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

1.1     ! bertrand    1:       SUBROUTINE DLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
        !             2: *
        !             3: *  -- LAPACK routine (version 3.2) --
        !             4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
        !             5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
        !             6: *     November 2006
        !             7: *
        !             8: *     .. Scalar Arguments ..
        !             9:       CHARACTER          SIDE
        !            10:       INTEGER            INCV, L, LDC, M, N
        !            11:       DOUBLE PRECISION   TAU
        !            12: *     ..
        !            13: *     .. Array Arguments ..
        !            14:       DOUBLE PRECISION   C( LDC, * ), V( * ), WORK( * )
        !            15: *     ..
        !            16: *
        !            17: *  Purpose
        !            18: *  =======
        !            19: *
        !            20: *  DLARZ applies a real elementary reflector H to a real M-by-N
        !            21: *  matrix C, from either the left or the right. H is represented in the
        !            22: *  form
        !            23: *
        !            24: *        H = I - tau * v * v'
        !            25: *
        !            26: *  where tau is a real scalar and v is a real vector.
        !            27: *
        !            28: *  If tau = 0, then H is taken to be the unit matrix.
        !            29: *
        !            30: *
        !            31: *  H is a product of k elementary reflectors as returned by DTZRZF.
        !            32: *
        !            33: *  Arguments
        !            34: *  =========
        !            35: *
        !            36: *  SIDE    (input) CHARACTER*1
        !            37: *          = 'L': form  H * C
        !            38: *          = 'R': form  C * H
        !            39: *
        !            40: *  M       (input) INTEGER
        !            41: *          The number of rows of the matrix C.
        !            42: *
        !            43: *  N       (input) INTEGER
        !            44: *          The number of columns of the matrix C.
        !            45: *
        !            46: *  L       (input) INTEGER
        !            47: *          The number of entries of the vector V containing
        !            48: *          the meaningful part of the Householder vectors.
        !            49: *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
        !            50: *
        !            51: *  V       (input) DOUBLE PRECISION array, dimension (1+(L-1)*abs(INCV))
        !            52: *          The vector v in the representation of H as returned by
        !            53: *          DTZRZF. V is not used if TAU = 0.
        !            54: *
        !            55: *  INCV    (input) INTEGER
        !            56: *          The increment between elements of v. INCV <> 0.
        !            57: *
        !            58: *  TAU     (input) DOUBLE PRECISION
        !            59: *          The value tau in the representation of H.
        !            60: *
        !            61: *  C       (input/output) DOUBLE PRECISION array, dimension (LDC,N)
        !            62: *          On entry, the M-by-N matrix C.
        !            63: *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
        !            64: *          or C * H if SIDE = 'R'.
        !            65: *
        !            66: *  LDC     (input) INTEGER
        !            67: *          The leading dimension of the array C. LDC >= max(1,M).
        !            68: *
        !            69: *  WORK    (workspace) DOUBLE PRECISION array, dimension
        !            70: *                         (N) if SIDE = 'L'
        !            71: *                      or (M) if SIDE = 'R'
        !            72: *
        !            73: *  Further Details
        !            74: *  ===============
        !            75: *
        !            76: *  Based on contributions by
        !            77: *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
        !            78: *
        !            79: *  =====================================================================
        !            80: *
        !            81: *     .. Parameters ..
        !            82:       DOUBLE PRECISION   ONE, ZERO
        !            83:       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
        !            84: *     ..
        !            85: *     .. External Subroutines ..
        !            86:       EXTERNAL           DAXPY, DCOPY, DGEMV, DGER
        !            87: *     ..
        !            88: *     .. External Functions ..
        !            89:       LOGICAL            LSAME
        !            90:       EXTERNAL           LSAME
        !            91: *     ..
        !            92: *     .. Executable Statements ..
        !            93: *
        !            94:       IF( LSAME( SIDE, 'L' ) ) THEN
        !            95: *
        !            96: *        Form  H * C
        !            97: *
        !            98:          IF( TAU.NE.ZERO ) THEN
        !            99: *
        !           100: *           w( 1:n ) = C( 1, 1:n )
        !           101: *
        !           102:             CALL DCOPY( N, C, LDC, WORK, 1 )
        !           103: *
        !           104: *           w( 1:n ) = w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l )
        !           105: *
        !           106:             CALL DGEMV( 'Transpose', L, N, ONE, C( M-L+1, 1 ), LDC, V,
        !           107:      $                  INCV, ONE, WORK, 1 )
        !           108: *
        !           109: *           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
        !           110: *
        !           111:             CALL DAXPY( N, -TAU, WORK, 1, C, LDC )
        !           112: *
        !           113: *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
        !           114: *                               tau * v( 1:l ) * w( 1:n )'
        !           115: *
        !           116:             CALL DGER( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
        !           117:      $                 LDC )
        !           118:          END IF
        !           119: *
        !           120:       ELSE
        !           121: *
        !           122: *        Form  C * H
        !           123: *
        !           124:          IF( TAU.NE.ZERO ) THEN
        !           125: *
        !           126: *           w( 1:m ) = C( 1:m, 1 )
        !           127: *
        !           128:             CALL DCOPY( M, C, 1, WORK, 1 )
        !           129: *
        !           130: *           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
        !           131: *
        !           132:             CALL DGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
        !           133:      $                  V, INCV, ONE, WORK, 1 )
        !           134: *
        !           135: *           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
        !           136: *
        !           137:             CALL DAXPY( M, -TAU, WORK, 1, C, 1 )
        !           138: *
        !           139: *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
        !           140: *                               tau * w( 1:m ) * v( 1:l )'
        !           141: *
        !           142:             CALL DGER( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
        !           143:      $                 LDC )
        !           144: *
        !           145:          END IF
        !           146: *
        !           147:       END IF
        !           148: *
        !           149:       RETURN
        !           150: *
        !           151: *     End of DLARZ
        !           152: *
        !           153:       END