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 formP' * 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 (K1)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 Kth 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.