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version 1.4, 2010/12/21 13:53:28 version 1.5, 2011/11/21 20:42:54
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   *> \brief \b DLA_SYRPVGRW
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLA_SYRPVGRW + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_syrpvgrw.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_syrpvgrw.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_syrpvgrw.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       DOUBLE PRECISION FUNCTION DLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF,
   *                                               LDAF, IPIV, WORK )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER*1        UPLO
   *       INTEGER            N, INFO, LDA, LDAF
   *       ..
   *       .. Array Arguments ..
   *       INTEGER            IPIV( * )
   *       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), WORK( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> 
   *> DLA_SYRPVGRW 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] N
   *> \verbatim
   *>          N is INTEGER
   *>     The number of linear equations, i.e., the order of the
   *>     matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>     The value of INFO returned from DSYTRF, .i.e., the pivot in
   *>     column INFO is exactly 0.
   *> \endverbatim
   *>
   *> \param[in] A
   *> \verbatim
   *>          A is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDAF,N)
   *>     The block diagonal matrix D and the multipliers used to
   *>     obtain the factor U or L as computed by DSYTRF.
   *> \endverbatim
   *>
   *> \param[in] LDAF
   *> \verbatim
   *>          LDAF is INTEGER
   *>     The leading dimension of the array AF.  LDAF >= max(1,N).
   *> \endverbatim
   *>
   *> \param[in] IPIV
   *> \verbatim
   *>          IPIV is INTEGER array, dimension (N)
   *>     Details of the interchanges and the block structure of D
   *>     as determined by DSYTRF.
   *> \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 November 2011
   *
   *> \ingroup doubleSYcomputational
   *
   *  =====================================================================
       DOUBLE PRECISION FUNCTION DLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF,        DOUBLE PRECISION FUNCTION DLA_SYRPVGRW( UPLO, N, INFO, A, LDA, AF,
      $                                        LDAF, IPIV, WORK )       $                                        LDAF, IPIV, WORK )
 *  *
 *     -- LAPACK routine (version 3.2.2)                                 --  *  -- LAPACK computational routine (version 3.4.0) --
 *     -- Contributed by James Demmel, Deaglan Halligan, Yozo Hida and --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *     -- Jason Riedy of Univ. of California Berkeley.                 --  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     -- June 2010                                                    --  *     November 2011
 *  *
 *     -- LAPACK is a software package provided by Univ. of Tennessee, --  
 *     -- Univ. of California Berkeley and NAG Ltd.                    --  
 *  
       IMPLICIT NONE  
 *     ..  
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER*1        UPLO        CHARACTER*1        UPLO
       INTEGER            N, INFO, LDA, LDAF        INTEGER            N, INFO, LDA, LDAF
Line 20 Line 136
       DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), WORK( * )        DOUBLE PRECISION   A( LDA, * ), AF( LDAF, * ), WORK( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *   
 *  DLA_SYRPVGRW 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.  
 *  
 *     N       (input) INTEGER  
 *     The number of linear equations, i.e., the order of the  
 *     matrix A.  N >= 0.  
 *  
 *     INFO    (input) INTEGER  
 *     The value of INFO returned from DSYTRF, .i.e., the pivot in  
 *     column INFO is exactly 0.  
 *  
 *     NCOLS   (input) INTEGER  
 *     The number of columns of the matrix A. NCOLS >= 0.  
 *  
 *     A       (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDAF,N)  
 *     The block diagonal matrix D and the multipliers used to  
 *     obtain the factor U or L as computed by DSYTRF.  
 *  
 *     LDAF    (input) INTEGER  
 *     The leading dimension of the array AF.  LDAF >= max(1,N).  
 *  
 *     IPIV    (input) INTEGER array, dimension (N)  
 *     Details of the interchanges and the block structure of D  
 *     as determined by DSYTRF.  
 *  
 *     WORK    (input) DOUBLE PRECISION array, dimension (2*N)  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.4  
changed lines
  Added in v.1.5

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