72 lines
2.4 KiB
Markdown
72 lines
2.4 KiB
Markdown
|
# 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](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/sytrf.html), [HETRF](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/hetrf.html).
|
|||
|
|
|
|||
|
|
Computing for type matrix<double>
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
bool matrix::FactorizationLDL(
|
|||
|
|
matrix& L, // lower or upper triangular matrix
|
|||
|
|
matrix& D // diagonal matrix D
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
Computing for type matrix<float>
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
bool matrix::FactorizationLDL(
|
|||
|
|
matrixf& L, // lower or upper triangular matrix
|
|||
|
|
matrixf& D // diagonal matrix D
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
Computing for type matrix<complex>
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
bool matrix::FactorizationLDL(
|
|||
|
|
matrixc& L, // lower or upper triangular matrix
|
|||
|
|
matrixc& D // diagonal matrix D
|
|||
|
|
);
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
|
|||
|
|
Computing for type matrix<complexf>
|
|||
|
|
|
|||
|
|
```
|
|||
|
|
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](/en/docs/constants/errorswarnings/errorcodes).
|
|||
|
|
|
|||
|
|
Note
|
|||
|
|
|
|||
|
|
The input can be a symmetric (Hermitian), [upper triangular](/en/docs/matrix/matrix_manipulations/matrix_triu) or [lower triangular](/en/docs/matrix/matrix_manipulations/matrix_tril) 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.
|