dlaqge.f

          SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
         $                   EQUED )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          EQUED
          INTEGER            LDA, M, N
          DOUBLE PRECISION   AMAX, COLCND, ROWCND
    *     ..
    *     .. Array Arguments ..
          DOUBLE PRECISION   A( LDA, * ), C( * ), R( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  DLAQGE equilibrates a general M by N matrix A using the row and
    *  column 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.
    *
    *  A       (input/output) 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.
    *
    *  LDA     (input) INTEGER
    *          The leading dimension of the array A.  LDA >= max(M,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 ..
          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