slarf.f

          SUBROUTINE SLARF( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
    *
    *  -- LAPACK auxiliary routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          SIDE
          INTEGER            INCV, LDC, M, N
          REAL               TAU
    *     ..
    *     .. Array Arguments ..
          REAL               C( LDC, * ), V( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  SLARF applies a real elementary reflector H to a real 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 real scalar and v is a real vector.
    *
    *  If tau = 0, then H is taken to be the unit matrix.
    *
    *  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.
    *
    *  V       (input) REAL array, dimension
    *                     (1 + (M-1)*abs(INCV)) if SIDE = 'L'
    *                  or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
    *          The vector v in the representation of H. V is not used if
    *          TAU = 0.
    *
    *  INCV    (input) INTEGER
    *          The increment between elements of v. INCV <> 0.
    *
    *  TAU     (input) REAL
    *          The value tau in the representation of H.
    *
    *  C       (input/output) REAL 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) REAL array, dimension
    *                         (N) if SIDE = 'L'
    *                      or (M) if SIDE = 'R'
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SGEMV, SGER
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Executable Statements ..
    *
          IF( LSAME( SIDE, 'L' ) ) THEN
    *
    *        Form  H * C
    *
             IF( TAU.NE.ZERO ) THEN
    *
    *           w := C' * v
    *
                CALL SGEMV( 'Transpose', M, N, ONE, C, LDC, V, INCV, ZERO,
         $                  WORK, 1 )
    *
    *           C := C - v * w'
    *
                CALL SGER( M, N, -TAU, V, INCV, WORK, 1, C, LDC )
             END IF
          ELSE
    *
    *        Form  C * H
    *
             IF( TAU.NE.ZERO ) THEN
    *
    *           w := C * v
    *
                CALL SGEMV( 'No transpose', M, N, ONE, C, LDC, V, INCV,
         $                  ZERO, WORK, 1 )
    *
    *           C := C - w * v'
    *
                CALL SGER( M, N, -TAU, WORK, 1, V, INCV, C, LDC )
             END IF
          END IF
          RETURN
    *
    *     End of SLARF
    *
          END