trace_dot() [3/3]

template<typename Mat1 , typename Mat2 , require_all_matrix_t< Mat1, Mat2 > * = nullptr, require_any_rev_matrix_t< Mat1, Mat2 > * = nullptr>

var stan::math::trace_dot ( Mat1 &&  A, Mat2 &&  B  )

inline

Compute the trace of the product of two matrices with autodiff support.

\( \text{tr}(A \cdot B) = \sum_{i,j} A_{ij} B_{ji} \)

The gradients are: \( \frac{\partial}{\partial A} \text{tr}(A B) = B^T \), \( \frac{\partial}{\partial B} \text{tr}(A B) = A^T \).

Template Parameters

Mat1	A type either inheriting from Eigen::DenseBase or a var_value with an inner type inheriting from Eigen::DenseBase
Mat2	A type either inheriting from Eigen::DenseBase or a var_value with an inner type inheriting from Eigen::DenseBase

Parameters

A	first matrix (m x n)
B	second matrix (n x m)

Returns

trace of A * B

Exceptions

std::invalid_argument

if A and B have incompatible dimensions

Definition at line 36 of file trace_dot.hpp.