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Annotation of rpl/lapack/lapack/dlaqge.f, revision 1.2

1.1       bertrand    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