#pragma once
#include <cmath>
#include <fftw3.h>
#include <complex>
#include <vector>

using Real = double;
using Complex = std::complex<Real>;
using namespace std::complex_literals;

Real f(Real λ, unsigned p, unsigned s, Real q);
Real df(Real λ, unsigned p, unsigned s, Real q);
Real ddf(Real λ, unsigned p, unsigned s, Real q);

class FourierTransform {
private:
  std::vector<Real> a;
  std::vector<Complex> â;
  fftw_plan plan_r2c;
  fftw_plan plan_c2r;
  Real Δω;
  Real Δτ;
public:
  FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags = 0);
  ~FourierTransform();
  std::vector<Complex> fourier(const std::vector<Real>& c);
  std::vector<Real> inverse(const std::vector<Complex>& ĉ);
};

std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ);
Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ);
std::tuple<std::vector<Complex>, std::vector<Complex>> RddfCtdfCt(FourierTransform& fft, const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ);
Real estimateZ(FourierTransform& 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 y);