*> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ. * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DLAQGE + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, * EQUED ) * * .. Scalar Arguments .. * CHARACTER EQUED * INTEGER LDA, M, N * DOUBLE PRECISION AMAX, COLCND, ROWCND * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), C( * ), R( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DLAQGE equilibrates a general M by N matrix A using the row and *> column 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,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the M by N matrix A. *> On exit, the equilibrated matrix. See EQUED for the form of *> the equilibrated matrix. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= max(M,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 December 2016 * *> \ingroup doubleGEauxiliary * * ===================================================================== SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX, \$ EQUED ) * * -- LAPACK auxiliary routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. CHARACTER EQUED INTEGER LDA, M, N DOUBLE PRECISION AMAX, COLCND, ROWCND * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), 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 * .. * .. 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 = 1, M A( I, J ) = CJ*A( I, 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 = 1, M A( I, J ) = R( I )*A( I, J ) 30 CONTINUE 40 CONTINUE EQUED = 'R' ELSE * * Row and column scaling * DO 60 J = 1, N CJ = C( J ) DO 50 I = 1, M A( I, J ) = CJ*R( I )*A( I, J ) 50 CONTINUE 60 CONTINUE EQUED = 'B' END IF * RETURN * * End of DLAQGE * END