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Diff for /rpl/lapack/lapack/zla_porpvgrw.f between versions 1.4 and 1.14

version 1.4, 2010/12/21 13:53:48 version 1.14, 2017/06/17 11:06:51
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       DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,   *> \brief \b ZLA_PORPVGRW computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.
      $                                        LDAF, WORK )  
 *  *
 *     -- LAPACK routine (version 3.2.2)                                 --  *  =========== DOCUMENTATION ===========
 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --  
 *     -- Jason Riedy of Univ. of California Berkeley.                 --  
 *     -- June 2010                                                    --  
 *  *
 *     -- LAPACK is a software package provided by Univ. of Tennessee, --  * Online html documentation available at
 *     -- Univ. of California Berkeley and NAG Ltd.                    --  *            http://www.netlib.org/lapack/explore-html/
   *
   *> \htmlonly
   *> Download ZLA_PORPVGRW + dependencies
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zla_porpvgrw.f">
   *> [TGZ]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zla_porpvgrw.f">
   *> [ZIP]</a>
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zla_porpvgrw.f">
   *> [TXT]</a>
   *> \endhtmlonly
   *
   *  Definition:
   *  ===========
   *
   *       DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
   *                                               LDAF, WORK )
   *
   *       .. Scalar Arguments ..
   *       CHARACTER*1        UPLO
   *       INTEGER            NCOLS, LDA, LDAF
   *       ..
   *       .. Array Arguments ..
   *       COMPLEX*16         A( LDA, * ), AF( LDAF, * )
   *       DOUBLE PRECISION   WORK( * )
   *       ..
   *
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *>
   *> ZLA_PORPVGRW computes the reciprocal pivot growth factor
   *> norm(A)/norm(U). The "max absolute element" norm is used. If this is
   *> much less than 1, the stability of the LU factorization of the
   *> (equilibrated) matrix A could be poor. This also means that the
   *> solution X, estimated condition numbers, and error bounds could be
   *> unreliable.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] UPLO
   *> \verbatim
   *>          UPLO is CHARACTER*1
   *>       = 'U':  Upper triangle of A is stored;
   *>       = 'L':  Lower triangle of A is stored.
   *> \endverbatim
   *>
   *> \param[in] NCOLS
   *> \verbatim
   *>          NCOLS is INTEGER
   *>     The number of columns of the matrix A. NCOLS >= 0.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is COMPLEX*16 array, dimension (LDA,N)
   *>     On entry, the N-by-N matrix A.
   *> \endverbatim
   *>
   *> \param[in] LDA
   *> \verbatim
   *>          LDA is INTEGER
   *>     The leading dimension of the array A.  LDA >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] AF
   *> \verbatim
   *>          AF is COMPLEX*16 array, dimension (LDAF,N)
   *>     The triangular factor U or L from the Cholesky factorization
   *>     A = U**T*U or A = L*L**T, as computed by ZPOTRF.
   *> \endverbatim
   *>
   *> \param[in] LDAF
   *> \verbatim
   *>          LDAF is INTEGER
   *>     The leading dimension of the array AF.  LDAF >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] WORK
   *> \verbatim
   *>          WORK is DOUBLE PRECISION array, dimension (2*N)
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee
   *> \author Univ. of California Berkeley
   *> \author Univ. of Colorado Denver
   *> \author NAG Ltd.
   *
   *> \date June 2016
   *
   *> \ingroup complex16POcomputational
   *
   *  =====================================================================
         DOUBLE PRECISION FUNCTION ZLA_PORPVGRW( UPLO, NCOLS, A, LDA, AF,
        $                                        LDAF, WORK )
   *
   *  -- LAPACK computational routine (version 3.7.0) --
   *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
   *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
   *     June 2016
 *  *
       IMPLICIT NONE  
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER*1        UPLO        CHARACTER*1        UPLO
       INTEGER            NCOLS, LDA, LDAF        INTEGER            NCOLS, LDA, LDAF
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       DOUBLE PRECISION   WORK( * )        DOUBLE PRECISION   WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *   
 *  ZLA_PORPVGRW computes the reciprocal pivot growth factor  
 *  norm(A)/norm(U). The "max absolute element" norm is used. If this is  
 *  much less than 1, the stability of the LU factorization of the  
 *  (equilibrated) matrix A could be poor. This also means that the  
 *  solution X, estimated condition numbers, and error bounds could be  
 *  unreliable.  
 *  
 *  Arguments  
 *  =========  
 *  
 *     UPLO    (input) CHARACTER*1  
 *       = 'U':  Upper triangle of A is stored;  
 *       = 'L':  Lower triangle of A is stored.  
 *  
 *     NCOLS   (input) INTEGER  
 *     The number of columns of the matrix A. NCOLS >= 0.  
 *  
 *     A       (input) COMPLEX*16 array, dimension (LDA,N)  
 *     On entry, the N-by-N matrix A.  
 *  
 *     LDA     (input) INTEGER  
 *     The leading dimension of the array A.  LDA >= max(1,N).  
 *  
 *     AF      (input) COMPLEX*16 array, dimension (LDAF,N)  
 *     The triangular factor U or L from the Cholesky factorization  
 *     A = U**T*U or A = L*L**T, as computed by ZPOTRF.  
 *  
 *     LDAF    (input) INTEGER  
 *     The leading dimension of the array AF.  LDAF >= max(1,N).  
 *  
 *     WORK    (input) COMPLEX*16 array, dimension (2*N)  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
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       COMPLEX*16         ZDUM        COMPLEX*16         ZDUM
 *     ..  *     ..
 *     .. External Functions ..  *     .. External Functions ..
       EXTERNAL           LSAME, ZLASET        EXTERNAL           LSAME
       LOGICAL            LSAME        LOGICAL            LSAME
 *     ..  *     ..
 *     .. Intrinsic Functions ..  *     .. Intrinsic Functions ..
Removed from v.1.4  
changed lines
  Added in v.1.14

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