LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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zlatzm.f
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1*> \brief \b ZLATZM
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZLATZM + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zlatzm.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zlatzm.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlatzm.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLATZM( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
22*
23* .. Scalar Arguments ..
24* CHARACTER SIDE
25* INTEGER INCV, LDC, M, N
26* COMPLEX*16 TAU
27* ..
28* .. Array Arguments ..
29* COMPLEX*16 C1( LDC, * ), C2( LDC, * ), V( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> This routine is deprecated and has been replaced by routine ZUNMRZ.
39*>
40*> ZLATZM applies a Householder matrix generated by ZTZRQF to a matrix.
41*>
42*> Let P = I - tau*u*u**H, u = ( 1 ),
43*> ( v )
44*> where v is an (m-1) vector if SIDE = 'L', or a (n-1) vector if
45*> SIDE = 'R'.
46*>
47*> If SIDE equals 'L', let
48*> C = [ C1 ] 1
49*> [ C2 ] m-1
50*> n
51*> Then C is overwritten by P*C.
52*>
53*> If SIDE equals 'R', let
54*> C = [ C1, C2 ] m
55*> 1 n-1
56*> Then C is overwritten by C*P.
57*> \endverbatim
58*
59* Arguments:
60* ==========
61*
62*> \param[in] SIDE
63*> \verbatim
64*> SIDE is CHARACTER*1
65*> = 'L': form P * C
66*> = 'R': form C * P
67*> \endverbatim
68*>
69*> \param[in] M
70*> \verbatim
71*> M is INTEGER
72*> The number of rows of the matrix C.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The number of columns of the matrix C.
79*> \endverbatim
80*>
81*> \param[in] V
82*> \verbatim
83*> V is COMPLEX*16 array, dimension
84*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
85*> (1 + (N-1)*abs(INCV)) if SIDE = 'R'
86*> The vector v in the representation of P. V is not used
87*> if TAU = 0.
88*> \endverbatim
89*>
90*> \param[in] INCV
91*> \verbatim
92*> INCV is INTEGER
93*> The increment between elements of v. INCV <> 0
94*> \endverbatim
95*>
96*> \param[in] TAU
97*> \verbatim
98*> TAU is COMPLEX*16
99*> The value tau in the representation of P.
100*> \endverbatim
101*>
102*> \param[in,out] C1
103*> \verbatim
104*> C1 is COMPLEX*16 array, dimension
105*> (LDC,N) if SIDE = 'L'
106*> (M,1) if SIDE = 'R'
107*> On entry, the n-vector C1 if SIDE = 'L', or the m-vector C1
108*> if SIDE = 'R'.
109*>
110*> On exit, the first row of P*C if SIDE = 'L', or the first
111*> column of C*P if SIDE = 'R'.
112*> \endverbatim
113*>
114*> \param[in,out] C2
115*> \verbatim
116*> C2 is COMPLEX*16 array, dimension
117*> (LDC, N) if SIDE = 'L'
118*> (LDC, N-1) if SIDE = 'R'
119*> On entry, the (m - 1) x n matrix C2 if SIDE = 'L', or the
120*> m x (n - 1) matrix C2 if SIDE = 'R'.
121*>
122*> On exit, rows 2:m of P*C if SIDE = 'L', or columns 2:m of C*P
123*> if SIDE = 'R'.
124*> \endverbatim
125*>
126*> \param[in] LDC
127*> \verbatim
128*> LDC is INTEGER
129*> The leading dimension of the arrays C1 and C2.
130*> LDC >= max(1,M).
131*> \endverbatim
132*>
133*> \param[out] WORK
134*> \verbatim
135*> WORK is COMPLEX*16 array, dimension
136*> (N) if SIDE = 'L'
137*> (M) if SIDE = 'R'
138*> \endverbatim
139*
140* Authors:
141* ========
142*
143*> \author Univ. of Tennessee
144*> \author Univ. of California Berkeley
145*> \author Univ. of Colorado Denver
146*> \author NAG Ltd.
147*
148*> \ingroup latzm
149*
150* =====================================================================
151 SUBROUTINE zlatzm( SIDE, M, N, V, INCV, TAU, C1, C2, LDC, WORK )
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*
222 END
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 zgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV
Definition zgemv.f:160
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 zlacgv(n, x, incx)
ZLACGV conjugates a complex vector.
Definition zlacgv.f:74
subroutine zlatzm(side, m, n, v, incv, tau, c1, c2, ldc, work)
ZLATZM
Definition zlatzm.f:152