?pstrf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 3/22/2024

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?pstrf

Computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix.

Syntax

lapack_int LAPACKE_spstrf( int matrix_layout, char uplo, lapack_int n, float* a, lapack_int lda, lapack_int* piv, lapack_int* rank, float tol );

lapack_int LAPACKE_dpstrf( int matrix_layout, char uplo, lapack_int n, double* a, lapack_int lda, lapack_int* piv, lapack_int* rank, double tol );

lapack_int LAPACKE_cpstrf( int matrix_layout, char uplo, lapack_int n, lapack_complex_float* a, lapack_int lda, lapack_int* piv, lapack_int* rank, float tol );

lapack_int LAPACKE_zpstrf( int matrix_layout, char uplo, lapack_int n, lapack_complex_double* a, lapack_int lda, lapack_int* piv, lapack_int* rank, double tol );

Include Files

mkl.h

Description

The routine computes the Cholesky factorization with complete pivoting of a real symmetric (complex Hermitian) positive semidefinite matrix. The form of the factorization is:

P^T * A * P = U^T * U, if uplo ='U' for real flavors,
P^T * A * P = U^H * U, if uplo ='U' for complex flavors,
P^T * A * P = L * L^T, if uplo ='L' for real flavors,
P^T * A * P = L * L^H, if uplo ='L' for complex flavors,

where P is a permutation matrix stored as vector piv, and U and L are upper and lower triangular matrices, respectively.

This algorithm does not attempt to check that A is positive semidefinite. This version of the algorithm calls level 3 BLAS.

Input Parameters

matrix_layout	Specifies whether matrix storage layout is row major (LAPACK_ROW_MAJOR) or column major (LAPACK_COL_MAJOR).
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`, and the strictly lower triangular part of the matrix is not referenced. If `uplo = 'L'`, the array a stores the lower triangular part of the matrix `A`, and the strictly upper triangular part of the matrix is not referenced.
n	The order of matrix `A`; `n`≥ 0.
a	Array a, size max(1,lda*n). The array a contains either the upper or the lower triangular part of the matrix `A` (see uplo). .
tol	User defined tolerance. If tol < 0, then nεmax(`A`_k,k), where ε is the machine precision, will be used (see Error Analysis for the definition of machine precision). The algorithm terminates at the `(k-1)`-st step, if the pivot ≤tol.
lda	The leading dimension of a; at least `max(1, n)`.

Output Parameters

a	If `info = 0`, the factor U or L from the Cholesky factorization is as described in Description.
piv	Array, size at least `max(1, n)`. The array piv is such that the nonzero entries are `P`_piv[k-1],k (1 ≤`k`≤`n`).
rank	The rank of a given by the number of steps the algorithm completed.

Return Values

This function returns a value info.

If info = 0, the execution is successful.

If info = -k, the k-th argument had an illegal value.

If info > 0, the matrix A is either rank deficient with a computed rank as returned in rank, or is not positive semidefinite.

Parent topic: Matrix Factorization: LAPACK Computational Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?pstrf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

See Also