poisson_log_glm_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_POISSON_LOG_GLM_LPMF_HPP
#define STAN_MATH_PRIM_PROB_POISSON_LOG_GLM_LPMF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/multiply.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/constants.hpp>
#include <stan/math/prim/fun/dot_product.hpp>
#include <stan/math/prim/fun/exp.hpp>
#include <stan/math/prim/fun/isfinite.hpp>
#include <stan/math/prim/fun/lgamma.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 {
 
template <bool propto, typename T_y, typename T_x, typename T_alpha,
          typename T_beta, require_matrix_t<T_x>* = nullptr>
inline return_type_t<T_x, T_alpha, T_beta> poisson_log_glm_lpmf(
    const T_y& y, const T_x& x, const T_alpha& alpha, const T_beta& beta) {
  using Eigen::Array;
  using Eigen::Dynamic;
  using Eigen::Matrix;
  using std::exp;
  using std::isfinite;
  constexpr int T_x_rows = T_x::RowsAtCompileTime;
  using T_partials_return = partials_return_t<T_y, T_x, T_alpha, T_beta>;
  using T_theta_tmp =
      typename std::conditional_t<T_x_rows == 1, T_partials_return,
                                  Array<T_partials_return, Dynamic, 1>>;
  using T_x_ref = ref_type_if_not_constant_t<T_x>;
  using T_alpha_ref = ref_type_if_not_constant_t<T_alpha>;
  using T_beta_ref = ref_type_if_not_constant_t<T_beta>;
 
  const size_t N_instances = T_x_rows == 1 ? stan::math::size(y) : x.rows();
  const size_t N_attributes = x.cols();
 
  static constexpr const char* function = "poisson_log_glm_lpmf";
  check_consistent_size(function, "Vector of dependent variables", y,
                        N_instances);
  check_consistent_size(function, "Weight vector", beta, N_attributes);
  check_consistent_size(function, "Vector of intercepts", alpha, N_instances);
  const auto& y_ref = to_ref(y);
  check_nonnegative(function, "Vector of dependent variables", y_ref);
 
  if (size_zero(y)) {
    return 0;
  }
  if constexpr (!include_summand<propto, T_x, T_alpha, T_beta>::value) {
    return 0;
  }
 
  T_x_ref x_ref = x;
  T_alpha_ref alpha_ref = alpha;
  T_beta_ref beta_ref = beta;
 
  const auto& y_val = value_of(y_ref);
  const auto& x_val = to_ref_if<is_autodiff_v<T_beta>>(value_of(x_ref));
  const auto& alpha_val = value_of(alpha_ref);
  const auto& beta_val = value_of(beta_ref);
 
  const auto& y_val_vec = to_ref(as_column_vector_or_scalar(y_val));
  const auto& alpha_val_vec = as_column_vector_or_scalar(alpha_val);
  const auto& beta_val_vec
      = to_ref_if<is_autodiff_v<T_x>>(as_column_vector_or_scalar(beta_val));
 
  Array<T_partials_return, Dynamic, 1> theta(N_instances);
  if constexpr (T_x_rows == 1) {
    T_theta_tmp theta_tmp = (x_val * beta_val_vec).coeff(0, 0);
    theta = theta_tmp + as_array_or_scalar(alpha_val_vec);
  } else {
    theta = multiply(x_val, beta_val_vec);
    theta += as_array_or_scalar(alpha_val_vec);
  }
 
  Matrix<T_partials_return, Dynamic, 1> theta_derivative
      = as_array_or_scalar(y_val_vec) - exp(theta.array());
  T_partials_return theta_derivative_sum = sum(theta_derivative);
  if (!isfinite(theta_derivative_sum)) {
    check_finite(function, "Weight vector", beta);
    check_finite(function, "Intercept", alpha);
    check_finite(function, "Matrix of independent variables", theta);
  }
 
  T_partials_return logp(0);
  if constexpr (include_summand<propto>::value) {
    logp -= sum(lgamma(as_array_or_scalar(y_val_vec) + 1));
  }
 
  logp += sum(as_array_or_scalar(y_val_vec) * theta.array()
              - exp(theta.array()));
 
  auto ops_partials = make_partials_propagator(x_ref, alpha_ref, beta_ref);
  // Compute the necessary derivatives.
  if constexpr (is_autodiff_v<T_beta>) {
    if constexpr (T_x_rows == 1) {
      edge<2>(ops_partials).partials_ = theta_derivative.sum() * x_val;
    } else if constexpr (T_x::ColsAtCompileTime == 1) {
      partials<2>(ops_partials)[0] = dot_product(x_val, theta_derivative);
    } else {
      partials<2>(ops_partials) = multiply(x_val.transpose(), theta_derivative);
    }
  }
  if constexpr (is_autodiff_v<T_x>) {
    if constexpr (T_x_rows == 1) {
      edge<0>(ops_partials).partials_ = beta_val_vec * theta_derivative.sum();
    } else {
      edge<0>(ops_partials).partials_
          = (beta_val_vec * theta_derivative.transpose()).transpose();
    }
  }
  if constexpr (is_autodiff_v<T_alpha>) {
    if constexpr (is_vector<T_alpha>::value) {
      partials<1>(ops_partials) = theta_derivative;
    } else {
      partials<1>(ops_partials)[0] = theta_derivative_sum;
    }
  }
  return ops_partials.build(logp);
}
 
template <typename T_y, typename T_x, typename T_alpha, typename T_beta>
inline return_type_t<T_x, T_alpha, T_beta> poisson_log_glm_lpmf(
    const T_y& y, const T_x& x, const T_alpha& alpha, const T_beta& beta) {
  return poisson_log_glm_lpmf<false>(y, x, alpha, beta);
}
 
}  // namespace math
}  // namespace stan
#endif