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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/StormEigen/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 StormEigen;
template < typename T> complex<long double> promote(complex<T> x) { return complex<long double>(x.real(),x.imag()); }
complex<long double> promote(float x) { return complex<long double>( x); } complex<long double> promote(double x) { return complex<long double>( x); } complex<long double> promote(long double x) { return complex<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 = -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 += (numext::abs2( buf1[k] ) + numext::abs2(buf2[k]) )/2.; difpower += 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( 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( 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( 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( dif_rmse(tbuf,tbuf3) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled); fft.inv( tbuf2 , freqBuf); VERIFY( 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( fft_rmse(outbuf,inbuf) < test_precision<T>() );// gross check
fft.inv( buf3 , outbuf);
VERIFY( 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( dif_rmse(inbuf,buf4) < test_precision<T>() );// gross check
// verify that ClearFlag works
fft.ClearFlag(fft.Unscaled); fft.inv( buf3 , outbuf); VERIFY( 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 StormEigen::FFT<T>::Complex Complex; FFT<T> fft; StormEigen::Matrix<Complex,nrows,ncols> src,src2,dst,dst2;
src = StormEigen::Matrix<Complex,nrows,ncols>::Random(); //src = StormEigen::Matrix<Complex,nrows,ncols>::Identity();
for (int k=0;k<ncols;k++) { StormEigen::Matrix<Complex,nrows,1> tmpOut; fft.fwd( tmpOut,src.col(k) ); dst2.col(k) = tmpOut; }
for (int k=0;k<nrows;k++) { StormEigen::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 STORMEIGEN_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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