// Copyright © 2016-2020 Thomas Nagler and Thibault Vatter
//
// This file is part of the vinecopulib library and licensed under the terms of
// the MIT license. For a copy, see the LICENSE file in the root directory of
// vinecopulib or https://vinecopulib.github.io/vinecopulib/.

#include <boost/math/special_functions/log1p.hpp>
#include <vinecopulib/misc/tools_eigen.hpp>

namespace vinecopulib {
inline ClaytonBicop::ClaytonBicop()
{
  family_ = BicopFamily::clayton;
  parameters_ = Eigen::VectorXd(1);
  parameters_lower_bounds_ = Eigen::VectorXd(1);
  parameters_upper_bounds_ = Eigen::VectorXd(1);
  parameters_ << 1e-10;
  parameters_lower_bounds_ << 1e-10;
  parameters_upper_bounds_ << 28;
}

inline double
ClaytonBicop::generator(const double& u)
{
  double theta = double(this->parameters_(0));
  return (std::pow(u, -theta) - 1) / theta;
}

inline double
ClaytonBicop::generator_inv(const double& u)
{
  double theta = double(this->parameters_(0));
  return std::pow(1 + theta * u, -1 / theta);
}

inline double
ClaytonBicop::generator_derivative(const double& u)
{
  return (-1) * std::pow(u, -1 - this->parameters_(0));
}

// inline double ClaytonBicop::generator_derivative2(const double &u)
//{
//    double theta = double(this->parameters_(0));
//    return (1 + theta) * std::pow(u, -2 - theta);
//}

inline Eigen::VectorXd
ClaytonBicop::pdf_raw(const Eigen::MatrixXd& u)
{
  double theta = static_cast<double>(parameters_(0));
  // avoid numerical issues when copula is too close to independence
  if (theta < 1e-10) {
    auto f = [](const double&, const double&) { return 1.0; };
    return tools_eigen::binaryExpr_or_nan(u, f);
  }

  auto f = [theta](const double& u1, const double& u2) {
    double temp = boost::math::log1p(theta) - (1.0 + theta) * std::log(u1 * u2);
    temp = temp - (2.0 + 1.0 / (theta)) *
                    std::log(std::pow(u1, -theta) + std::pow(u2, -theta) - 1.0);
    return std::exp(temp);
  };
  return tools_eigen::binaryExpr_or_nan(u, f);
}

inline Eigen::VectorXd
ClaytonBicop::hinv1_raw(const Eigen::MatrixXd& u)
{
  double theta = double(this->parameters_(0));
  Eigen::VectorXd hinv = u.col(0).array().pow(theta + 1.0);
  if (theta < 75) {
    hinv = u.col(1).cwiseProduct(hinv);
    hinv = hinv.array().pow(-theta / (theta + 1.0));
    Eigen::VectorXd x = u.col(0);
    x = x.array().pow(-theta);
    hinv = hinv - x + Eigen::VectorXd::Ones(x.size());
    hinv = hinv.array().pow(-1 / theta);
  } else {
    hinv = hinv1_num(u);
  }
  return hinv;
}

inline Eigen::MatrixXd
ClaytonBicop::tau_to_parameters(const double& tau)
{
  Eigen::VectorXd parameters(1);
  parameters(0) = 2 * std::fabs(tau) / (1 - std::fabs(tau));
  return parameters;
}

inline double
ClaytonBicop::parameters_to_tau(const Eigen::MatrixXd& parameters)
{
  return parameters(0) / (2 + std::fabs(parameters(0)));
}

inline Eigen::VectorXd
ClaytonBicop::get_start_parameters(const double tau)
{
  Eigen::VectorXd par = tau_to_parameters(tau);
  par = par.cwiseMax(parameters_lower_bounds_);
  par = par.cwiseMin(parameters_upper_bounds_);
  return par;
}
}
