SRC/zpstf2.f(3)            Library Functions Manual            SRC/zpstf2.f(3)

NAME
       SRC/zpstf2.f

SYNOPSIS
   Functions/Subroutines
       subroutine zpstf2 (uplo, n, a, lda, piv, rank, tol, work, info)
           ZPSTF2 computes the Cholesky factorization with complete pivoting
           of a complex Hermitian positive semidefinite matrix.

Function/Subroutine Documentation
   subroutine zpstf2 (character uplo, integer n, complex*16, dimension( lda, *
       ) a, integer lda, integer, dimension( n ) piv, integer rank, double
       precision tol, double precision, dimension( 2*n ) work, integer info)
       ZPSTF2 computes the Cholesky factorization with complete pivoting of a
       complex Hermitian positive semidefinite matrix.

       Purpose:


            ZPSTF2 computes the Cholesky factorization with complete
            pivoting of a complex Hermitian positive semidefinite matrix A.

            The factorization has the form
               P**T * A * P = U**H * U ,  if UPLO = 'U',
               P**T * A * P = L  * L**H,  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 COMPLEX*16 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 not positive semidefinite. 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.

       Definition at line 141 of file zpstf2.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                 SRC/zpstf2.f(3)