fft_test_shared.h

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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>
inline 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>
inline complex<long double> promote(complex<T> x) {
  return complex<long double>((long double)x.real(), (long double)x.imag());
}
 
inline complex<long double> promote(float x) { return complex<long double>((long double)x); }
inline complex<long double> promote(double x) { return complex<long double>((long double)x); }
inline 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_strided(int nfft) {
  typedef typename FFT<T>::Complex Complex;
  typedef typename Eigen::Vector<Complex, Dynamic> ComplexVector;
  constexpr int kInputStride = 3;
  constexpr int kOutputStride = 7;
  constexpr int kInvOutputStride = 13;
 
  FFT<T> fft;
 
  ComplexVector inbuf(nfft * kInputStride);
  inbuf.setRandom();
  ComplexVector outbuf(nfft * kOutputStride);
  outbuf.setRandom();
  ComplexVector invoutbuf(nfft * kInvOutputStride);
  invoutbuf.setRandom();
 
  using StridedComplexVector = Map<ComplexVector, /*MapOptions=*/0, InnerStride<Dynamic>>;
  StridedComplexVector input(inbuf.data(), nfft, InnerStride<Dynamic>(kInputStride));
  StridedComplexVector output(outbuf.data(), nfft, InnerStride<Dynamic>(kOutputStride));
  StridedComplexVector inv_output(invoutbuf.data(), nfft, InnerStride<Dynamic>(kInvOutputStride));
 
  for (int k = 0; k < nfft; ++k)
    input[k] = Complex((T)(rand() / (double)RAND_MAX - .5), (T)(rand() / (double)RAND_MAX - .5));
  fft.fwd(output, input);
 
  VERIFY(T(fft_rmse(output, input)) < test_precision<T>());  // gross check
  fft.inv(inv_output, output);
  VERIFY(T(dif_rmse(inv_output, input)) < 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);
  test_complex_strided<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>());
}
 
inline 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>());
}
 
EIGEN_DECLARE_TEST(FFTW) {
  CALL_SUBTEST(test_return_by_value(32));
  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));
 
#if defined EIGEN_HAS_FFTWL || defined EIGEN_POCKETFFT_DEFAULT
  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));
 
  CALL_SUBTEST((test_complex2d<long double, 2 * 3 * 4, 2 * 3 * 4>()));
  CALL_SUBTEST((test_complex2d<long double, 3 * 4 * 5, 3 * 4 * 5>()));
  CALL_SUBTEST((test_complex2d<long double, 24, 60>()));
  CALL_SUBTEST((test_complex2d<long double, 60, 24>()));
// fail to build since Eigen limit the stack allocation size,too big here.
// CALL_SUBTEST( ( test_complex2d<long double, 256, 256> () ) );
#endif
#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
  CALL_SUBTEST((test_complex2d<float, 24, 24>()));
  CALL_SUBTEST((test_complex2d<float, 60, 60>()));
  CALL_SUBTEST((test_complex2d<float, 24, 60>()));
  CALL_SUBTEST((test_complex2d<float, 60, 24>()));
#endif
#if defined EIGEN_FFTW_DEFAULT || defined EIGEN_POCKETFFT_DEFAULT || defined EIGEN_MKL_DEFAULT
  CALL_SUBTEST((test_complex2d<double, 24, 24>()));
  CALL_SUBTEST((test_complex2d<double, 60, 60>()));
  CALL_SUBTEST((test_complex2d<double, 24, 60>()));
  CALL_SUBTEST((test_complex2d<double, 60, 24>()));
#endif
}