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version 1.7, 2010/12/21 13:53:24 version 1.8, 2011/11/21 20:42:49
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   *> \brief \b DGBEQU
   *
   *  =========== DOCUMENTATION ===========
   *
   * Online html documentation available at 
   *            http://www.netlib.org/lapack/explore-html/ 
   *
   *> \htmlonly
   *> Download DGBEQU + dependencies 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgbequ.f"> 
   *> [TGZ]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgbequ.f"> 
   *> [ZIP]</a> 
   *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgbequ.f"> 
   *> [TXT]</a>
   *> \endhtmlonly 
   *
   *  Definition:
   *  ===========
   *
   *       SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
   *                          AMAX, INFO )
   * 
   *       .. Scalar Arguments ..
   *       INTEGER            INFO, KL, KU, LDAB, M, N
   *       DOUBLE PRECISION   AMAX, COLCND, ROWCND
   *       ..
   *       .. Array Arguments ..
   *       DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )
   *       ..
   *  
   *
   *> \par Purpose:
   *  =============
   *>
   *> \verbatim
   *>
   *> DGBEQU computes row and column scalings intended to equilibrate an
   *> M-by-N band matrix A and reduce its condition number.  R returns the
   *> row scale factors and C the column scale factors, chosen to try to
   *> make the largest element in each row and column of the matrix B with
   *> elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.
   *>
   *> R(i) and C(j) are restricted to be between SMLNUM = smallest safe
   *> number and BIGNUM = largest safe number.  Use of these scaling
   *> factors is not guaranteed to reduce the condition number of A but
   *> works well in practice.
   *> \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] AB
   *> \verbatim
   *>          AB is DOUBLE PRECISION array, dimension (LDAB,N)
   *>          The band matrix A, stored 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).
   *> \endverbatim
   *>
   *> \param[in] LDAB
   *> \verbatim
   *>          LDAB is INTEGER
   *>          The leading dimension of the array AB.  LDAB >= KL+KU+1.
   *> \endverbatim
   *>
   *> \param[out] R
   *> \verbatim
   *>          R is DOUBLE PRECISION array, dimension (M)
   *>          If INFO = 0, or INFO > M, R contains the row scale factors
   *>          for A.
   *> \endverbatim
   *>
   *> \param[out] C
   *> \verbatim
   *>          C is DOUBLE PRECISION array, dimension (N)
   *>          If INFO = 0, C contains the column scale factors for A.
   *> \endverbatim
   *>
   *> \param[out] ROWCND
   *> \verbatim
   *>          ROWCND is DOUBLE PRECISION
   *>          If INFO = 0 or INFO > M, ROWCND contains the ratio of the
   *>          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and
   *>          AMAX is neither too large nor too small, it is not worth
   *>          scaling by R.
   *> \endverbatim
   *>
   *> \param[out] COLCND
   *> \verbatim
   *>          COLCND is DOUBLE PRECISION
   *>          If INFO = 0, COLCND contains the ratio of the smallest
   *>          C(i) to the largest C(i).  If COLCND >= 0.1, it is not
   *>          worth scaling by C.
   *> \endverbatim
   *>
   *> \param[out] AMAX
   *> \verbatim
   *>          AMAX is DOUBLE PRECISION
   *>          Absolute value of largest matrix element.  If AMAX is very
   *>          close to overflow or very close to underflow, the matrix
   *>          should be scaled.
   *> \endverbatim
   *>
   *> \param[out] INFO
   *> \verbatim
   *>          INFO is INTEGER
   *>          = 0:  successful exit
   *>          < 0:  if INFO = -i, the i-th argument had an illegal value
   *>          > 0:  if INFO = i, and i is
   *>                <= M:  the i-th row of A is exactly zero
   *>                >  M:  the (i-M)-th column of A is exactly zero
   *> \endverbatim
   *
   *  Authors:
   *  ========
   *
   *> \author Univ. of Tennessee 
   *> \author Univ. of California Berkeley 
   *> \author Univ. of Colorado Denver 
   *> \author NAG Ltd. 
   *
   *> \date November 2011
   *
   *> \ingroup doubleGBcomputational
   *
   *  =====================================================================
       SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,        SUBROUTINE DGBEQU( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
      $                   AMAX, INFO )       $                   AMAX, INFO )
 *  *
 *  -- LAPACK routine (version 3.2) --  *  -- LAPACK computational 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 ..
       INTEGER            INFO, KL, KU, LDAB, M, N        INTEGER            INFO, KL, KU, LDAB, M, N
Line 14 Line 166
       DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )        DOUBLE PRECISION   AB( LDAB, * ), C( * ), R( * )
 *     ..  *     ..
 *  *
 *  Purpose  
 *  =======  
 *  
 *  DGBEQU computes row and column scalings intended to equilibrate an  
 *  M-by-N band matrix A and reduce its condition number.  R returns the  
 *  row scale factors and C the column scale factors, chosen to try to  
 *  make the largest element in each row and column of the matrix B with  
 *  elements B(i,j)=R(i)*A(i,j)*C(j) have absolute value 1.  
 *  
 *  R(i) and C(j) are restricted to be between SMLNUM = smallest safe  
 *  number and BIGNUM = largest safe number.  Use of these scaling  
 *  factors is not guaranteed to reduce the condition number of A but  
 *  works well in practice.  
 *  
 *  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) DOUBLE PRECISION array, dimension (LDAB,N)  
 *          The band matrix A, stored 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).  
 *  
 *  LDAB    (input) INTEGER  
 *          The leading dimension of the array AB.  LDAB >= KL+KU+1.  
 *  
 *  R       (output) DOUBLE PRECISION array, dimension (M)  
 *          If INFO = 0, or INFO > M, R contains the row scale factors  
 *          for A.  
 *  
 *  C       (output) DOUBLE PRECISION array, dimension (N)  
 *          If INFO = 0, C contains the column scale factors for A.  
 *  
 *  ROWCND  (output) DOUBLE PRECISION  
 *          If INFO = 0 or INFO > M, ROWCND contains the ratio of the  
 *          smallest R(i) to the largest R(i).  If ROWCND >= 0.1 and  
 *          AMAX is neither too large nor too small, it is not worth  
 *          scaling by R.  
 *  
 *  COLCND  (output) DOUBLE PRECISION  
 *          If INFO = 0, COLCND contains the ratio of the smallest  
 *          C(i) to the largest C(i).  If COLCND >= 0.1, it is not  
 *          worth scaling by C.  
 *  
 *  AMAX    (output) DOUBLE PRECISION  
 *          Absolute value of largest matrix element.  If AMAX is very  
 *          close to overflow or very close to underflow, the matrix  
 *          should be scaled.  
 *  
 *  INFO    (output) INTEGER  
 *          = 0:  successful exit  
 *          < 0:  if INFO = -i, the i-th argument had an illegal value  
 *          > 0:  if INFO = i, and i is  
 *                <= M:  the i-th row of A is exactly zero  
 *                >  M:  the (i-M)-th column of A is exactly zero  
 *  
 *  =====================================================================  *  =====================================================================
 *  *
 *     .. Parameters ..  *     .. Parameters ..
Removed from v.1.7  
changed lines
  Added in v.1.8

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