LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cunmlq.f
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1*> \brief \b CUNMLQ
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/cunmlq.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmlq.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmlq.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22* WORK, LWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER SIDE, TRANS
26* INTEGER INFO, K, LDA, LDC, LWORK, M, N
27* ..
28* .. Array Arguments ..
29* COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
30* \$ WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CUNMLQ overwrites the general complex M-by-N matrix C with
40*>
41*> SIDE = 'L' SIDE = 'R'
42*> TRANS = 'N': Q * C C * Q
43*> TRANS = 'C': Q**H * C C * Q**H
44*>
45*> where Q is a complex unitary matrix defined as the product of k
46*> elementary reflectors
47*>
48*> Q = H(k)**H . . . H(2)**H H(1)**H
49*>
50*> as returned by CGELQF. Q is of order M if SIDE = 'L' and of order N
51*> if SIDE = 'R'.
52*> \endverbatim
53*
54* Arguments:
55* ==========
56*
57*> \param[in] SIDE
58*> \verbatim
59*> SIDE is CHARACTER*1
60*> = 'L': apply Q or Q**H from the Left;
61*> = 'R': apply Q or Q**H from the Right.
62*> \endverbatim
63*>
64*> \param[in] TRANS
65*> \verbatim
66*> TRANS is CHARACTER*1
67*> = 'N': No transpose, apply Q;
68*> = 'C': Conjugate transpose, apply Q**H.
69*> \endverbatim
70*>
71*> \param[in] M
72*> \verbatim
73*> M is INTEGER
74*> The number of rows of the matrix C. M >= 0.
75*> \endverbatim
76*>
77*> \param[in] N
78*> \verbatim
79*> N is INTEGER
80*> The number of columns of the matrix C. N >= 0.
81*> \endverbatim
82*>
83*> \param[in] K
84*> \verbatim
85*> K is INTEGER
86*> The number of elementary reflectors whose product defines
87*> the matrix Q.
88*> If SIDE = 'L', M >= K >= 0;
89*> if SIDE = 'R', N >= K >= 0.
90*> \endverbatim
91*>
92*> \param[in] A
93*> \verbatim
94*> A is COMPLEX array, dimension
95*> (LDA,M) if SIDE = 'L',
96*> (LDA,N) if SIDE = 'R'
97*> The i-th row must contain the vector which defines the
98*> elementary reflector H(i), for i = 1,2,...,k, as returned by
99*> CGELQF in the first k rows of its array argument A.
100*> \endverbatim
101*>
102*> \param[in] LDA
103*> \verbatim
104*> LDA is INTEGER
105*> The leading dimension of the array A. LDA >= max(1,K).
106*> \endverbatim
107*>
108*> \param[in] TAU
109*> \verbatim
110*> TAU is COMPLEX array, dimension (K)
111*> TAU(i) must contain the scalar factor of the elementary
112*> reflector H(i), as returned by CGELQF.
113*> \endverbatim
114*>
115*> \param[in,out] C
116*> \verbatim
117*> C is COMPLEX array, dimension (LDC,N)
118*> On entry, the M-by-N matrix C.
119*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
120*> \endverbatim
121*>
122*> \param[in] LDC
123*> \verbatim
124*> LDC is INTEGER
125*> The leading dimension of the array C. LDC >= max(1,M).
126*> \endverbatim
127*>
128*> \param[out] WORK
129*> \verbatim
130*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
131*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
132*> \endverbatim
133*>
134*> \param[in] LWORK
135*> \verbatim
136*> LWORK is INTEGER
137*> The dimension of the array WORK.
138*> If SIDE = 'L', LWORK >= max(1,N);
139*> if SIDE = 'R', LWORK >= max(1,M).
140*> For good performance, LWORK should generally be larger.
141*>
142*> If LWORK = -1, then a workspace query is assumed; the routine
143*> only calculates the optimal size of the WORK array, returns
144*> this value as the first entry of the WORK array, and no error
145*> message related to LWORK is issued by XERBLA.
146*> \endverbatim
147*>
148*> \param[out] INFO
149*> \verbatim
150*> INFO is INTEGER
151*> = 0: successful exit
152*> < 0: if INFO = -i, the i-th argument had an illegal value
153*> \endverbatim
154*
155* Authors:
156* ========
157*
158*> \author Univ. of Tennessee
159*> \author Univ. of California Berkeley
160*> \author Univ. of Colorado Denver
161*> \author NAG Ltd.
162*
163*> \ingroup unmlq
164*
165* =====================================================================
166 SUBROUTINE cunmlq( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
167 \$ WORK, LWORK, INFO )
168*
169* -- LAPACK computational routine --
170* -- LAPACK is a software package provided by Univ. of Tennessee, --
171* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
172*
173* .. Scalar Arguments ..
174 CHARACTER SIDE, TRANS
175 INTEGER INFO, K, LDA, LDC, LWORK, M, N
176* ..
177* .. Array Arguments ..
178 COMPLEX A( LDA, * ), C( LDC, * ), TAU( * ),
179 \$ work( * )
180* ..
181*
182* =====================================================================
183*
184* .. Parameters ..
185 INTEGER NBMAX, LDT, TSIZE
186 parameter( nbmax = 64, ldt = nbmax+1,
187 \$ tsize = ldt*nbmax )
188* ..
189* .. Local Scalars ..
190 LOGICAL LEFT, LQUERY, NOTRAN
191 CHARACTER TRANST
192 INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK,
193 \$ lwkopt, mi, nb, nbmin, ni, nq, nw
194* ..
195* .. External Functions ..
196 LOGICAL LSAME
197 INTEGER ILAENV
198 REAL SROUNDUP_LWORK
199 EXTERNAL lsame, ilaenv, sroundup_lwork
200* ..
201* .. External Subroutines ..
202 EXTERNAL clarfb, clarft, cunml2, xerbla
203* ..
204* .. Intrinsic Functions ..
205 INTRINSIC max, min
206* ..
207* .. Executable Statements ..
208*
209* Test the input arguments
210*
211 info = 0
212 left = lsame( side, 'L' )
213 notran = lsame( trans, 'N' )
214 lquery = ( lwork.EQ.-1 )
215*
216* NQ is the order of Q and NW is the minimum dimension of WORK
217*
218 IF( left ) THEN
219 nq = m
220 nw = max( 1, n )
221 ELSE
222 nq = n
223 nw = max( 1, m )
224 END IF
225 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
226 info = -1
227 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
228 info = -2
229 ELSE IF( m.LT.0 ) THEN
230 info = -3
231 ELSE IF( n.LT.0 ) THEN
232 info = -4
233 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
234 info = -5
235 ELSE IF( lda.LT.max( 1, k ) ) THEN
236 info = -7
237 ELSE IF( ldc.LT.max( 1, m ) ) THEN
238 info = -10
239 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
240 info = -12
241 END IF
242*
243 IF( info.EQ.0 ) THEN
244*
245* Compute the workspace requirements
246*
247 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
248 lwkopt = 1
249 ELSE
250 nb = min( nbmax, ilaenv( 1, 'CUNMLQ', side // trans, m, n,
251 \$ k, -1 ) )
252 lwkopt = nw*nb + tsize
253 END IF
254 work( 1 ) = sroundup_lwork(lwkopt)
255 END IF
256*
257 IF( info.NE.0 ) THEN
258 CALL xerbla( 'CUNMLQ', -info )
259 RETURN
260 ELSE IF( lquery ) THEN
261 RETURN
262 END IF
263*
264* Quick return if possible
265*
266 IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 ) THEN
267 RETURN
268 END IF
269*
270* Determine the block size
271*
272 nbmin = 2
273 ldwork = nw
274 IF( nb.GT.1 .AND. nb.LT.k ) THEN
275 IF( lwork.LT.lwkopt ) THEN
276 nb = (lwork-tsize) / ldwork
277 nbmin = max( 2, ilaenv( 2, 'CUNMLQ', side // trans, m, n, k,
278 \$ -1 ) )
279 END IF
280 END IF
281*
282 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
283*
284* Use unblocked code
285*
286 CALL cunml2( side, trans, m, n, k, a, lda, tau, c, ldc, work,
287 \$ iinfo )
288 ELSE
289*
290* Use blocked code
291*
292 iwt = 1 + nw*nb
293 IF( ( left .AND. notran ) .OR.
294 \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
295 i1 = 1
296 i2 = k
297 i3 = nb
298 ELSE
299 i1 = ( ( k-1 ) / nb )*nb + 1
300 i2 = 1
301 i3 = -nb
302 END IF
303*
304 IF( left ) THEN
305 ni = n
306 jc = 1
307 ELSE
308 mi = m
309 ic = 1
310 END IF
311*
312 IF( notran ) THEN
313 transt = 'C'
314 ELSE
315 transt = 'N'
316 END IF
317*
318 DO 10 i = i1, i2, i3
319 ib = min( nb, k-i+1 )
320*
321* Form the triangular factor of the block reflector
322* H = H(i) H(i+1) . . . H(i+ib-1)
323*
324 CALL clarft( 'Forward', 'Rowwise', nq-i+1, ib, a( i, i ),
325 \$ lda, tau( i ), work( iwt ), ldt )
326 IF( left ) THEN
327*
328* H or H**H is applied to C(i:m,1:n)
329*
330 mi = m - i + 1
331 ic = i
332 ELSE
333*
334* H or H**H is applied to C(1:m,i:n)
335*
336 ni = n - i + 1
337 jc = i
338 END IF
339*
340* Apply H or H**H
341*
342 CALL clarfb( side, transt, 'Forward', 'Rowwise', mi, ni, ib,
343 \$ a( i, i ), lda, work( iwt ), ldt,
344 \$ c( ic, jc ), ldc, work, ldwork )
345 10 CONTINUE
346 END IF
347 work( 1 ) = sroundup_lwork(lwkopt)
348 RETURN
349*
350* End of CUNMLQ
351*
352 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine clarfb(side, trans, direct, storev, m, n, k, v, ldv, t, ldt, c, ldc, work, ldwork)
CLARFB applies a block reflector or its conjugate-transpose to a general rectangular matrix.
Definition clarfb.f:197
subroutine clarft(direct, storev, n, k, v, ldv, tau, t, ldt)
CLARFT forms the triangular factor T of a block reflector H = I - vtvH
Definition clarft.f:163
subroutine cunml2(side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNML2 multiplies a general matrix by the unitary matrix from a LQ factorization determined by cgelqf...
Definition cunml2.f:159
subroutine cunmlq(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMLQ
Definition cunmlq.f:168