log_softmax() [5/5]

template<typename Container , require_st_arithmetic< Container > * = nullptr, require_container_t< Container > * = nullptr, require_not_t< bool_constant< is_eigen< std::decay_t< Container > >::value &&!is_eigen_vector< std::decay_t< Container > >::value > > * = nullptr>

auto stan::math::log_softmax ( Container &&  x )

inline

Return the natural logarithm of the softmax of the specified vector, or of each vector in a container.

\( \log \mbox{softmax}(y) \ = \ y - \log \sum_{k=1}^K \exp(y_k) \ = \ y - \mbox{log\_sum\_exp}(y). \)

For the log softmax function, the entries in the Jacobian are \( \frac{\partial}{\partial y_m} \log\mbox{softmax}(y)[k] = \left\{ \begin{array}{ll} 1 - \mbox{softmax}(y)[m] & \mbox{ if } m = k, \mbox{ and} \\[6pt] -\mbox{softmax}(y)[m] & \mbox{ if } m \neq k. \end{array} \right. \)

Template Parameters

Container

type of input: an Eigen vector, std::vector of doubles, or nested container whose scalar type is arithmetic

Parameters

[in]

x

vector or container of vectors to transform

Returns

log softmax of the input, preserving the container structure

Exceptions

std::domain_error

if any input vector is empty

Definition at line 49 of file log_softmax.hpp.