SYNOPSIS

SUBROUTINE SPSTRF(

UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )

    

REAL TOL

    

INTEGER INFO, LDA, N, RANK

    

CHARACTER UPLO

    

REAL A( LDA, * ), WORK( 2*N )

    

INTEGER PIV( N )

PURPOSE

SPSTRF computes the Cholesky factorization with complete pivoting of a real symmetric positive semidefinite matrix A. The factorization has the form

   P' * A * P = U' * U ,  if UPLO = 'U',

   P' * A * P = L  * L',  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 3 BLAS.

ARGUMENTS

UPLO (input) CHARACTER*1

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

N (input) INTEGER

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

A (input/output) 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 (output) INTEGER array, dimension (N)

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

RANK (output) INTEGER

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

TOL (input) 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 (input) INTEGER

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

WORK REAL array, dimension (2*N)

Work space.

INFO (output) 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.