!>
!> SPSTRF 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 3 BLAS.
!> 

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.
!> 

LDA

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

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.
!> 

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 not positive semidefinite. See
!>               Section 7 of LAPACK Working Note #161 for further
!>               information.
!> 

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