LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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slamtsqr.f
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1*> \brief \b SLAMTSQR
2*
3* Definition:
4* ===========
5*
6* SUBROUTINE SLAMTSQR( 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*> SLAMTSQR 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
29*> of blocked elementary reflectors computed by tall skinny
30*> QR factorization (SLATSQR)
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 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 SLATSQR)
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 REAL 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 SLATSQR 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 REAL 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 REAL array, dimension (LDC,N)
119*> On entry, the M-by-N matrix C.
120*> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T 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) REAL array, dimension (MAX(1,LWORK))
132*>
133*> \endverbatim
134*> \param[in] LWORK
135*> \verbatim
136*> LWORK is INTEGER
137*> The dimension of the array WORK.
138*>
139*> If SIDE = 'L', LWORK >= max(1,N)*NB;
140*> if SIDE = 'R', LWORK >= max(1,MB)*NB.
141*> If LWORK = -1, then a workspace query is assumed; the routine
142*> only calculates the optimal size of the WORK array, returns
143*> this value as the first entry of the WORK array, and no error
144*> message related to LWORK is issued by XERBLA.
145*>
146*> \endverbatim
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*> \par Further Details:
163* =====================
164*>
165*> \verbatim
166*> Tall-Skinny QR (TSQR) performs QR by a sequence of orthogonal transformations,
167*> representing Q as a product of other orthogonal matrices
168*> Q = Q(1) * Q(2) * . . . * Q(k)
169*> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
170*> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
171*> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
172*> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
173*> . . .
174*>
175*> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
176*> stored under the diagonal of rows 1:MB of A, and by upper triangular
177*> block reflectors, stored in array T(1:LDT,1:N).
179*>
180*> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
181*> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
182*> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
183*> The last Q(k) may use fewer rows.
185*>
186*> For more details of the overall algorithm, see the description of
187*> Sequential TSQR in Section 2.2 of [1].
188*>
189*> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
190*> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
191*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
192*> \endverbatim
193*>
194* =====================================================================
195 SUBROUTINE slamtsqr( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
196 \$ LDT, C, LDC, WORK, LWORK, INFO )
197*
198* -- LAPACK computational routine --
199* -- LAPACK is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 CHARACTER SIDE, TRANS
204 INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
205* ..
206* .. Array Arguments ..
207 REAL A( LDA, * ), WORK( * ), C(LDC, * ),
208 \$ t( ldt, * )
209* ..
210*
211* =====================================================================
212*
213* ..
214* .. Local Scalars ..
215 LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
216 INTEGER I, II, KK, LW, CTR, Q
217* ..
218* .. External Functions ..
219 LOGICAL LSAME
220 EXTERNAL lsame
221* .. External Subroutines ..
222 EXTERNAL sgemqrt, stpmqrt, xerbla
223* ..
224* .. Executable Statements ..
225*
226* Test the input arguments
227*
228 lquery = lwork.LT.0
229 notran = lsame( trans, 'N' )
230 tran = lsame( trans, 'T' )
231 left = lsame( side, 'L' )
232 right = lsame( side, 'R' )
233 IF (left) THEN
234 lw = n * nb
235 q = m
236 ELSE
237 lw = mb * nb
238 q = n
239 END IF
240*
241 info = 0
242 IF( .NOT.left .AND. .NOT.right ) THEN
243 info = -1
244 ELSE IF( .NOT.tran .AND. .NOT.notran ) THEN
245 info = -2
246 ELSE IF( m.LT.k ) THEN
247 info = -3
248 ELSE IF( n.LT.0 ) THEN
249 info = -4
250 ELSE IF( k.LT.0 ) THEN
251 info = -5
252 ELSE IF( k.LT.nb .OR. nb.LT.1 ) THEN
253 info = -7
254 ELSE IF( lda.LT.max( 1, q ) ) THEN
255 info = -9
256 ELSE IF( ldt.LT.max( 1, nb) ) THEN
257 info = -11
258 ELSE IF( ldc.LT.max( 1, m ) ) THEN
259 info = -13
260 ELSE IF(( lwork.LT.max(1,lw)).AND.(.NOT.lquery)) THEN
261 info = -15
262 END IF
263*
264* Determine the block size if it is tall skinny or short and wide
265*
266 IF( info.EQ.0) THEN
267 work(1) = lw
268 END IF
269*
270 IF( info.NE.0 ) THEN
271 CALL xerbla( 'SLAMTSQR', -info )
272 RETURN
273 ELSE IF (lquery) THEN
274 RETURN
275 END IF
276*
277* Quick return if possible
278*
279 IF( min(m,n,k).EQ.0 ) THEN
280 RETURN
281 END IF
282*
283 IF((mb.LE.k).OR.(mb.GE.max(m,n,k))) THEN
284 CALL sgemqrt( side, trans, m, n, k, nb, a, lda,
285 \$ t, ldt, c, ldc, work, info)
286 RETURN
287 END IF
288*
289 IF(left.AND.notran) THEN
290*
291* Multiply Q to the last block of C
292*
293 kk = mod((m-k),(mb-k))
294 ctr = (m-k)/(mb-k)
295 IF (kk.GT.0) THEN
296 ii=m-kk+1
297 CALL stpmqrt('L','N',kk , n, k, 0, nb, a(ii,1), lda,
298 \$ t(1,ctr*k+1),ldt , c(1,1), ldc,
299 \$ c(ii,1), ldc, work, info )
300 ELSE
301 ii=m+1
302 END IF
303*
304 DO i=ii-(mb-k),mb+1,-(mb-k)
305*
306* Multiply Q to the current block of C (I:I+MB,1:N)
307*
308 ctr = ctr - 1
309 CALL stpmqrt('L','N',mb-k , n, k, 0,nb, a(i,1), lda,
310 \$ t(1, ctr * k + 1), ldt, c(1,1), ldc,
311 \$ c(i,1), ldc, work, info )
312*
313 END DO
314*
315* Multiply Q to the first block of C (1:MB,1:N)
316*
317 CALL sgemqrt('L','N',mb , n, k, nb, a(1,1), lda, t
318 \$ ,ldt ,c(1,1), ldc, work, info )
319*
320 ELSE IF (left.AND.tran) THEN
321*
322* Multiply Q to the first block of C
323*
324 kk = mod((m-k),(mb-k))
325 ii=m-kk+1
326 ctr = 1
327 CALL sgemqrt('L','T',mb , n, k, nb, a(1,1), lda, t
328 \$ ,ldt ,c(1,1), ldc, work, info )
329*
330 DO i=mb+1,ii-mb+k,(mb-k)
331*
332* Multiply Q to the current block of C (I:I+MB,1:N)
333*
334 CALL stpmqrt('L','T',mb-k , n, k, 0,nb, a(i,1), lda,
335 \$ t(1,ctr * k + 1),ldt, c(1,1), ldc,
336 \$ c(i,1), ldc, work, info )
337 ctr = ctr + 1
338*
339 END DO
340 IF(ii.LE.m) THEN
341*
342* Multiply Q to the last block of C
343*
344 CALL stpmqrt('L','T',kk , n, k, 0,nb, a(ii,1), lda,
345 \$ t(1, ctr * k + 1), ldt, c(1,1), ldc,
346 \$ c(ii,1), ldc, work, info )
347*
348 END IF
349*
350 ELSE IF(right.AND.tran) THEN
351*
352* Multiply Q to the last block of C
353*
354 kk = mod((n-k),(mb-k))
355 ctr = (n-k)/(mb-k)
356 IF (kk.GT.0) THEN
357 ii=n-kk+1
358 CALL stpmqrt('R','T',m , kk, k, 0, nb, a(ii,1), lda,
359 \$ t(1, ctr * k + 1), ldt, c(1,1), ldc,
360 \$ c(1,ii), ldc, work, info )
361 ELSE
362 ii=n+1
363 END IF
364*
365 DO i=ii-(mb-k),mb+1,-(mb-k)
366*
367* Multiply Q to the current block of C (1:M,I:I+MB)
368*
369 ctr = ctr - 1
370 CALL stpmqrt('R','T',m , mb-k, k, 0,nb, a(i,1), lda,
371 \$ t(1, ctr * k + 1), ldt, c(1,1), ldc,
372 \$ c(1,i), ldc, work, info )
373*
374 END DO
375*
376* Multiply Q to the first block of C (1:M,1:MB)
377*
378 CALL sgemqrt('R','T',m , mb, k, nb, a(1,1), lda, t
379 \$ ,ldt ,c(1,1), ldc, work, info )
380*
381 ELSE IF (right.AND.notran) THEN
382*
383* Multiply Q to the first block of C
384*
385 kk = mod((n-k),(mb-k))
386 ii=n-kk+1
387 ctr = 1
388 CALL sgemqrt('R','N', m, mb , k, nb, a(1,1), lda, t
389 \$ ,ldt ,c(1,1), ldc, work, info )
390*
391 DO i=mb+1,ii-mb+k,(mb-k)
392*
393* Multiply Q to the current block of C (1:M,I:I+MB)
394*
395 CALL stpmqrt('R','N', m, mb-k, k, 0,nb, a(i,1), lda,
396 \$ t(1, ctr * k + 1),ldt, c(1,1), ldc,
397 \$ c(1,i), ldc, work, info )
398 ctr = ctr + 1
399*
400 END DO
401 IF(ii.LE.n) THEN
402*
403* Multiply Q to the last block of C
404*
405 CALL stpmqrt('R','N', m, kk , k, 0,nb, a(ii,1), lda,
406 \$ t(1, ctr * k + 1),ldt, c(1,1), ldc,
407 \$ c(1,ii), ldc, work, info )
408*
409 END IF
410*
411 END IF
412*
413 work(1) = lw
414 RETURN
415*
416* End of SLAMTSQR
417*
418 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine sgemqrt(SIDE, TRANS, M, N, K, NB, V, LDV, T, LDT, C, LDC, WORK, INFO)
SGEMQRT
Definition: sgemqrt.f:168
subroutine stpmqrt(SIDE, TRANS, M, N, K, L, NB, V, LDV, T, LDT, A, LDA, B, LDB, WORK, INFO)
STPMQRT
Definition: stpmqrt.f:216
subroutine slamtsqr(SIDE, TRANS, M, N, K, MB, NB, A, LDA, T, LDT, C, LDC, WORK, LWORK, INFO)
SLAMTSQR
Definition: slamtsqr.f:197