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Annotation of rpl/lapack/lapack/zlaqge.f, revision 1.3

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