poisson_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_POISSON_LPMF_HPP
#define STAN_MATH_PRIM_PROB_POISSON_LPMF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.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/lgamma.hpp>
#include <stan/math/prim/fun/lmultiply.hpp>
#include <stan/math/prim/fun/max_size.hpp>
#include <stan/math/prim/fun/promote_scalar.hpp>
#include <stan/math/prim/fun/scalar_seq_view.hpp>
#include <stan/math/prim/fun/size.hpp>
#include <stan/math/prim/fun/size_zero.hpp>
#include <stan/math/prim/fun/sum.hpp>
#include <stan/math/prim/functor/partials_propagator.hpp>
 
namespace stan {
namespace math {
 
// Poisson(n|lambda)  [lambda > 0;  n >= 0]
template <bool propto, typename T_n, typename T_rate,
          require_all_not_nonscalar_prim_or_rev_kernel_expression_t<
              T_n, T_rate>* = nullptr>
inline return_type_t<T_rate> poisson_lpmf(const T_n& n, const T_rate& lambda) {
  using T_partials_return = partials_return_t<T_n, T_rate>;
  using T_n_ref = ref_type_if_not_constant_t<T_n>;
  using T_lambda_ref = ref_type_if_not_constant_t<T_rate>;
  using std::isinf;
  static constexpr const char* function = "poisson_lpmf";
  check_consistent_sizes(function, "Random variable", n, "Rate parameter",
                         lambda);
 
  T_n_ref n_ref = n;
  T_lambda_ref lambda_ref = lambda;
 
  decltype(auto) n_val = to_ref(as_value_column_array_or_scalar(n_ref));
  decltype(auto) lambda_val
      = to_ref(as_value_column_array_or_scalar(lambda_ref));
 
  check_nonnegative(function, "Random variable", n_val);
  check_nonnegative(function, "Rate parameter", lambda_val);
 
  if (size_zero(n, lambda)) {
    return 0.0;
  }
  if constexpr (!include_summand<propto, T_rate>::value) {
    return 0.0;
  }
  if (sum(promote_scalar<int>(isinf(lambda_val)))) {
    return LOG_ZERO;
  }
 
  size_t N = max_size(n, lambda);
  scalar_seq_view<decltype(n_val)> n_vec(n_val);
  scalar_seq_view<decltype(lambda_val)> lambda_vec(lambda_val);
  for (size_t i = 0; i < N; i++) {
    if (lambda_vec[i] == 0 && n_vec[i] != 0) {
      return LOG_ZERO;
    }
  }
 
  auto ops_partials = make_partials_propagator(lambda_ref);
 
  T_partials_return logp = stan::math::sum(lmultiply(n_val, lambda_val));
  if constexpr (include_summand<propto, T_rate>::value) {
    logp -= sum(lambda_val) * N / math::size(lambda);
  }
  if constexpr (include_summand<propto>::value) {
    logp -= sum(lgamma(n_val + 1.0)) * N / math::size(n);
  }
 
  if constexpr (is_autodiff_v<T_rate>) {
    partials<0>(ops_partials) = n_val / lambda_val - 1.0;
  }
 
  return ops_partials.build(logp);
}
 
template <typename T_n, typename T_rate>
inline return_type_t<T_rate> poisson_lpmf(const T_n& n, const T_rate& lambda) {
  return poisson_lpmf<false>(n, lambda);
}
 
}  // namespace math
}  // namespace stan
#endif