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