SPSTF2(3)      LAPACK routine of NEC Numeric Library Collection      SPSTF2(3)



NAME
       SPSTF2

SYNOPSIS
       SUBROUTINE SPSTF2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)



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

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

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

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

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

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                      SPSTF2(3)