exp_mod_normal_cdf.hpp

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#ifndef STAN_MATH_OPENCL_PRIM_DOUBLE_EXP_MOD_NORMAL_CDF_HPP
#define STAN_MATH_OPENCL_PRIM_DOUBLE_EXP_MOD_NORMAL_CDF_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/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_cdf(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_cdf(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 1.0;
  }
 
  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 inv_sigma = elt_divide(1.0, sigma_val);
  auto diff = y_val - mu_val;
  auto v = elt_multiply(lambda_val, sigma_val);
  auto scaled_diff = elt_multiply(diff, inv_sigma * INV_SQRT_TWO);
  auto scaled_diff_diff = scaled_diff - v * INV_SQRT_TWO;
  auto erf_calc = 0.5 * (1.0 + erf(scaled_diff_diff));
  auto exp_term = exp(0.5 * square(v) - elt_multiply(lambda_val, diff));
  auto cdf_n = 0.5 + 0.5 * erf(scaled_diff) - elt_multiply(exp_term, erf_calc);
  auto cdf_expr = colwise_prod(cdf_n);
 
  auto exp_term_2 = exp(-square(scaled_diff_diff));
  auto deriv_1 = elt_multiply(elt_multiply(lambda_val, exp_term), erf_calc);
  auto deriv_2 = INV_SQRT_TWO_PI
                 * elt_multiply(elt_multiply(exp_term, exp_term_2), inv_sigma);
  auto deriv_3
      = INV_SQRT_TWO_PI * elt_multiply(exp(-square(scaled_diff)), inv_sigma);
  auto mu_deriv1 = elt_divide(deriv_2 - deriv_1 - deriv_3, cdf_n);
  auto sigma_deriv1 = elt_divide(
      -elt_multiply(deriv_1 - deriv_2, v)
          + elt_multiply(deriv_3 - deriv_2, scaled_diff) * SQRT_TWO,
      cdf_n);
  auto lambda_deriv1 = 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, erf_calc)),
      cdf_n);
 
  matrix_cl<char> any_y_neg_inf_cl;
  matrix_cl<double> cdf_cl;
  matrix_cl<double> y_deriv_cl;
  matrix_cl<double> mu_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, cdf_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, cdf_expr,
                    calc_if<is_any_autodiff_v<T_y_cl, T_loc_cl, T_scale_cl,
                                              T_inv_scale_cl>>(cdf_n),
                    calc_if<is_any_autodiff_v<T_y_cl, T_loc_cl>>(mu_deriv1),
                    calc_if<is_autodiff_v<T_scale_cl>>(sigma_deriv1),
                    calc_if<is_autodiff_v<T_inv_scale_cl>>(lambda_deriv1));
 
  if (from_matrix_cl(any_y_neg_inf_cl).maxCoeff()) {
    return 0.0;
  }
 
  T_partials_return cdf = (from_matrix_cl(cdf_cl)).prod();
 
  auto ops_partials
      = make_partials_propagator(y_col, mu_col, sigma_col, lambda_col);
  if constexpr (is_any_autodiff_v<T_y_cl, T_loc_cl, T_scale_cl,
                                  T_inv_scale_cl>) {
    auto mu_deriv = elt_multiply(
        static_select<is_constant_all<T_y_cl, T_loc_cl>::value>(0, mu_deriv_cl),
        cdf);
    auto y_deriv = -mu_deriv;
    auto sigma_deriv = elt_multiply(
        static_select<is_constant_v<T_scale_cl>>(0, sigma_deriv_cl), cdf);
    auto lambda_deriv = elt_multiply(
        static_select<is_constant_v<T_inv_scale_cl>>(0, lambda_deriv_cl), cdf);
 
    results(y_deriv_cl, mu_deriv_cl, sigma_deriv_cl, lambda_deriv_cl)
        = expressions(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 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);
}
 
}  // namespace math
}  // namespace stan
#endif
#endif