#include "log-fourier.hpp"

LogarithmicFourierTransform::LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad) : N(N), pad(pad), k(k), Δτ(Δτ) {
  τₛ = -0.5 * N;
  ωₛ = -0.5 * N;
  sₛ = -0.5 * pad * N;
  a = reinterpret_cast<Complex*>(fftw_alloc_complex(pad*N));
  â = reinterpret_cast<Complex*>(fftw_alloc_complex(pad*N));
  fftw_import_wisdom_from_filename("fftw.wisdom");
  a_to_â = fftw_plan_dft_1d(pad*N, reinterpret_cast<fftw_complex*>(a), reinterpret_cast<fftw_complex*>(â), FFTW_BACKWARD, 0);
  â_to_a = fftw_plan_dft_1d(pad*N, reinterpret_cast<fftw_complex*>(â), reinterpret_cast<fftw_complex*>(a), FFTW_BACKWARD, 0);
  fftw_export_wisdom_to_filename("fftw.wisdom");
}

LogarithmicFourierTransform::~LogarithmicFourierTransform() {
  fftw_destroy_plan(a_to_â);
  fftw_destroy_plan(â_to_a);
  fftw_free(a);
  fftw_free(â);
  fftw_cleanup();
}

Real LogarithmicFourierTransform::τ(unsigned n) const {
  return Δτ * (n + τₛ);
}

Real LogarithmicFourierTransform::ω(unsigned n) const {
  return Δτ * (n + ωₛ);
}

Real LogarithmicFourierTransform::s(unsigned n) const {
  return (n + sₛ) * 2*M_PI / (pad * N * Δτ);
}

Real LogarithmicFourierTransform::t(unsigned n) const {
  return exp(τ(n));
}

Real LogarithmicFourierTransform::ν(unsigned n) const {
  return exp(ω(n));
}

Complex gamma(Complex z) {
  gsl_sf_result logΓ;
  gsl_sf_result argΓ;

  gsl_sf_lngamma_complex_e(z.real(), z.imag(), &logΓ, &argΓ);

  return exp(logΓ.val + 1i * argΓ.val);
}

std::vector<Complex> LogarithmicFourierTransform::fourier(const std::vector<Real>& c, bool symmetric) {
  std::vector<Complex> ĉ(N);
  std::vector<Real> σs = {1};
  if (symmetric){
    σs.push_back(-1);
  }
  for (Real σ : σs) {
    for (unsigned n = 0; n < pad*N; n++) {
      if (n < N) {
        a[n] = c[n] * exp((1 - k) * τ(n));
      } else {
        a[n] = 0;
      }
    }
    fftw_execute(a_to_â);
    for (unsigned n = 0; n < pad*N; n++) {
      â[(pad*N / 2 + n) % (pad*N)] *= pow(1i * σ, 1i * s(n) - k) * gamma(k - 1i * s(n));
    }
    fftw_execute(â_to_a);
    for (unsigned n = 0; n < N; n++) {
      ĉ[n] += exp(-k * ω(n)) * a[(pad - 1)*N+n] / (Real)(pad*N);
    }
  }

  return ĉ;
}

std::vector<Real> LogarithmicFourierTransform::inverse(const std::vector<Complex>& ĉ) {
  std::vector<Real> c(N);
  std::vector<Real> σs = {1, -1};
  for (Real σ : σs) {
    for (unsigned n = 0; n < pad * N; n++) {
      if (n < N) {
        a[n] = ĉ[n] * exp((1 - k) * ω(n));
      } else {
        a[n] = 0;
      }
    }
    fftw_execute(a_to_â);
    for (unsigned n = 0; n < pad*N; n++) {
      â[(pad*N / 2 + n) % (pad*N)] *= pow(-1i * σ, 1i * s(n) - k) * gamma(k - 1i * s(n));
    }
    fftw_execute(â_to_a);
    for (unsigned n = 0; n < N; n++) {
      c[n] += exp(-k * τ(n)) * a[(pad - 1)*N+n].real() / (Real)(pad*N) / (2 * M_PI);
    }
  }

  return c;
}