# FactorizationCholesky

Computes the factorization of a real symmetric or complex Hermitian positive-definite matrix A. The factorization has the form:

A = L *  L**T in case of lower triangular or symmetric matrix A

or

A = U**T  * U in case of upper triangular matrix A

where L is lower triangular, U is upper triangular. LAPACK function [POTRF](https://www.intel.com/content/www/us/en/docs/onemkl/developer-reference-fortran/2025-2/potrf.html).

Computing for type matrix<double>

```
bool  matrix::FactorizationCholesky(
   matrix&         L             // lower or upper triangular matrix
   );

```

Computing for type matrix<float>

```
bool  matrix::FactorizationCholesky(
   matrixf&        L             // lower or upper triangular matrix
   );

```

Computing for type matrix<complex>

```
bool  matrix::FactorizationCholesky(
   matrixc&        L             // lower or upper triangular matrix
   );

```

Computing for type matrix<complexf>

```
bool  matrix::FactorizationCholesky(
   matrixcf&       L             // lower or upper triangular matrix
   );

```

Parameters

L

[out]  Lower or upper triangular matrix.

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).

Matrices L and D can be used for further calculations with methods [LDLSyTridPDLinearEquationsSolution](/en/docs/matrix/openblas/factored_calculations/ldlsytridpdlinearequations) and [LDLSyTridPDCondNumReciprocal](/en/docs/matrix/openblas/factored_calculations/ldlsytridpdcondnumreciprocal).