dpstf2 man page on Scientific

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DPSTF2(1)	    LAPACK PROTOTYPE routine (version 3.2)	     DPSTF2(1)

NAME
       DPSTF2  - computes the Cholesky factorization with complete pivoting of
       a real symmetric positive semidefinite matrix A

SYNOPSIS
       SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )

	   DOUBLE	  PRECISION TOL

	   INTEGER	  INFO, LDA, N, RANK

	   CHARACTER	  UPLO

	   DOUBLE	  PRECISION A( LDA, * ), WORK( 2*N )

	   INTEGER	  PIV( N )

PURPOSE
       DPSTF2 computes the Cholesky factorization with complete pivoting of  a
       real  symmetric	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 2 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) 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     (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) 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     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,N).

       WORK    DOUBLE PRECISION 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 PROTOTYPE routine (versioNovember 2008			     DPSTF2(1)
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