multinomial_logit_lpmf.hpp

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#ifndef STAN_MATH_PRIM_PROB_MULTINOMIAL_LOGIT_LPMF_HPP
#define STAN_MATH_PRIM_PROB_MULTINOMIAL_LOGIT_LPMF_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/err.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/lgamma.hpp>
#include <stan/math/prim/fun/log_sum_exp.hpp>
#include <stan/math/prim/fun/to_ref.hpp>
#include <stan/math/prim/fun/as_array_or_scalar.hpp>
#include <cmath>
#include <vector>
 
namespace stan {
namespace math {
 
template <bool propto, typename T_beta, typename T_prob = scalar_type_t<T_beta>,
          require_eigen_col_vector_t<T_beta>* = nullptr>
inline return_type_t<T_prob> multinomial_logit_lpmf(const std::vector<int>& ns,
                                                    const T_beta& beta) {
  static constexpr const char* function = "multinomial_logit_lpmf";
  check_size_match(function, "Size of number of trials variable", ns.size(),
                   "rows of log-probabilities parameter", beta.rows());
  check_nonnegative(function, "Number of trials variable", ns);
  const auto& beta_ref = to_ref(beta);
 
  // An empty beta forces ns to be empty (checked above)
  if (beta_ref.size() == 0) {
    return 0.0;
  }
 
  // Autodiff args must be finite data may be +/-inf
  if constexpr (is_constant_v<T_beta>) {
    // Data Case: Throws in nan and all -inf case
    check_not_nan(function, "log-probabilities parameter", beta_ref);
    check_greater(function, "log-probabilities parameter", beta_ref.maxCoeff(),
                  NEGATIVE_INFTY);
  } else {
    // Autodiff Case: Throws in non-finite case
    check_finite(function, "log-probabilities parameter", beta_ref);
  }
 
  return_type_t<T_prob> lp(0.0);
 
  decltype(auto) ns_map = as_array_or_scalar(ns);
 
  if constexpr (include_summand<propto>::value) {
    lp += lgamma(1 + ns_map.sum()) - lgamma(1 + ns_map).sum();
  }
 
  if constexpr (include_summand<propto, T_prob>::value) {
    // softmax is NaN with +inf, so split probability evenly over the
    // +inf entries and give every other entry zero probability
    if constexpr (is_constant_v<T_beta>) {
      int num_infty = (beta_ref.array() == INFTY).count();
      if (num_infty > 0) {
        for (unsigned int i = 0; i < ns.size(); ++i) {
          if (ns[i] != 0) {
            if (beta_ref.coeff(i) != INFTY) {
              return NEGATIVE_INFTY;
            }
            lp -= ns[i] * std::log(num_infty);
          }
        }
        return lp;
      }
    }
 
    T_prob alpha = log_sum_exp(beta_ref);
    for (unsigned int i = 0; i < ns.size(); ++i) {
      if (ns[i] != 0) {
        lp += ns[i] * (beta_ref.coeff(i) - alpha);
      }
    }
  }
 
  return lp;
}
 
template <typename T_beta, require_eigen_col_vector_t<T_beta>* = nullptr>
inline return_type_t<T_beta> multinomial_logit_lpmf(const std::vector<int>& ns,
                                                    const T_beta& beta) {
  return multinomial_logit_lpmf<false>(ns, beta);
}
 
}  // namespace math
}  // namespace stan
#endif