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version 1.4, 2010/12/21 13:53:28 version 1.5, 2011/11/21 20:42:53
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   *> \brief \b DLA_GBRPVGRW
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DLA_GBRPVGRW + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dla_gbrpvgrw.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dla_gbrpvgrw.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dla_gbrpvgrw.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
   *                                               LDAB, AFB, LDAFB )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            N, KL, KU, NCOLS, LDAB, LDAFB
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * ), AFB( LDAFB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DLA_GBRPVGRW 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] N
   *> \verbatim
   *>          N is INTEGER
   *>     The number of linear equations, i.e., the order of the
   *>     matrix A.  N >= 0.
   *> \endverbatim
   *>
   *> \param[in] KL
   *> \verbatim
   *>          KL is INTEGER
   *>     The number of subdiagonals within the band of A.  KL >= 0.
   *> \endverbatim
   *>
   *> \param[in] KU
   *> \verbatim
   *>          KU is INTEGER
   *>     The number of superdiagonals within the band of A.  KU >= 0.
   *> \endverbatim
   *>
   *> \param[in] NCOLS
   *> \verbatim
   *>          NCOLS is INTEGER
   *>     The number of columns of the matrix A.  NCOLS >= 0.
   *> \endverbatim
   *>
   *> \param[in] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   *>     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.
   *>     The j-th column of A is stored in the j-th column of the
   *>     array AB as follows:
   *>     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>     The leading dimension of the array AB.  LDAB >= KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] AFB
   *> \verbatim
   *>          AFB is DOUBLE PRECISION array, dimension (LDAFB,N)
   *>     Details of the LU factorization of the band matrix A, as
   *>     computed by DGBTRF.  U is stored as an upper triangular
   *>     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,
   *>     and the multipliers used during the factorization are stored
   *>     in rows KL+KU+2 to 2*KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] LDAFB
   *> \verbatim
   *>          LDAFB is INTEGER
   *>     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGBcomputational
   *
   *  =====================================================================
       DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,        DOUBLE PRECISION FUNCTION DLA_GBRPVGRW( N, KL, KU, NCOLS, AB,
      $                                        LDAB, AFB, LDAFB )       $                                        LDAB, AFB, LDAFB )
 *  *
 *     -- 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 ..
       INTEGER            N, KL, KU, NCOLS, LDAB, LDAFB        INTEGER            N, KL, KU, NCOLS, LDAB, LDAFB
 *     ..  *     ..
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       DOUBLE PRECISION   AB( LDAB, * ), AFB( LDAFB, * )        DOUBLE PRECISION   AB( LDAB, * ), AFB( LDAFB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DLA_GBRPVGRW 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  
 *  =========  
 *  
 *     N       (input) INTEGER  
 *     The number of linear equations, i.e., the order of the  
 *     matrix A.  N >= 0.  
 *  
 *     KL      (input) INTEGER  
 *     The number of subdiagonals within the band of A.  KL >= 0.  
 *  
 *     KU      (input) INTEGER  
 *     The number of superdiagonals within the band of A.  KU >= 0.  
 *  
 *     NCOLS   (input) INTEGER  
 *     The number of columns of the matrix A.  NCOLS >= 0.  
 *  
 *     AB      (input) DOUBLE PRECISION array, dimension (LDAB,N)  
 *     On entry, the matrix A in band storage, in rows 1 to KL+KU+1.  
 *     The j-th column of A is stored in the j-th column of the  
 *     array AB as follows:  
 *     AB(KU+1+i-j,j) = A(i,j) for max(1,j-KU)<=i<=min(N,j+kl)  
 *  
 *     LDAB    (input) INTEGER  
 *     The leading dimension of the array AB.  LDAB >= KL+KU+1.  
 *  
 *     AFB     (input) DOUBLE PRECISION array, dimension (LDAFB,N)  
 *     Details of the LU factorization of the band matrix A, as  
 *     computed by DGBTRF.  U is stored as an upper triangular  
 *     band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1,  
 *     and the multipliers used during the factorization are stored  
 *     in rows KL+KU+2 to 2*KL+KU+1.  
 *  
 *     LDAFB   (input) INTEGER  
 *     The leading dimension of the array AFB.  LDAFB >= 2*KL+KU+1.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Local Scalars ..  *     .. Local Scalars ..
Removed from v.1.4  
changed lines
  Added in v.1.5

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