LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ clatzm()

 subroutine clatzm ( character side, integer m, integer n, complex, dimension( * ) v, integer incv, complex tau, complex, dimension( ldc, * ) c1, complex, dimension( ldc, * ) c2, integer ldc, complex, dimension( * ) work )

CLATZM

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``` This routine is deprecated and has been replaced by routine CUNMRZ.

CLATZM applies a Householder matrix generated by CTZRQF 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 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 The value tau in the representation of P.``` [in,out] C1 ``` C1 is COMPLEX 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 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 array, dimension (N) if SIDE = 'L' (M) if SIDE = 'R'```

Definition at line 151 of file clatzm.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 TAU
161* ..
162* .. Array Arguments ..
163 COMPLEX C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
164* ..
165*
166* =====================================================================
167*
168* .. Parameters ..
169 COMPLEX ONE, ZERO
170 parameter( one = ( 1.0e+0, 0.0e+0 ),
171 \$ zero = ( 0.0e+0, 0.0e+0 ) )
172* ..
173* .. External Subroutines ..
174 EXTERNAL caxpy, ccopy, cgemv, cgerc, cgeru, clacgv
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 ccopy( n, c1, ldc, work, 1 )
193 CALL clacgv( n, work, 1 )
194 CALL cgemv( '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 clacgv( n, work, 1 )
201 CALL caxpy( n, -tau, work, 1, c1, ldc )
202 CALL cgeru( 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 ccopy( m, c1, 1, work, 1 )
209 CALL cgemv( '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 caxpy( m, -tau, work, 1, c1, 1 )
215 CALL cgerc( m, n-1, -tau, work, 1, v, incv, c2, ldc )
216 END IF
217*
218 RETURN
219*
220* End of CLATZM
221*
subroutine caxpy(n, ca, cx, incx, cy, incy)
CAXPY
Definition caxpy.f:88
subroutine ccopy(n, cx, incx, cy, incy)
CCOPY
Definition ccopy.f:81
subroutine cgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
CGEMV
Definition cgemv.f:160
subroutine cgerc(m, n, alpha, x, incx, y, incy, a, lda)
CGERC
Definition cgerc.f:130
subroutine cgeru(m, n, alpha, x, incx, y, incy, a, lda)
CGERU
Definition cgeru.f:130
subroutine clacgv(n, x, incx)
CLACGV conjugates a complex vector.
Definition clacgv.f:74
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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