr << oddshift << " or odd ny" << std::endl;
exit(1);
}
}
fftw() : plan(NULL) {}
fftw(size_t doubles, int sign, size_t threads,
size_t n=0) :
doubles(doubles), sign(sign), threads(threads),
norm(1.0/(n ? n : doubles/2)), plan(NULL) {
#ifndef FFTWPP_SINGLE_THREAD
fftw_init_threads();
#endif
}
virtual ~fftw() {
if(plan)
fftw_destroy_plan(plan);
}
virtual fftw_plan Plan(Complex *in, Complex *out) {return NULL;};
inline void CheckAlign(Complex *p, const char *s) {
if((size_t) p % sizeof(Complex) == 0) return;
std::cerr << "WARNING: " << s << " array is not " << sizeof(Complex)
<< "-byte aligned: address " << p << std::endl;
}
void noplan() {
std::cerr << "Unable to construct FFTW plan" << std::endl;
exit(1);
}
static void planThreads(size_t threads) {
#ifndef FFTWPP_SINGLE_THREAD
omp_set_num_threads(fftw::maxthreads);
fftw_plan_with_nthreads(threads);
#endif
}
inline Complex *CheckAlign(Complex *in, Complex *out, bool constructor=true)
{
#ifndef NO_CHECK_ALIGN
CheckAlign(in,constructor ? "constructor input" : "input");
if(out) CheckAlign(out,constructor ? "constructor output" : "output");
else out=in;
#else
if(!out) out=in;
#endif
return out;
}
void Setup(Complex *in, Complex *out=NULL) {
bool alloc=!in;
if(alloc) in=utils::ComplexAlign((doubles+1)/2);
out=CheckAlign(in,out);
inplace=(out==in);
parallel::Threshold(threads);
if(doubles < 2*threshold)
threads=1;
planThreads(threads);
plan=(*planner)(this,in,out);
if(!plan) noplan();
if(alloc) Array::deleteAlign(in,(doubles+1)/2);
#ifdef FFTWPP_VERBOSE
if(threads > 1)
std::cout << "Using " << threads << " threads." << std::endl;
#endif
}
void Setup(Complex *in, double *out) {
parallel::Threshold(threads);
if(doubles < 4*threshold)
threads=1;
Setup(in,(Complex *) out);
}
void Setup(double *in, Complex *out=NULL) {
parallel::Threshold(threads);
if(doubles < 4*threshold)
threads=1;
Setup((Complex *) in,out);
}
virtual void Execute(Complex *in, Complex *out, bool=false) {
fftw_execute_dft(plan,(fftw_complex *) in,(fftw_complex *) out);
}
Complex *Setout(Complex *in, Complex *out) {
out=CheckAlign(in,out,false);
if(inplace ^ (out == in)) {
std::cerr << "ERROR: fft " << inout << std::endl;
exit(1);
}
return out;
}
void fft(Complex *in, Complex *out=NULL) {
out=Setout(in,out);
Execute(in,out);
}
void fft(double *in, Complex *out=NULL) {
fft((Complex *) in,out);
}
void fft(Complex *in, double *out) {
fft(in,(Complex *) out);
}
void fft0(Complex *in, Complex *out=NULL) {
out=Setout(in,out);
Execute(in,out,true);
}
void fft0(double *in, Complex *out=NULL) {
fft0((Complex *) in,out);
}
void fft0(Complex *in, double *out) {
fft0(in,(Complex *) out);
}
void Normalize(Complex *out) {
size_t stop=doubles/2;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=0; i < stop; i++) out[i] *= norm;
}
void Normalize(double *out) {
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=0; i < doubles; i++) out[i] *= norm;
}
void fftNormalized(Complex *in, Complex *out=NULL)
{
out=Setout(in,out);
Execute(in,out);
Normalize(out);
}
void fftNormalized(Complex *in, double *out) {
out=(double *) Setout(in,(Complex *) out);
Execute(in,(Complex *) out);
Normalize(out);
}
void fftNormalized(double *in, Complex *out) {
out=Setout((Complex *) in,out);
Execute((Complex *) in,out);
Normalize(out);
}
void fft0Normalized(Complex *in, Complex *out=NULL)
{
out=Setout(in,out);
Execute(in,out,true);
Normalize(out);
}
void fft0Normalized(Complex *in, double *out) {
out=(double *) Setout(in,(Complex *) out);
Execute(in,(Complex *) out,true);
Normalize(out);
}
void fft0Normalized(double *in, Complex *out) {
out=Setout((Complex *) in,out);
Execute((Complex *) in,out,true);
Normalize(out);
}
template<class O>
void Normalize(size_t nx, size_t M, size_t ostride,
size_t odist, O *out) {
size_t stop=nx*ostride;
O *outMdist=out+M*odist;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(threads)
#endif
for(size_t i=0; i < stop; i += ostride) {
O *pstop=outMdist+i;
for(O *p=out+i; p < pstop; p += odist) {
*p *= norm;
}
}
}
template<class I, class O>
void fftNormalized(size_t nx, size_t M, size_t ostride,
size_t odist, I *in, O *out) {
out=(O *) Setout((Complex *) in,(Complex *) out);
Execute((Complex *) in,(Complex *) out);
Normalize(nx,M,ostride,odist,out);
}
}; // class fftw
class Transpose {
fftw_plan plan;
bool inplace;
public:
template<class T>
Transpose(size_t rows, size_t cols, size_t length,
T *in, T *out=NULL, size_t threads=fftw::maxthreads) {
size_t size=sizeof(T);
if(size % sizeof(double) != 0) {
std::cerr << "ERROR: Transpose is not implemented for type of size "
<< size;
exit(1);
}
plan=NULL;
if(!out) out=in;
inplace=(out==in);
if(rows == 0 || cols == 0) return;
size /= sizeof(double);
length *= size;
parallel::Threshold(threads);
if(length*rows*cols/2 < threshold)
threads=1;
fftw::planThreads(threads);
fftw_iodim dims[3];
dims[0].n=rows;
dims[0].is=cols*length;
dims[0].os=length;
dims[1].n=cols;
dims[1].is=length;
dims[1].os=rows*length;
dims[2].n=length;
dims[2].is=1;
dims[2].os=1;
// A plan with rank=0 is a transpose.
plan=fftw_plan_guru_r2r(0,NULL,3,dims,(double *) in,(double *) out,
NULL,fftw::effort);
}
~Transpose() {
if(plan)
fftw_destroy_plan(plan);
}
template<class T>
void transpose(T *in, T *out=NULL) {
if(!plan) return;
if(!out) out=in;
if(inplace ^ (out == in)) {
std::cerr << "ERROR: Transpose " << inout << std::endl;
exit(1);
}
fftw_execute_r2r(plan,(double *) in,(double*) out);
}
};
template<class T, class L>
class Threadtable {
public:
typedef std::map<T,size_t,L> Table;
size_t Lookup(Table& table, T key) {
typename Table::iterator p=table.find(key);
return p == table.end() ? 0 : p->second;
}
void Store(Table& threadtable, T key, size_t t) {
threadtable[key]=t;
}
};
struct keytype {
size_t nx;
size_t M;
size_t threads;
bool inplace;
keytype(size_t nx, size_t M, size_t threads,
bool inplace) :
nx(nx), M(M), threads(threads), inplace(inplace) {}
};
struct keyless {
bool operator()(const keytype& a, const keytype& b) const {
return a.nx < b.nx || (a.nx == b.nx &&
(a.M < b.M || (a.M == b.M &&
(a.threads < b.threads ||
(a.threads == b.threads &&
a.inplace < b.inplace)))));
}
};
// Compute the complex Fourier transform of n complex values.
// Before calling fft(), the arrays in and out (which may coincide) must be
// allocated as Complex[n].
//
// Out-of-place usage:
//
// fft1d Forward(n,-1,in,out);
// Forward.fft(in,out);
//
// fft1d Backward(n,1,in,out);
// Backward.fft(in,out);
//
// fft1d Backward(n,1,in,out);
// Backward.fftNormalized(in,out); // True inverse of Forward.fft(out,in);
//
// In-place usage:
//
// fft1d Forward(n,-1);
// Forward.fft(in);
//
// fft1d Backward(n,1);
// Backward.fft(in);
//
class fft1d : public fftw {
size_t nx;
public:
fft1d(size_t nx, int sign, Complex *in=NULL, Complex *out=NULL,
size_t threads=maxthreads)
: fftw(2*nx,sign,threads), nx(nx) {Setup(in,out);}
#ifdef __Array_h__
fft1d(int sign, const Array::array1<Complex>& in,
const Array::array1<Complex>& out=Array::NULL1,
size_t threads=maxthreads)
: fftw(2*in.Nx(),sign,threads), nx(in.Nx()) {Setup(in,out);}
#endif
fftw_plan Plan(Complex *in, Complex *out) {
return fftw_plan_dft_1d(nx,(fftw_complex *) in,(fftw_complex *) out,
sign,effort);
}
};
template<class I, class O>
class fftwblock : public virtual fftw,
public virtual Threadtable<keytype,keyless> {
public:
int nx;
size_t M;
size_t istride,ostride;
size_t idist,odist;
fftw_plan plan1,plan2;
size_t T,Q,R;
fftwblock() : plan1(NULL), plan2(NULL) {}
fftwblock(size_t nx, size_t M,
size_t istride, size_t ostride, size_t idist, size_t odist)
: fftw(), nx(nx), M(M), istride(istride), ostride(ostride),
idist(Dist(nx,istride,idist)), odist(Dist(nx,ostride,odist)),
plan1(NULL), plan2(NULL) {}
void init(Complex *in, Complex *out, size_t Threads,
Table& threadtable) {
T=1;
Q=M;
R=0;
if(Threads > M && M > 1) Threads=M;
threads=Threads;
Setup(in,out);
Threads=threads;
size_t T0=Threads;
if(T0 > 1) {
size_t nxp=nx/2+1;
size_t olength=0;
size_t ilength=0;
if(typeid(I) == typeid(double)) {
ilength=nx;
olength=nxp;
}
if(typeid(O) == typeid(double)) {
ilength=nxp;
olength=nx;
}
if(!inplace ||
(ostride*olength*sizeof(O) <= idist*sizeof(I) &&
odist*sizeof(O) >= istride*ilength*sizeof(I))) {
T=T0;
Q=T > 0 ? M/T : 0;
R=M-Q*T;
size_t data=Lookup(threadtable,keytype(nx,M,Threads,inplace));
if(data == 1)
T0=1;
else {
fftw_plan planFFTW=plan;
threads=1;
Setup(in,out);
plan1=plan;
if(data == T) {
plan=NULL;
return;
}
plan=planFFTW;
}
} else T0=1;
}
if(T0 == 1 || time(in,out)) { // Use FFTW's multithreading
T=1;
if(plan1) {
fftw_destroy_plan(plan1);
plan1=NULL;
if(plan2) {
fftw_destroy_plan(plan2);
plan2=NULL;
}
threads=Threads;
Store(threadtable,keytype(nx,M,Threads,inplace),T);
}
} else { // Do the multithreading ourselves
T=T0;
threads=T;
Store(threadtable,keytype(nx,M,Threads,inplace),T);
}
}
bool time0(Complex *in, Complex *out) {
utils::statistics S(true),ST(true);
utils::statistics medianS(true),medianST(true);
double eps=0.02;
size_t T0=T;
do {
T=1; // FFTW
utils::cpuTimer C;
inplace ? fftNormalized(in,out) : fft(in,out);
S.add(C.nanoseconds());
T=T0; // BLOCK
utils::cpuTimer CT;
inplace ? fftNormalized(in,out) : fft(in,out);
ST.add(CT.nanoseconds());
if(S.count() >= 4 && ST.min() >= S.max())
return true;
if(S.count() >= 4 && S.min() >= ST.max())
return false;
medianS.add(S.median());
medianST.add(ST.median());
} while(S.count() < 5 || medianS.stderror() > eps*medianS.mean() ||
medianST.stderror() > eps*medianST.mean());
return S.median() <= ST.median();
}
bool time(Complex *in, Complex *out) {
bool alloc=!in;
if(alloc) in=utils::ComplexAlign((doubles+1)/2);
bool result=time0(in,out);
if(alloc) Array::deleteAlign(in,(doubles+1)/2);
return result;
}
fftw_plan Plan(int Q, fftw_complex *in, fftw_complex *out) {
return fftw_plan_many_dft(1,&nx,Q,in,NULL,istride,idist,
out,NULL,ostride,odist,sign,effort);
}
fftw_plan Plan(int Q, double *in, fftw_complex *out) {
return fftw_plan_many_dft_r2c(1,&nx,Q,in,NULL,istride,idist,
out,NULL,ostride,odist,effort);
}
fftw_plan Plan(int Q, fftw_complex *in, double *out) {
return fftw_plan_many_dft_c2r(1,&nx,Q,in,NULL,istride,idist,
out,NULL,ostride,odist,effort);
}
fftw_plan Plan(Complex *in, Complex *out) {
if(R > 0) {
plan2=Plan(Q+1,(I *) in,(O *) out);
if(!plan2) return NULL;
}
return Plan(Q,(I *) in,(O *) out);
}
void Execute(fftw_plan plan, fftw_complex *in, fftw_complex *out) {
fftw_execute_dft(plan,in,out);
}
void Execute(fftw_plan plan, double *in, fftw_complex *out) {
fftw_execute_dft_r2c(plan,in,out);
}
void Execute(fftw_plan plan, fftw_complex *in, double *out) {
fftw_execute_dft_c2r(plan,in,out);
}
void Execute(Complex *in, Complex *out, bool=false) {
if(T == 1)
Execute(plan,(I *) in,(O *) out);
else {
size_t extra=T-R;
#ifndef FFTWPP_SINGLE_THREAD
#pragma omp parallel for num_threads(T)
#endif
for(size_t i=0; i < T; ++i) {
size_t iQ=i*Q;
if(i < extra)
Execute(plan1,(I *) in+iQ*idist,(O *) out+iQ*odist);
else {
size_t offset=iQ+i-extra;
Execute(plan2,(I *) in+offset*idist,(O *) out+offset*odist);
}
}
}
}
size_t Threads() {return std::max(T,threads);}
~fftwblock() {
if(plan1)
fftw_destroy_plan(plan1);
if(plan2)
fftw_destroy_plan(plan2);
}
};
class Mfft1d : public fftwblock<fftw_complex,fftw_complex>,
public virtual Threadtable<keytype,keyless> {
static Table threadtable;
public:
Mfft1d(size_t nx, int sign, size_t M=1,
Complex *in=NULL, Complex *out=NULL,
size_t threads=maxthreads) :
fftw(2*((nx-1)+(M-1)*nx+1),sign,threads,nx),
fftwblock<fftw_complex,fftw_complex>(nx,M,1,1,nx,nx) {
init(in,out,threads,threadtable);
}
Mfft1d(size_t nx, int sign, size_t M, size_t stride=1,
size_t dist=0, Complex *in=NULL, Complex *out=NULL,
size_t threads=maxthreads) :
fftw(2*((nx-1)*stride+(M-1)*Dist(nx,stride,dist)+1),sign,threads,nx),
fftwblock<fftw_complex,fftw_complex>
(nx,M,stride,stride,dist,dist) {
init(in,out,threads,threadtable);
}
Mfft1d(size_t nx, int sign, size_t M,
size_t istride, size_t ostride, size_t idist, size_t odist,
Complex *in, Complex *out, size_t threads=maxthreads):
fftw(std::max(2*((nx-1)*istride+(M-1)*Dist(nx,istride,idist)+1),
2*((nx-1)*ostride+(M-1)*Dist(nx,ostride,odist)+1)),sign,
threads,nx),
fftwblock<fftw_complex,fftw_complex>(nx,M,istride,ostride,idist,odist)
{
init(in,out,threads,threadtable);
}
};
// Compute the complex Fourier transform of M complex vectors, each of
// length n.
// Before calling fft(), the arrays in and out (which may coincide) must be
// allocated as Complex[M*n].
//
// Out-of-place usage:
//
// mfft1d Forward(n,-1,M,stride,dist,in,out);
// Forward.fft(in,out);
//
// mfft1d Forward(n,-1,M,istride,ostride,idist,odist,in,out);
// Forward.fft(in,out);
//
// In-place usage:
//
// mfft1d Forward(n,-1,M,stride,dist);
// Forward.fft(in);
//
//
//
// Notes:
// stride is the spacing between the elements of each Complex vector;
// dist is the spacing between the first elements of the vectors.
//
//
class mfft1d {
bool single;
fft1d *fft1;
Mfft1d *fftm;
public:
mfft1d(size_t nx, int sign, size_t M=1,
Complex *in=NULL, Complex *out=NULL,
size_t threads=fftw::maxthreads) : single(M == 1) {
if(single)
fft1=new fft1d(nx,sign,in,out,threads);
else
fftm=new Mfft1d(nx,sign,M,in,out,threads);
}
mfft1d(size_t nx, int sign, size_t M, size_t stride=1,
size_t dist=0, Complex *in=NULL, Complex *out=NULL,
size_t threads=fftw::maxthreads) :
single(M == 1 && stride == 1) {
if(single)
fft1=new fft1d(nx,sign,in,out,threads);
else
fftm=new Mfft1d(nx,sign,M,stride,dist,in,out,threads);
}
mfft1d(size_t nx, int sign, size_t M,
size_t istride, size_t ostride, size_t idist, size_t odist,
Complex *in, Complex *out, size_t threads=fftw::maxthreads) :
single(M == 1 && istride == 1 && ostride == 1) {
if(single)
fft1=new fft1d(nx,sign,in,out,threads);
else
fftm=new Mfft1d(nx,sign,M,istride,ostride,idist,odist,in,out,threads);
}
size_t Threads() {
return single ? fft1->Threads() : fftm->Threads();
}
template<class I>
void fft(I in) {
single ? fft1->fft(in) : fftm->fft(in);
}
template<class I, class O>
void fft(I in, O out) {
single ? fft1->fft(in,out) : fftm->fft(in,out);
}
template<class I>
void fftNormalized(I in) {
single ? fft1->fftNormalized(in) : fftm->fftNormalized(in);
}
template<class I, class O>
void fftNormalized(I in, O out) {
single ? fft1->fftNormalized(in,out) : fftm->fftNormalized(in,out);
}
template<class O>
void Normalize(O out) {
single ? fft1->Normalize(out) : fftm->Normalize(out);
}
~mfft1d() {
if(single)
delete fft1;
else
delete fftm;
}
};
// Compute the complex Fourier transform of n real values, using phase sign -1.
// Before calling fft(), the array in must be allocated as double[n] and
// the array out must be allocated as Complex[n/2+1]. The arrays in and out
// may coincide, allocated as Complex[n/2+1].
//
// Out-of-place usage:
//
// rcfft1d Forward(n,in,out);
// Forward.fft(in,out);
//
// In-place usage:
//
// rcfft1d Forward(n);
// Forward.fft(out);
//
// Notes:
// in contains the n real values stored as a Complex array;
// out contains the first n/2+1 Complex Fourier values.
//
class rcfft1d : public fftw {
size_t nx;
public:
rcfft1d(size_t nx, Complex *out=NULL, size_t threads=maxthreads)
: fftw(2*(nx/2+1),-1,threads,nx), nx(nx) {Setup(out,(double*) NULL);}
rcfft1d(size_t nx, double *in, Complex *out=NULL,
size_t threads=maxthreads)
: fftw(2*(nx/2+1),-1,threads,nx), nx(nx) {Setup(in,out);}
fftw_plan Plan(Complex *in, Complex *out) {
return fftw_plan_dft_r2c_1d(nx,(double *) in,(fftw_complex *) out, effort);
}
void Execute(Complex *in, Complex *out, bool=false) {
fftw_execute_dft_r2c(plan,(double *) in,(fftw_complex *) out);
}
};
// Compute the real inverse Fourier transform of the n/2+1 Complex values
// corresponding to the non-negative part of the frequency spectrum, using
// phase sign +1.
// Before calling fft(), the array in must be allocated as Complex[n/2+1]
// and the array out must be allocated as double[n]. The arrays in and out
// may coincide, allocated as Complex[n/2+1].
//
// Out-of-place usage (input destroyed):
//
// crfft1d Backward(n,in,out);
// Backward.fft(in,out);
//
// In-place usage:
//
// crfft1d Backward(n);
// Backward.fft(in);
//
// Notes:
// in contains the first n/2+1 Complex Fourier values.
// out contains the n real values stored as a Complex array;
//
class crfft1d : public fftw {
size_t nx;
public:
crfft1d(size_t nx, double *out=NULL, size_t threads=maxthreads)
: fftw(2*(nx/2+1),1,threads,nx), nx(nx) {Setup(out);}
crfft1d(size_t nx, Complex *in, double *out=NULL,
size_t threads=maxthreads)
: fftw(realsize(nx,Inplace(in,out)),1,threads,nx), nx(nx) {Setup(in,out);}
fftw_plan Plan(Complex *in, Complex *out) {
return fftw_plan_dft_c2r_1d(nx,(fftw_complex *) in,(double *) out,effort);
}
void Execute(Complex *in, Complex *out, bool=false) {
fftw_execute_dft_c2r(plan,(fftw_complex *) in,(double *) out);
}
};
class Mrcfft1d : public fftwblock<double,fftw_complex>,
public virtual Threadtable<keytype,keyless> {
static Table threadtable;
public:
Mrcfft1d(size_t nx, size_t M, size_t istride, size_t ostride,
size_t idist, size_t odist, double *in=NULL, Complex *out=NULL,
size_t threads=maxthreads)
: fftw(Doubles(nx,M,istride,ostride,idist,odist,Inplace(in,out)).csize,
-1,threads,nx),
fftwblock<double,fftw_complex>
(nx,M,istride,ostride,idist,odist) {
init((Complex *) in,out,threads,threadtable);
}
void Normalize(Complex *out) {
fftw::Normalize<Complex>(nx/2+1,M,ostride,odist,out);
}
void fftNormalized(double *in, Complex *out=NULL) {
fftw::fftNormalized<double,Complex>(nx/2+1,M,ostride,odist,in,out);
}
};
// Compute the real Fourier transform of M real vectors, each of length n,
// using phase sign -1. Before calling fft(), the array in must be
// allocated as double[M*n] and the array out must be allocated as
// Complex[M*(n/2+1)]. The arrays in and out may coincide,
// allocated as Complex[M*(n/2+1)].
//
// Out-of-place usage:
//