lognormal_lpdf.hpp

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#ifndef STAN_MATH_PRIM_PROB_LOGNORMAL_LPDF_HPP
#define STAN_MATH_PRIM_PROB_LOGNORMAL_LPDF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/as_column_vector_or_scalar.hpp>
#include <stan/math/prim/fun/as_array_or_scalar.hpp>
#include <stan/math/prim/fun/as_value_column_array_or_scalar.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/inv.hpp>
#include <stan/math/prim/fun/log.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/promote_scalar.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/value_of.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
#include <cmath>
 
namespace stan {
namespace math {
 
// LogNormal(y|mu, sigma)  [y >= 0;  sigma > 0]
template <bool propto, typename T_y, typename T_loc, typename T_scale,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_y, T_loc, T_scale>* = nullptr>
inline return_type_t<T_y, T_loc, T_scale> lognormal_lpdf(const T_y& y,
                                                         const T_loc& mu,
                                                         const T_scale& sigma) {
  using T_partials_return = partials_return_t<T_y, T_loc, T_scale>;
  using T_y_ref = ref_type_if_not_constant_t<T_y>;
  using T_mu_ref = ref_type_if_not_constant_t<T_loc>;
  using T_sigma_ref = ref_type_if_not_constant_t<T_scale>;
  static constexpr const char* function = "lognormal_lpdf";
  check_consistent_sizes(function, "Random variable", y, "Location parameter",
                         mu, "Scale parameter", sigma);
 
  T_y_ref y_ref = y;
  T_mu_ref mu_ref = mu;
  T_sigma_ref sigma_ref = sigma;
 
  decltype(auto) y_val = to_ref(as_value_column_array_or_scalar(y_ref));
  decltype(auto) mu_val = to_ref(as_value_column_array_or_scalar(mu_ref));
  decltype(auto) sigma_val = to_ref(as_value_column_array_or_scalar(sigma_ref));
 
  check_nonnegative(function, "Random variable", y_val);
  check_finite(function, "Location parameter", mu_val);
  check_positive_finite(function, "Scale parameter", sigma_val);
 
  if (size_zero(y, mu, sigma)) {
    return 0;
  }
  if constexpr (!include_summand<propto, T_y, T_loc, T_scale>::value) {
    return 0;
  }
 
  auto ops_partials = make_partials_propagator(y_ref, mu_ref, sigma_ref);
 
  if (sum(promote_scalar<int>(y_val == 0))) {
    return ops_partials.build(LOG_ZERO);
  }
 
  const auto& inv_sigma = to_ref_if<is_autodiff_v<T_scale>>(inv(sigma_val));
  const auto& inv_sigma_sq
      = to_ref_if<is_any_autodiff_v<T_y, T_loc, T_scale>>(square(inv_sigma));
  const auto& log_y
      = to_ref_if<include_summand<propto, T_y>::value>(log(y_val));
  const auto& logy_m_mu = to_ref(log_y - mu_val);
 
  size_t N = max_size(y, mu, sigma);
  T_partials_return logp
      = N * NEG_LOG_SQRT_TWO_PI - 0.5 * sum(square(logy_m_mu) * inv_sigma_sq);
  if constexpr (include_summand<propto, T_scale>::value) {
    logp -= sum(log(sigma_val)) * N / math::size(sigma);
  }
  if constexpr (include_summand<propto, T_y>::value) {
    logp -= sum(log_y) * N / math::size(y);
  }
 
  if constexpr (is_any_autodiff_v<T_y, T_loc, T_scale>) {
    const auto& logy_m_mu_div_sigma = to_ref_if<
        is_autodiff_v<
            T_y> + is_autodiff_v<T_loc> + is_autodiff_v<T_scale> >= 2>(
        logy_m_mu * inv_sigma_sq);
    if constexpr (is_autodiff_v<T_y>) {
      partials<0>(ops_partials) = -(1 + logy_m_mu_div_sigma) / y_val;
    }
    if constexpr (is_autodiff_v<T_loc>) {
      partials<1>(ops_partials) = logy_m_mu_div_sigma;
    }
    if constexpr (is_autodiff_v<T_scale>) {
      edge<2>(ops_partials).partials_
          = (logy_m_mu_div_sigma * logy_m_mu - 1) * inv_sigma;
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_loc, typename T_scale>
inline return_type_t<T_y, T_loc, T_scale> lognormal_lpdf(const T_y& y,
                                                         const T_loc& mu,
                                                         const T_scale& sigma) {
  return lognormal_lpdf<false>(y, mu, sigma);
}
 
}  // namespace math
}  // namespace stan
#endif