LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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cunmql.f
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1*> \brief \b CUNMQL
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/cunmql.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cunmql.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cunmql.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CUNMQL( 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*> CUNMQL 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(2) H(1)
49*>
50*> as returned by CGEQLF. 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 (LDA,K)
95*> The i-th column must contain the vector which defines the
96*> elementary reflector H(i), for i = 1,2,...,k, as returned by
97*> CGEQLF in the last k columns of its array argument A.
98*> \endverbatim
99*>
100*> \param[in] LDA
101*> \verbatim
102*> LDA is INTEGER
103*> The leading dimension of the array A.
104*> If SIDE = 'L', LDA >= max(1,M);
105*> if SIDE = 'R', LDA >= max(1,N).
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 CGEQLF.
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 unmql
164*
165* =====================================================================
166 SUBROUTINE cunmql( 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 INTEGER I, I1, I2, I3, IB, IINFO, IWT, LDWORK, LWKOPT,
192 \$ mi, nb, nbmin, ni, nq, nw
193* ..
194* .. External Functions ..
195 LOGICAL LSAME
196 INTEGER ILAENV
197 REAL SROUNDUP_LWORK
198 EXTERNAL lsame, ilaenv, sroundup_lwork
199* ..
200* .. External Subroutines ..
201 EXTERNAL clarfb, clarft, cunm2l, xerbla
202* ..
203* .. Intrinsic Functions ..
204 INTRINSIC max, min
205* ..
206* .. Executable Statements ..
207*
208* Test the input arguments
209*
210 info = 0
211 left = lsame( side, 'L' )
212 notran = lsame( trans, 'N' )
213 lquery = ( lwork.EQ.-1 )
214*
215* NQ is the order of Q and NW is the minimum dimension of WORK
216*
217 IF( left ) THEN
218 nq = m
219 nw = max( 1, n )
220 ELSE
221 nq = n
222 nw = max( 1, m )
223 END IF
224 IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
225 info = -1
226 ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'C' ) ) THEN
227 info = -2
228 ELSE IF( m.LT.0 ) THEN
229 info = -3
230 ELSE IF( n.LT.0 ) THEN
231 info = -4
232 ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
233 info = -5
234 ELSE IF( lda.LT.max( 1, nq ) ) THEN
235 info = -7
236 ELSE IF( ldc.LT.max( 1, m ) ) THEN
237 info = -10
238 ELSE IF( lwork.LT.nw .AND. .NOT.lquery ) THEN
239 info = -12
240 END IF
241*
242 IF( info.EQ.0 ) THEN
243*
244* Compute the workspace requirements
245*
246 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
247 lwkopt = 1
248 ELSE
249 nb = min( nbmax, ilaenv( 1, 'CUNMQL', side // trans, m, n,
250 \$ k, -1 ) )
251 lwkopt = nw*nb + tsize
252 END IF
253 work( 1 ) = sroundup_lwork(lwkopt)
254 END IF
255*
256 IF( info.NE.0 ) THEN
257 CALL xerbla( 'CUNMQL', -info )
258 RETURN
259 ELSE IF( lquery ) THEN
260 RETURN
261 END IF
262*
263* Quick return if possible
264*
265 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
266 RETURN
267 END IF
268*
269* Determine the block size
270*
271 nbmin = 2
272 ldwork = nw
273 IF( nb.GT.1 .AND. nb.LT.k ) THEN
274 IF( lwork.LT.lwkopt ) THEN
275 nb = (lwork-tsize) / ldwork
276 nbmin = max( 2, ilaenv( 2, 'CUNMQL', side // trans, m, n, k,
277 \$ -1 ) )
278 END IF
279 END IF
280*
281 IF( nb.LT.nbmin .OR. nb.GE.k ) THEN
282*
283* Use unblocked code
284*
285 CALL cunm2l( side, trans, m, n, k, a, lda, tau, c, ldc, work,
286 \$ iinfo )
287 ELSE
288*
289* Use blocked code
290*
291 iwt = 1 + nw*nb
292 IF( ( left .AND. notran ) .OR.
293 \$ ( .NOT.left .AND. .NOT.notran ) ) THEN
294 i1 = 1
295 i2 = k
296 i3 = nb
297 ELSE
298 i1 = ( ( k-1 ) / nb )*nb + 1
299 i2 = 1
300 i3 = -nb
301 END IF
302*
303 IF( left ) THEN
304 ni = n
305 ELSE
306 mi = m
307 END IF
308*
309 DO 10 i = i1, i2, i3
310 ib = min( nb, k-i+1 )
311*
312* Form the triangular factor of the block reflector
313* H = H(i+ib-1) . . . H(i+1) H(i)
314*
315 CALL clarft( 'Backward', 'Columnwise', nq-k+i+ib-1, ib,
316 \$ a( 1, i ), lda, tau( i ), work( iwt ), ldt )
317 IF( left ) THEN
318*
319* H or H**H is applied to C(1:m-k+i+ib-1,1:n)
320*
321 mi = m - k + i + ib - 1
322 ELSE
323*
324* H or H**H is applied to C(1:m,1:n-k+i+ib-1)
325*
326 ni = n - k + i + ib - 1
327 END IF
328*
329* Apply H or H**H
330*
331 CALL clarfb( side, trans, 'Backward', 'Columnwise', mi, ni,
332 \$ ib, a( 1, i ), lda, work( iwt ), ldt, c, ldc,
333 \$ work, ldwork )
334 10 CONTINUE
335 END IF
336 work( 1 ) = sroundup_lwork(lwkopt)
337 RETURN
338*
339* End of CUNMQL
340*
341 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 cunm2l(side, trans, m, n, k, a, lda, tau, c, ldc, work, info)
CUNM2L multiplies a general matrix by the unitary matrix from a QL factorization determined by cgeqlf...
Definition cunm2l.f:159
subroutine cunmql(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMQL
Definition cunmql.f:168