#include "fourier.hpp"
#include "p-spin.hpp"
#include <fftw3.h>

FourierTransform::FourierTransform(unsigned n, Real Δω, Real Δτ, unsigned flags) : n(n), Δω(Δω), Δτ(Δτ) {
  a = fftw_alloc_real(2 * n);
  â = reinterpret_cast<Complex*>(fftw_alloc_complex(n + 1));
//  fftw_init_threads();
//  fftw_plan_with_nthreads(FFTW_THREADS);
  fftw_import_wisdom_from_filename("fftw.wisdom");
  plan_r2c = fftw_plan_dft_r2c_1d(2 * n, a, reinterpret_cast<fftw_complex*>(â), flags);
  plan_c2r = fftw_plan_dft_c2r_1d(2 * n, reinterpret_cast<fftw_complex*>(â), a, flags);
  fftw_export_wisdom_to_filename("fftw.wisdom");
}

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

std::vector<Complex> FourierTransform::fourier(const std::vector<Real>& c) {
  for (unsigned i = 0; i < 2 * n; i++) {
    a[i] = c[i];
  }
  fftw_execute(plan_r2c);
  std::vector<Complex> ĉ(n + 1);
  for (unsigned i = 0; i < n + 1; i++) {
    ĉ[i] = â[i] * (Δτ * M_PI);
  }
  return ĉ;
}

std::vector<Complex> FourierTransform::fourier() {
  fftw_execute(plan_r2c);
  std::vector<Complex> ĉ(n+1);
  for (unsigned i = 0; i < n+1; i++) {
    ĉ[i] = â[i] * (Δτ * M_PI);
  }
  return ĉ;
}

std::vector<Real> FourierTransform::convolve(const std::vector<Real>& Γh, const std::vector<Real>& R) {
  a[0] = 0;
  for (unsigned i = 1; i < n; i++) {
    a[i] = R[i];
    a[2 * n - i] = -R[i];
  }
  fftw_execute(plan_r2c);
  for (unsigned i = 1; i < n + 1; i++) {
    â[i] *= Γh[i] * (Δτ * M_PI);
  }
  fftw_execute(plan_c2r);
  std::vector<Real> dC(n);
  for (unsigned i = 0; i < n; i++) {
    dC[i] = a[i] * (Δω / (2 * M_PI));
  }

  return dC;
}

std::vector<Real> FourierTransform::inverse(const std::vector<Complex>& ĉ) {
  for (unsigned i = 0; i < n + 1; i++) {
    â[i] = ĉ[i];
  }
  fftw_execute(plan_c2r);
  std::vector<Real> c(2*n);
  for (unsigned i = 0; i < 2*n; i++) {
    c[i] = a[i] * (Δω / (2 * M_PI));
  }
  return c;
}

void FourierTransform::writeToA(unsigned i, Real ai) {
  a[i] = ai;
}

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

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

  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 τ₀, Real y) {
  auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
  Real Γ₀ = 1 + τ₀ / 2;

  return ((Γ₀ * std::conj(Rt[0]) + pow(y, 2) * (RddfCt[0] * Ct[0] + dfCt[0] * std::conj(Rt[0]))) / Ct[0]).real();
}