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clamtsqr.f File Reference

Go to the source code of this file.

Functions/Subroutines

subroutine clamtsqr (side, trans, m, n, k, mb, nb, a, lda, t, ldt, c, ldc, work, lwork, info)
 CLAMTSQR

Function/Subroutine Documentation

◆ clamtsqr()

subroutine clamtsqr ( character side,
character trans,
integer m,
integer n,
integer k,
integer mb,
integer nb,
complex, dimension( lda, * ) a,
integer lda,
complex, dimension( ldt, * ) t,
integer ldt,
complex, dimension(ldc, * ) c,
integer ldc,
complex, dimension( * ) work,
integer lwork,
integer info )

CLAMTSQR

Purpose:
!>
!>      CLAMTSQR overwrites the general complex M-by-N matrix C with
!>
!>
!>                 SIDE = 'L'     SIDE = 'R'
!> TRANS = 'N':      Q * C          C * Q
!> TRANS = 'C':      Q**H * C       C * Q**H
!>      where Q is a complex unitary matrix defined as the product
!>      of blocked elementary reflectors computed by tall skinny
!>      QR factorization (CLATSQR)
!>
Parameters
[in]SIDE
!>          SIDE is CHARACTER*1
!>          = 'L': apply Q or Q**H from the Left;
!>          = 'R': apply Q or Q**H from the Right.
!>
[in]TRANS
!>          TRANS is CHARACTER*1
!>          = 'N':  No transpose, apply Q;
!>          = 'C':  Conjugate Transpose, apply Q**H.
!>
[in]M
!>          M is INTEGER
!>          The number of rows of the matrix A.  M >=0.
!>
[in]N
!>          N is INTEGER
!>          The number of columns of the matrix C. N >= 0.
!>
[in]K
!>          K is INTEGER
!>          The number of elementary reflectors whose product defines
!>          the matrix Q. M >= K >= 0;
!>
!>
[in]MB
!>          MB is INTEGER
!>          The block size to be used in the blocked QR.
!>          MB > N. (must be the same as CLATSQR)
!>
[in]NB
!>          NB is INTEGER
!>          The column block size to be used in the blocked QR.
!>          N >= NB >= 1.
!>
[in]A
!>          A is COMPLEX array, dimension (LDA,K)
!>          The i-th column must contain the vector which defines the
!>          blockedelementary reflector H(i), for i = 1,2,...,k, as
!>          returned by CLATSQR in the first k columns of
!>          its array argument A.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.
!>          If SIDE = 'L', LDA >= max(1,M);
!>          if SIDE = 'R', LDA >= max(1,N).
!>
[in]T
!>          T is COMPLEX array, dimension
!>          ( N * Number of blocks(CEIL(M-K/MB-K)),
!>          The blocked upper triangular block reflectors stored in compact form
!>          as a sequence of upper triangular blocks.  See below
!>          for further details.
!>
[in]LDT
!>          LDT is INTEGER
!>          The leading dimension of the array T.  LDT >= NB.
!>
[in,out]C
!>          C is COMPLEX array, dimension (LDC,N)
!>          On entry, the M-by-N matrix C.
!>          On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q.
!>
[in]LDC
!>          LDC is INTEGER
!>          The leading dimension of the array C. LDC >= max(1,M).
!>
[out]WORK
!>         (workspace) COMPLEX array, dimension (MAX(1,LWORK))
!>
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>
!>          If SIDE = 'L', LWORK >= max(1,N)*NB;
!>          if SIDE = 'R', LWORK >= max(1,MB)*NB.
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal size of the WORK array, returns
!>          this value as the first entry of the WORK array, and no error
!>          message related to LWORK is issued by XERBLA.
!>
!>
[out]INFO
!>          INFO is INTEGER
!>          = 0:  successful exit
!>          < 0:  if INFO = -i, the i-th argument had an illegal value
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Further Details:
!> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
!> representing Q as a product of other unitary matrices
!>   Q = Q(1) * Q(2) * . . . * Q(k)
!> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
!>   Q(1) zeros out the subdiagonal entries of rows 1:MB of A
!>   Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
!>   Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
!>   . . .
!>
!> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
!> stored under the diagonal of rows 1:MB of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,1:N).
!> For more information see Further Details in GEQRT.
!>
!> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
!> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
!> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
!> The last Q(k) may use fewer rows.
!> For more information see Further Details in TPQRT.
!>
!> For more details of the overall algorithm, see the description of
!> Sequential TSQR in Section 2.2 of [1].
!>
!> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
!>     J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
!>     SIAM J. Sci. Comput, vol. 34, no. 1, 2012
!>

Definition at line 195 of file clamtsqr.f.

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 COMPLEX 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 cgemqrt, ctpmqrt, 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, 'C' )
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 = m * 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( 'CLAMTSQR', -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 cgemqrt( 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 ctpmqrt('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 ctpmqrt('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 cgemqrt('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 cgemqrt('L','C',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 ctpmqrt('L','C',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 ctpmqrt('L','C',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 ctpmqrt('R','C',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 ctpmqrt('R','C',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 END DO
374*
375* Multiply Q to the first block of C (1:M,1:MB)
376*
377 CALL cgemqrt('R','C',m , mb, k, nb, a(1,1), lda, t
378 $ ,ldt ,c(1,1), ldc, work, info )
379*
380 ELSE IF (right.AND.notran) THEN
381*
382* Multiply Q to the first block of C
383*
384 kk = mod((n-k),(mb-k))
385 ii=n-kk+1
386 ctr = 1
387 CALL cgemqrt('R','N', m, mb , k, nb, a(1,1), lda, t
388 $ ,ldt ,c(1,1), ldc, work, info )
389*
390 DO i=mb+1,ii-mb+k,(mb-k)
391*
392* Multiply Q to the current block of C (1:M,I:I+MB)
393*
394 CALL ctpmqrt('R','N', m, mb-k, k, 0,nb, a(i,1), lda,
395 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
396 $ c(1,i), ldc, work, info )
397 ctr = ctr + 1
398*
399 END DO
400 IF(ii.LE.n) THEN
401*
402* Multiply Q to the last block of C
403*
404 CALL ctpmqrt('R','N', m, kk , k, 0,nb, a(ii,1), lda,
405 $ t(1,ctr*k+1),ldt, c(1,1), ldc,
406 $ c(1,ii), ldc, work, info )
407*
408 END IF
409*
410 END IF
411*
412 work(1) = lw
413 RETURN
414*
415* End of CLAMTSQR
416*
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:53
cgemqrt
subroutine cgemqrt(side, trans, m, n, k, nb, v, ldv, t, ldt, c, ldc, work, info)
CGEMQRT
Definition cgemqrt.f:168
ctpmqrt
subroutine ctpmqrt(side, trans, m, n, k, l, nb, v, ldv, t, ldt, a, lda, b, ldb, work, info)
CTPMQRT
Definition ctpmqrt.f:216
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21