cxx11_tensor_fft.cpp File Reference

#include "main.h"
#include <Eigen/CXX11/Tensor>

Functions
template<int DataLayout>
static void	test_fft_2D_golden ()
static void	test_fft_complex_input_golden ()
static void	test_fft_real_input_golden ()
template<int DataLayout, typename RealScalar , bool isComplexInput, int FFTResultType, int FFTDirection, int TensorRank>
static void	test_fft_real_input_energy ()
template<typename RealScalar >
static void	test_fft_non_power_of_2_round_trip (int exponent)
	EIGEN_DECLARE_TEST (cxx11_tensor_fft)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

cxx11_tensor_fft

)

                                     {
  test_fft_complex_input_golden();
  test_fft_real_input_golden();
 
  test_fft_2D_golden<ColMajor>();
  test_fft_2D_golden<RowMajor>();
 
  test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 1>();
 
  test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 2>();
 
  test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 3>();
 
  test_fft_real_input_energy<ColMajor, float, true, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<ColMajor, double, true, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<ColMajor, float, false, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<ColMajor, double, false, Eigen::BothParts, FFT_FORWARD, 4>();
 
  test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 1>();
  test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 1>();
 
  test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 2>();
  test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 2>();
 
  test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 3>();
  test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 3>();
 
  test_fft_real_input_energy<RowMajor, float, true, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<RowMajor, double, true, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<RowMajor, float, false, Eigen::BothParts, FFT_FORWARD, 4>();
  test_fft_real_input_energy<RowMajor, double, false, Eigen::BothParts, FFT_FORWARD, 4>();
 
  test_fft_non_power_of_2_round_trip<float>(7);
  test_fft_non_power_of_2_round_trip<double>(7);
}

References test_fft_complex_input_golden(), and test_fft_real_input_golden().

test_fft_2D_golden()

template<int DataLayout>

static void test_fft_2D_golden ( )

static

                                 {
  Tensor<float, 2, DataLayout> input(2, 3);
  input(0, 0) = 1;
  input(0, 1) = 2;
  input(0, 2) = 3;
  input(1, 0) = 4;
  input(1, 1) = 5;
  input(1, 2) = 6;
 
  array<ptrdiff_t, 2> fft;
  fft[0] = 0;
  fft[1] = 1;
 
  Tensor<std::complex<float>, 2, DataLayout> output = input.template fft<Eigen::BothParts, Eigen::FFT_FORWARD>(fft);
 
  std::complex<float> output_golden[6];  // in ColMajor order
  output_golden[0] = std::complex<float>(21, 0);
  output_golden[1] = std::complex<float>(-9, 0);
  output_golden[2] = std::complex<float>(-3, 1.73205);
  output_golden[3] = std::complex<float>(0, 0);
  output_golden[4] = std::complex<float>(-3, -1.73205);
  output_golden[5] = std::complex<float>(0, 0);
 
  std::complex<float> c_offset = std::complex<float>(1.0, 1.0);
 
  if (DataLayout == ColMajor) {
    VERIFY_IS_APPROX(output(0) + c_offset, output_golden[0] + c_offset);
    VERIFY_IS_APPROX(output(1) + c_offset, output_golden[1] + c_offset);
    VERIFY_IS_APPROX(output(2) + c_offset, output_golden[2] + c_offset);
    VERIFY_IS_APPROX(output(3) + c_offset, output_golden[3] + c_offset);
    VERIFY_IS_APPROX(output(4) + c_offset, output_golden[4] + c_offset);
    VERIFY_IS_APPROX(output(5) + c_offset, output_golden[5] + c_offset);
  } else {
    VERIFY_IS_APPROX(output(0) + c_offset, output_golden[0] + c_offset);
    VERIFY_IS_APPROX(output(1) + c_offset, output_golden[2] + c_offset);
    VERIFY_IS_APPROX(output(2) + c_offset, output_golden[4] + c_offset);
    VERIFY_IS_APPROX(output(3) + c_offset, output_golden[1] + c_offset);
    VERIFY_IS_APPROX(output(4) + c_offset, output_golden[3] + c_offset);
    VERIFY_IS_APPROX(output(5) + c_offset, output_golden[5] + c_offset);
  }
}

References Eigen::ColMajor, DataLayout, output(), and VERIFY_IS_APPROX.

test_fft_complex_input_golden()

static void test_fft_complex_input_golden ( )

static

                                            {
  Tensor<std::complex<float>, 1, ColMajor> input(5);
  input(0) = std::complex<float>(1, 1);
  input(1) = std::complex<float>(2, 2);
  input(2) = std::complex<float>(3, 3);
  input(3) = std::complex<float>(4, 4);
  input(4) = std::complex<float>(5, 5);
 
  array<ptrdiff_t, 1> fft;
  fft[0] = 0;
 
  Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);
  Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);
 
  Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);
  Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);
 
  Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);
  Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);
 
  VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));
 
  VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));
 
  VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));
 
  std::complex<float> forward_golden_result[5];
  std::complex<float> reverse_golden_result[5];
 
  forward_golden_result[0] = std::complex<float>(15.000000000000000, +15.000000000000000);
  forward_golden_result[1] = std::complex<float>(-5.940954801177935, +0.940954801177934);
  forward_golden_result[2] = std::complex<float>(-3.312299240582266, -1.687700759417735);
  forward_golden_result[3] = std::complex<float>(-1.687700759417735, -3.312299240582266);
  forward_golden_result[4] = std::complex<float>(0.940954801177934, -5.940954801177935);
 
  reverse_golden_result[0] = std::complex<float>(3.000000000000000, +3.000000000000000);
  reverse_golden_result[1] = std::complex<float>(0.188190960235587, -1.188190960235587);
  reverse_golden_result[2] = std::complex<float>(-0.337540151883547, -0.662459848116453);
  reverse_golden_result[3] = std::complex<float>(-0.662459848116453, -0.337540151883547);
  reverse_golden_result[4] = std::complex<float>(-1.188190960235587, +0.188190960235587);
 
  for (int i = 0; i < 5; ++i) {
    VERIFY_IS_APPROX(forward_output_both_parts(i), forward_golden_result[i]);
    VERIFY_IS_APPROX(forward_output_real_part(i), forward_golden_result[i].real());
    VERIFY_IS_APPROX(forward_output_imag_part(i), forward_golden_result[i].imag());
  }
 
  for (int i = 0; i < 5; ++i) {
    VERIFY_IS_APPROX(reverse_output_both_parts(i), reverse_golden_result[i]);
    VERIFY_IS_APPROX(reverse_output_real_part(i), reverse_golden_result[i].real());
    VERIFY_IS_APPROX(reverse_output_imag_part(i), reverse_golden_result[i].imag());
  }
}

References Eigen::BothParts, Eigen::ColMajor, Eigen::Tensor< Scalar_, NumIndices_, Options_, IndexType_ >::dimension(), Eigen::FFT_FORWARD, Eigen::FFT_REVERSE, i, imag(), Eigen::ImagPart, Eigen::RealPart, VERIFY_IS_APPROX, and VERIFY_IS_EQUAL.

Referenced by EIGEN_DECLARE_TEST().

test_fft_non_power_of_2_round_trip()

template<typename RealScalar >

static void test_fft_non_power_of_2_round_trip ( int  exponent )

static

                                                             {
  int n = (1 << exponent) + 1;
 
  Eigen::DSizes<ptrdiff_t, 1> dimensions;
  dimensions[0] = n;
  const DSizes<ptrdiff_t, 1> arr = dimensions;
  Tensor<RealScalar, 1, ColMajor, ptrdiff_t> input;
 
  input.resize(arr);
  input.setRandom();
 
  array<int, 1> fft;
  fft[0] = 0;
 
  Tensor<std::complex<RealScalar>, 1, ColMajor> forward = input.template fft<BothParts, FFT_FORWARD>(fft);
 
  Tensor<RealScalar, 1, ColMajor, ptrdiff_t> output = forward.template fft<RealPart, FFT_REVERSE>(fft);
 
  for (int i = 0; i < n; ++i) {
    RealScalar tol = test_precision<RealScalar>() * (std::abs(input[i]) + std::abs(output[i]) + 1);
    VERIFY_IS_APPROX_OR_LESS_THAN(std::abs(input[i] - output[i]), tol);
  }
}

References abs(), Eigen::ColMajor, i, n, output(), Eigen::Tensor< Scalar_, NumIndices_, Options_, IndexType_ >::resize(), Eigen::TensorBase< Derived, AccessLevel >::setRandom(), and VERIFY_IS_APPROX_OR_LESS_THAN.

test_fft_real_input_energy()

template<int DataLayout, typename RealScalar , bool isComplexInput, int FFTResultType, int FFTDirection, int TensorRank>

static void test_fft_real_input_energy ( )

static

                                         {
  Eigen::DSizes<ptrdiff_t, TensorRank> dimensions;
  ptrdiff_t total_size = 1;
  for (int i = 0; i < TensorRank; ++i) {
    dimensions[i] = rand() % 20 + 1;
    total_size *= dimensions[i];
  }
  const DSizes<ptrdiff_t, TensorRank> arr = dimensions;
 
  typedef std::conditional_t<isComplexInput == true, std::complex<RealScalar>, RealScalar> InputScalar;
 
  Tensor<InputScalar, TensorRank, DataLayout> input;
  input.resize(arr);
  input.setRandom();
 
  array<ptrdiff_t, TensorRank> fft;
  for (int i = 0; i < TensorRank; ++i) {
    fft[i] = i;
  }
 
  typedef std::conditional_t<FFTResultType == Eigen::BothParts, std::complex<RealScalar>, RealScalar> OutputScalar;
  Tensor<OutputScalar, TensorRank, DataLayout> output;
  output = input.template fft<FFTResultType, FFTDirection>(fft);
 
  for (int i = 0; i < TensorRank; ++i) {
    VERIFY_IS_EQUAL(output.dimension(i), input.dimension(i));
  }
 
  RealScalar energy_original = 0.0;
  RealScalar energy_after_fft = 0.0;
 
  for (int i = 0; i < total_size; ++i) {
    energy_original += numext::abs2(input(i));
  }
 
  for (int i = 0; i < total_size; ++i) {
    energy_after_fft += numext::abs2(output(i));
  }
 
  if (FFTDirection == FFT_FORWARD) {
    VERIFY_IS_APPROX(energy_original, energy_after_fft / total_size);
  } else {
    VERIFY_IS_APPROX(energy_original, energy_after_fft * total_size);
  }
}

References Eigen::numext::abs2(), Eigen::Tensor< Scalar_, NumIndices_, Options_, IndexType_ >::dimension(), Eigen::FFT_FORWARD, i, output(), Eigen::Tensor< Scalar_, NumIndices_, Options_, IndexType_ >::resize(), Eigen::TensorBase< Derived, AccessLevel >::setRandom(), VERIFY_IS_APPROX, and VERIFY_IS_EQUAL.

test_fft_real_input_golden()

static void test_fft_real_input_golden ( )

static

                                         {
  Tensor<float, 1, ColMajor> input(5);
  input(0) = 1.0;
  input(1) = 2.0;
  input(2) = 3.0;
  input(3) = 4.0;
  input(4) = 5.0;
 
  array<ptrdiff_t, 1> fft;
  fft[0] = 0;
 
  Tensor<std::complex<float>, 1, ColMajor> forward_output_both_parts = input.fft<BothParts, FFT_FORWARD>(fft);
  Tensor<std::complex<float>, 1, ColMajor> reverse_output_both_parts = input.fft<BothParts, FFT_REVERSE>(fft);
 
  Tensor<float, 1, ColMajor> forward_output_real_part = input.fft<RealPart, FFT_FORWARD>(fft);
  Tensor<float, 1, ColMajor> reverse_output_real_part = input.fft<RealPart, FFT_REVERSE>(fft);
 
  Tensor<float, 1, ColMajor> forward_output_imag_part = input.fft<ImagPart, FFT_FORWARD>(fft);
  Tensor<float, 1, ColMajor> reverse_output_imag_part = input.fft<ImagPart, FFT_REVERSE>(fft);
 
  VERIFY_IS_EQUAL(forward_output_both_parts.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_both_parts.dimension(0), input.dimension(0));
 
  VERIFY_IS_EQUAL(forward_output_real_part.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_real_part.dimension(0), input.dimension(0));
 
  VERIFY_IS_EQUAL(forward_output_imag_part.dimension(0), input.dimension(0));
  VERIFY_IS_EQUAL(reverse_output_imag_part.dimension(0), input.dimension(0));
 
  std::complex<float> forward_golden_result[5];
  std::complex<float> reverse_golden_result[5];
 
  forward_golden_result[0] = std::complex<float>(15, 0);
  forward_golden_result[1] = std::complex<float>(-2.5, +3.44095480117793);
  forward_golden_result[2] = std::complex<float>(-2.5, +0.81229924058227);
  forward_golden_result[3] = std::complex<float>(-2.5, -0.81229924058227);
  forward_golden_result[4] = std::complex<float>(-2.5, -3.44095480117793);
 
  reverse_golden_result[0] = std::complex<float>(3.0, 0);
  reverse_golden_result[1] = std::complex<float>(-0.5, -0.688190960235587);
  reverse_golden_result[2] = std::complex<float>(-0.5, -0.162459848116453);
  reverse_golden_result[3] = std::complex<float>(-0.5, +0.162459848116453);
  reverse_golden_result[4] = std::complex<float>(-0.5, +0.688190960235587);
 
  std::complex<float> c_offset(1.0, 1.0);
  float r_offset = 1.0;
 
  for (int i = 0; i < 5; ++i) {
    VERIFY_IS_APPROX(forward_output_both_parts(i) + c_offset, forward_golden_result[i] + c_offset);
    VERIFY_IS_APPROX(forward_output_real_part(i) + r_offset, forward_golden_result[i].real() + r_offset);
    VERIFY_IS_APPROX(forward_output_imag_part(i) + r_offset, forward_golden_result[i].imag() + r_offset);
  }
 
  for (int i = 0; i < 5; ++i) {
    VERIFY_IS_APPROX(reverse_output_both_parts(i) + c_offset, reverse_golden_result[i] + c_offset);
    VERIFY_IS_APPROX(reverse_output_real_part(i) + r_offset, reverse_golden_result[i].real() + r_offset);
    VERIFY_IS_APPROX(reverse_output_imag_part(i) + r_offset, reverse_golden_result[i].imag() + r_offset);
  }
}

References Eigen::BothParts, Eigen::ColMajor, Eigen::Tensor< Scalar_, NumIndices_, Options_, IndexType_ >::dimension(), Eigen::FFT_FORWARD, Eigen::FFT_REVERSE, i, imag(), Eigen::ImagPart, Eigen::RealPart, VERIFY_IS_APPROX, and VERIFY_IS_EQUAL.

Referenced by EIGEN_DECLARE_TEST().