?pstrf

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?pstrf

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

Syntax

call spstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call dpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call cpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

call zpstrf( uplo, n, a, lda, piv, rank, tol, work, info )

Include Files

mkl.fi, lapack.f90

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

uplo	CHARACTER*1. 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	INTEGER. The order of matrix `A`; `n`≥ 0.
a	REAL for spstrf DOUBLE PRECISION for dpstrf COMPLEX for cpstrf DOUBLE COMPLEX for zpstrf. Array a, size `(lda,*)`. The array a contains either the upper or the lower triangular part of the matrix `A` (see uplo). The second dimension of a must be at least `max(1, n)`.
work	REAL for spstrf and cpstrf DOUBLE PRECISION for dpstrf and zpstrf. work() is a workspace array. The dimension of work is at least `max(1,2n)`.
tol	REAL for single precision flavors DOUBLE PRECISION for double precision flavors. 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	INTEGER. 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	INTEGER. Array, size at least `max(1, n)`. The array piv is such that the nonzero entries are `P`_piv(k),k (1 ≤`k`≤`n`).
rank	INTEGER. The rank of a given by the number of steps the algorithm completed.
info	INTEGER. 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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