LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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clamtsqr.f
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1*> \brief \b CLAMTSQR
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE CLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
7* $ LDT, C, LDC, WORK, LWORK, INFO )
8*
9*
10* .. Scalar Arguments ..
11* CHARACTER SIDE, TRANS
12* INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
13* ..
14* .. Array Arguments ..
15* COMPLEX A( LDA, * ), WORK( * ), C(LDC, * ),
16* $ T( LDT, * )
17*> \par Purpose:
18* =============
19*>
20*> \verbatim
21*>
22*> CLAMTSQR overwrites the general complex M-by-N matrix C with
23*>
24*>
25*> SIDE = 'L' SIDE = 'R'
26*> TRANS = 'N': Q * C C * Q
27*> TRANS = 'C': Q**H * C C * Q**H
28*> where Q is a complex unitary matrix defined as the product
29*> of blocked elementary reflectors computed by tall skinny
30*> QR factorization (CLATSQR)
31*> \endverbatim
32*
33* Arguments:
34* ==========
35*
36*> \param[in] SIDE
37*> \verbatim
38*> SIDE is CHARACTER*1
39*> = 'L': apply Q or Q**H from the Left;
40*> = 'R': apply Q or Q**H from the Right.
41*> \endverbatim
42*>
43*> \param[in] TRANS
44*> \verbatim
45*> TRANS is CHARACTER*1
46*> = 'N': No transpose, apply Q;
47*> = 'C': Conjugate Transpose, apply Q**H.
48*> \endverbatim
49*>
50*> \param[in] M
51*> \verbatim
52*> M is INTEGER
53*> The number of rows of the matrix A. M >=0.
54*> \endverbatim
55*>
56*> \param[in] N
57*> \verbatim
58*> N is INTEGER
59*> The number of columns of the matrix C. N >= 0.
60*> \endverbatim
61*>
62*> \param[in] K
63*> \verbatim
64*> K is INTEGER
65*> The number of elementary reflectors whose product defines
66*> the matrix Q. M >= K >= 0;
67*>
68*> \endverbatim
69*>
70*> \param[in] MB
71*> \verbatim
72*> MB is INTEGER
73*> The block size to be used in the blocked QR.
74*> MB > N. (must be the same as CLATSQR)
75*> \endverbatim
76*>
77*> \param[in] NB
78*> \verbatim
79*> NB is INTEGER
80*> The column block size to be used in the blocked QR.
81*> N >= NB >= 1.
82*> \endverbatim
83*>
84*> \param[in] A
85*> \verbatim
86*> A is COMPLEX array, dimension (LDA,K)
87*> The i-th column must contain the vector which defines the
88*> blockedelementary reflector H(i), for i = 1,2,...,k, as
89*> returned by CLATSQR in the first k columns of
90*> its array argument A.
91*> \endverbatim
92*>
93*> \param[in] LDA
94*> \verbatim
95*> LDA is INTEGER
96*> The leading dimension of the array A.
97*> If SIDE = 'L', LDA >= max(1,M);
98*> if SIDE = 'R', LDA >= max(1,N).
99*> \endverbatim
100*>
101*> \param[in] T
102*> \verbatim
103*> T is COMPLEX array, dimension
104*> ( N * Number of blocks(CEIL(M-K/MB-K)),
105*> The blocked upper triangular block reflectors stored in compact form
106*> as a sequence of upper triangular blocks. See below
107*> for further details.
108*> \endverbatim
109*>
110*> \param[in] LDT
111*> \verbatim
112*> LDT is INTEGER
113*> The leading dimension of the array T. LDT >= NB.
114*> \endverbatim
115*>
116*> \param[in,out] C
117*> \verbatim
118*> C is COMPLEX array, dimension (LDC,N)
119*> On entry, the M-by-N matrix C.
120*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
121*> \endverbatim
122*>
123*> \param[in] LDC
124*> \verbatim
125*> LDC is INTEGER
126*> The leading dimension of the array C. LDC >= max(1,M).
127*> \endverbatim
128*>
129*> \param[out] WORK
130*> \verbatim
131*> (workspace) COMPLEX array, dimension (MAX(1,LWORK))
132*> On exit, if INFO = 0, WORK(1) returns the minimal LWORK.
133*> \endverbatim
134*>
135*> \param[in] LWORK
136*> \verbatim
137*> LWORK is INTEGER
138*> The dimension of the array WORK.
139*> If MIN(M,N,K) = 0, LWORK >= 1.
140*> If SIDE = 'L', LWORK >= max(1,N*NB).
141*> If SIDE = 'R', LWORK >= max(1,MB*NB).
142*>
143*> If LWORK = -1, then a workspace query is assumed; the routine
144*> only calculates the minimal size of the WORK array, returns
145*> this value as the first entry of the WORK array, and no error
146*> message related to LWORK is issued by XERBLA.
147*> \endverbatim
148*>
149*> \param[out] INFO
150*> \verbatim
151*> INFO is INTEGER
152*> = 0: successful exit
153*> < 0: if INFO = -i, the i-th argument had an illegal value
154*> \endverbatim
155*
156* Authors:
157* ========
158*
159*> \author Univ. of Tennessee
160*> \author Univ. of California Berkeley
161*> \author Univ. of Colorado Denver
162*> \author NAG Ltd.
163*
164*> \par Further Details:
165* =====================
166*>
167*> \verbatim
168*> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
169*> representing Q as a product of other unitary matrices
170*> Q = Q(1) * Q(2) * . . . * Q(k)
171*> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
172*> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
173*> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
174*> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
175*> . . .
176*>
177*> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
178*> stored under the diagonal of rows 1:MB of A, and by upper triangular
179*> block reflectors, stored in array T(1:LDT,1:N).
180*> For more information see Further Details in GEQRT.
181*>
182*> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
183*> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
184*> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
185*> The last Q(k) may use fewer rows.
186*> For more information see Further Details in TPQRT.
187*>
188*> For more details of the overall algorithm, see the description of
189*> Sequential TSQR in Section 2.2 of [1].
190*>
191*> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
192*> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
193*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
194*> \endverbatim
195*>
196*> \ingroup lamtsqr
197*>
198* =====================================================================
199 SUBROUTINE clamtsqr( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
200 $ LDT, C, LDC, WORK, LWORK, INFO )
201*
202* -- LAPACK computational routine --
203* -- LAPACK is a software package provided by Univ. of Tennessee, --
204* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205*
206* .. Scalar Arguments ..
207 CHARACTER SIDE, TRANS
208 INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
209* ..
210* .. Array Arguments ..
211 COMPLEX A( LDA, * ), WORK( * ), C( LDC, * ),
212 $ t( ldt, * )
213* ..
214*
215* =====================================================================
216*
217* ..
218* .. Local Scalars ..
219 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
220 INTEGER I, II, KK, LW, CTR, Q, MINMNK, LWMIN
221* ..
222* .. External Functions ..
223 LOGICAL LSAME
224 REAL SROUNDUP_LWORK
225 EXTERNAL lsame, sroundup_lwork
226* ..
227* .. External Subroutines ..
228 EXTERNAL cgemqrt, ctpmqrt, xerbla
229* ..
230* .. Executable Statements ..
231*
232* Test the input arguments
233*
234 info = 0
235 lquery = ( lwork.EQ.-1 )
236 notran = lsame( trans, 'N' )
237 tran = lsame( trans, 'C' )
238 left = lsame( side, 'L' )
239 right = lsame( side, 'R' )
240 IF( left ) THEN
241 lw = n * nb
242 q = m
243 ELSE
244 lw = m * nb
245 q = n
246 END IF
247*
248 minmnk = min( m, n, k )
249 IF( minmnk.EQ.0 ) THEN
250 lwmin = 1
251 ELSE
252 lwmin = max( 1, lw )
253 END IF
254*
255 IF( .NOT.left .AND. .NOT.right ) THEN
256 info = -1
257 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
258 info = -2
259 ELSE IF( m.LT.k ) THEN
260 info = -3
261 ELSE IF( n.LT.0 ) THEN
262 info = -4
263 ELSE IF( k.LT.0 ) THEN
264 info = -5
265 ELSE IF( k.LT.nb .OR. nb.LT.1 ) THEN
266 info = -7
267 ELSE IF( lda.LT.max( 1, q ) ) THEN
268 info = -9
269 ELSE IF( ldt.LT.max( 1, nb ) ) THEN
270 info = -11
271 ELSE IF( ldc.LT.max( 1, m ) ) THEN
272 info = -13
273 ELSE IF( lwork.LT.lwmin .AND. (.NOT.lquery) ) THEN
274 info = -15
275 END IF
276*
277 IF( info.EQ.0 ) THEN
278 work( 1 ) = sroundup_lwork( lwmin )
279 END IF
280*
281 IF( info.NE.0 ) THEN
282 CALL xerbla( 'CLAMTSQR', -info )
283 RETURN
284 ELSE IF( lquery ) THEN
285 RETURN
286 END IF
287*
288* Quick return if possible
289*
290 IF( minmnk.EQ.0 ) THEN
291 RETURN
292 END IF
293*
294* Determine the block size if it is tall skinny or short and wide
295*
296 IF((mb.LE.k).OR.(mb.GE.max(m,n,k))) THEN
297 CALL cgemqrt( side, trans, m, n, k, nb, a, lda,
298 $ t, ldt, c, ldc, work, info )
299 RETURN
300 END IF
301*
302 IF(left.AND.notran) THEN
303*
304* Multiply Q to the last block of C
305*
306 kk = mod((m-k),(mb-k))
307 ctr = (m-k)/(mb-k)
308 IF (kk.GT.0) THEN
309 ii=m-kk+1
310 CALL ctpmqrt('L','N',kk , n, k, 0, nb, a(ii,1), lda,
311 $ t(1, ctr*k+1),ldt , c(1,1), ldc,
312 $ c(ii,1), ldc, work, info )
313 ELSE
314 ii=m+1
315 END IF
316*
317 DO i=ii-(mb-k),mb+1,-(mb-k)
318*
319* Multiply Q to the current block of C (I:I+MB,1:N)
320*
321 ctr = ctr - 1
322 CALL ctpmqrt('L','N',mb-k , n, k, 0,nb, a(i,1), lda,
323 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
324 $ c(i,1), ldc, work, info )
325
326 END DO
327*
328* Multiply Q to the first block of C (1:MB,1:N)
329*
330 CALL cgemqrt('L','N',mb , n, k, nb, a(1,1), lda, t
331 $ ,ldt ,c(1,1), ldc, work, info )
332*
333 ELSE IF (left.AND.tran) THEN
334*
335* Multiply Q to the first block of C
336*
337 kk = mod((m-k),(mb-k))
338 ii=m-kk+1
339 ctr = 1
340 CALL cgemqrt('L','C',mb , n, k, nb, a(1,1), lda, t
341 $ ,ldt ,c(1,1), ldc, work, info )
342*
343 DO i=mb+1,ii-mb+k,(mb-k)
344*
345* Multiply Q to the current block of C (I:I+MB,1:N)
346*
347 CALL ctpmqrt('L','C',mb-k , n, k, 0,nb, a(i,1), lda,
348 $ t(1, ctr*k+1),ldt, c(1,1), ldc,
349 $ c(i,1), ldc, work, info )
350 ctr = ctr + 1
351*
352 END DO
353 IF(ii.LE.m) THEN
354*
355* Multiply Q to the last block of C
356*
357 CALL ctpmqrt('L','C',kk , n, k, 0,nb, a(ii,1), lda,
358 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
359 $ c(ii,1), ldc, work, info )
360*
361 END IF
362*
363 ELSE IF(right.AND.tran) THEN
364*
365* Multiply Q to the last block of C
366*
367 kk = mod((n-k),(mb-k))
368 ctr = (n-k)/(mb-k)
369 IF (kk.GT.0) THEN
370 ii=n-kk+1
371 CALL ctpmqrt('R','C',m , kk, k, 0, nb, a(ii,1), lda,
372 $ t(1, ctr*k+1), ldt, c(1,1), ldc,
373 $ c(1,ii), ldc, work, info )
374 ELSE
375 ii=n+1
376 END IF
377*
378 DO i=ii-(mb-k),mb+1,-(mb-k)
379*
380* Multiply Q to the current block of C (1:M,I:I+MB)
381*
382 ctr = ctr - 1
383 CALL ctpmqrt('R','C',m , mb-k, k, 0,nb, a(i,1), lda,
384 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
385 $ c(1,i), ldc, work, info )
386 END DO
387*
388* Multiply Q to the first block of C (1:M,1:MB)
389*
390 CALL cgemqrt('R','C',m , mb, k, nb, a(1,1), lda, t
391 $ ,ldt ,c(1,1), ldc, work, info )
392*
393 ELSE IF (right.AND.notran) THEN
394*
395* Multiply Q to the first block of C
396*
397 kk = mod((n-k),(mb-k))
398 ii=n-kk+1
399 ctr = 1
400 CALL cgemqrt('R','N', m, mb , k, nb, a(1,1), lda, t
401 $ ,ldt ,c(1,1), ldc, work, info )
402*
403 DO i=mb+1,ii-mb+k,(mb-k)
404*
405* Multiply Q to the current block of C (1:M,I:I+MB)
406*
407 CALL ctpmqrt('R','N', m, mb-k, k, 0,nb, a(i,1), lda,
408 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
409 $ c(1,i), ldc, work, info )
410 ctr = ctr + 1
411*
412 END DO
413 IF(ii.LE.n) THEN
414*
415* Multiply Q to the last block of C
416*
417 CALL ctpmqrt('R','N', m, kk , k, 0,nb, a(ii,1), lda,
418 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
419 $ c(1,ii), ldc, work, info )
420*
421 END IF
422*
423 END IF
424*
425 work( 1 ) = sroundup_lwork( lwmin )
426 RETURN
427*
428* End of CLAMTSQR
429*
430 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine cgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
CGEMQRT
Definition cgemqrt.f:166
subroutine clamtsqr(side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
CLAMTSQR
Definition clamtsqr.f:201
subroutine ctpmqrt(side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
CTPMQRT
Definition ctpmqrt.f:215