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CPSTRF(1)		 LAPACK routine (version 3.2)		     CPSTRF(1)

NAME
       CPSTRF  - computes the Cholesky factorization with complete pivoting of
       a complex Hermitian positive semidefinite matrix A

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

	   REAL		  TOL

	   INTEGER	  INFO, LDA, N, RANK

	   CHARACTER	  UPLO

	   COMPLEX	  A( LDA, * )

	   REAL		  WORK( 2*N )

	   INTEGER	  PIV( N )

PURPOSE
       CPSTRF computes the Cholesky factorization with complete pivoting of  a
       complex	Hermitian  positive  semidefinite matrix A.  The factorization
       has the form
	  P' * A * P = U' * U ,	 if UPLO = 'U',
	  P' * A * P = L  * L',	 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 semidefi‐
       nite. This version of the algorithm calls level 3 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) COMPLEX 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  com‐
	       pleted.

       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    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 routine (version 3.2)	 November 2008			     CPSTRF(1)
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