#pragma once

#include <array>

#include <eigen3/unsupported/Eigen/CXX11/Tensor>

#include "factorial.hpp"

template <class Scalar, unsigned p, std::size_t... Indices>
Eigen::Tensor<Scalar, p> initializeJ(unsigned N, std::index_sequence<Indices...>) {
  std::array<unsigned, p> Ns;
  std::fill_n(Ns.begin(), p, N);
  return Eigen::Tensor<Scalar, p>(std::get<Indices>(Ns)...);
}

template <class Scalar, unsigned p, class Distribution, class Generator, std::size_t... Indices>
void populateCouplings(Eigen::Tensor<Scalar, p>& J, unsigned N, unsigned l,
                       std::array<unsigned, p> is, Distribution d, Generator& r,
                       std::index_sequence<Indices...> ii) {
  if (l == 0) {
    Scalar z = d(r);
    do {
      J(std::get<Indices>(is)...) = z;
    } while (std::next_permutation(is.begin(), is.end()));
  } else {
    unsigned iMin;
    if (l == p) {
      iMin = 0;
    } else {
      iMin = is[p - l - 1];
    }
    for (unsigned i = iMin; i < N; i++) {
      std::array<unsigned, p> js = is;
      js[p - l] = i;
      populateCouplings<Scalar, p>(J, N, l - 1, js, d, r, ii);
    }
  }
}

template <class Scalar, unsigned p, class Distribution, class Generator>
Eigen::Tensor<Scalar, p> generateCouplings(unsigned N, Distribution d, Generator& r) {
  Eigen::Tensor<Scalar, p> J = initializeJ<Scalar, p>(N, std::make_index_sequence<p>());

  std::array<unsigned, p> is;
  populateCouplings<Scalar, p>(J, N, p, is, d, r, std::make_index_sequence<p>());

  return J;
}

template <class Scalar>
Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>
contractDown(const Eigen::Tensor<Scalar, 2>& J, const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& z) {
  return Eigen::Map<const Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>>(J.data(), z.size(), z.size());
}

const std::array<Eigen::IndexPair<int>, 1> ip00 = {Eigen::IndexPair<int>(0, 0)};

template <class Scalar, int r>
Eigen::Matrix<Scalar, Eigen::Dynamic, Eigen::Dynamic>
contractDown(const Eigen::Tensor<Scalar, r>& J, const Eigen::Matrix<Scalar, Eigen::Dynamic, 1>& z) {
  Eigen::Tensor<Scalar, 1> zT = Eigen::TensorMap<Eigen::Tensor<const Scalar, 1>>(z.data(), {z.size()});
  Eigen::Tensor<Scalar, r - 1> Jz = J.contract(zT, ip00);
  return contractDown(Jz, z);
}