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*> \brief \b DLAQGB scales a general band matrix, using row and column scaling factors computed by sgbequ.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DLAQGB + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqgb.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqgb.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqgb.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DLAQGB( 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 AB( LDAB, * ), C( * ), R( * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DLAQGB 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 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(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 doubleGBauxiliary
*
* =====================================================================
SUBROUTINE DLAQGB( M, N, KL, KU, AB, LDAB, R, C, ROWCND, COLCND,
$ AMAX, EQUED )
*
* -- LAPACK auxiliary routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
CHARACTER EQUED
INTEGER KL, KU, LDAB, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
DOUBLE PRECISION AB( LDAB, * ), C( * ), R( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, THRESH
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
* ..
* .. Local Scalars ..
INTEGER I, J
DOUBLE PRECISION CJ, LARGE, SMALL
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Initialize LARGE and SMALL.
*
SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
LARGE = ONE / SMALL
*
IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
$ THEN
*
* No row scaling
*
IF( COLCND.GE.THRESH ) THEN
*
* No column scaling
*
EQUED = 'N'
ELSE
*
* Column scaling
*
DO 20 J = 1, N
CJ = C( J )
DO 10 I = MAX( 1, J-KU ), MIN( M, J+KL )
AB( KU+1+I-J, J ) = CJ*AB( KU+1+I-J, J )
10 CONTINUE
20 CONTINUE
EQUED = 'C'
END IF
ELSE IF( COLCND.GE.THRESH ) THEN
*
* Row scaling, no column scaling
*
DO 40 J = 1, N
DO 30 I = MAX( 1, J-KU ), MIN( M, J+KL )
AB( KU+1+I-J, J ) = R( I )*AB( KU+1+I-J, J )
30 CONTINUE
40 CONTINUE
EQUED = 'R'
ELSE
*
* Row and column scaling
*
DO 60 J = 1, N
CJ = C( J )
DO 50 I = MAX( 1, J-KU ), MIN( M, J+KL )
AB( KU+1+I-J, J ) = CJ*R( I )*AB( KU+1+I-J, J )
50 CONTINUE
60 CONTINUE
EQUED = 'B'
END IF
*
RETURN
*
* End of DLAQGB
*
END
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