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version 1.5, 2011/07/22 07:38:10 version 1.6, 2011/11/21 20:43:02
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   *> \brief \b DPSTF2
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DPSTF2 + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dpstf2.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dpstf2.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dpstf2.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
   * 
   *       .. Scalar Arguments ..
   *       DOUBLE PRECISION   TOL
   *       INTEGER            INFO, LDA, N, RANK
   *       CHARACTER          UPLO
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   A( LDA, * ), WORK( 2*N )
   *       INTEGER            PIV( N )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 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.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          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
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The order of the matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in,out] A
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[out] PIV
   *> \verbatim
   *>          PIV is INTEGER array, dimension (N)
   *>          PIV is such that the nonzero entries are P( PIV(K), K ) = 1.
   *> \endverbatim
   *>
   *> \param[out] RANK
   *> \verbatim
   *>          RANK is INTEGER
   *>          The rank of A given by the number of steps the algorithm
   *>          completed.
   *> \endverbatim
   *>
   *> \param[in] TOL
   *> \verbatim
   *>          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.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>          The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[out] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (2*N)
   *>          Work space.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          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.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleOTHERcomputational
   *
   *  =====================================================================
       SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )        SUBROUTINE DPSTF2( UPLO, N, A, LDA, PIV, RANK, TOL, WORK, INFO )
 *  *
 *  -- LAPACK PROTOTYPE routine (version 3.2.2) --  *  -- LAPACK computational routine (version 3.4.0) --
 *     Craig Lucas, University of Manchester / NAG Ltd.  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *     October, 2008  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       DOUBLE PRECISION   TOL        DOUBLE PRECISION   TOL
Line 14 Line 155
       INTEGER            PIV( 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**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) 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  
 *          completed.  
 *  
 *  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    (workspace) 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.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.5  
changed lines
  Added in v.1.6

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