Stan Math Library  2.20.0
reverse mode automatic differentiation
trace_gen_inv_quad_form_ldlt.hpp
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1 #ifndef STAN_MATH_PRIM_MAT_FUN_TRACE_GEN_INV_QUAD_FORM_LDLT_HPP
2 #define STAN_MATH_PRIM_MAT_FUN_TRACE_GEN_INV_QUAD_FORM_LDLT_HPP
3 
13 
14 namespace stan {
15 namespace math {
16 
17 /*
18  * Compute the trace of an inverse quadratic form. I.E., this computes
19  * trace(D B^T A^-1 B)
20  * where D is a square matrix and the LDLT_factor of A is provided.
21  */
22 template <typename T1, typename T2, typename T3, int R1, int C1, int R2, int C2,
23  int R3, int C3>
24 inline typename std::enable_if<
27  typename boost::math::tools::promote_args<T1, T2, T3>::type>::type
28 trace_gen_inv_quad_form_ldlt(const Eigen::Matrix<T1, R1, C1> &D,
29  const LDLT_factor<T2, R2, C2> &A,
30  const Eigen::Matrix<T3, R3, C3> &B) {
31  check_square("trace_gen_inv_quad_form_ldlt", "D", D);
32  check_multiplicable("trace_gen_inv_quad_form_ldlt", "A", A, "B", B);
33  check_multiplicable("trace_gen_inv_quad_form_ldlt", "B", B, "D", D);
34 
35  return trace(multiply(multiply(D, transpose(B)), mdivide_left_ldlt(A, B)));
36 }
37 
38 } // namespace math
39 } // namespace stan
40 #endif
Defines a public enum named value which is defined to be false as the primitive scalar types cannot b...
Definition: is_var.hpp:10
Eigen::Matrix< fvar< T2 >, R1, C2 > mdivide_left_ldlt(const LDLT_factor< double, R1, C1 > &A, const Eigen::Matrix< fvar< T2 >, R2, C2 > &b)
Returns the solution of the system Ax=b given an LDLT_factor of A.
void check_square(const char *function, const char *name, const matrix_cl &y)
Check if the matrix_cl is square.
std::enable_if< !stan::is_var< T1 >::value &&!stan::is_var< T2 >::value &&!stan::is_var< T3 >::value, typename boost::math::tools::promote_args< T1, T2, T3 >::type >::type trace_gen_inv_quad_form_ldlt(const Eigen::Matrix< T1, R1, C1 > &D, const LDLT_factor< T2, R2, C2 > &A, const Eigen::Matrix< T3, R3, C3 > &B)
Eigen::Matrix< fvar< T >, R1, C1 > multiply(const Eigen::Matrix< fvar< T >, R1, C1 > &m, const fvar< T > &c)
Definition: multiply.hpp:14
void check_multiplicable(const char *function, const char *name1, const T1 &y1, const char *name2, const T2 &y2)
Check if the matrices can be multiplied.
matrix_cl transpose(const matrix_cl &src)
Takes the transpose of the matrix on the OpenCL device.
Definition: transpose.hpp:20
T trace(const Eigen::Matrix< T, Eigen::Dynamic, Eigen::Dynamic > &m)
Returns the trace of the specified matrix.
Definition: trace.hpp:19

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