 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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## ◆ zlatzm()

 subroutine zlatzm ( character SIDE, integer M, integer N, complex*16, dimension( * ) V, integer INCV, complex*16 TAU, complex*16, dimension( ldc, * ) C1, complex*16, dimension( ldc, * ) C2, integer LDC, complex*16, dimension( * ) WORK )

ZLATZM

Purpose:
``` This routine is deprecated and has been replaced by routine ZUNMRZ.

ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.

Let P = I - tau*u*u**H,   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 COMPLEX*16 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 COMPLEX*16 The value tau in the representation of P.``` [in,out] C1 ``` C1 is COMPLEX*16 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 COMPLEX*16 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 >= max(1,M).``` [out] WORK ``` WORK is COMPLEX*16 array, dimension (N) if SIDE = 'L' (M) if SIDE = 'R'```

Definition at line 151 of file zlatzm.f.

152*
153* -- LAPACK computational routine --
154* -- LAPACK is a software package provided by Univ. of Tennessee, --
155* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157* .. Scalar Arguments ..
158 CHARACTER SIDE
159 INTEGER INCV, LDC, M, N
160 COMPLEX*16 TAU
161* ..
162* .. Array Arguments ..
163 COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
164* ..
165*
166* =====================================================================
167*
168* .. Parameters ..
169 COMPLEX*16 ONE, ZERO
170 parameter( one = ( 1.0d+0, 0.0d+0 ),
171 \$ zero = ( 0.0d+0, 0.0d+0 ) )
172* ..
173* .. External Subroutines ..
174 EXTERNAL zaxpy, zcopy, zgemv, zgerc, zgeru, zlacgv
175* ..
176* .. External Functions ..
177 LOGICAL LSAME
178 EXTERNAL lsame
179* ..
180* .. Intrinsic Functions ..
181 INTRINSIC min
182* ..
183* .. Executable Statements ..
184*
185 IF( ( min( m, n ).EQ.0 ) .OR. ( tau.EQ.zero ) )
186 \$ RETURN
187*
188 IF( lsame( side, 'L' ) ) THEN
189*
190* w := ( C1 + v**H * C2 )**H
191*
192 CALL zcopy( n, c1, ldc, work, 1 )
193 CALL zlacgv( n, work, 1 )
194 CALL zgemv( 'Conjugate transpose', m-1, n, one, c2, ldc, v,
195 \$ incv, one, work, 1 )
196*
197* [ C1 ] := [ C1 ] - tau* [ 1 ] * w**H
198* [ C2 ] [ C2 ] [ v ]
199*
200 CALL zlacgv( n, work, 1 )
201 CALL zaxpy( n, -tau, work, 1, c1, ldc )
202 CALL zgeru( m-1, n, -tau, v, incv, work, 1, c2, ldc )
203*
204 ELSE IF( lsame( side, 'R' ) ) THEN
205*
206* w := C1 + C2 * v
207*
208 CALL zcopy( m, c1, 1, work, 1 )
209 CALL zgemv( 'No transpose', m, n-1, one, c2, ldc, v, incv, one,
210 \$ work, 1 )
211*
212* [ C1, C2 ] := [ C1, C2 ] - tau* w * [ 1 , v**H]
213*
214 CALL zaxpy( m, -tau, work, 1, c1, 1 )
215 CALL zgerc( m, n-1, -tau, work, 1, v, incv, c2, ldc )
216 END IF
217*
218 RETURN
219*
220* End of ZLATZM
221*
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:88
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:81
subroutine zgeru(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERU
Definition: zgeru.f:130
subroutine zgerc(M, N, ALPHA, X, INCX, Y, INCY, A, LDA)
ZGERC
Definition: zgerc.f:130
subroutine zgemv(TRANS, M, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY)
ZGEMV
Definition: zgemv.f:158
subroutine zlacgv(N, X, INCX)
ZLACGV conjugates a complex vector.
Definition: zlacgv.f:74
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