2.4 KiB
FactorizationLDL
Computes the factorization of a real symmetric or complex Hermitian matrix A using the Bunch-Kaufman diagonal pivoting method. The form of the factorization is:
A = L * D * L**T in case of lower triangular or symmetric matrix A
or
A = U * D * U**T in case of upper triangular matrix A
where L is lower triangular with unit diagonal elements, U is upper triangular with unit diagonal elements. D is a symmetric block-diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks. LAPACK functions SYTRF, HETRF.
Computing for type matrix
bool matrix::FactorizationLDL(
matrix& L, // lower or upper triangular matrix
matrix& D // diagonal matrix D
);
Computing for type matrix
bool matrix::FactorizationLDL(
matrixf& L, // lower or upper triangular matrix
matrixf& D // diagonal matrix D
);
Computing for type matrix
bool matrix::FactorizationLDL(
matrixc& L, // lower or upper triangular matrix
matrixc& D // diagonal matrix D
);
Computing for type matrix
bool matrix::FactorizationLDL(
matrixcf& L, // lower or upper triangular matrix
matrixcf& D // diagonal matrix D
);
Parameters
L
[out] Lower or upper triangular matrix with unit diagonal elements.
D
[out] Symmetric block-diagonal matrix D.
Return Value
Return true if successful, otherwise false in case of an error.
Note
The input can be a symmetric (Hermitian), upper triangular or lower triangular matrix. Triangular matrices are assumed to be symmetric (Hermitian conjugated).
As a result of the computations, the lower-triangular matrix L (or the upper-triangular matrix U) may become permuted.