#include "fourier.hpp"
#include <fftw3.h>

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) : 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;
}

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;
}

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();
}