clarz.f

          SUBROUTINE CLARZ( SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          SIDE
          INTEGER            INCV, L, LDC, M, N
          COMPLEX            TAU
    *     ..
    *     .. Array Arguments ..
          COMPLEX            C( LDC, * ), V( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CLARZ applies a complex elementary reflector H to a complex
    *  M-by-N matrix C, from either the left or the right. H is represented
    *  in the form
    *
    *        H = I - tau * v * v'
    *
    *  where tau is a complex scalar and v is a complex vector.
    *
    *  If tau = 0, then H is taken to be the unit matrix.
    *
    *  To apply H' (the conjugate transpose of H), supply conjg(tau) instead
    *  tau.
    *
    *  H is a product of k elementary reflectors as returned by CTZRZF.
    *
    *  Arguments
    *  =========
    *
    *  SIDE    (input) CHARACTER*1
    *          = 'L': form  H * C
    *          = 'R': form  C * H
    *
    *  M       (input) INTEGER
    *          The number of rows of the matrix C.
    *
    *  N       (input) INTEGER
    *          The number of columns of the matrix C.
    *
    *  L       (input) INTEGER
    *          The number of entries of the vector V containing
    *          the meaningful part of the Householder vectors.
    *          If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
    *
    *  V       (input) COMPLEX array, dimension (1+(L-1)*abs(INCV))
    *          The vector v in the representation of H as returned by
    *          CTZRZF. V is not used if TAU = 0.
    *
    *  INCV    (input) INTEGER
    *          The increment between elements of v. INCV <> 0.
    *
    *  TAU     (input) COMPLEX
    *          The value tau in the representation of H.
    *
    *  C       (input/output) COMPLEX array, dimension (LDC,N)
    *          On entry, the M-by-N matrix C.
    *          On exit, C is overwritten by the matrix H * C if SIDE = 'L',
    *          or C * H if SIDE = 'R'.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the array C. LDC >= max(1,M).
    *
    *  WORK    (workspace) COMPLEX array, dimension
    *                         (N) if SIDE = 'L'
    *                      or (M) if SIDE = 'R'
    *
    *  Further Details
    *  ===============
    *
    *  Based on contributions by
    *    A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          COMPLEX            ONE, ZERO
          PARAMETER          ( ONE = ( 1.0E+0, 0.0E+0 ),
         $                   ZERO = ( 0.0E+0, 0.0E+0 ) )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           CAXPY, CCOPY, CGEMV, CGERC, CGERU, CLACGV
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Executable Statements ..
    *
          IF( LSAME( SIDE, 'L' ) ) THEN
    *
    *        Form  H * C
    *
             IF( TAU.NE.ZERO ) THEN
    *
    *           w( 1:n ) = conjg( C( 1, 1:n ) )
    *
                CALL CCOPY( N, C, LDC, WORK, 1 )
                CALL CLACGV( N, WORK, 1 )
    *
    *           w( 1:n ) = conjg( w( 1:n ) + C( m-l+1:m, 1:n )' * v( 1:l ) )
    *
                CALL CGEMV( 'Conjugate transpose', L, N, ONE, C( M-L+1, 1 ),
         $                  LDC, V, INCV, ONE, WORK, 1 )
                CALL CLACGV( N, WORK, 1 )
    *
    *           C( 1, 1:n ) = C( 1, 1:n ) - tau * w( 1:n )
    *
                CALL CAXPY( N, -TAU, WORK, 1, C, LDC )
    *
    *           C( m-l+1:m, 1:n ) = C( m-l+1:m, 1:n ) - ...
    *                               tau * v( 1:l ) * conjg( w( 1:n )' )
    *
                CALL CGERU( L, N, -TAU, V, INCV, WORK, 1, C( M-L+1, 1 ),
         $                  LDC )
             END IF
    *
          ELSE
    *
    *        Form  C * H
    *
             IF( TAU.NE.ZERO ) THEN
    *
    *           w( 1:m ) = C( 1:m, 1 )
    *
                CALL CCOPY( M, C, 1, WORK, 1 )
    *
    *           w( 1:m ) = w( 1:m ) + C( 1:m, n-l+1:n, 1:n ) * v( 1:l )
    *
                CALL CGEMV( 'No transpose', M, L, ONE, C( 1, N-L+1 ), LDC,
         $                  V, INCV, ONE, WORK, 1 )
    *
    *           C( 1:m, 1 ) = C( 1:m, 1 ) - tau * w( 1:m )
    *
                CALL CAXPY( M, -TAU, WORK, 1, C, 1 )
    *
    *           C( 1:m, n-l+1:n ) = C( 1:m, n-l+1:n ) - ...
    *                               tau * w( 1:m ) * v( 1:l )'
    *
                CALL CGERC( M, L, -TAU, WORK, 1, V, INCV, C( 1, N-L+1 ),
         $                  LDC )
    *
             END IF
    *
          END IF
    *
          RETURN
    *
    *     End of CLARZ
    *
          END