#include <getopt.h>

#include "complex_normal.hpp"
#include "p-spin.hpp"
#include "dynamics.hpp"

#include "pcg-cpp/include/pcg_random.hpp"
#include "randutils/randutils.hpp"
#include "unsupported/Eigen/CXX11/src/Tensor/TensorFFT.h"

#define PSPIN_P 3
const int p = PSPIN_P; // polynomial degree of Hamiltonian
using Complex = std::complex<double>;
using ComplexVector = Vector<Complex>;
using ComplexMatrix = Matrix<Complex>;
using ComplexTensor = Tensor<Complex, p>;

using Rng = randutils::random_generator<pcg32>;

int main(int argc, char* argv[]) {
  // model parameters
  unsigned N = 10; // number of spins
  double T = 1;    // temperature
  double Rκ = 1;   // real part of distribution parameter
  double Iκ = 0;   // imaginary part of distribution parameter

  // simulation parameters
  double ε = 1e-4;
  double εJ = 1e-2;
  double δ = 1e-2;   // threshold for determining saddle
  double Δ = 1e-3;
  double γ = 1e-2;   // step size
  unsigned t = 1000; // number of Langevin steps
  unsigned M = 100;
  unsigned n = 100;

  int opt;

  while ((opt = getopt(argc, argv, "N:M:n:T:e:r:i:g:t:E:")) != -1) {
    switch (opt) {
    case 'N':
      N = (unsigned)atof(optarg);
      break;
    case 't':
      t = (unsigned)atof(optarg);
      break;
    case 'T':
      T = atof(optarg);
      break;
    case 'e':
      δ = atof(optarg);
      break;
    case 'E':
      ε = atof(optarg);
      break;
    case 'g':
      γ = atof(optarg);
    case 'r':
      Rκ = atof(optarg);
      break;
    case 'i':
      Iκ = atof(optarg);
      break;
    case 'n':
      n = (unsigned)atof(optarg);
      break;
    case 'M':
      M = (unsigned)atof(optarg);
      break;
    default:
      exit(1);
    }
  }

  Complex κ(Rκ, Iκ);
  double σ = sqrt(factorial(p) / (2.0 * pow(N, p - 1)));

  Rng r;

  complex_normal_distribution<> d(0, 1, 0);

  ComplexTensor J = generateCouplings<Complex, PSPIN_P>(N, complex_normal_distribution<>(0, σ, κ), r.engine());
  ComplexVector z0 = normalize(randomVector<Complex>(N, d, r.engine()));

  ComplexVector zSaddle = findSaddle(J, z0, ε);
  ComplexVector zSaddlePrev = ComplexVector::Zero(N);
  ComplexVector z = zSaddle;

  while (δ < (zSaddle - zSaddlePrev).norm()) { // Until we find two saddles sufficiently close...
    std::tie(std::ignore, z) = langevin(J, z, T, γ, M, d, r.engine());
    try {
      ComplexVector zSaddleNext = findSaddle(J, z, ε);
      if (Δ < (zSaddleNext - zSaddle).norm()) { // Ensure we are finding distinct saddles.
        zSaddlePrev = zSaddle;
        zSaddle = zSaddleNext;
      }
    } catch (std::exception& e) {
      std::cerr << "Could not find a saddle: " << e.what() << std::endl;
    }

    std::cerr << "Current saddles are " << (zSaddle - zSaddlePrev).norm() << " apart." << std::endl;
  }

  std::cerr << "Found sufficiently nearby saddles, perturbing J." << std::endl;

  complex_normal_distribution<> dJ(0, εJ * σ, 0);

  std::function<void(ComplexTensor&, std::array<unsigned, p>)> perturbJ =
    [&dJ, &r] (ComplexTensor& JJ, std::array<unsigned, p> ind) {
      Complex Ji = getJ<Complex, p>(JJ, ind);
      setJ<Complex, p>(JJ, ind, Ji + dJ(r.engine()));
    };

  for (unsigned i = 0; i < n; i++) {
    ComplexTensor Jp = J;

    iterateOver<Complex, p>(Jp, perturbJ);

    try {
      ComplexVector zSaddleNew = findSaddle(Jp, zSaddle, ε);
      ComplexVector zSaddlePrevNew = findSaddle(Jp, zSaddlePrev, ε);

      std::cout << zSaddleNew.transpose() << " " << zSaddlePrevNew.transpose() << std::endl;
    } catch (std::exception& e) {
      std::cerr << "Couldn't find a saddle with new couplings, skipping." << std::endl;
    }
  }

  return 0;
}