#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, Real Δτ, Real τ₀) {
  Real I = 0;
#pragma omp parallel for reduction(+:I)
  for (unsigned σ = 0; σ < C.size() - 1; σ++) {
    unsigned τ_σ = C.size() - 1 - σ;
    Real Cτ_σ = (C[τ_σ] + C[τ_σ - 1]) / 2;
    Real dCσ = (C[σ + 1] - C[σ]) / Δτ;

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

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;

  int opt;

  while ((opt = getopt(argc, argv, "d:T:t:y:")) != -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;
    default:
      exit(1);
    }
  }

  Real z = 0.5;
  Real Γ₀ = 0.5 * (2 * τ₀) / (sqrt(1 + 2 * τ₀) - 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) {
    τ += Δτ;
    Real dC = -z * C.back() - 2 / Γ₀ * pow(y, 2) * integrate(C, Δτ, τ₀);
    C.push_back(C.back() + Δτ * dC);
  }

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

  return 0;
}