 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ 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

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``` This routine is deprecated and has been replaced by routine DORMRZ.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'```

Definition at line 150 of file dlatzm.f.

151 *
152 * -- LAPACK computational routine --
153 * -- LAPACK is a software package provided by Univ. of Tennessee, --
154 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155 *
156 * .. Scalar Arguments ..
157  CHARACTER SIDE
158  INTEGER INCV, LDC, M, N
159  DOUBLE PRECISION TAU
160 * ..
161 * .. Array Arguments ..
162  DOUBLE PRECISION C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
163 * ..
164 *
165 * =====================================================================
166 *
167 * .. Parameters ..
168  DOUBLE PRECISION ONE, ZERO
169  parameter( one = 1.0d+0, zero = 0.0d+0 )
170 * ..
171 * .. External Subroutines ..
172  EXTERNAL daxpy, dcopy, dgemv, dger
173 * ..
174 * .. External Functions ..
175  LOGICAL LSAME
176  EXTERNAL lsame
177 * ..
178 * .. Intrinsic Functions ..
179  INTRINSIC min
180 * ..
181 * .. Executable Statements ..
182 *
183  IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
184  \$ RETURN
185 *
186  IF( lsame( side, 'L' ) ) THEN
187 *
188 * w := (C1 + v**T * C2)**T
189 *
190  CALL dcopy( n, c1, ldc, work, 1 )
191  CALL dgemv( 'Transpose', m-1, n, one, c2, ldc, v, incv, one,
192  \$ work, 1 )
193 *
194 * [ C1 ] := [ C1 ] - tau* [ 1 ] * w**T
195 * [ C2 ] [ C2 ] [ v ]
196 *
197  CALL daxpy( n, -tau, work, 1, c1, ldc )
198  CALL dger( m-1, n, -tau, v, incv, work, 1, c2, ldc )
199 *
200  ELSE IF( lsame( side, 'R' ) ) THEN
201 *
202 * w := C1 + C2 * v
203 *
204  CALL dcopy( m, c1, 1, work, 1 )
205  CALL dgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
206  \$ work, 1 )
207 *
208 * [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**T]
209 *
210  CALL daxpy( m, -tau, work, 1, c1, 1 )
211  CALL dger( m, n-1, -tau, work, 1, v, incv, c2, ldc )
212  END IF
213 *
214  RETURN
215 *
216 * End of DLATZM
217 *
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine daxpy(N, DA, DX, INCX, DY, INCY)
DAXPY
Definition: daxpy.f:89
subroutine dger(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
DGER
Definition: dger.f:130
subroutine dgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
DGEMV
Definition: dgemv.f:156
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