integrator.cpp


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

using Real = double;

class Point : public std::array<Real, 2> {
public:
  Real τ() const {
    return front();
  }
  Real C() const {
    return back();
  }
};

unsigned p = 3;

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<Point>& Cₜ) {
  Real I = 0;
  for (unsigned i = 0; i < Cₜ.size() - 1; i++) {
    unsigned j = Cₜ.size() - 1 - i;
    Real Δτ = Cₜ[i + 1].τ() - Cₜ[i].τ();
    Real C = (Cₜ[j].C() + Cₜ[j - 1].C()) / 2;
    Real dC = (Cₜ[i + 1].C() - Cₜ[i].C()) / Δτ;
    I += Δτ * df(C) * dC;
  }
  return I;
}

Real energy(const std::vector<Point>& Ct) {
  Real I = 0;
  for (unsigned i = 0; i < Ct.size() - 1; i++) {
    Real Δτ = Ct[i + 1].τ() - Ct[i].τ();
    Real C = (Ct[i].C() + Ct[i + 1].C()) / 2;
    Real dC = (Ct[i + 1].C() - Ct[i].C()) / Δτ;
    I += Δτ * df(C) * dC;
  }
  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 + 0.0 * pow(y, 2);

  std::vector<Point> Cₜ;
  Cₜ.reserve(τₘₐₓ / Δτ + 1);

  Cₜ.push_back({0, 1});

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

  std::cerr << - 2 * y * energy(Cₜ) << std::endl;

  return 0;
}