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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Mark Borgerding mark a borgerding net
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
#include "main.h"
#include <unsupported/Eigen/FFT>
template <typename T>
std::complex<T> RandomCpx() { return std::complex<T>( (T)(rand()/(T)RAND_MAX - .5), (T)(rand()/(T)RAND_MAX - .5) ); }
using namespace std;
using namespace Eigen;
template < typename T>
complex<long double> promote(complex<T> x) { return complex<long double>((long double)x.real(),(long double)x.imag()); }
complex<long double> promote(float x) { return complex<long double>((long double)x); }
complex<long double> promote(double x) { return complex<long double>((long double)x); }
complex<long double> promote(long double x) { return complex<long double>((long double)x); }
template <typename VT1,typename VT2>
long double fft_rmse( const VT1 & fftbuf,const VT2 & timebuf)
{
long double totalpower=0;
long double difpower=0;
long double pi = acos((long double)-1 );
for (size_t k0=0;k0<(size_t)fftbuf.size();++k0) {
complex<long double> acc = 0;
long double phinc = (long double)(-2.)*k0* pi / timebuf.size();
for (size_t k1=0;k1<(size_t)timebuf.size();++k1) {
acc += promote( timebuf[k1] ) * exp( complex<long double>(0,k1*phinc) );
}
totalpower += numext::abs2(acc);
complex<long double> x = promote(fftbuf[k0]);
complex<long double> dif = acc - x;
difpower += numext::abs2(dif);
//cerr << k0 << "\t" << acc << "\t" << x << "\t" << sqrt(numext::abs2(dif)) << endl;
}
cerr << "rmse:" << sqrt(difpower/totalpower) << endl;
return sqrt(difpower/totalpower);
}
template <typename VT1,typename VT2>
long double dif_rmse( const VT1 buf1,const VT2 buf2)
{
long double totalpower=0;
long double difpower=0;
size_t n = (min)( buf1.size(),buf2.size() );
for (size_t k=0;k<n;++k) {
totalpower += (long double)((numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2);
difpower += (long double)(numext::abs2(buf1[k] - buf2[k]));
}
return sqrt(difpower/totalpower);
}
enum { StdVectorContainer, EigenVectorContainer };
template<int Container, typename Scalar> struct VectorType;
template<typename Scalar> struct VectorType<StdVectorContainer,Scalar>
{
typedef vector<Scalar> type;
};
template<typename Scalar> struct VectorType<EigenVectorContainer,Scalar>
{
typedef Matrix<Scalar,Dynamic,1> type;
};
template <int Container, typename T>
void test_scalar_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename FFT<T>::Scalar Scalar;
typedef typename VectorType<Container,Scalar>::type ScalarVector;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ScalarVector tbuf(nfft);
ComplexVector freqBuf;
for (int k=0;k<nfft;++k)
tbuf[k]= (T)( rand()/(double)RAND_MAX - .5);
// make sure it DOESN'T give the right full spectrum answer
// if we've asked for half-spectrum
fft.SetFlag(fft.HalfSpectrum );
fft.fwd( freqBuf,tbuf);
VERIFY((size_t)freqBuf.size() == (size_t)( (nfft>>1)+1) );
VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>() );// gross check
fft.ClearFlag(fft.HalfSpectrum );
fft.fwd( freqBuf,tbuf);
VERIFY( (size_t)freqBuf.size() == (size_t)nfft);
VERIFY( T(fft_rmse(freqBuf,tbuf)) < test_precision<T>() );// gross check
if (nfft&1)
return; // odd FFTs get the wrong size inverse FFT
ScalarVector tbuf2;
fft.inv( tbuf2 , freqBuf);
VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>() );// gross check
// verify that the Unscaled flag takes effect
ScalarVector tbuf3;
fft.SetFlag(fft.Unscaled);
fft.inv( tbuf3 , freqBuf);
for (int k=0;k<nfft;++k)
tbuf3[k] *= T(1./nfft);
//for (size_t i=0;i<(size_t) tbuf.size();++i)
// cout << "freqBuf=" << freqBuf[i] << " in2=" << tbuf3[i] << " - in=" << tbuf[i] << " => " << (tbuf3[i] - tbuf[i] ) << endl;
VERIFY( T(dif_rmse(tbuf,tbuf3)) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled);
fft.inv( tbuf2 , freqBuf);
VERIFY( T(dif_rmse(tbuf,tbuf2)) < test_precision<T>() );// gross check
}
template <typename T>
void test_scalar(int nfft)
{
test_scalar_generic<StdVectorContainer,T>(nfft);
//test_scalar_generic<EigenVectorContainer,T>(nfft);
}
template <int Container, typename T>
void test_complex_generic(int nfft)
{
typedef typename FFT<T>::Complex Complex;
typedef typename VectorType<Container,Complex>::type ComplexVector;
FFT<T> fft;
ComplexVector inbuf(nfft);
ComplexVector outbuf;
ComplexVector buf3;
for (int k=0;k<nfft;++k)
inbuf[k]= Complex( (T)(rand()/(double)RAND_MAX - .5), (T)(rand()/(double)RAND_MAX - .5) );
fft.fwd( outbuf , inbuf);
VERIFY( T(fft_rmse(outbuf,inbuf)) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>() );// gross check
// verify that the Unscaled flag takes effect
ComplexVector buf4;
fft.SetFlag(fft.Unscaled);
fft.inv( buf4 , outbuf);
for (int k=0;k<nfft;++k)
buf4[k] *= T(1./nfft);
VERIFY( T(dif_rmse(inbuf,buf4)) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled);
fft.inv( buf3 , outbuf);
VERIFY( T(dif_rmse(inbuf,buf3)) < test_precision<T>() );// gross check
}
template <typename T>
void test_complex(int nfft)
{
test_complex_generic<StdVectorContainer,T>(nfft);
test_complex_generic<EigenVectorContainer,T>(nfft);
}
/*
template <typename T,int nrows,int ncols>
void test_complex2d()
{
typedef typename Eigen::FFT<T>::Complex Complex;
FFT<T> fft;
Eigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2;
src = Eigen::Matrix<Complex,nrows,ncols>::Random();
//src = Eigen::Matrix<Complex,nrows,ncols>::Identity();
for (int k=0;k<ncols;k++) {
Eigen::Matrix<Complex,nrows,1> tmpOut;
fft.fwd( tmpOut,src.col(k) );
dst2.col(k) = tmpOut;
}
for (int k=0;k<nrows;k++) {
Eigen::Matrix<Complex,1,ncols> tmpOut;
fft.fwd( tmpOut, dst2.row(k) );
dst2.row(k) = tmpOut;
}
fft.fwd2(dst.data(),src.data(),ncols,nrows);
fft.inv2(src2.data(),dst.data(),ncols,nrows);
VERIFY( (src-src2).norm() < test_precision<T>() );
VERIFY( (dst-dst2).norm() < test_precision<T>() );
}
*/
void test_return_by_value(int len)
{
VectorXf in;
VectorXf in1;
in.setRandom( len );
VectorXcf out1,out2;
FFT<float> fft;
fft.SetFlag(fft.HalfSpectrum );
fft.fwd(out1,in);
out2 = fft.fwd(in);
VERIFY( (out1-out2).norm() < test_precision<float>() );
in1 = fft.inv(out1);
VERIFY( (in1-in).norm() < test_precision<float>() );
}
void test_FFTW()
{
CALL_SUBTEST( test_return_by_value(32) );
//CALL_SUBTEST( ( test_complex2d<float,4,8> () ) ); CALL_SUBTEST( ( test_complex2d<double,4,8> () ) );
//CALL_SUBTEST( ( test_complex2d<long double,4,8> () ) );
CALL_SUBTEST( test_complex<float>(32) ); CALL_SUBTEST( test_complex<double>(32) );
CALL_SUBTEST( test_complex<float>(256) ); CALL_SUBTEST( test_complex<double>(256) );
CALL_SUBTEST( test_complex<float>(3*8) ); CALL_SUBTEST( test_complex<double>(3*8) );
CALL_SUBTEST( test_complex<float>(5*32) ); CALL_SUBTEST( test_complex<double>(5*32) );
CALL_SUBTEST( test_complex<float>(2*3*4) ); CALL_SUBTEST( test_complex<double>(2*3*4) );
CALL_SUBTEST( test_complex<float>(2*3*4*5) ); CALL_SUBTEST( test_complex<double>(2*3*4*5) );
CALL_SUBTEST( test_complex<float>(2*3*4*5*7) ); CALL_SUBTEST( test_complex<double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<float>(32) ); CALL_SUBTEST( test_scalar<double>(32) );
CALL_SUBTEST( test_scalar<float>(45) ); CALL_SUBTEST( test_scalar<double>(45) );
CALL_SUBTEST( test_scalar<float>(50) ); CALL_SUBTEST( test_scalar<double>(50) );
CALL_SUBTEST( test_scalar<float>(256) ); CALL_SUBTEST( test_scalar<double>(256) );
CALL_SUBTEST( test_scalar<float>(2*3*4*5*7) ); CALL_SUBTEST( test_scalar<double>(2*3*4*5*7) );
#ifdef EIGEN_HAS_FFTWL
CALL_SUBTEST( test_complex<long double>(32) );
CALL_SUBTEST( test_complex<long double>(256) );
CALL_SUBTEST( test_complex<long double>(3*8) );
CALL_SUBTEST( test_complex<long double>(5*32) );
CALL_SUBTEST( test_complex<long double>(2*3*4) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5) );
CALL_SUBTEST( test_complex<long double>(2*3*4*5*7) );
CALL_SUBTEST( test_scalar<long double>(32) );
CALL_SUBTEST( test_scalar<long double>(45) );
CALL_SUBTEST( test_scalar<long double>(50) );
CALL_SUBTEST( test_scalar<long double>(256) );
CALL_SUBTEST( test_scalar<long double>(2*3*4*5*7) );
#endif
}
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