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

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