#include <getopt.h>
#include <vector>
#include <cmath>
#include <iostream>

using Real = double;

unsigned p = 2;

Real f(Real q) {
  return 0.5 * pow(q, p);
}

Real df(Real q) {
  return 0.5 * p * pow(q, p - 1);
}

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

Real integrate(const std::vector<Real>& C, signed τ = std::numeric_limits<unsigned>::max()) {
  Real I = 0;
  if (τ > C.size() - 1) {
    τ = C.size() - 1;
  }
#pragma omp parallel for reduction(+:I)
  for (unsigned σ = 0; σ < τ; σ++) {
    unsigned τ_σ = τ - σ;
    Real Cτ_σ = (C[τ_σ] + C[τ_σ - 1]) / 2;
    Real dCσ = C[σ + 1] - C[σ];

    I += df(Cτ_σ) * dCσ;
  }
  return I;
}

Real integratePast(const std::vector<Real>& C, signed τ) {
  Real I = 0;
#pragma omp parallel for reduction(+:I)
  for (signed σ = -C.size() + τ + 3; σ < τ - 2; σ++) {
    signed τ_σ = τ - σ;

    Real Cτ_σ = (C[abs(τ_σ)] + C[abs(τ_σ) - 1]) / 2;
    Real Cσ = (C[abs(σ) + 1] + C[abs(σ)]) / 2;
    Real dddC;
    if (τ_σ != 0) {
      dddC = (τ_σ / abs(τ_σ)) * (C[abs(τ_σ)+2] - 2 * C[abs(τ_σ)+1] + 2 * C[abs(τ_σ)-1] - C[abs(τ_σ)-2]) / 2;
    } else {
      dddC = 0;
    }

    I += dddC * ddf(Cτ_σ) * Cσ;
  }
#pragma omp parallel for reduction(+:I)
  for (signed σ = -C.size() + τ + 3; σ < -1; σ++) {
    signed τ_σ = τ - σ;

    Real Cτ_σ = (C[abs(τ_σ)] + C[abs(τ_σ) - 1]) / 2;
    Real dddC;
    if (σ != 0) {
      dddC = -(σ / abs(σ)) * (C[abs(σ)+2] - 2 * C[abs(σ)+1] + 2 * C[abs(σ)-1] - C[abs(σ)-2]) / 2;
    } else {
      dddC = 0;
    }

    I += dddC * df(Cτ_σ);
  }
  return I;
}

Real integrateDelay(const std::vector<Real>& C, unsigned τ, Real Δτ, Real τ₀) {
  Real I = 0;
#pragma omp parallel for reduction(+:I)
  for (signed σ = 2; σ < C.size() - τ - 2; σ++) {
    unsigned τ_σ = τ + σ;
    Real dC = -(C[σ+1] - C[σ-1]) / 2;
    Real dddC = -(C[σ+2] - 2 * C[σ+1] + 2 * C[σ-1] - C[σ-2]) / 2;

    I += (dC - pow(τ₀ / Δτ, 2) * dddC) * exp(-(τ_σ * Δτ / τ₀));
  }
  return I  / τ₀;
}

Real energy(const std::vector<Real>& C, Real Δτ, Real τ₀) {
  Real I = 0;
  for (unsigned σ = 0; σ < C.size() - 1; σ++) {
    Real Cσ = (C[σ] + C[σ + 1]) / 2;
    Real dC = (C[σ + 1] - C[σ]) / Δτ;

    Real dddC = 0;
    if (σ > 1 && σ < C.size() - 2 && C.size() > 3) {
      dddC = (C[σ+1] - 3 * C[σ] + 3 * C[σ-1] - C[σ-2]) / pow(Δτ, 3);
    }
    I += Δτ * df(Cσ) * (dC - pow(τ₀, 2) * dddC);
  }
  return I;
}

int main(int argc, char* argv[]) {
  Real Δτ = 1e-3;
  Real τₘₐₓ = 1e3;
  Real τ₀ = 0;
  Real y = 0.5;
  unsigned iterations = 10;

  int opt;

  while ((opt = getopt(argc, argv, "d:T:t:y:I:")) != -1) {
    switch (opt) {
    case 'd':
      Δτ = atof(optarg);
      break;
    case 'T':
      τₘₐₓ = atof(optarg);
      break;
    case 't':
      τ₀ = atof(optarg);
      break;
    case 'y':
      y = atof(optarg);
      break;
    case 'I':
      iterations = (unsigned)atof(optarg);
      break;
    default:
      exit(1);
    }
  }

  Real z = 0.5;
  Real Γ₀ = 1;

  Real τ = 0;
  std::vector<Real> C;
  C.reserve(τₘₐₓ / Δτ + 1);

  C.push_back(1);

//  while (std::cout << τ << " " << C.back() << std::endl, τ < τₘₐₓ) {
  while (τ < τₘₐₓ) {
    τ += Δτ;
    Real dC = -(z - 2 * pow(y, 2)) * C.back() - 2 / Γ₀ * pow(y, 2) * integrate(C);
    C.push_back(C.back() + Δτ * dC);
  }


  for (unsigned it = 0; it < iterations; it++) {

    τ = 0;
    std::vector<Real> C2;
    C2.reserve(τₘₐₓ / Δτ + 1);
    C2.push_back(1);
    while (τ < τₘₐₓ) {
      τ += Δτ;
      Real dC = -(z - 2 * pow(y, 2)) * C2.back() + integrateDelay(C, C2.size() - 1, Δτ, τ₀) - 2 / Γ₀ * pow(y, 2) * (integrate(C2) - pow(τ₀ / Δτ, 2) * integratePast(C, C2.size()-1));
      C2.push_back(C2.back() + Δτ * dC);
    }

    Real error = 0;

    for (unsigned i = 0; i < std::min(C.size(), C2.size()); i++) {
      error += pow(C[i] - C2[i], 2);
    }

    std::cerr << "Iteration " << it << ": " << sqrt(error / C.size()) << " " << z << std::endl;

    C = C2;
  }
  /*
    Real zNew = (2.0 * ((C[2] - 2 * C[1] + C[0]) / pow(Δτ, 2) - pow(τ₀, 2) * (C[4] - 4 * C[3] + 6 * C[2] - 4 * C[1] + C[0]) / pow(Δτ, 4)));
    Real zNew = (2.0 * ((C[2] - 2 * C[1] + C[0]) / pow(Δτ, 2) - pow(τ₀, 2) * (C[4] - 4 * C[3] + 6 * C[2] - 4 * C[1] + C[0]) / pow(Δτ, 4)));
//    Real zNew = (2.0 * ((83 * C[6] - 245 * C[5] + 101 * C[4] + 254 * C[3] - 31 * C[2] - 377 * C[1] + 215 * C[0]) / (132 * pow(Δτ, 2)) - pow(τ₀, 2) * (3 * C[6] - 7 * C[5] + C[4] + 6 * C[3] + C[2] - 7 * C[1] + 3 * C[0]) / (11 * pow(Δτ, 4))));
    z = z / zNew;
  τ = 0;
  C.clear();
  C.reserve(τₘₐₓ / Δτ + 1);

  C.push_back(1);

//  while (std::cout << τ << " " << C.back() << std::endl, τ < τₘₐₓ) {
  while (τ < τₘₐₓ) {
    τ += Δτ;
    Real dC = -z * C.back() - 2 / Γ₀ * pow(y, 2) * integrate(C);
    C.push_back(C.back() + Δτ * dC);
  }
  */

  τ = 0;
  for (Real Ci : C) {
    std::cout << τ << " " << Ci << std::endl;
    τ += Δτ;
  }

  std::cerr << - 2 * y / Γ₀ * energy(C, Δτ, τ₀) << std::endl;

  return 0;
}