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FFT results of c++ vs MATLAB

Pages: 12
mbozzi (3933)
I just I am trying to reproduce it using FFTW library and sort of failing


See the following. The important part is just the examples of how to make the plans.

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#include <cmath>
#include <cassert>
#include <iostream> 
#include <iomanip>
#include <utility>
#include <complex>

#include "fftw3.h"

int constexpr ny = 11;
int constexpr nx = 10;
int constexpr nxk = nx / 2 + 1;
int constexpr nyk = ny / 2 + 1;

unsigned constexpr flags = FFTW_ESTIMATE;

double const pi = 3.1415926535897932384626433;

struct cplx_buffer
{
  fftw_complex* a;
  int rows;
  int cols;

  fftw_complex& operator()(int i, int j) const { return a[i * cols + j]; }
};

struct real_buffer
{
  double* a;
  int rows;
  int cols;

  double& operator()(int i, int j) const { return a[i * cols + j]; }
};

real_buffer my_fftw_allocate_real(int x, int y) { return real_buffer{ fftw_alloc_real(x * y), x, y }; }
cplx_buffer my_fftw_allocate_cplx(int x, int y) { return cplx_buffer{ fftw_alloc_complex(x * y), x, y }; }


void print_matrix(real_buffer const& m)
{
  std::cout << std::fixed << std::setprecision(2);

  for (int i = 0; i < m.rows; i++)
  {
    for (int j = 0; j < m.cols; j++)
    {
      std::cout << std::setw(16) << m(i, j);
    }
    std::cout << '\n';
  }
  std::cout << '\n';
}

void print_matrix(cplx_buffer const& m)
{
  std::cout << std::fixed << std::setprecision(2);

  for (int i = 0; i < m.rows; i++)
  {
    for (int j = 0; j < m.cols; j++)
    {
      std::cout << std::setw(16) << std::complex<double> { m(i, j)[0], m(i, j)[1] };
    }
    std::cout << '\n';
  }
  std::cout << '\n';
}

int main()
{
  real_buffer in = my_fftw_allocate_real(ny, nx);
  for (int i = 0; i < ny; ++i)
    for (int j = 0; j < nx; ++j)
    {
      double const XXij = +std::sin(j * 2.0 * pi / nx);
      double const YYij = -std::cos(i * pi / ny) - 0.5;
      in(i, j) = YYij * YYij * XXij;
    }
  std::cout << "input matrix\n"; print_matrix(in);

  { // Transform the first row
    cplx_buffer out = my_fftw_allocate_cplx(1, nxk);
    fftw_execute(fftw_plan_dft_r2c_1d(nx, in.a, out.a, flags));
    std::cout << "DFT of first row of input\n"; print_matrix(out);
  }

  { // Transform all the rows
    cplx_buffer out = my_fftw_allocate_cplx(ny, nxk);
    fftw_execute(fftw_plan_many_dft_r2c(1, &nx, in.rows, in.a, &in.cols, 1, in.cols, out.a, &in.cols, 1, out.cols, flags));
    std::cout << "DFT of input, row-wise\n"; print_matrix(out);
  }

  { // Transform the first column 
    cplx_buffer out = my_fftw_allocate_cplx(nyk, 1);
    fftw_execute(fftw_plan_many_dft_r2c(1, &in.rows, 1, in.a, &in.rows, in.cols, 1, out.a, &in.rows, out.cols, 1, flags));
    std::cout << "DFT of first column of input\n";  print_matrix(out);
  }

  { // Transform all the columns: 
    cplx_buffer out = my_fftw_allocate_cplx(nyk, nx);
    fftw_execute(fftw_plan_many_dft_r2c(1, &in.rows, in.cols, in.a, &in.rows, in.cols, 1, out.a, &in.rows, out.cols, 1, flags));
    std::cout << "DFT of input, column-wise\n"; print_matrix(out);
  }

  { // Do a 2D FFT the hard way, first rows, then columns
    cplx_buffer tmp = my_fftw_allocate_cplx(ny, nxk);
    cplx_buffer out = my_fftw_allocate_cplx(ny, nxk);
    fftw_execute(fftw_plan_many_dft_r2c(1, &in.cols, in.rows, in.a, &in.cols, 1, in.cols, tmp.a, &in.cols, 1, tmp.cols, flags));
    fftw_execute(fftw_plan_many_dft(1, &in.rows, tmp.cols, tmp.a, &in.rows, tmp.cols, 1, out.a, &in.rows, out.cols, 1, FFTW_FORWARD, flags));
    std::cout << "2D transform, the hard way\n"; print_matrix(out);
  }

  { // Do a 2D FFT the easy way:
    cplx_buffer out = my_fftw_allocate_cplx(ny, nxk);
    fftw_execute(fftw_plan_dft_r2c_2d(in.rows, in.cols, in.a, out.a, flags));
    std::cout << "2D transform, the easy way\n"; print_matrix(out);
  }

  return 0;
}

Last edited on
mbozzi (3933)
Here's a version of the program that doesn't leak memory or fftw_plans, is a little more ergonomic, and marginally less error prone. As before the important part is the main function. 

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#include <cmath>
#include <cassert>
#include <iostream> 
#include <iomanip>
#include <utility>
#include <complex>

#include "fftw3.h"

template <typename T>
  class my_fftw_buffer_base
  {
    T* a;
    int m; 
    int n;
  
  protected:
    ~my_fftw_buffer_base() { if (a) fftw_free(a); };
  
  public:
    using value_type = T;
  
    my_fftw_buffer_base(int m, int n)
      : a{(T*)fftw_malloc(m * n * sizeof T)}, m{ m }, n{ n }
    {       
      if (a == nullptr) abort(); 
    }
  
    my_fftw_buffer_base& operator=(my_fftw_buffer_base const&) = delete;
    my_fftw_buffer_base(my_fftw_buffer_base const&) = delete;
  
    my_fftw_buffer_base& operator=(my_fftw_buffer_base&& that) noexcept
    {
      if (this == &that) return;
      this->a = std::exchange(that.a, nullptr);
      this->m = std::exchange(that.m, 0);
      this->n = std::exchange(that.n, 0);
      return *this;
    }
    
    my_fftw_buffer_base(my_fftw_buffer_base&& that) noexcept
    {
      *this = std::move(that);
    }
  
    int rows() const noexcept { return m; }
    int cols() const noexcept { return n; }
  
    T&       operator[](int n)              { return checked_access(n); }
    T const& operator[](int n) const        { return checked_access(n); }
    T&       operator()(int n)              { return checked_access(n); }
    T const& operator()(int n) const        { return checked_access(n); }
    T&       operator()(int i, int j)       { return checked_access(i, j); }
    T const& operator()(int i, int j) const { return checked_access(i, j); }
  
    T*       data()      noexcept       { return a; }
    T const* data()      const noexcept { return a; }
    operator T* ()       noexcept       { return a; }
    operator T const* () const noexcept { return a; }
  
    int size() const noexcept { return m * n; }
  
  private:
    T& checked_access(int i, int j) const
    { 
      assert(i >= 0 && i < m);
      assert(j >= 0 && j < n);
      return a[i * n + j];
    }
  
    T& checked_access(int i) const
    {
      assert(i >= 0 && i < size());
      return a[i];
    }
  
  protected: 
    T* unsafe_get_ptr() const noexcept { return a; };
  };

template <typename T>
  struct my_fftw_buffer_impl : my_fftw_buffer_base<T>
  { 
    using base_type = my_fftw_buffer_base<T>;
    using base_type::base_type;
    operator bool() = delete; 
    operator bool() const = delete;
  };

struct my_fftw_buffer_real
  : public my_fftw_buffer_impl<double>
{
  using base_type = my_fftw_buffer_impl<double>;
  using base_type::base_type;
};

struct my_fftw_buffer_complex 
  : public my_fftw_buffer_impl<std::complex<double>>
{
  using base_type = my_fftw_buffer_impl<std::complex<double>>;
  using base_type::base_type;

  fftw_complex* data()            noexcept       { return array_oriented(); }
  fftw_complex const* data()      const noexcept { return array_oriented(); }
  operator fftw_complex* ()       noexcept       { return array_oriented(); }
  operator fftw_complex const* () const noexcept { return array_oriented(); }

private:
  fftw_complex* array_oriented() const 
  { // This conversion is likely okay, see [complex.numbers.general]/4
    return reinterpret_cast<fftw_complex*>(unsafe_get_ptr()); 
  }
};

class my_fftw_plan
{
  fftw_plan p;

public:
  ~my_fftw_plan() { if (p) fftw_destroy_plan(p); }

  explicit my_fftw_plan(fftw_plan p)
        : p(p) { if (!p) abort(); }

  my_fftw_plan& operator=(my_fftw_plan&& that) noexcept
  { if (this != &that) this->p = std::exchange(that.p, nullptr); }
  my_fftw_plan(my_fftw_plan&& that) noexcept { *this = std::move(that); }
  my_fftw_plan& operator=(my_fftw_plan const&) = delete;
  my_fftw_plan(my_fftw_plan const&) = delete;
  operator fftw_plan() const noexcept { return p; }
};

template <typename T>
  void print_matrix(T const& m, typename T::value_type q = 1.0)
  {
    std::cout << std::fixed << std::setprecision(2); 
  
    for (int i = 0; i < m.rows(); i++)
    {
      for (int j = 0; j < m.cols(); j++) 
      {
        std::cout << std::setw(16) << (m(i, j) / q);
      }
      std::cout << '\n';
    }
    std::cout << '\n';
  }

int constexpr ny = 11;
int constexpr nx = 10;
int constexpr nxk = nx / 2 + 1;
int constexpr nyk = ny / 2 + 1;

unsigned constexpr flags = FFTW_ESTIMATE;

double const pi = 3.1415926535897932384626433;

int main()
{
  my_fftw_buffer_real in(ny, nx);
  for (int i = 0; i < ny; ++i)
    for (int j = 0; j < nx; ++j)
    {
      double const XXij = +std::sin(j * 2.0 * pi / nx);
      double const YYij = -std::cos(i * pi / ny) - 0.5;
      in(i, j) = YYij * YYij * XXij;
    }
  std::cout << "input matrix\n"; print_matrix(in);

  { // Transform the first row
    my_fftw_buffer_complex out{ 1, nxk };
    fftw_execute(my_fftw_plan{ fftw_plan_dft_r2c_1d(nx, in, out, flags) });
    std::cout << "DFT of first row of input\n"; print_matrix(out);
  }

  { // Transform all the rows
    my_fftw_buffer_complex out{ ny, nxk };
    fftw_execute(my_fftw_plan{ fftw_plan_many_dft_r2c(1, &nx, in.rows(), in, &nx, 1, nx, out, &nx, 1, out.cols(), flags) });
    std::cout << "DFT of input, row-wise\n"; print_matrix(out);
  }

  { // Transform the first column 
    my_fftw_buffer_complex out{ nyk, 1 };
    fftw_execute(my_fftw_plan{ fftw_plan_many_dft_r2c(1, &ny, 1, in, &ny, in.cols(), 1, out, &ny, out.cols(), 1, flags) });
    std::cout << "DFT of first column of input\n";  print_matrix(out);
  }

  { // Transform all the columns: 
    my_fftw_buffer_complex out{ nyk, nx };
    fftw_execute(my_fftw_plan{ fftw_plan_many_dft_r2c(1, &ny, in.cols(), in, &ny, in.cols(), 1, out, &ny, out.cols(), 1, flags)});
    std::cout << "DFT of input, column-wise\n"; print_matrix(out);
  }

  { // Do a 2D FFT the hard way, first rows, then columns
    my_fftw_buffer_complex tmp{ ny, nxk };
    my_fftw_buffer_complex out{ ny, nxk };
    fftw_execute(my_fftw_plan{ fftw_plan_many_dft_r2c(1, &nx, in.rows(), in, &nx, 1, nx, tmp, &nx, 1, tmp.cols(), flags) });
    fftw_execute(my_fftw_plan{ fftw_plan_many_dft(1, &ny, tmp.cols(), tmp, &ny, tmp.cols(), 1, out, &ny, out.cols(), 1, FFTW_FORWARD, flags) });
    std::cout << "2D transform, the hard way\n"; print_matrix(out);
  }

  { // Do a 2D FFT the easy way:
    my_fftw_buffer_complex out{ ny, nxk };
    fftw_execute(my_fftw_plan{ fftw_plan_dft_r2c_2d(in.rows(), in.cols(), in, out, flags) });
    std::cout << "2D transform, the easy way\n"; print_matrix(out);
  }
}

Last edited on
JamieAl (236)
This is pretty HELPFUL, thanks a lot everyone!
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