exp_mod_normal_lcdf.hpp

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#ifndef STAN_MATH_OPENCL_PRIM_DOUBLE_EXP_MOD_NORMAL_LCDF_HPP
#define STAN_MATH_OPENCL_PRIM_DOUBLE_EXP_MOD_NORMAL_LCDF_HPP
#ifdef STAN_OPENCL
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/elt_divide.hpp>
#include <stan/math/prim/fun/elt_multiply.hpp>
#include <stan/math/opencl/kernel_generator.hpp>
#include <stan/math/opencl/prim/std_normal_lcdf.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
 
namespace stan {
namespace math {
 
template <typename T_y_cl, typename T_loc_cl, typename T_scale_cl,
          typename T_inv_scale_cl,
          require_all_prim_or_rev_kernel_expression_t<
              T_y_cl, T_loc_cl, T_scale_cl, T_inv_scale_cl>* = nullptr,
          require_any_not_stan_scalar_t<T_y_cl, T_loc_cl, T_scale_cl,
                                        T_inv_scale_cl>* = nullptr>
inline return_type_t<T_y_cl, T_loc_cl, T_scale_cl, T_inv_scale_cl>
exp_mod_normal_lcdf(const T_y_cl& y, const T_loc_cl& mu,
                    const T_scale_cl& sigma, const T_inv_scale_cl& lambda) {
  static constexpr const char* function = "exp_mod_normal_lcdf(OpenCL)";
  using T_partials_return
      = partials_return_t<T_y_cl, T_loc_cl, T_scale_cl, T_inv_scale_cl>;
  using std::isfinite;
  using std::isnan;
 
  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Scale parameter", sigma);
  const size_t N = max_size(y, mu, sigma);
  if (N == 0) {
    return 0.0;
  }
 
  const auto& y_col = as_column_vector_or_scalar(y);
  const auto& mu_col = as_column_vector_or_scalar(mu);
  const auto& sigma_col = as_column_vector_or_scalar(sigma);
  const auto& lambda_col = as_column_vector_or_scalar(lambda);
 
  const auto& y_val = value_of(y_col);
  const auto& mu_val = value_of(mu_col);
  const auto& sigma_val = value_of(sigma_col);
  const auto& lambda_val = value_of(lambda_col);
 
  auto check_y_not_nan
      = check_cl(function, "Random variable", y_val, "not NaN");
  auto y_not_nan_expr = !isnan(y_val);
  auto check_mu_finite
      = check_cl(function, "Location parameter", mu_val, "finite");
  auto mu_finite_expr = isfinite(mu_val);
  auto check_sigma_positive_finite
      = check_cl(function, "Scale parameter", sigma_val, "positive finite");
  auto sigma_positive_finite_expr = 0 < sigma_val && isfinite(sigma_val);
  auto check_lambda_positive_finite
      = check_cl(function, "Inv_cale parameter", lambda_val, "positive finite");
  auto lambda_positive_finite_expr = 0 < lambda_val && isfinite(lambda_val);
 
  auto any_y_neg_inf = colwise_max(cast<char>(y_val == NEGATIVE_INFTY));
  auto any_y_pos_inf = colwise_max(cast<char>(y_val == INFTY));
  auto sigma_inv = elt_divide(1.0, sigma_val);
  auto diff = y_val - mu_val;
  auto scaled_diff = elt_multiply(diff * INV_SQRT_TWO, sigma_inv);
  auto v = elt_multiply(lambda_val, sigma_val);
  auto scaled_diff_diff = scaled_diff - v * INV_SQRT_TWO;
  auto cdf_term_1 = 0.5 + 0.5 * erf(scaled_diff);
  auto cdf_term_2_phi = 0.5 * (1.0 + erf(scaled_diff_diff));
  auto log_exp_term = 0.5 * square(v) - elt_multiply(lambda_val, diff);
  auto exp_term = exp(log_exp_term);
  auto cdf_term_2 = elt_multiply(exp_term, cdf_term_2_phi);
  auto cdf_n = cdf_term_1 - cdf_term_2;
  auto use_stable = cdf_n <= 0.0 || !isfinite(cdf_n);
 
  auto exp_term_2 = exp(-square(scaled_diff_diff));
  auto deriv_1
      = elt_multiply(elt_multiply(lambda_val, exp_term), cdf_term_2_phi);
  auto deriv_2 = INV_SQRT_TWO_PI
                 * elt_multiply(elt_multiply(exp_term, exp_term_2), sigma_inv);
  auto deriv_3
      = INV_SQRT_TWO_PI * elt_multiply(exp(-square(scaled_diff)), sigma_inv);
  auto direct_cdf_log = log(cdf_n);
  auto direct_y_deriv = elt_divide(deriv_1 - deriv_2 + deriv_3, cdf_n);
  auto direct_mu_deriv = -direct_y_deriv;
  auto direct_sigma_deriv = -elt_divide(
      elt_multiply(deriv_1 - deriv_2, v)
          + elt_multiply(deriv_3 - deriv_2, scaled_diff) * SQRT_TWO,
      cdf_n);
  auto direct_lambda_deriv = elt_divide(
      elt_multiply(exp_term,
                   INV_SQRT_TWO_PI * elt_multiply(sigma_val, exp_term_2)
                       - elt_multiply(elt_multiply(v, sigma_val) - diff,
                                      cdf_term_2_phi)),
      cdf_n);
 
  auto log_cdf_term_1 = std_normal_lcdf_scaled_impl(scaled_diff);
  auto dlog_cdf_term_1 = std_normal_lcdf_dscaled_impl(scaled_diff);
  auto log_cdf_term_2_phi = std_normal_lcdf_scaled_impl(scaled_diff_diff);
  auto dlog_cdf_term_2_phi = std_normal_lcdf_dscaled_impl(scaled_diff_diff);
  auto log_cdf_term_2 = log_exp_term + log_cdf_term_2_phi;
  auto log_cdf_n = log_diff_exp(log_cdf_term_1, log_cdf_term_2);
  auto cdf_term_1_weight = exp(log_cdf_term_1 - log_cdf_n);
  auto cdf_term_2_weight = exp(log_cdf_term_2 - log_cdf_n);
  auto scaled_diff_deriv
      = elt_multiply(dlog_cdf_term_1, sigma_inv * INV_SQRT_TWO);
  auto scaled_diff_diff_deriv
      = elt_multiply(dlog_cdf_term_2_phi, sigma_inv * INV_SQRT_TWO);
  auto stable_y_deriv
      = elt_multiply(cdf_term_1_weight, scaled_diff_deriv)
        - elt_multiply(cdf_term_2_weight, -lambda_val + scaled_diff_diff_deriv);
  auto stable_mu_deriv = -stable_y_deriv;
  auto stable_sigma_deriv
      = elt_multiply(cdf_term_1_weight,
                     -elt_multiply(dlog_cdf_term_1,
                                   elt_multiply(scaled_diff, sigma_inv)))
        - elt_multiply(
            cdf_term_2_weight,
            elt_multiply(lambda_val, v)
                - elt_multiply(
                    dlog_cdf_term_2_phi,
                    elt_multiply(scaled_diff + v * INV_SQRT_TWO, sigma_inv)));
  auto stable_lambda_deriv = -elt_multiply(
      cdf_term_2_weight,
      elt_multiply(v, sigma_val) - diff
          - elt_multiply(dlog_cdf_term_2_phi, sigma_val * INV_SQRT_TWO));
  auto cdf_log_expr
      = colwise_sum(select(use_stable, log_cdf_n, direct_cdf_log));
  auto y_deriv = select(use_stable, stable_y_deriv, direct_y_deriv);
  auto mu_deriv = select(use_stable, stable_mu_deriv, direct_mu_deriv);
  auto sigma_deriv = select(use_stable, stable_sigma_deriv, direct_sigma_deriv);
  auto lambda_deriv
      = select(use_stable, stable_lambda_deriv, direct_lambda_deriv);
 
  matrix_cl<char> any_y_neg_inf_cl;
  matrix_cl<char> any_y_pos_inf_cl;
  matrix_cl<double> cdf_log_cl;
  matrix_cl<double> mu_deriv_cl;
  matrix_cl<double> y_deriv_cl;
  matrix_cl<double> sigma_deriv_cl;
  matrix_cl<double> lambda_deriv_cl;
 
  results(check_y_not_nan, check_mu_finite, check_sigma_positive_finite,
          check_lambda_positive_finite, any_y_neg_inf_cl, any_y_pos_inf_cl,
          cdf_log_cl, y_deriv_cl, mu_deriv_cl, sigma_deriv_cl, lambda_deriv_cl)
      = expressions(y_not_nan_expr, mu_finite_expr, sigma_positive_finite_expr,
                    lambda_positive_finite_expr, any_y_neg_inf, any_y_pos_inf,
                    cdf_log_expr, calc_if<is_autodiff_v<T_y_cl>>(y_deriv),
                    calc_if<is_autodiff_v<T_loc_cl>>(mu_deriv),
                    calc_if<is_autodiff_v<T_scale_cl>>(sigma_deriv),
                    calc_if<is_autodiff_v<T_inv_scale_cl>>(lambda_deriv));
 
  if (from_matrix_cl(any_y_pos_inf_cl).maxCoeff()) {
    return 0.0;
  }
 
  if (from_matrix_cl(any_y_neg_inf_cl).maxCoeff()) {
    return NEGATIVE_INFTY;
  }
 
  T_partials_return cdf_log = (from_matrix_cl(cdf_log_cl)).sum();
 
  auto ops_partials
      = make_partials_propagator(y_col, mu_col, sigma_col, lambda_col);
 
  if constexpr (is_autodiff_v<T_y_cl>) {
    partials<0>(ops_partials) = std::move(y_deriv_cl);
  }
  if constexpr (is_autodiff_v<T_loc_cl>) {
    partials<1>(ops_partials) = std::move(mu_deriv_cl);
  }
  if constexpr (is_autodiff_v<T_scale_cl>) {
    partials<2>(ops_partials) = std::move(sigma_deriv_cl);
  }
  if constexpr (is_autodiff_v<T_inv_scale_cl>) {
    partials<3>(ops_partials) = std::move(lambda_deriv_cl);
  }
  return ops_partials.build(cdf_log);
}
 
}  // namespace math
}  // namespace stan
#endif
#endif