Provided by: liblapack-doc_3.3.1-1_all

#### NAME

```       LAPACK-3  - computes the Cholesky factorization with complete pivoting of a real symmetric
positive semidefinite matrix A

```

#### SYNOPSIS

```       SUBROUTINE SPSTF2( 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

```       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.

```

#### 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    (workspace) 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.

LAPACK PROTOTYPE routine (version 3.2.2)   April 2011                            SPSTF2(3lapack)
```