72 lines
2.7 KiB
Markdown
72 lines
2.7 KiB
Markdown
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# FactorizationLDLRaw
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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:
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A = L * D * L**T in case of lower triangular or symmetric matrix A
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or
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A = U**T * D * U in case of upper triangular matrix A
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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).
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Computing for type matrix<double>
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```
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bool matrix::FactorizationLDLRaw(
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matrix& AF, // factored matrix A
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long[]& ipiv // pivot indices array
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);
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```
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Computing for type matrix<float>
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```
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bool matrixf::FactorizationLDLRaw(
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matrixf& AF, // factored matrix A
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long[]& ipiv // pivot indices array
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);
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```
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Computing for type matrix<complex>
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```
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bool matrixc::FactorizationLDLRaw(
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matrixc& AF, // factored matrix A
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long[]& ipiv // pivot indices array
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);
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```
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Computing for type matrix<complexf>
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```
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bool matrixcf::FactorizationLDLRaw(
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matrixcf& AF, // factored matrix A
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long[]& ipiv // pivot indices array
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);
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```
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Parameters
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AF
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[out] Factored matrix A. The block diagonal matrix D and factor L or U.
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ipiv
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[out] Pivot indices array of size N; details of the interchanges and the block structure of D.
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Return Value
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Return true if successful, otherwise false in case of an [error](/en/docs/constants/errorswarnings/errorcodes).
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Note
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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).
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Matrix AF and pivot indices array ipiv[] are raw output of the SYTRF (HETRF) function and can be used for further calculations with methods [LDLLinearEquationsSolution](/en/docs/matrix/openblas/factored_calculations/ldllinearequationssolution), [LDLInverse](/en/docs/matrix/openblas/factored_calculations/ldlinverse) and [LDLCondNumReciprocal](/en/docs/matrix/openblas/factored_calculations/ldlcondnumreciprocal).
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