log_sum_exp.hpp

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#ifndef STAN_MATH_PRIM_FUN_LOG_SUM_EXP_HPP
#define STAN_MATH_PRIM_FUN_LOG_SUM_EXP_HPP
 
#include <stan/math/prim/meta.hpp>
#include <stan/math/prim/fun/constants.hpp>
#include <stan/math/prim/fun/Eigen.hpp>
#include <stan/math/prim/fun/log1p_exp.hpp>
#include <stan/math/prim/functor/apply_scalar_binary.hpp>
#include <cmath>
#include <vector>
 
namespace stan {
namespace math {
 
template <typename T1, typename T2, require_all_not_st_var<T1, T2>* = nullptr,
          require_all_stan_scalar_t<T1, T2>* = nullptr>
inline return_type_t<T1, T2> log_sum_exp(const T2& a, const T1& b) {
  if (a == NEGATIVE_INFTY) {
    return b;
  }
  if (a == INFTY && b == INFTY) {
    return INFTY;
  }
  if (a > b) {
    return a + log1p_exp(b - a);
  }
  return b + log1p_exp(a - b);
}
 
template <typename T, require_container_st<std::is_arithmetic, T>* = nullptr>
inline auto log_sum_exp(const T& x) {
  return apply_vector_unary<T>::reduce(x, [&](const auto& v) {
    if (v.size() == 0) {
      return NEGATIVE_INFTY;
    }
    const auto& v_ref = to_ref(v);
    const double max = v_ref.maxCoeff();
    if (!std::isfinite(max)) {
      return max;
    }
    return max + std::log((v_ref.array() - max).exp().sum());
  });
}
 
template <typename T1, typename T2, require_any_container_t<T1, T2>* = nullptr>
inline auto log_sum_exp(const T1& a, const T2& b) {
  return apply_scalar_binary(
      a, b, [](const auto& c, const auto& d) { return log_sum_exp(c, d); });
}
 
}  // namespace math
}  // namespace stan
 
#endif