LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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zunmr3.f
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1*> \brief \b ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf (unblocked algorithm).
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmr3.f">
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunmr3.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZUNMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
22* WORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER INFO, K, L, LDA, LDC, M, N
27* ..
28* .. Array Arguments ..
29* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZUNMR3 overwrites the general complex m by n matrix C with
39*>
40*> Q * C if SIDE = 'L' and TRANS = 'N', or
41*>
42*> Q**H* C if SIDE = 'L' and TRANS = 'C', or
43*>
44*> C * Q if SIDE = 'R' and TRANS = 'N', or
45*>
46*> C * Q**H if SIDE = 'R' and TRANS = 'C',
47*>
48*> where Q is a complex unitary matrix defined as the product of k
49*> elementary reflectors
50*>
51*> Q = H(1) H(2) . . . H(k)
52*>
53*> as returned by ZTZRZF. Q is of order m if SIDE = 'L' and of order n
54*> if SIDE = 'R'.
55*> \endverbatim
56*
57* Arguments:
58* ==========
59*
60*> \param[in] SIDE
61*> \verbatim
62*> SIDE is CHARACTER*1
63*> = 'L': apply Q or Q**H from the Left
64*> = 'R': apply Q or Q**H from the Right
65*> \endverbatim
66*>
67*> \param[in] TRANS
68*> \verbatim
69*> TRANS is CHARACTER*1
70*> = 'N': apply Q (No transpose)
71*> = 'C': apply Q**H (Conjugate transpose)
72*> \endverbatim
73*>
74*> \param[in] M
75*> \verbatim
76*> M is INTEGER
77*> The number of rows of the matrix C. M >= 0.
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*> N is INTEGER
83*> The number of columns of the matrix C. N >= 0.
84*> \endverbatim
85*>
86*> \param[in] K
87*> \verbatim
88*> K is INTEGER
89*> The number of elementary reflectors whose product defines
90*> the matrix Q.
91*> If SIDE = 'L', M >= K >= 0;
92*> if SIDE = 'R', N >= K >= 0.
93*> \endverbatim
94*>
95*> \param[in] L
96*> \verbatim
97*> L is INTEGER
98*> The number of columns of the matrix A containing
99*> the meaningful part of the Householder reflectors.
100*> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
101*> \endverbatim
102*>
103*> \param[in] A
104*> \verbatim
105*> A is COMPLEX*16 array, dimension
106*> (LDA,M) if SIDE = 'L',
107*> (LDA,N) if SIDE = 'R'
108*> The i-th row must contain the vector which defines the
109*> elementary reflector H(i), for i = 1,2,...,k, as returned by
110*> ZTZRZF in the last k rows of its array argument A.
111*> A is modified by the routine but restored on exit.
112*> \endverbatim
113*>
114*> \param[in] LDA
115*> \verbatim
116*> LDA is INTEGER
117*> The leading dimension of the array A. LDA >= max(1,K).
118*> \endverbatim
119*>
120*> \param[in] TAU
121*> \verbatim
122*> TAU is COMPLEX*16 array, dimension (K)
123*> TAU(i) must contain the scalar factor of the elementary
124*> reflector H(i), as returned by ZTZRZF.
125*> \endverbatim
126*>
127*> \param[in,out] C
128*> \verbatim
129*> C is COMPLEX*16 array, dimension (LDC,N)
130*> On entry, the m-by-n matrix C.
131*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
132*> \endverbatim
133*>
134*> \param[in] LDC
135*> \verbatim
136*> LDC is INTEGER
137*> The leading dimension of the array C. LDC >= max(1,M).
138*> \endverbatim
139*>
140*> \param[out] WORK
141*> \verbatim
142*> WORK is COMPLEX*16 array, dimension
143*> (N) if SIDE = 'L',
144*> (M) if SIDE = 'R'
145*> \endverbatim
146*>
147*> \param[out] INFO
148*> \verbatim
149*> INFO is INTEGER
150*> = 0: successful exit
151*> < 0: if INFO = -i, the i-th argument had an illegal value
152*> \endverbatim
153*
154* Authors:
155* ========
156*
157*> \author Univ. of Tennessee
158*> \author Univ. of California Berkeley
159*> \author Univ. of Colorado Denver
160*> \author NAG Ltd.
161*
162*> \ingroup unmr3
163*
164*> \par Contributors:
165* ==================
166*>
167*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
168*
169*> \par Further Details:
170* =====================
171*>
172*> \verbatim
173*> \endverbatim
174*>
175* =====================================================================
176 SUBROUTINE zunmr3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
177 \$ WORK, INFO )
178*
179* -- LAPACK computational routine --
180* -- LAPACK is a software package provided by Univ. of Tennessee, --
181* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182*
183* .. Scalar Arguments ..
184 CHARACTER SIDE, TRANS
185 INTEGER INFO, K, L, LDA, LDC, M, N
186* ..
187* .. Array Arguments ..
188 COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
189* ..
190*
191* =====================================================================
192*
193* .. Local Scalars ..
194 LOGICAL LEFT, NOTRAN
195 INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
196 COMPLEX*16 TAUI
197* ..
198* .. External Functions ..
199 LOGICAL LSAME
200 EXTERNAL lsame
201* ..
202* .. External Subroutines ..
203 EXTERNAL xerbla, zlarz
204* ..
205* .. Intrinsic Functions ..
206 INTRINSIC dconjg, max
207* ..
208* .. Executable Statements ..
209*
210* Test the input arguments
211*
212 info = 0
213 left = lsame( side, 'L' )
214 notran = lsame( trans, 'N' )
215*
216* NQ is the order of Q
217*
218 IF( left ) THEN
219 nq = m
220 ELSE
221 nq = n
222 END IF
223 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
224 info = -1
225 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
226 info = -2
227 ELSE IF( m.LT.0 ) THEN
228 info = -3
229 ELSE IF( n.LT.0 ) THEN
230 info = -4
231 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
232 info = -5
233 ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
234 \$ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
235 info = -6
236 ELSE IF( lda.LT.max( 1, k ) ) THEN
237 info = -8
238 ELSE IF( ldc.LT.max( 1, m ) ) THEN
239 info = -11
240 END IF
241 IF( info.NE.0 ) THEN
242 CALL xerbla( 'ZUNMR3', -info )
243 RETURN
244 END IF
245*
246* Quick return if possible
247*
248 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
249 \$ RETURN
250*
251 IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
252 i1 = 1
253 i2 = k
254 i3 = 1
255 ELSE
256 i1 = k
257 i2 = 1
258 i3 = -1
259 END IF
260*
261 IF( left ) THEN
262 ni = n
263 ja = m - l + 1
264 jc = 1
265 ELSE
266 mi = m
267 ja = n - l + 1
268 ic = 1
269 END IF
270*
271 DO 10 i = i1, i2, i3
272 IF( left ) THEN
273*
274* H(i) or H(i)**H is applied to C(i:m,1:n)
275*
276 mi = m - i + 1
277 ic = i
278 ELSE
279*
280* H(i) or H(i)**H is applied to C(1:m,i:n)
281*
282 ni = n - i + 1
283 jc = i
284 END IF
285*
286* Apply H(i) or H(i)**H
287*
288 IF( notran ) THEN
289 taui = tau( i )
290 ELSE
291 taui = dconjg( tau( i ) )
292 END IF
293 CALL zlarz( side, mi, ni, l, a( i, ja ), lda, taui,
294 \$ c( ic, jc ), ldc, work )
295*
296 10 CONTINUE
297*
298 RETURN
299*
300* End of ZUNMR3
301*
302 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zlarz(side, m, n, l, v, incv, tau, c, ldc, work)
ZLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition zlarz.f:147
subroutine zunmr3(side, trans, m, n, k, l, a, lda, tau, c, ldc, work, info)
ZUNMR3 multiplies a general matrix by the unitary matrix from a RZ factorization determined by ctzrzf...
Definition zunmr3.f:178