//  To use the simple FFT implementation
//  g++ -o demofft -I.. -Wall -O3 FFT.cpp

//  To use the FFTW implementation
//  g++ -o demofft -I.. -DUSE_FFTW -Wall -O3 FFT.cpp -lfftw3 -lfftw3f -lfftw3l

#ifdef USE_FFTW
#include <fftw3.h>
#endif

#include <vector>
#include <complex>
#include <algorithm>
#include <iterator>
#include <iostream>
#include <Eigen/Core>
#include <unsupported/Eigen/FFT>

using namespace std;
using namespace Eigen;

template <typename T>
T mag2(T a) {
  return a * a;
}
template <typename T>
T mag2(std::complex<T> a) {
  return norm(a);
}

template <typename T>
T mag2(const std::vector<T>& vec) {
  T out = 0;
  for (size_t k = 0; k < vec.size(); ++k) out += mag2(vec[k]);
  return out;
}

template <typename T>
T mag2(const std::vector<std::complex<T> >& vec) {
  T out = 0;
  for (size_t k = 0; k < vec.size(); ++k) out += mag2(vec[k]);
  return out;
}

template <typename T>
vector<T> operator-(const vector<T>& a, const vector<T>& b) {
  vector<T> c(a);
  for (size_t k = 0; k < b.size(); ++k) c[k] -= b[k];
  return c;
}

template <typename T>
void RandomFill(std::vector<T>& vec) {
  for (size_t k = 0; k < vec.size(); ++k) vec[k] = T(rand()) / T(RAND_MAX) - T(.5);
}

template <typename T>
void RandomFill(std::vector<std::complex<T> >& vec) {
  for (size_t k = 0; k < vec.size(); ++k)
    vec[k] = std::complex<T>(T(rand()) / T(RAND_MAX) - T(.5), T(rand()) / T(RAND_MAX) - T(.5));
}

template <typename T_time, typename T_freq>
void fwd_inv(size_t nfft) {
  typedef typename NumTraits<T_freq>::Real Scalar;
  vector<T_time> timebuf(nfft);
  RandomFill(timebuf);

  vector<T_freq> freqbuf;
  static FFT<Scalar> fft;
  fft.fwd(freqbuf, timebuf);

  vector<T_time> timebuf2;
  fft.inv(timebuf2, freqbuf);

  T_time rmse = mag2(timebuf - timebuf2) / mag2(timebuf);
  cout << "roundtrip rmse: " << rmse << endl;
}

template <typename T_scalar>
void two_demos(int nfft) {
  cout << "     scalar ";
  fwd_inv<T_scalar, std::complex<T_scalar> >(nfft);
  cout << "    complex ";
  fwd_inv<std::complex<T_scalar>, std::complex<T_scalar> >(nfft);
}

void demo_all_types(int nfft) {
  cout << "nfft=" << nfft << endl;
  cout << "   float" << endl;
  two_demos<float>(nfft);
  cout << "   double" << endl;
  two_demos<double>(nfft);
  cout << "   long double" << endl;
  two_demos<long double>(nfft);
}

int main() {
  demo_all_types(2 * 3 * 4 * 5 * 7);
  demo_all_types(2 * 9 * 16 * 25);
  demo_all_types(1024);
  return 0;
}