#pragma once
#include "types.hpp"

#include <cmath>
#include <fftw3.h>
#include <vector>
#include <tuple>
#include <gsl/gsl_sf_gamma.h>

class LogarithmicFourierTransform {
private:
  Complex* a;
  Complex* â;
  FFTW_PLAN a_to_â;
  FFTW_PLAN â_to_a;
  unsigned N;
  unsigned pad;
  Real k;
  Real Δτ;
  Real τₛ;
  Real ωₛ;
  Real sₛ;
public:
  Real shift;
  LogarithmicFourierTransform(unsigned N, Real k, Real Δτ, unsigned pad = 4, Real shift = 0.5);
  ~LogarithmicFourierTransform();
  Real τ(unsigned n) const;
  Real ω(unsigned n) const;
  Real t(unsigned n) const;
  Real ν(unsigned n) const;
  Real s(unsigned n) const;
  std::vector<Complex> fourier(const std::vector<Real>& c, bool symmetric);
  std::vector<Real> inverse(const std::vector<Complex>& ĉ);
};

std::string logFourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real shift);

void logFourierSave(const std::vector<Real>& C, const std::vector<Real>& R, const std::vector<Complex>& Ct, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real shift);

bool logFourierLoad(std::vector<Real>& C, std::vector<Real>& R, std::vector<Complex>& Ct, std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β, unsigned log2n, Real Δτ, Real shift);

std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ);

Real estimateZ(LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Complex>& Ct, const std::vector<Real>& R, const std::vector<Complex>& Rt, unsigned p, unsigned s, Real λ, Real τ₀, Real β);

Real energy(const LogarithmicFourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real β);

Real C0(const LogarithmicFourierTransform& fft, const std::vector<Complex>& Ĉ);