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    1:       SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
    2:      $                   EQUED )
    3: *
    4: *  -- LAPACK auxiliary routine (version 3.2) --
    5: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    6: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    7: *     November 2006
    8: *
    9: *     .. Scalar Arguments ..
   10:       CHARACTER          EQUED
   11:       INTEGER            LDA, M, N
   12:       DOUBLE PRECISION   AMAX, COLCND, ROWCND
   13: *     ..
   14: *     .. Array Arguments ..
   15:       DOUBLE PRECISION   A( LDA, * ), C( * ), R( * )
   16: *     ..
   17: *
   18: *  Purpose
   19: *  =======
   20: *
   21: *  DLAQGE equilibrates a general M by N matrix A using the row and
   22: *  column scaling factors in the vectors R and C.
   23: *
   24: *  Arguments
   25: *  =========
   26: *
   27: *  M       (input) INTEGER
   28: *          The number of rows of the matrix A.  M >= 0.
   29: *
   30: *  N       (input) INTEGER
   31: *          The number of columns of the matrix A.  N >= 0.
   32: *
   33: *  A       (input/output) DOUBLE PRECISION array, dimension (LDA,N)
   34: *          On entry, the M by N matrix A.
   35: *          On exit, the equilibrated matrix.  See EQUED for the form of
   36: *          the equilibrated matrix.
   37: *
   38: *  LDA     (input) INTEGER
   39: *          The leading dimension of the array A.  LDA >= max(M,1).
   40: *
   41: *  R       (input) DOUBLE PRECISION array, dimension (M)
   42: *          The row scale factors for A.
   43: *
   44: *  C       (input) DOUBLE PRECISION array, dimension (N)
   45: *          The column scale factors for A.
   46: *
   47: *  ROWCND  (input) DOUBLE PRECISION
   48: *          Ratio of the smallest R(i) to the largest R(i).
   49: *
   50: *  COLCND  (input) DOUBLE PRECISION
   51: *          Ratio of the smallest C(i) to the largest C(i).
   52: *
   53: *  AMAX    (input) DOUBLE PRECISION
   54: *          Absolute value of largest matrix entry.
   55: *
   56: *  EQUED   (output) CHARACTER*1
   57: *          Specifies the form of equilibration that was done.
   58: *          = 'N':  No equilibration
   59: *          = 'R':  Row equilibration, i.e., A has been premultiplied by
   60: *                  diag(R).
   61: *          = 'C':  Column equilibration, i.e., A has been postmultiplied
   62: *                  by diag(C).
   63: *          = 'B':  Both row and column equilibration, i.e., A has been
   64: *                  replaced by diag(R) * A * diag(C).
   65: *
   66: *  Internal Parameters
   67: *  ===================
   68: *
   69: *  THRESH is a threshold value used to decide if row or column scaling
   70: *  should be done based on the ratio of the row or column scaling
   71: *  factors.  If ROWCND < THRESH, row scaling is done, and if
   72: *  COLCND < THRESH, column scaling is done.
   73: *
   74: *  LARGE and SMALL are threshold values used to decide if row scaling
   75: *  should be done based on the absolute size of the largest matrix
   76: *  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
   77: *
   78: *  =====================================================================
   79: *
   80: *     .. Parameters ..
   81:       DOUBLE PRECISION   ONE, THRESH
   82:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
   83: *     ..
   84: *     .. Local Scalars ..
   85:       INTEGER            I, J
   86:       DOUBLE PRECISION   CJ, LARGE, SMALL
   87: *     ..
   88: *     .. External Functions ..
   89:       DOUBLE PRECISION   DLAMCH
   90:       EXTERNAL           DLAMCH
   91: *     ..
   92: *     .. Executable Statements ..
   93: *
   94: *     Quick return if possible
   95: *
   96:       IF( M.LE.0 .OR. N.LE.0 ) THEN
   97:          EQUED = 'N'
   98:          RETURN
   99:       END IF
  100: *
  101: *     Initialize LARGE and SMALL.
  102: *
  103:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  104:       LARGE = ONE / SMALL
  105: *
  106:       IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
  107:      $     THEN
  108: *
  109: *        No row scaling
  110: *
  111:          IF( COLCND.GE.THRESH ) THEN
  112: *
  113: *           No column scaling
  114: *
  115:             EQUED = 'N'
  116:          ELSE
  117: *
  118: *           Column scaling
  119: *
  120:             DO 20 J = 1, N
  121:                CJ = C( J )
  122:                DO 10 I = 1, M
  123:                   A( I, J ) = CJ*A( I, J )
  124:    10          CONTINUE
  125:    20       CONTINUE
  126:             EQUED = 'C'
  127:          END IF
  128:       ELSE IF( COLCND.GE.THRESH ) THEN
  129: *
  130: *        Row scaling, no column scaling
  131: *
  132:          DO 40 J = 1, N
  133:             DO 30 I = 1, M
  134:                A( I, J ) = R( I )*A( I, J )
  135:    30       CONTINUE
  136:    40    CONTINUE
  137:          EQUED = 'R'
  138:       ELSE
  139: *
  140: *        Row and column scaling
  141: *
  142:          DO 60 J = 1, N
  143:             CJ = C( J )
  144:             DO 50 I = 1, M
  145:                A( I, J ) = CJ*R( I )*A( I, J )
  146:    50       CONTINUE
  147:    60    CONTINUE
  148:          EQUED = 'B'
  149:       END IF
  150: *
  151:       RETURN
  152: *
  153: *     End of DLAQGE
  154: *
  155:       END