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    1: *> \brief \b DLAQGE scales a general rectangular matrix, using row and column scaling factors computed by sgeequ.
    2: *
    3: *  =========== DOCUMENTATION ===========
    4: *
    5: * Online html documentation available at
    6: *            http://www.netlib.org/lapack/explore-html/
    7: *
    8: *> \htmlonly
    9: *> Download DLAQGE + dependencies
   10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlaqge.f">
   11: *> [TGZ]</a>
   12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlaqge.f">
   13: *> [ZIP]</a>
   14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlaqge.f">
   15: *> [TXT]</a>
   16: *> \endhtmlonly
   17: *
   18: *  Definition:
   19: *  ===========
   20: *
   21: *       SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
   22: *                          EQUED )
   23: *
   24: *       .. Scalar Arguments ..
   25: *       CHARACTER          EQUED
   26: *       INTEGER            LDA, M, N
   27: *       DOUBLE PRECISION   AMAX, COLCND, ROWCND
   28: *       ..
   29: *       .. Array Arguments ..
   30: *       DOUBLE PRECISION   A( LDA, * ), C( * ), R( * )
   31: *       ..
   32: *
   33: *
   34: *> \par Purpose:
   35: *  =============
   36: *>
   37: *> \verbatim
   38: *>
   39: *> DLAQGE equilibrates a general M by N matrix A using the row and
   40: *> column scaling factors in the vectors R and C.
   41: *> \endverbatim
   42: *
   43: *  Arguments:
   44: *  ==========
   45: *
   46: *> \param[in] M
   47: *> \verbatim
   48: *>          M is INTEGER
   49: *>          The number of rows of the matrix A.  M >= 0.
   50: *> \endverbatim
   51: *>
   52: *> \param[in] N
   53: *> \verbatim
   54: *>          N is INTEGER
   55: *>          The number of columns of the matrix A.  N >= 0.
   56: *> \endverbatim
   57: *>
   58: *> \param[in,out] A
   59: *> \verbatim
   60: *>          A is DOUBLE PRECISION array, dimension (LDA,N)
   61: *>          On entry, the M by N matrix A.
   62: *>          On exit, the equilibrated matrix.  See EQUED for the form of
   63: *>          the equilibrated matrix.
   64: *> \endverbatim
   65: *>
   66: *> \param[in] LDA
   67: *> \verbatim
   68: *>          LDA is INTEGER
   69: *>          The leading dimension of the array A.  LDA >= max(M,1).
   70: *> \endverbatim
   71: *>
   72: *> \param[in] R
   73: *> \verbatim
   74: *>          R is DOUBLE PRECISION array, dimension (M)
   75: *>          The row scale factors for A.
   76: *> \endverbatim
   77: *>
   78: *> \param[in] C
   79: *> \verbatim
   80: *>          C is DOUBLE PRECISION array, dimension (N)
   81: *>          The column scale factors for A.
   82: *> \endverbatim
   83: *>
   84: *> \param[in] ROWCND
   85: *> \verbatim
   86: *>          ROWCND is DOUBLE PRECISION
   87: *>          Ratio of the smallest R(i) to the largest R(i).
   88: *> \endverbatim
   89: *>
   90: *> \param[in] COLCND
   91: *> \verbatim
   92: *>          COLCND is DOUBLE PRECISION
   93: *>          Ratio of the smallest C(i) to the largest C(i).
   94: *> \endverbatim
   95: *>
   96: *> \param[in] AMAX
   97: *> \verbatim
   98: *>          AMAX is DOUBLE PRECISION
   99: *>          Absolute value of largest matrix entry.
  100: *> \endverbatim
  101: *>
  102: *> \param[out] EQUED
  103: *> \verbatim
  104: *>          EQUED is CHARACTER*1
  105: *>          Specifies the form of equilibration that was done.
  106: *>          = 'N':  No equilibration
  107: *>          = 'R':  Row equilibration, i.e., A has been premultiplied by
  108: *>                  diag(R).
  109: *>          = 'C':  Column equilibration, i.e., A has been postmultiplied
  110: *>                  by diag(C).
  111: *>          = 'B':  Both row and column equilibration, i.e., A has been
  112: *>                  replaced by diag(R) * A * diag(C).
  113: *> \endverbatim
  114: *
  115: *> \par Internal Parameters:
  116: *  =========================
  117: *>
  118: *> \verbatim
  119: *>  THRESH is a threshold value used to decide if row or column scaling
  120: *>  should be done based on the ratio of the row or column scaling
  121: *>  factors.  If ROWCND < THRESH, row scaling is done, and if
  122: *>  COLCND < THRESH, column scaling is done.
  123: *>
  124: *>  LARGE and SMALL are threshold values used to decide if row scaling
  125: *>  should be done based on the absolute size of the largest matrix
  126: *>  element.  If AMAX > LARGE or AMAX < SMALL, row scaling is done.
  127: *> \endverbatim
  128: *
  129: *  Authors:
  130: *  ========
  131: *
  132: *> \author Univ. of Tennessee
  133: *> \author Univ. of California Berkeley
  134: *> \author Univ. of Colorado Denver
  135: *> \author NAG Ltd.
  136: *
  137: *> \ingroup doubleGEauxiliary
  138: *
  139: *  =====================================================================
  140:       SUBROUTINE DLAQGE( M, N, A, LDA, R, C, ROWCND, COLCND, AMAX,
  141:      $                   EQUED )
  142: *
  143: *  -- LAPACK auxiliary routine --
  144: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  145: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  146: *
  147: *     .. Scalar Arguments ..
  148:       CHARACTER          EQUED
  149:       INTEGER            LDA, M, N
  150:       DOUBLE PRECISION   AMAX, COLCND, ROWCND
  151: *     ..
  152: *     .. Array Arguments ..
  153:       DOUBLE PRECISION   A( LDA, * ), C( * ), R( * )
  154: *     ..
  155: *
  156: *  =====================================================================
  157: *
  158: *     .. Parameters ..
  159:       DOUBLE PRECISION   ONE, THRESH
  160:       PARAMETER          ( ONE = 1.0D+0, THRESH = 0.1D+0 )
  161: *     ..
  162: *     .. Local Scalars ..
  163:       INTEGER            I, J
  164:       DOUBLE PRECISION   CJ, LARGE, SMALL
  165: *     ..
  166: *     .. External Functions ..
  167:       DOUBLE PRECISION   DLAMCH
  168:       EXTERNAL           DLAMCH
  169: *     ..
  170: *     .. Executable Statements ..
  171: *
  172: *     Quick return if possible
  173: *
  174:       IF( M.LE.0 .OR. N.LE.0 ) THEN
  175:          EQUED = 'N'
  176:          RETURN
  177:       END IF
  178: *
  179: *     Initialize LARGE and SMALL.
  180: *
  181:       SMALL = DLAMCH( 'Safe minimum' ) / DLAMCH( 'Precision' )
  182:       LARGE = ONE / SMALL
  183: *
  184:       IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
  185:      $     THEN
  186: *
  187: *        No row scaling
  188: *
  189:          IF( COLCND.GE.THRESH ) THEN
  190: *
  191: *           No column scaling
  192: *
  193:             EQUED = 'N'
  194:          ELSE
  195: *
  196: *           Column scaling
  197: *
  198:             DO 20 J = 1, N
  199:                CJ = C( J )
  200:                DO 10 I = 1, M
  201:                   A( I, J ) = CJ*A( I, J )
  202:    10          CONTINUE
  203:    20       CONTINUE
  204:             EQUED = 'C'
  205:          END IF
  206:       ELSE IF( COLCND.GE.THRESH ) THEN
  207: *
  208: *        Row scaling, no column scaling
  209: *
  210:          DO 40 J = 1, N
  211:             DO 30 I = 1, M
  212:                A( I, J ) = R( I )*A( I, J )
  213:    30       CONTINUE
  214:    40    CONTINUE
  215:          EQUED = 'R'
  216:       ELSE
  217: *
  218: *        Row and column scaling
  219: *
  220:          DO 60 J = 1, N
  221:             CJ = C( J )
  222:             DO 50 I = 1, M
  223:                A( I, J ) = CJ*R( I )*A( I, J )
  224:    50       CONTINUE
  225:    60    CONTINUE
  226:          EQUED = 'B'
  227:       END IF
  228: *
  229:       RETURN
  230: *
  231: *     End of DLAQGE
  232: *
  233:       END