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version 1.7, 2010/12/21 13:53:50 version 1.8, 2011/11/21 20:43:16
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   *> \brief \b ZLAQGB
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download ZLAQGB + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlaqgb.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlaqgb.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlaqgb.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
   *                          AMAX, EQUED )
   * 
   *       .. Scalar Arguments ..
   *       CHARACTER          EQUED
   *       INTEGER            KL, KU, LDAB, M, N
   *       DOUBLE PRECISION   AMAX, COLCND, ROWCND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   C( * ), R( * )
   *       COMPLEX*16         AB( LDAB, * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> ZLAQGB equilibrates a general M by N band matrix A with KL
   *> subdiagonals and KU superdiagonals using the row and scaling factors
   *> in the vectors R and C.
   *> \endverbatim
   *
   *  Arguments:
   *  ==========
   *
   *> \param[in] M
   *> \verbatim
   *>          M is INTEGER
   *>          The number of rows of the matrix A.  M >= 0.
   *> \endverbatim
   *>
   *> \param[in] N
   *> \verbatim
   *>          N is INTEGER
   *>          The number of columns 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,out] AB
   *> \verbatim
   *>          AB is COMPLEX*16 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(m,j+kl)
   *>
   *>          On exit, the equilibrated matrix, in the same storage format
   *>          as A.  See EQUED for the form of the equilibrated matrix.
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDA >= KL+KU+1.
   *> \endverbatim
   *>
   *> \param[in] R
   *> \verbatim
   *>          R is DOUBLE PRECISION array, dimension (M)
   *>          The row scale factors for A.
   *> \endverbatim
   *>
   *> \param[in] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (N)
   *>          The column scale factors for A.
   *> \endverbatim
   *>
   *> \param[in] ROWCND
   *> \verbatim
   *>          ROWCND is DOUBLE PRECISION
   *>          Ratio of the smallest R(i) to the largest R(i).
   *> \endverbatim
   *>
   *> \param[in] COLCND
   *> \verbatim
   *>          COLCND is DOUBLE PRECISION
   *>          Ratio of the smallest C(i) to the largest C(i).
   *> \endverbatim
   *>
   *> \param[in] AMAX
   *> \verbatim
   *>          AMAX is DOUBLE PRECISION
   *>          Absolute value of largest matrix entry.
   *> \endverbatim
   *>
   *> \param[out] EQUED
   *> \verbatim
   *>          EQUED is CHARACTER*1
   *>          Specifies the form of equilibration that was done.
   *>          = 'N':  No equilibration
   *>          = 'R':  Row equilibration, i.e., A has been premultiplied by
   *>                  diag(R).
   *>          = 'C':  Column equilibration, i.e., A has been postmultiplied
   *>                  by diag(C).
   *>          = 'B':  Both row and column equilibration, i.e., A has been
   *>                  replaced by diag(R) * A * diag(C).
   *> \endverbatim
   *
   *> \par Internal Parameters:
   *  =========================
   *>
   *> \verbatim
   *>  THRESH is a threshold value used to decide if row or column scaling
   *>  should be done based on the ratio of the row or column scaling
   *>  factors.  If ROWCND < THRESH, row scaling is done, and if
   *>  COLCND < THRESH, column scaling is done.
   *>
   *>  LARGE and SMALL are threshold values used to decide if row scaling
   *>  should be done based on the absolute size of the largest matrix
   *>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup complex16GBauxiliary
   *
   *  =====================================================================
       SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,        SUBROUTINE ZLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
      $                   AMAX, EQUED )       $                   AMAX, EQUED )
 *  *
 *  -- LAPACK auxiliary routine (version 3.2) --  *  -- LAPACK auxiliary routine (version 3.4.0) --
 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --  *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--  *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
 *     November 2006  *     November 2011
 *  *
 *     .. Scalar Arguments ..  *     .. Scalar Arguments ..
       CHARACTER          EQUED        CHARACTER          EQUED
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       COMPLEX*16         AB( LDAB, * )        COMPLEX*16         AB( LDAB, * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  ZLAQGB equilibrates a general M by N band matrix A with KL  
 *  subdiagonals and KU superdiagonals using the row and scaling factors  
 *  in the vectors R and C.  
 *  
 *  Arguments  
 *  =========  
 *  
 *  M       (input) INTEGER  
 *          The number of rows of the matrix A.  M >= 0.  
 *  
 *  N       (input) INTEGER  
 *          The number of columns 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.  
 *  
 *  AB      (input/output) COMPLEX*16 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(m,j+kl)  
 *  
 *          On exit, the equilibrated matrix, in the same storage format  
 *          as A.  See EQUED for the form of the equilibrated matrix.  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDA >= KL+KU+1.  
 *  
 *  R       (input) DOUBLE PRECISION array, dimension (M)  
 *          The row scale factors for A.  
 *  
 *  C       (input) DOUBLE PRECISION array, dimension (N)  
 *          The column scale factors for A.  
 *  
 *  ROWCND  (input) DOUBLE PRECISION  
 *          Ratio of the smallest R(i) to the largest R(i).  
 *  
 *  COLCND  (input) DOUBLE PRECISION  
 *          Ratio of the smallest C(i) to the largest C(i).  
 *  
 *  AMAX    (input) DOUBLE PRECISION  
 *          Absolute value of largest matrix entry.  
 *  
 *  EQUED   (output) CHARACTER*1  
 *          Specifies the form of equilibration that was done.  
 *          = 'N':  No equilibration  
 *          = 'R':  Row equilibration, i.e., A has been premultiplied by  
 *                  diag(R).  
 *          = 'C':  Column equilibration, i.e., A has been postmultiplied  
 *                  by diag(C).  
 *          = 'B':  Both row and column equilibration, i.e., A has been  
 *                  replaced by diag(R) * A * diag(C).  
 *  
 *  Internal Parameters  
 *  ===================  
 *  
 *  THRESH is a threshold value used to decide if row or column scaling  
 *  should be done based on the ratio of the row or column scaling  
 *  factors.  If ROWCND < THRESH, row scaling is done, and if  
 *  COLCND < THRESH, column scaling is done.  
 *  
 *  LARGE and SMALL are threshold values used to decide if row scaling  
 *  should be done based on the absolute size of the largest matrix  
 *  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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