Return to zlaqge.f CVS log

Up to [local] / rpl / lapack / lapack

Annotation of rpl/lapack/lapack/zlaqge.f, revision 1.1

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