log_sum_exp() [4/13]

template<typename T , require_container_st< is_fvar, T > * = nullptr>

auto stan::math::log_sum_exp ( const T &  x )

inline

Return the log of the sum of the exponentiated values of the specified matrix of values.

Returns the log sum of exponentials.

The matrix may be a full matrix, a vector, a row vector, or a container of these.

The function is defined as follows to prevent overflow in exponential calculations.

\(\log \sum_{n=1}^N \exp(x_n) = \max(x) + \log \sum_{n=1}^N \exp(x_n - \max(x))\).

Template Parameters

T	Type of input vector or matrix.

Parameters

[in]

x

Matrix of specified values.

Returns

The log of the sum of the exponentiated vector values.

The matrix may be a full matrix, a vector, a row vector, or a container of these.

The function is defined as follows to prevent overflow in exponential calculations.

\(\log \sum_{n=1}^N \exp(x_n) = \max(x) + \log \sum_{n=1}^N \exp(x_n - \max(x))\).

Template Parameters

T	type of input vector or matrix

Parameters

[in]

x

matrix of specified values

Returns

The log of the sum of the exponentiated vector values.

Template Parameters

T	Type of input vector or matrix.

Parameters

x

matrix

Definition at line 55 of file log_sum_exp.hpp.