#include "fourier.hpp"

inline Real fP(unsigned p, Real q) {
  return 0.5 * pow(q, p);
}

inline Real dfP(unsigned p, Real q) {
  return 0.5 * p * pow(q, p - 1);
}

inline Real ddfP(unsigned p, Real q) {
  return 0.5 * p * (p - 1) * pow(q, p - 2);
}

Real f(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * fP(p, q) + λ * fP(s, q);
}

Real df(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * dfP(p, q) + λ * dfP(s, q);
}

Real ddf(Real λ, unsigned p, unsigned s, Real q) {
  return (1 - λ) * ddfP(p, q) + λ * ddfP(s, q);
}

FourierTransform::FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags) : a(2 * n), â(n + 1), Δω(Δω), Δτ(Δτ) {
  plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a.data(), reinterpret_cast<fftw_complex*>(â.data()), flags);
  plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â.data()), a.data(), flags);
}

FourierTransform::~FourierTransform() {
  fftw_destroy_plan(plan_r2c);
  fftw_destroy_plan(plan_c2r);
  fftw_cleanup();
}

std::vector<Complex> FourierTransform::fourier(const std::vector<Real>& c) {
  a = c;
  fftw_execute(plan_r2c);
  std::vector<Complex> ĉ(â.size());
  for (unsigned i = 0; i < â.size(); i++) {
    ĉ[i] = â[i] * (Δτ * M_PI);
  }
  return ĉ;
}

std::vector<Real> FourierTransform::inverse(const std::vector<Complex>& ĉ) {
  â = ĉ;
  fftw_execute(plan_c2r);
  std::vector<Real> c(a.size());
  for (unsigned i = 0; i < a.size(); i++) {
    c[i] = a[i] * (Δω / (2 * M_PI));
  }
  return c;
}

std::string fourierFile(std::string prefix, unsigned p, unsigned s, Real λ, Real τ₀, Real y, unsigned log2n, Real τₘₐₓ) {
  return prefix + "_" + std::to_string(p) + "_" + std::to_string(s) + "_" + std::to_string(λ) + "_" + std::to_string(τ₀) + "_" + std::to_string(y) + "_" + std::to_string(log2n) + "_" + std::to_string(τₘₐₓ) + ".dat";
}

Real energy(const std::vector<Real>& C, const std::vector<Real>& R, unsigned p, unsigned s, Real λ, Real y, Real Δτ) {
  Real e = 0;

  for (unsigned i = 0; i < C.size() / 2; i++) {
    e += y * R[i] * df(λ, p, s, C[i]) * M_PI * Δτ;
  }

  return e;
}

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) {
  std::vector<Real> RddfC(C.size());
  for (unsigned i = 0; i < C.size() / 2; i++) {
    RddfC[i] = R[i] * ddf(λ, p, s, C[i]);
  }
  std::vector<Complex> RddfCt = fft.fourier(RddfC);

  std::vector<Real> dfC(C.size());
  for (unsigned i = 0; i < C.size(); i++) {
    dfC[i] = df(λ, p, s, C[i]);
  }
  std::vector<Complex> dfCt = fft.fourier(dfC);

  return {RddfCt, dfCt};
}

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) {
  auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);

  return ((std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
}