dlatzm.f

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*> \brief \b DLATZM
*
*  =========== DOCUMENTATION ===========
*
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*
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*
*  Definition:
*  ===========
*
*       SUBROUTINE DLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
*       .. Scalar Arguments ..
*       CHARACTER          SIDE
*       INTEGER            INCV, LDC, M, N
*       DOUBLE PRECISION   TAU
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> This routine is deprecated and has been replaced by routine DORMRZ.
*>
*> DLATZM applies a Householder matrix generated by DTZRQF to a matrix.
*>
*> Let P = I - tau*u*u**T,   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.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] SIDE
*> \verbatim
*>          SIDE is CHARACTER*1
*>          = 'L': form P * C
*>          = 'R': form C * P
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix C.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix C.
*> \endverbatim
*>
*> \param[in] V
*> \verbatim
*>          V is DOUBLE PRECISION 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.
*> \endverbatim
*>
*> \param[in] INCV
*> \verbatim
*>          INCV is INTEGER
*>          The increment between elements of v. INCV <> 0
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION
*>          The value tau in the representation of P.
*> \endverbatim
*>
*> \param[in,out] C1
*> \verbatim
*>          C1 is DOUBLE PRECISION 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'.
*> \endverbatim
*>
*> \param[in,out] C2
*> \verbatim
*>          C2 is DOUBLE PRECISION 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'.
*> \endverbatim
*>
*> \param[in] LDC
*> \verbatim
*>          LDC is INTEGER
*>          The leading dimension of the arrays C1 and C2. LDC >= (1,M).
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION array, dimension
*>                      (N) if SIDE = 'L'
*>                      (M) if SIDE = 'R'
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup doubleOTHERcomputational
*
*  =====================================================================
      SUBROUTINE dlatzm( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. Scalar Arguments ..
      CHARACTER          SIDE
      INTEGER            INCV, LDC, M, N
      DOUBLE PRECISION   TAU
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ONE, ZERO
      parameter( one = 1.0d+0, zero = 0.0d+0 )
*     ..
*     .. External Subroutines ..
      EXTERNAL           daxpy, dcopy, dgemv, dger
*     ..
*     .. 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**T * C2)**T
*
         CALL dcopy( n, c1, ldc, work, 1 )
         CALL dgemv( 'Transpose', m-1, n, one, c2, ldc, v, incv, one,
     $               work, 1 )
*
*        [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
*        [ C2 ]    [ C2 ]        [ v ]
*
         CALL daxpy( n, -tau, work, 1, c1, ldc )
         CALL dger( m-1, n, -tau, v, incv, work, 1, c2, ldc )
*
      ELSE IF( lsame( side, 'R' ) ) THEN
*
*        w := C1 + C2 * v
*
         CALL dcopy( m, c1, 1, work, 1 )
         CALL dgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
     $               work, 1 )
*
*        [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
*
         CALL daxpy( m, -tau, work, 1, c1, 1 )
         CALL dger( m, n-1, -tau, work, 1, v, incv, c2, ldc )
      END IF
*
      RETURN
*
*     End of DLATZM
*
      END