slatzm.f

          SUBROUTINE SLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, 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, LDC, M, N
          REAL               TAU
    *     ..
    *     .. Array Arguments ..
          REAL               C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  This routine is deprecated and has been replaced by routine SORMRZ.
    *
    *  SLATZM applies a Householder matrix generated by STZRQF to a matrix.
    *
    *  Let P = I - tau*u*u',   u = ( 1 ),
    *                              ( v )
    *  where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
    *  SIDE = 'R'.
    *
    *  If SIDE equals 'L', let
    *         C = [ C1 ] 1
    *             [ C2 ] m-1
    *               n
    *  Then C is overwritten by P*C.
    *
    *  If SIDE equals 'R', let
    *         C = [ C1, C2 ] m
    *                1  n-1
    *  Then C is overwritten by C*P.
    *
    *  Arguments
    *  =========
    *
    *  SIDE    (input) CHARACTER*1
    *          = 'L': form P * C
    *          = 'R': form C * P
    *
    *  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'
    *                  (1 + (N-1)*abs(INCV)) if SIDE = 'R'
    *          The vector v in the representation of P. 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 P.
    *
    *  C1      (input/output) REAL array, dimension
    *                         (LDC,N) if SIDE = 'L'
    *                         (M,1)   if SIDE = 'R'
    *          On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
    *          if SIDE = 'R'.
    *
    *          On exit, the first row of P*C if SIDE = 'L', or the first
    *          column of C*P if SIDE = 'R'.
    *
    *  C2      (input/output) REAL array, dimension
    *                         (LDC, N)   if SIDE = 'L'
    *                         (LDC, N-1) if SIDE = 'R'
    *          On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
    *          m x (n - 1) matrix C2 if SIDE = 'R'.
    *
    *          On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
    *          if SIDE = 'R'.
    *
    *  LDC     (input) INTEGER
    *          The leading dimension of the arrays C1 and C2. LDC >= (1,M).
    *
    *  WORK    (workspace) REAL array, dimension
    *                      (N) if SIDE = 'L'
    *                      (M) if SIDE = 'R'
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           SAXPY, SCOPY, SGEMV, SGER
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MIN
    *     ..
    *     .. Executable Statements ..
    *
          IF( ( MIN( M, N ).EQ.0 ) .OR. ( TAU.EQ.ZERO ) )
         $   RETURN
    *
          IF( LSAME( SIDE, 'L' ) ) THEN
    *
    *        w := C1 + v' * C2
    *
             CALL SCOPY( N, C1, LDC, WORK, 1 )
             CALL SGEMV( 'Transpose', M-1, N, ONE, C2, LDC, V, INCV, ONE,
         $               WORK, 1 )
    *
    *        [ C1 ] := [ C1 ] - tau* [ 1 ] * w'
    *        [ C2 ]    [ C2 ]        [ v ]
    *
             CALL SAXPY( N, -TAU, WORK, 1, C1, LDC )
             CALL SGER( M-1, N, -TAU, V, INCV, WORK, 1, C2, LDC )
    *
          ELSE IF( LSAME( SIDE, 'R' ) ) THEN
    *
    *        w := C1 + C2 * v
    *
             CALL SCOPY( M, C1, 1, WORK, 1 )
             CALL SGEMV( 'No transpose', M, N-1, ONE, C2, LDC, V, INCV, ONE,
         $               WORK, 1 )
    *
    *        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v']
    *
             CALL SAXPY( M, -TAU, WORK, 1, C1, 1 )
             CALL SGER( M, N-1, -TAU, WORK, 1, V, INCV, C2, LDC )
          END IF
    *
          RETURN
    *
    *     End of SLATZM
    *
          END