dlatzm()

subroutine dlatzm	(	character	side,
		integer	m,
		integer	n,
		double precision, dimension( * )	v,
		integer	incv,
		double precision	tau,
		double precision, dimension( ldc, * )	c1,
		double precision, dimension( ldc, * )	c2,
		integer	ldc,
		double precision, dimension( * )	work )

DLATZM

Download DLATZM + dependencies [TGZ] [ZIP] [TXT]

Purpose:

!>
!> This routine is deprecated and has been replaced by routine DORMRZ.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.
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': form P * C !> = 'R': form C * P !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix C. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix C. !>
[in]	V	!> 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. !>
[in]	INCV	!> INCV is INTEGER !> The increment between elements of v. INCV <> 0 !>
[in]	TAU	!> TAU is DOUBLE PRECISION !> The value tau in the representation of P. !>
[in,out]	C1	!> 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'. !>
[in,out]	C2	!> 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'. !>
[in]	LDC	!> LDC is INTEGER !> The leading dimension of the arrays C1 and C2. LDC >= (1,M). !>
[out]	WORK	!> WORK is DOUBLE PRECISION array, dimension !> (N) if SIDE = 'L' !> (M) if SIDE = 'R' !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 148 of file dlatzm.f.

*
*  -- LAPACK computational routine --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
*     .. 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
*

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