?pftrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/31/2023

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?pftrf

Computes the Cholesky factorization of a symmetric (Hermitian) positive-definite matrix using the Rectangular Full Packed (RFP) format .

Syntax

lapack_int LAPACKE_spftrf (int matrix_layout , char transr , char uplo , lapack_int n , float * a );

lapack_int LAPACKE_dpftrf (int matrix_layout , char transr , char uplo , lapack_int n , double * a );

lapack_int LAPACKE_cpftrf (int matrix_layout , char transr , char uplo , lapack_int n , lapack_complex_float * a );

lapack_int LAPACKE_zpftrf (int matrix_layout , char transr , char uplo , lapack_int n , lapack_complex_double * a );

Include Files

mkl.h

Description

The routine forms the Cholesky factorization of a symmetric positive-definite or, for complex data, a Hermitian positive-definite matrix A:

`A = U^TU` for real data, `A = U^HU` for complex data	if `uplo='U'`
`A = LL^T` for real data, `A = LL^H` for complex data	if `uplo='L'`

where L is a lower triangular matrix and U is upper triangular.

The matrix A is in the Rectangular Full Packed (RFP) format. For the description of the RFP format, see Matrix Storage Schemes.

This is the block version of the algorithm, calling Level 3 BLAS.

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
transr	Must be 'N', 'T' (for real data) or 'C' (for complex data). If transr = 'N', the Normal transr of RFP `A` is stored. If transr = 'T', the Transpose transr of RFP `A` is stored. If transr = 'C', the Conjugate-Transpose transr of RFP `A` is stored.
uplo	Must be 'U' or 'L'. Indicates whether the upper or lower triangular part of `A` is stored: If uplo = 'U', the array a stores the upper triangular part of the matrix `A`. If uplo = 'L', the array a stores the lower triangular part of the matrix `A`.
n	The order of the matrix `A`; n≥ 0.
a	Array, size `(n*(n+1)/2)`. The array a contains the matrix `A` in the RFP format.

Output Parameters

a	a is overwritten by the Cholesky factor `U` or `L`, as specified by uplo and trans.

Return Values

This function returns a value info.

If info=0, the execution is successful.

If info = -i, parameter i had an illegal value.

If info = i, the leading minor of order i (and therefore the matrix A itself) is not positive-definite, and the factorization could not be completed. This may indicate an error in forming the matrix A.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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