spstf2.f man page

spstf2.f —

Synopsis

Functions/Subroutines

subroutine spstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

Function/Subroutine Documentation

subroutine spstf2 (characterUPLO, integerN, real, dimension( lda, * )A, integerLDA, integer, dimension( n )PIV, integerRANK, realTOL, real, dimension( 2*n )WORK, integerINFO)

SPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or complex Hermitian positive semi-definite matrix.

Purpose:

SPSTF2 computes the Cholesky factorization with complete
pivoting of a real symmetric positive semidefinite matrix A.

The factorization has the form
   P**T * A * P = U**T * U ,  if UPLO = 'U',
   P**T * A * P = L  * L**T,  if UPLO = 'L',
where U is an upper triangular matrix and L is lower triangular, and
P is stored as vector PIV.

This algorithm does not attempt to check that A is positive
semidefinite. This version of the algorithm calls level 2 BLAS.

Parameters:

UPLO

UPLO is CHARACTER*1
Specifies whether the upper or lower triangular part of the
symmetric matrix A is stored.
= 'U':  Upper triangular
= 'L':  Lower triangular

N

N is INTEGER
The order of the matrix A.  N >= 0.

A

A is REAL array, dimension (LDA,N)
On entry, the symmetric matrix A.  If UPLO = 'U', the leading
n by n upper triangular part of 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 A contains the lower
triangular part of the matrix A, and the strictly upper
triangular part of A is not referenced.

On exit, if INFO = 0, the factor U or L from the Cholesky
factorization as above.

PIV

PIV is INTEGER array, dimension (N)
PIV is such that the nonzero entries are P( PIV(K), K ) = 1.

RANK

RANK is INTEGER
The rank of A given by the number of steps the algorithm
completed.

TOL

TOL is REAL
User defined tolerance. If TOL < 0, then N*U*MAX( A( K,K ) )
will be used. The algorithm terminates at the (K-1)st step
if the pivot <= TOL.

LDA

LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,N).

WORK

WORK is REAL array, dimension (2*N)
Work space.

INFO

INFO is INTEGER
< 0: If INFO = -K, the K-th argument had an illegal value,
= 0: algorithm completed successfully, and
> 0: the matrix A is either rank deficient with computed rank
     as returned in RANK, or is indefinite.  See Section 7 of
     LAPACK Working Note #161 for further information.

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

Definition at line 141 of file spstf2.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

spstf2(3) is an alias of spstf2.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK