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Référence MQL5Méthodes sur les Matrices et les VecteursOpenBLASFactorizationsFactorizationLDL 

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**T * D * U 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<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.

Note

The input can be a symmetric (Hermitian), upper triangular or lower triangular matrix. Triangular matrices are assumed to be symmetric (Hermitian conjugated).