LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ cungtsqr_row()

 subroutine cungtsqr_row ( integer m, integer n, integer mb, integer nb, complex, dimension( lda, * ) a, integer lda, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( * ) work, integer lwork, integer info )

CUNGTSQR_ROW

Purpose:
``` CUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
orthonormal columns from the output of CLATSQR. These N orthonormal
columns are the first N columns of a product of complex unitary
matrices Q(k)_in of order M, which are returned by CLATSQR in
a special format.

Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).

The input matrices Q(k)_in are stored in row and column blocks in A.
See the documentation of CLATSQR for more details on the format of
Q(k)_in, where each Q(k)_in is represented by block Householder
transformations. This routine calls an auxiliary routine CLARFB_GETT,
where the computation is performed on each individual block. The
algorithm first sweeps NB-sized column blocks from the right to left
starting in the bottom row block and continues to the top row block
(hence _ROW in the routine name). This sweep is in reverse order of
the order in which CLATSQR generates the output blocks.```
Parameters
 [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 A. M >= N >= 0.``` [in] MB ``` MB is INTEGER The row block size used by CLATSQR to return arrays A and T. MB > N. (Note that if MB > M, then M is used instead of MB as the row block size).``` [in] NB ``` NB is INTEGER The column block size used by CLATSQR to return arrays A and T. NB >= 1. (Note that if NB > N, then N is used instead of NB as the column block size).``` [in,out] A ``` A is COMPLEX array, dimension (LDA,N) On entry: The elements on and above the diagonal are not used as input. The elements below the diagonal represent the unit lower-trapezoidal blocked matrix V computed by CLATSQR that defines the input matrices Q_in(k) (ones on the diagonal are not stored). See CLATSQR for more details. On exit: The array A contains an M-by-N orthonormal matrix Q_out, i.e the columns of A are orthogonal unit vectors.``` [in] LDA ``` LDA is INTEGER The leading dimension of the array A. LDA >= max(1,M).``` [in] T ``` T is COMPLEX array, dimension (LDT, N * NIRB) where NIRB = Number_of_input_row_blocks = MAX( 1, CEIL((M-N)/(MB-N)) ) Let NICB = Number_of_input_col_blocks = CEIL(N/NB) The upper-triangular block reflectors used to define the input matrices Q_in(k), k=(1:NIRB*NICB). The block reflectors are stored in compact form in NIRB block reflector sequences. Each of the NIRB block reflector sequences is stored in a larger NB-by-N column block of T and consists of NICB smaller NB-by-NB upper-triangular column blocks. See CLATSQR for more details on the format of T.``` [in] LDT ``` LDT is INTEGER The leading dimension of the array T. LDT >= max(1,min(NB,N)).``` [out] WORK ``` (workspace) COMPLEX array, dimension (MAX(1,LWORK)) On exit, if INFO = 0, WORK(1) returns the optimal LWORK.``` [in] LWORK ``` The dimension of the array WORK. LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)), where NBLOCAL=MIN(NB,N). 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```
Contributors:
``` November 2020, Igor Kozachenko,
Computer Science Division,
University of California, Berkeley```

Definition at line 186 of file cungtsqr_row.f.

188 IMPLICIT NONE
189*
190* -- LAPACK computational routine --
191* -- LAPACK is a software package provided by Univ. of Tennessee, --
192* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
193*
194* .. Scalar Arguments ..
195 INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
196* ..
197* .. Array Arguments ..
198 COMPLEX A( LDA, * ), T( LDT, * ), WORK( * )
199* ..
200*
201* =====================================================================
202*
203* .. Parameters ..
204 COMPLEX CONE, CZERO
205 parameter( cone = ( 1.0e+0, 0.0e+0 ),
206 \$ czero = ( 0.0e+0, 0.0e+0 ) )
207* ..
208* .. Local Scalars ..
209 LOGICAL LQUERY
210 INTEGER NBLOCAL, MB2, M_PLUS_ONE, ITMP, IB_BOTTOM,
211 \$ LWORKOPT, NUM_ALL_ROW_BLOCKS, JB_T, IB, IMB,
212 \$ KB, KB_LAST, KNB, MB1
213* ..
214* .. Local Arrays ..
215 COMPLEX DUMMY( 1, 1 )
216* ..
217* .. External Subroutines ..
218 EXTERNAL clarfb_gett, claset, xerbla
219* ..
220* .. Intrinsic Functions ..
221 INTRINSIC cmplx, max, min
222* ..
223* .. Executable Statements ..
224*
225* Test the input parameters
226*
227 info = 0
228 lquery = lwork.EQ.-1
229 IF( m.LT.0 ) THEN
230 info = -1
231 ELSE IF( n.LT.0 .OR. m.LT.n ) THEN
232 info = -2
233 ELSE IF( mb.LE.n ) THEN
234 info = -3
235 ELSE IF( nb.LT.1 ) THEN
236 info = -4
237 ELSE IF( lda.LT.max( 1, m ) ) THEN
238 info = -6
239 ELSE IF( ldt.LT.max( 1, min( nb, n ) ) ) THEN
240 info = -8
241 ELSE IF( lwork.LT.1 .AND. .NOT.lquery ) THEN
242 info = -10
243 END IF
244*
245 nblocal = min( nb, n )
246*
247* Determine the workspace size.
248*
249 IF( info.EQ.0 ) THEN
250 lworkopt = nblocal * max( nblocal, ( n - nblocal ) )
251 END IF
252*
253* Handle error in the input parameters and handle the workspace query.
254*
255 IF( info.NE.0 ) THEN
256 CALL xerbla( 'CUNGTSQR_ROW', -info )
257 RETURN
258 ELSE IF ( lquery ) THEN
259 work( 1 ) = cmplx( lworkopt )
260 RETURN
261 END IF
262*
263* Quick return if possible
264*
265 IF( min( m, n ).EQ.0 ) THEN
266 work( 1 ) = cmplx( lworkopt )
267 RETURN
268 END IF
269*
270* (0) Set the upper-triangular part of the matrix A to zero and
271* its diagonal elements to one.
272*
273 CALL claset('U', m, n, czero, cone, a, lda )
274*
275* KB_LAST is the column index of the last column block reflector
276* in the matrices T and V.
277*
278 kb_last = ( ( n-1 ) / nblocal ) * nblocal + 1
279*
280*
281* (1) Bottom-up loop over row blocks of A, except the top row block.
282* NOTE: If MB>=M, then the loop is never executed.
283*
284 IF ( mb.LT.m ) THEN
285*
286* MB2 is the row blocking size for the row blocks before the
287* first top row block in the matrix A. IB is the row index for
288* the row blocks in the matrix A before the first top row block.
289* IB_BOTTOM is the row index for the last bottom row block
290* in the matrix A. JB_T is the column index of the corresponding
291* column block in the matrix T.
292*
293* Initialize variables.
294*
295* NUM_ALL_ROW_BLOCKS is the number of row blocks in the matrix A
296* including the first row block.
297*
298 mb2 = mb - n
299 m_plus_one = m + 1
300 itmp = ( m - mb - 1 ) / mb2
301 ib_bottom = itmp * mb2 + mb + 1
302 num_all_row_blocks = itmp + 2
303 jb_t = num_all_row_blocks * n + 1
304*
305 DO ib = ib_bottom, mb+1, -mb2
306*
307* Determine the block size IMB for the current row block
308* in the matrix A.
309*
310 imb = min( m_plus_one - ib, mb2 )
311*
312* Determine the column index JB_T for the current column block
313* in the matrix T.
314*
315 jb_t = jb_t - n
316*
317* Apply column blocks of H in the row block from right to left.
318*
319* KB is the column index of the current column block reflector
320* in the matrices T and V.
321*
322 DO kb = kb_last, 1, -nblocal
323*
324* Determine the size of the current column block KNB in
325* the matrices T and V.
326*
327 knb = min( nblocal, n - kb + 1 )
328*
329 CALL clarfb_gett( 'I', imb, n-kb+1, knb,
330 \$ t( 1, jb_t+kb-1 ), ldt, a( kb, kb ), lda,
331 \$ a( ib, kb ), lda, work, knb )
332*
333 END DO
334*
335 END DO
336*
337 END IF
338*
339* (2) Top row block of A.
340* NOTE: If MB>=M, then we have only one row block of A of size M
341* and we work on the entire matrix A.
342*
343 mb1 = min( mb, m )
344*
345* Apply column blocks of H in the top row block from right to left.
346*
347* KB is the column index of the current block reflector in
348* the matrices T and V.
349*
350 DO kb = kb_last, 1, -nblocal
351*
352* Determine the size of the current column block KNB in
353* the matrices T and V.
354*
355 knb = min( nblocal, n - kb + 1 )
356*
357 IF( mb1-kb-knb+1.EQ.0 ) THEN
358*
359* In SLARFB_GETT parameters, when M=0, then the matrix B
360* does not exist, hence we need to pass a dummy array
361* reference DUMMY(1,1) to B with LDDUMMY=1.
362*
363 CALL clarfb_gett( 'N', 0, n-kb+1, knb,
364 \$ t( 1, kb ), ldt, a( kb, kb ), lda,
365 \$ dummy( 1, 1 ), 1, work, knb )
366 ELSE
367 CALL clarfb_gett( 'N', mb1-kb-knb+1, n-kb+1, knb,
368 \$ t( 1, kb ), ldt, a( kb, kb ), lda,
369 \$ a( kb+knb, kb), lda, work, knb )
370
371 END IF
372*
373 END DO
374*
375 work( 1 ) = cmplx( lworkopt )
376 RETURN
377*
378* End of CUNGTSQR_ROW
379*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine clarfb_gett(ident, m, n, k, t, ldt, a, lda, b, ldb, work, ldwork)
CLARFB_GETT
subroutine claset(uplo, m, n, alpha, beta, a, lda)
CLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition claset.f:106
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