NAME

       dpstf2.f -

SYNOPSIS

   Functions/Subroutines
       subroutine dpstf2 (UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO)
           DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric
           or complex Hermitian positive semi-definite matrix.

Function/Subroutine Documentation

   subroutine dpstf2 (characterUPLO, integerN, double precision, dimension( lda, * )A,
       integerLDA, integer, dimension( n )PIV, integerRANK, double precisionTOL, double
       precision, dimension( 2*n )WORK, integerINFO)
       DPSTF2 computes the Cholesky factorization with complete pivoting of a real symmetric or
       complex Hermitian positive semi-definite matrix.

       Purpose:

            DPSTF2 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.

       Parameters:
           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 DOUBLE PRECISION 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

                     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 DOUBLE PRECISION
                     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

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

           WORK

                     WORK is DOUBLE PRECISION 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 indefinite.  See Section 7 of
                          LAPACK Working Note #161 for further information.

       Author:
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Date:
           September 2012

       Definition at line 141 of file dpstf2.f.

Author

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