LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zlarf.f
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1*> \brief \b ZLARF applies an elementary reflector to a general rectangular matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zlarf.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZLARF( SIDE, M, N, V, INCV, TAU, C, 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 C( LDC, * ), V( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZLARF applies a complex elementary reflector H to a complex M-by-N
39*> matrix C, from either the left or the right. H is represented in the
40*> form
41*>
42*> H = I - tau * v * v**H
43*>
44*> where tau is a complex scalar and v is a complex vector.
45*>
46*> If tau = 0, then H is taken to be the unit matrix.
47*>
48*> To apply H**H, supply conjg(tau) instead
49*> tau.
50*> \endverbatim
51*
52* Arguments:
53* ==========
54*
55*> \param[in] SIDE
56*> \verbatim
57*> SIDE is CHARACTER*1
58*> = 'L': form H * C
59*> = 'R': form C * H
60*> \endverbatim
61*>
62*> \param[in] M
63*> \verbatim
64*> M is INTEGER
65*> The number of rows of the matrix C.
66*> \endverbatim
67*>
68*> \param[in] N
69*> \verbatim
70*> N is INTEGER
71*> The number of columns of the matrix C.
72*> \endverbatim
73*>
74*> \param[in] V
75*> \verbatim
76*> V is COMPLEX*16 array, dimension
77*> (1 + (M-1)*abs(INCV)) if SIDE = 'L'
78*> or (1 + (N-1)*abs(INCV)) if SIDE = 'R'
79*> The vector v in the representation of H. V is not used if
80*> TAU = 0.
81*> \endverbatim
82*>
83*> \param[in] INCV
84*> \verbatim
85*> INCV is INTEGER
86*> The increment between elements of v. INCV <> 0.
87*> \endverbatim
88*>
89*> \param[in] TAU
90*> \verbatim
91*> TAU is COMPLEX*16
92*> The value tau in the representation of H.
93*> \endverbatim
94*>
95*> \param[in,out] C
96*> \verbatim
97*> C is COMPLEX*16 array, dimension (LDC,N)
98*> On entry, the M-by-N matrix C.
99*> On exit, C is overwritten by the matrix H * C if SIDE = 'L',
100*> or C * H if SIDE = 'R'.
101*> \endverbatim
102*>
103*> \param[in] LDC
104*> \verbatim
105*> LDC is INTEGER
106*> The leading dimension of the array C. LDC >= max(1,M).
107*> \endverbatim
108*>
109*> \param[out] WORK
110*> \verbatim
111*> WORK is COMPLEX*16 array, dimension
112*> (N) if SIDE = 'L'
113*> or (M) if SIDE = 'R'
114*> \endverbatim
115*
116* Authors:
117* ========
118*
119*> \author Univ. of Tennessee
120*> \author Univ. of California Berkeley
121*> \author Univ. of Colorado Denver
122*> \author NAG Ltd.
123*
124*> \ingroup larf
125*
126* =====================================================================
127 SUBROUTINE zlarf( SIDE, M, N, V, INCV, TAU, C, LDC, WORK )
128*
129* -- LAPACK auxiliary routine --
130* -- LAPACK is a software package provided by Univ. of Tennessee, --
131* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
132*
133* .. Scalar Arguments ..
134 CHARACTER SIDE
135 INTEGER INCV, LDC, M, N
136 COMPLEX*16 TAU
137* ..
138* .. Array Arguments ..
139 COMPLEX*16 C( LDC, * ), V( * ), WORK( * )
140* ..
141*
142* =====================================================================
143*
144* .. Parameters ..
145 COMPLEX*16 ONE, ZERO
146 parameter( one = ( 1.0d+0, 0.0d+0 ),
147 \$ zero = ( 0.0d+0, 0.0d+0 ) )
148* ..
149* .. Local Scalars ..
150 LOGICAL APPLYLEFT
151 INTEGER I, LASTV, LASTC
152* ..
153* .. External Subroutines ..
154 EXTERNAL zgemv, zgerc
155* ..
156* .. External Functions ..
157 LOGICAL LSAME
158 INTEGER ILAZLR, ILAZLC
159 EXTERNAL lsame, ilazlr, ilazlc
160* ..
161* .. Executable Statements ..
162*
163 applyleft = lsame( side, 'L' )
164 lastv = 0
165 lastc = 0
166 IF( tau.NE.zero ) THEN
167* Set up variables for scanning V. LASTV begins pointing to the end
168* of V.
169 IF( applyleft ) THEN
170 lastv = m
171 ELSE
172 lastv = n
173 END IF
174 IF( incv.GT.0 ) THEN
175 i = 1 + (lastv-1) * incv
176 ELSE
177 i = 1
178 END IF
179* Look for the last non-zero row in V.
180 DO WHILE( lastv.GT.0 .AND. v( i ).EQ.zero )
181 lastv = lastv - 1
182 i = i - incv
183 END DO
184 IF( applyleft ) THEN
185* Scan for the last non-zero column in C(1:lastv,:).
186 lastc = ilazlc(lastv, n, c, ldc)
187 ELSE
188* Scan for the last non-zero row in C(:,1:lastv).
189 lastc = ilazlr(m, lastv, c, ldc)
190 END IF
191 END IF
192* Note that lastc.eq.0 renders the BLAS operations null; no special
193* case is needed at this level.
194 IF( applyleft ) THEN
195*
196* Form H * C
197*
198 IF( lastv.GT.0 ) THEN
199*
200* w(1:lastc,1) := C(1:lastv,1:lastc)**H * v(1:lastv,1)
201*
202 CALL zgemv( 'Conjugate transpose', lastv, lastc, one,
203 \$ c, ldc, v, incv, zero, work, 1 )
204*
205* C(1:lastv,1:lastc) := C(...) - v(1:lastv,1) * w(1:lastc,1)**H
206*
207 CALL zgerc( lastv, lastc, -tau, v, incv, work, 1, c, ldc )
208 END IF
209 ELSE
210*
211* Form C * H
212*
213 IF( lastv.GT.0 ) THEN
214*
215* w(1:lastc,1) := C(1:lastc,1:lastv) * v(1:lastv,1)
216*
217 CALL zgemv( 'No transpose', lastc, lastv, one, c, ldc,
218 \$ v, incv, zero, work, 1 )
219*
220* C(1:lastc,1:lastv) := C(...) - w(1:lastc,1) * v(1:lastv,1)**H
221*
222 CALL zgerc( lastc, lastv, -tau, work, 1, v, incv, c, ldc )
223 END IF
224 END IF
225 RETURN
226*
227* End of ZLARF
228*
229 END
subroutine zgemv(trans, m, n, alpha, a, lda, x, incx, beta, y, incy)
ZGEMV
Definition zgemv.f:160
subroutine zgerc(m, n, alpha, x, incx, y, incy, a, lda)
ZGERC
Definition zgerc.f:130
subroutine zlarf(side, m, n, v, incv, tau, c, ldc, work)
ZLARF applies an elementary reflector to a general rectangular matrix.
Definition zlarf.f:128