LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
slamswlq.f
Go to the documentation of this file.
1*> \brief \b SLAMSWLQ
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE SLAMSWLQ( 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* DOUBLE A( LDA, * ), WORK( * ), C(LDC, * ),
16* $ T( LDT, * )
17*> \par Purpose:
18* =============
19*>
20*> \verbatim
21*>
22*> SLAMSWLQ overwrites the general real M-by-N matrix C with
23*>
24*>
25*> SIDE = 'L' SIDE = 'R'
26*> TRANS = 'N': Q * C C * Q
27*> TRANS = 'T': Q**T * C C * Q**T
28*> where Q is a real orthogonal matrix defined as the product of blocked
29*> elementary reflectors computed by short wide LQ
30*> factorization (SLASWLQ)
31*> \endverbatim
32*
33* Arguments:
34* ==========
35*
36*> \param[in] SIDE
37*> \verbatim
38*> SIDE is CHARACTER*1
39*> = 'L': apply Q or Q**T from the Left;
40*> = 'R': apply Q or Q**T from the Right.
41*> \endverbatim
42*>
43*> \param[in] TRANS
44*> \verbatim
45*> TRANS is CHARACTER*1
46*> = 'N': No transpose, apply Q;
47*> = 'T': Transpose, apply Q**T.
48*> \endverbatim
49*>
50*> \param[in] M
51*> \verbatim
52*> M is INTEGER
53*> The number of rows of the matrix C. 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.
67*> M >= K >= 0;
68*>
69*> \endverbatim
70*> \param[in] MB
71*> \verbatim
72*> MB is INTEGER
73*> The row block size to be used in the blocked LQ.
74*> M >= MB >= 1
75*> \endverbatim
76*>
77*> \param[in] NB
78*> \verbatim
79*> NB is INTEGER
80*> The column block size to be used in the blocked LQ.
81*> NB > M.
82*> \endverbatim
83*>
84*> \param[in] A
85*> \verbatim
86*> A is REAL array, dimension
87*> (LDA,M) if SIDE = 'L',
88*> (LDA,N) if SIDE = 'R'
89*> The i-th row must contain the vector which defines the blocked
90*> elementary reflector H(i), for i = 1,2,...,k, as returned by
91*> SLASWLQ in the first k rows of its array argument A.
92*> \endverbatim
93*>
94*> \param[in] LDA
95*> \verbatim
96*> LDA is INTEGER
97*> The leading dimension of the array A. LDA >= max(1,K).
98*> \endverbatim
99*>
100*> \param[in] T
101*> \verbatim
102*> T is REAL array, dimension
103*> ( M * Number of blocks(CEIL(N-K/NB-K)),
104*> The blocked upper triangular block reflectors stored in compact form
105*> as a sequence of upper triangular blocks. See below
106*> for further details.
107*> \endverbatim
108*>
109*> \param[in] LDT
110*> \verbatim
111*> LDT is INTEGER
112*> The leading dimension of the array T. LDT >= MB.
113*> \endverbatim
114*>
115*> \param[in,out] C
116*> \verbatim
117*> C is REAL array, dimension (LDC,N)
118*> On entry, the M-by-N matrix C.
119*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T 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*> (workspace) REAL array, dimension (MAX(1,LWORK))
131*> \endverbatim
132*>
133*> \param[in] LWORK
134*> \verbatim
135*> LWORK is INTEGER
136*> The dimension of the array WORK.
137*> If SIDE = 'L', LWORK >= max(1,NB) * MB;
138*> if SIDE = 'R', LWORK >= max(1,M) * MB.
139*> If LWORK = -1, then a workspace query is assumed; the routine
140*> only calculates the optimal size of the WORK array, returns
141*> this value as the first entry of the WORK array, and no error
142*> message related to LWORK is issued by XERBLA.
143*> \endverbatim
144*>
145*> \param[out] INFO
146*> \verbatim
147*> INFO is INTEGER
148*> = 0: successful exit
149*> < 0: if INFO = -i, the i-th argument had an illegal value
150*> \endverbatim
151*
152* Authors:
153* ========
154*
155*> \author Univ. of Tennessee
156*> \author Univ. of California Berkeley
157*> \author Univ. of Colorado Denver
158*> \author NAG Ltd.
159*
160*> \par Further Details:
161* =====================
162*>
163*> \verbatim
164*> Short-Wide LQ (SWLQ) performs LQ by a sequence of orthogonal transformations,
165*> representing Q as a product of other orthogonal matrices
166*> Q = Q(1) * Q(2) * . . . * Q(k)
167*> where each Q(i) zeros out upper diagonal entries of a block of NB rows of A:
168*> Q(1) zeros out the upper diagonal entries of rows 1:NB of A
169*> Q(2) zeros out the bottom MB-N rows of rows [1:M,NB+1:2*NB-M] of A
170*> Q(3) zeros out the bottom MB-N rows of rows [1:M,2*NB-M+1:3*NB-2*M] of A
171*> . . .
172*>
173*> Q(1) is computed by GELQT, which represents Q(1) by Householder vectors
174*> stored under the diagonal of rows 1:MB of A, and by upper triangular
175*> block reflectors, stored in array T(1:LDT,1:N).
176*> For more information see Further Details in GELQT.
177*>
178*> Q(i) for i>1 is computed by TPLQT, which represents Q(i) by Householder vectors
179*> stored in columns [(i-1)*(NB-M)+M+1:i*(NB-M)+M] of A, and by upper triangular
180*> block reflectors, stored in array T(1:LDT,(i-1)*M+1:i*M).
181*> The last Q(k) may use fewer rows.
182*> For more information see Further Details in TPLQT.
183*>
184*> For more details of the overall algorithm, see the description of
185*> Sequential TSQR in Section 2.2 of [1].
186*>
187*> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
188*> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
189*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
190*> \endverbatim
191*>
192* =====================================================================
193 SUBROUTINE slamswlq( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
194 $ LDT, C, LDC, WORK, LWORK, INFO )
195*
196* -- LAPACK computational routine --
197* -- LAPACK is a software package provided by Univ. of Tennessee, --
198* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
199*
200* .. Scalar Arguments ..
201 CHARACTER SIDE, TRANS
202 INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
203* ..
204* .. Array Arguments ..
205 REAL A( LDA, * ), WORK( * ), C(LDC, * ),
206 $ t( ldt, * )
207* ..
208*
209* =====================================================================
210*
211* ..
212* .. Local Scalars ..
213 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
214 INTEGER I, II, KK, LW, CTR
215* ..
216* .. External Functions ..
217 LOGICAL LSAME
218 EXTERNAL lsame
219* .. External Subroutines ..
220 EXTERNAL stpmlqt, sgemlqt, xerbla
221* ..
222* .. Executable Statements ..
223*
224* Test the input arguments
225*
226 lquery = lwork.LT.0
227 notran = lsame( trans, 'N' )
228 tran = lsame( trans, 'T' )
229 left = lsame( side, 'L' )
230 right = lsame( side, 'R' )
231 IF (left) THEN
232 lw = n * mb
233 ELSE
234 lw = m * mb
235 END IF
236*
237 info = 0
238 IF( .NOT.left .AND. .NOT.right ) THEN
239 info = -1
240 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
241 info = -2
242 ELSE IF( k.LT.0 ) THEN
243 info = -5
244 ELSE IF( m.LT.k ) THEN
245 info = -3
246 ELSE IF( n.LT.0 ) THEN
247 info = -4
248 ELSE IF( k.LT.mb .OR. mb.LT.1) THEN
249 info = -6
250 ELSE IF( lda.LT.max( 1, k ) ) THEN
251 info = -9
252 ELSE IF( ldt.LT.max( 1, mb) ) THEN
253 info = -11
254 ELSE IF( ldc.LT.max( 1, m ) ) THEN
255 info = -13
256 ELSE IF(( lwork.LT.max(1,lw)).AND.(.NOT.lquery)) THEN
257 info = -15
258 END IF
259*
260 IF( info.NE.0 ) THEN
261 CALL xerbla( 'SLAMSWLQ', -info )
262 work(1) = lw
263 RETURN
264 ELSE IF (lquery) THEN
265 work(1) = lw
266 RETURN
267 END IF
268*
269* Quick return if possible
270*
271 IF( min(m,n,k).EQ.0 ) THEN
272 RETURN
273 END IF
274*
275 IF((nb.LE.k).OR.(nb.GE.max(m,n,k))) THEN
276 CALL sgemlqt( side, trans, m, n, k, mb, a, lda,
277 $ t, ldt, c, ldc, work, info)
278 RETURN
279 END IF
280*
281 IF(left.AND.tran) THEN
282*
283* Multiply Q to the last block of C
284*
285 kk = mod((m-k),(nb-k))
286 ctr = (m-k)/(nb-k)
287*
288 IF (kk.GT.0) THEN
289 ii=m-kk+1
290 CALL stpmlqt('L','T',kk , n, k, 0, mb, a(1,ii), lda,
291 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
292 $ c(ii,1), ldc, work, info )
293 ELSE
294 ii=m+1
295 END IF
296*
297 DO i=ii-(nb-k),nb+1,-(nb-k)
298*
299* Multiply Q to the current block of C (1:M,I:I+NB)
300*
301 ctr = ctr - 1
302 CALL stpmlqt('L','T',nb-k , n, k, 0,mb, a(1,i), lda,
303 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
304 $ c(i,1), ldc, work, info )
305 END DO
306*
307* Multiply Q to the first block of C (1:M,1:NB)
308*
309 CALL sgemlqt('L','T',nb , n, k, mb, a(1,1), lda, t
310 $ ,ldt ,c(1,1), ldc, work, info )
311*
312 ELSE IF (left.AND.notran) THEN
313*
314* Multiply Q to the first block of C
315*
316 kk = mod((m-k),(nb-k))
317 ii=m-kk+1
318 ctr = 1
319 CALL sgemlqt('L','N',nb , n, k, mb, a(1,1), lda, t
320 $ ,ldt ,c(1,1), ldc, work, info )
321*
322 DO i=nb+1,ii-nb+k,(nb-k)
323*
324* Multiply Q to the current block of C (I:I+NB,1:N)
325*
326 CALL stpmlqt('L','N',nb-k , n, k, 0,mb, a(1,i), lda,
327 $ t(1,ctr * k+1), ldt, c(1,1), ldc,
328 $ c(i,1), ldc, work, info )
329 ctr = ctr + 1
330*
331 END DO
332 IF(ii.LE.m) THEN
333*
334* Multiply Q to the last block of C
335*
336 CALL stpmlqt('L','N',kk , n, k, 0, mb, a(1,ii), lda,
337 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
338 $ c(ii,1), ldc, work, info )
339*
340 END IF
341*
342 ELSE IF(right.AND.notran) THEN
343*
344* Multiply Q to the last block of C
345*
346 kk = mod((n-k),(nb-k))
347 ctr = (n-k)/(nb-k)
348 IF (kk.GT.0) THEN
349 ii=n-kk+1
350 CALL stpmlqt('R','N',m , kk, k, 0, mb, a(1, ii), lda,
351 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
352 $ c(1,ii), ldc, work, info )
353 ELSE
354 ii=n+1
355 END IF
356*
357 DO i=ii-(nb-k),nb+1,-(nb-k)
358*
359* Multiply Q to the current block of C (1:M,I:I+MB)
360*
361 ctr = ctr - 1
362 CALL stpmlqt('R','N', m, nb-k, k, 0, mb, a(1, i), lda,
363 $ t(1,ctr*k+1), ldt, c(1,1), ldc,
364 $ c(1,i), ldc, work, info )
365
366 END DO
367*
368* Multiply Q to the first block of C (1:M,1:MB)
369*
370 CALL sgemlqt('R','N',m , nb, k, mb, a(1,1), lda, t
371 $ ,ldt ,c(1,1), ldc, work, info )
372*
373 ELSE IF (right.AND.tran) THEN
374*
375* Multiply Q to the first block of C
376*
377 kk = mod((n-k),(nb-k))
378 ii=n-kk+1
379 ctr = 1
380 CALL sgemlqt('R','T',m , nb, k, mb, a(1,1), lda, t
381 $ ,ldt ,c(1,1), ldc, work, info )
382*
383 DO i=nb+1,ii-nb+k,(nb-k)
384*
385* Multiply Q to the current block of C (1:M,I:I+MB)
386*
387 CALL stpmlqt('R','T',m , nb-k, k, 0,mb, a(1,i), lda,
388 $ t(1, ctr*k+1), ldt, c(1,1), ldc,
389 $ c(1,i), ldc, work, info )
390 ctr = ctr + 1
391*
392 END DO
393 IF(ii.LE.n) THEN
394*
395* Multiply Q to the last block of C
396*
397 CALL stpmlqt('R','T',m , kk, k, 0,mb, a(1,ii), lda,
398 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
399 $ c(1,ii), ldc, work, info )
400*
401 END IF
402*
403 END IF
404*
405 work(1) = lw
406 RETURN
407*
408* End of SLAMSWLQ
409*
410 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgemlqt(SIDE, TRANS, M, N, K, MB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMLQT
Definition: sgemlqt.f:153
subroutine stpmlqt(SIDE, TRANS, M, N, K, L, MB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
STPMLQT
Definition: stpmlqt.f:214
subroutine slamswlq(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
SLAMSWLQ
Definition: slamswlq.f:195