234 lines
6.1 KiB
Fortran
234 lines
6.1 KiB
Fortran
*> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLAQGE + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqge.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqge.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqge.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
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* EQUED )
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*
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* .. Scalar Arguments ..
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* CHARACTER EQUED
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* INTEGER LDA, M, N
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* DOUBLE PRECISION AMAX, COLCND, ROWCND
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DLAQGE equilibrates a general M by N matrix A using the row and
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*> column scaling factors in the vectors R and C.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the M by N matrix A.
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*> On exit, the equilibrated matrix. See EQUED for the form of
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*> the equilibrated matrix.
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(M,1).
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*> \endverbatim
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*>
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*> \param[in] R
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*> \verbatim
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*> R is DOUBLE PRECISION array, dimension (M)
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*> The row scale factors for A.
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is DOUBLE PRECISION array, dimension (N)
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*> The column scale factors for A.
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*> \endverbatim
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*>
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*> \param[in] ROWCND
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*> \verbatim
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*> ROWCND is DOUBLE PRECISION
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*> Ratio of the smallest R(i) to the largest R(i).
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*> \endverbatim
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*>
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*> \param[in] COLCND
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*> \verbatim
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*> COLCND is DOUBLE PRECISION
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*> Ratio of the smallest C(i) to the largest C(i).
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*> \endverbatim
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*>
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*> \param[in] AMAX
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*> \verbatim
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*> AMAX is DOUBLE PRECISION
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*> Absolute value of largest matrix entry.
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*> \endverbatim
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*>
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*> \param[out] EQUED
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*> \verbatim
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*> EQUED is CHARACTER*1
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*> Specifies the form of equilibration that was done.
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*> = 'N': No equilibration
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*> = 'R': Row equilibration, i.e., A has been premultiplied by
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*> diag(R).
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*> = 'C': Column equilibration, i.e., A has been postmultiplied
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*> by diag(C).
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*> = 'B': Both row and column equilibration, i.e., A has been
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*> replaced by diag(R) * A * diag(C).
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*> \endverbatim
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*
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*> \par Internal Parameters:
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* =========================
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*>
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*> \verbatim
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*> THRESH is a threshold value used to decide if row or column scaling
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*> should be done based on the ratio of the row or column scaling
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*> factors. If ROWCND < THRESH, row scaling is done, and if
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*> COLCND < THRESH, column scaling is done.
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*>
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*> LARGE and SMALL are threshold values used to decide if row scaling
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*> should be done based on the absolute size of the largest matrix
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*> element. If AMAX > LARGE or AMAX < SMALL, row scaling is done.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup doubleGEauxiliary
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*
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* =====================================================================
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SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
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$ EQUED )
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*
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* -- LAPACK auxiliary routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER EQUED
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INTEGER LDA, M, N
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DOUBLE PRECISION AMAX, COLCND, ROWCND
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), C( * ), R( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, THRESH
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PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I, J
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DOUBLE PRECISION CJ, LARGE, SMALL
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLAMCH
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EXTERNAL DLAMCH
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* ..
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* .. Executable Statements ..
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*
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* Quick return if possible
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*
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IF( M.LE.0 .OR. N.LE.0 ) THEN
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EQUED = 'N'
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RETURN
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END IF
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*
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* Initialize LARGE and SMALL.
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*
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SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
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LARGE = ONE / SMALL
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*
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IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
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$ THEN
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*
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* No row scaling
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*
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IF( COLCND.GE.THRESH ) THEN
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*
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* No column scaling
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*
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EQUED = 'N'
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ELSE
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*
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* Column scaling
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*
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DO 20 J = 1, N
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CJ = C( J )
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DO 10 I = 1, M
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A( I, J ) = CJ*A( I, J )
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10 CONTINUE
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20 CONTINUE
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EQUED = 'C'
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END IF
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ELSE IF( COLCND.GE.THRESH ) THEN
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*
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* Row scaling, no column scaling
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*
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DO 40 J = 1, N
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DO 30 I = 1, M
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A( I, J ) = R( I )*A( I, J )
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30 CONTINUE
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40 CONTINUE
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EQUED = 'R'
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ELSE
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*
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* Row and column scaling
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*
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DO 60 J = 1, N
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CJ = C( J )
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DO 50 I = 1, M
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A( I, J ) = CJ*R( I )*A( I, J )
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50 CONTINUE
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60 CONTINUE
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EQUED = 'B'
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END IF
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*
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RETURN
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*
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* End of DLAQGE
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*
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END
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