?pstf2

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?pstf2

Computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

Syntax

call spstf2( uplo, n, a, lda, piv, rank, tol, work, info )

call dpstf2( uplo, n, a, lda, piv, rank, tol, work, info )

call cpstf2( uplo, n, a, lda, piv, rank, tol, work, info )

call zpstf2( uplo, n, a, lda, piv, rank, tol, work, info )

Include Files

mkl.fi

Description

The real flavors spstf2 and dpstf2 compute the Cholesky factorization with complete pivoting of a real symmetric positive semi-definite matrix A. The complex flavors cpstf2 and zpstf2 compute the Cholesky factorization with complete pivoting of a complex Hermitian positive semi-definite matrix A. The factorization has the form:

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 U is an upper triangular matrix and L is lower triangular, and P is stored as vector piv.

This algorithm does not check that A is positive semi-definite. This version of the algorithm calls level 2 BLAS.

Input Parameters

uplo

CHARACTER*1.

Specifies whether the upper or lower triangular part of the symmetric or Hermitian matrix A is stored:

= 'U': Upper triangular,

= 'L': Lower triangular.

n

INTEGER. The order of the matrix A. n≥ 0.

a

REAL for spstf2,

DOUBLE PRECISION for dpstf2,

COMPLEX for cpstf2,

DOUBLE COMPLEX for zpstf2.

Array, DIMENSION (lda, *).

On entry, the symmetric matrix A. If uplo = 'U', the leading n-by-n upper triangular part of the array a contains the upper triangular part of the matrix A, and the strictly lower triangular part of a is not referenced. If uplo = 'L', the leading n-by-n lower triangular part of the array a contains the lower triangular part of the matrix A, and the strictly upper triangular part of a is not referenced.

tol

REAL for spstf2 and cpstf2,

DOUBLE PRECISION for dpstf2 and zpstf2.

A user-defined tolerance.

If tol < 0, n*ulp*max(A(k,k)) will be used (ulp is the Unit in the Last Place, or Unit of Least Precision). The algorithm terminates at the (k - 1)-st step if the pivot is not greater than tol.

lda

INTEGER. The leading dimension of the matrix A. lda ≥ max(1,n).

work

REAL for spstf2 and cpstf2,

DOUBLE PRECISION for dpstf2 and zpstf2.

Workspace array, DIMENSION at least max (1, 2*n).

Output Parameters

piv

INTEGER. Array. DIMENSION at least max (1,n).

piv is such that the non-zero entries are P ( piv (k), k ) = 1.

a

On exit, if info = 0, the factor U or L from the Cholesky factorization stored the same way as the matrix A is stored on entry.

rank

INTEGER.

The rank of A, determined by the number of steps the algorithm completed.

info

INTEGER.

< 0: if info = -k, the k-th parameter had an illegal value,

=0: the algorithm completed successfully,

> 0: the matrix A is rank-deficient with the computed rank, returned in rank, or indefinite.

Parent topic: LAPACK Auxiliary Routines

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