#ifndef STAN_MATH_PRIM_MAT_FUN_SOFTMAX_HPP
#define STAN_MATH_PRIM_MAT_FUN_SOFTMAX_HPP

#include <stan/math/prim/arr/err/check_nonzero_size.hpp>
#include <stan/math/prim/mat/fun/Eigen.hpp>
#include <cmath>

namespace stan {
namespace math {

/**
 * Return the softmax of the specified vector.
 *
 * <p>
 * \f$
 * \mbox{softmax}(y)
 * = \frac{\exp(y)}
 * {\sum_{k=1}^K \exp(y_k)},
 * \f$
 *
 * <p>The entries in the Jacobian of the softmax function are given by
 * \f$
 * \begin{array}{l}
 * \displaystyle
 * \frac{\partial}{\partial y_m} \mbox{softmax}(y)[k]
 * \\[8pt]
 * \displaystyle
 * \mbox{ } \ \ \ = \left\{
 * \begin{array}{ll}
 * \mbox{softmax}(y)[k] - \mbox{softmax}(y)[k] \times \mbox{softmax}(y)[m]
 * & \mbox{ if } m = k, \mbox{ and}
 * \\[6pt]
 * \mbox{softmax}(y)[k] * \mbox{softmax}(y)[m]
 * & \mbox{ if } m \neq k.
 * \end{array}
 * \right.
 * \end{array}
 * \f$
 *
 * @tparam T Scalar type of values in vector.
 * @param[in] v Vector to transform.
 * @return Unit simplex result of the softmax transform of the vector.
 */
template <typename T>
inline Eigen::Matrix<T, Eigen::Dynamic, 1> softmax(
    const Eigen::Matrix<T, Eigen::Dynamic, 1>& v) {
  using std::exp;
  check_nonzero_size("softmax", "v", v);
  Eigen::Matrix<T, Eigen::Dynamic, 1> theta(v.size());
  T sum(0.0);
  T max_v = v.maxCoeff();
  for (int i = 0; i < v.size(); ++i) {
    theta(i) = exp(v(i) - max_v);  // extra work for (v[i] == max_v)
    sum += theta(i);               // extra work vs. sum() w. auto-diff
  }
  for (int i = 0; i < v.size(); ++i)
    theta(i) /= sum;
  return theta;
}

}  // namespace math
}  // namespace stan
#endif
