LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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zungtsqr_row.f
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1*> \brief \b ZUNGTSQR_ROW
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download ZUNGTSQR_ROW + dependencies
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14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zunrgtsqr_row.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE ZUNGTSQR_ROW( M, N, MB, NB, A, LDA, T, LDT, WORK,
22* $ LWORK, INFO )
23* IMPLICIT NONE
24*
25* .. Scalar Arguments ..
26* INTEGER INFO, LDA, LDT, LWORK, M, N, MB, NB
27* ..
28* .. Array Arguments ..
29* COMPLEX*16 A( LDA, * ), T( LDT, * ), WORK( * )
30* ..
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> ZUNGTSQR_ROW generates an M-by-N complex matrix Q_out with
38*> orthonormal columns from the output of ZLATSQR. These N orthonormal
39*> columns are the first N columns of a product of complex unitary
40*> matrices Q(k)_in of order M, which are returned by ZLATSQR in
41*> a special format.
42*>
43*> Q_out = first_N_columns_of( Q(1)_in * Q(2)_in * ... * Q(k)_in ).
44*>
45*> The input matrices Q(k)_in are stored in row and column blocks in A.
46*> See the documentation of ZLATSQR for more details on the format of
47*> Q(k)_in, where each Q(k)_in is represented by block Householder
48*> transformations. This routine calls an auxiliary routine ZLARFB_GETT,
49*> where the computation is performed on each individual block. The
50*> algorithm first sweeps NB-sized column blocks from the right to left
51*> starting in the bottom row block and continues to the top row block
52*> (hence _ROW in the routine name). This sweep is in reverse order of
53*> the order in which ZLATSQR generates the output blocks.
54*> \endverbatim
55*
56* Arguments:
57* ==========
58*
59*> \param[in] M
60*> \verbatim
61*> M is INTEGER
62*> The number of rows of the matrix A. M >= 0.
63*> \endverbatim
64*>
65*> \param[in] N
66*> \verbatim
67*> N is INTEGER
68*> The number of columns of the matrix A. M >= N >= 0.
69*> \endverbatim
70*>
71*> \param[in] MB
72*> \verbatim
73*> MB is INTEGER
74*> The row block size used by ZLATSQR to return
75*> arrays A and T. MB > N.
76*> (Note that if MB > M, then M is used instead of MB
77*> as the row block size).
78*> \endverbatim
79*>
80*> \param[in] NB
81*> \verbatim
82*> NB is INTEGER
83*> The column block size used by ZLATSQR to return
84*> arrays A and T. NB >= 1.
85*> (Note that if NB > N, then N is used instead of NB
86*> as the column block size).
87*> \endverbatim
88*>
89*> \param[in,out] A
90*> \verbatim
91*> A is COMPLEX*16 array, dimension (LDA,N)
92*>
93*> On entry:
94*>
95*> The elements on and above the diagonal are not used as
96*> input. The elements below the diagonal represent the unit
97*> lower-trapezoidal blocked matrix V computed by ZLATSQR
98*> that defines the input matrices Q_in(k) (ones on the
99*> diagonal are not stored). See ZLATSQR for more details.
100*>
101*> On exit:
102*>
103*> The array A contains an M-by-N orthonormal matrix Q_out,
104*> i.e the columns of A are orthogonal unit vectors.
105*> \endverbatim
106*>
107*> \param[in] LDA
108*> \verbatim
109*> LDA is INTEGER
110*> The leading dimension of the array A. LDA >= max(1,M).
111*> \endverbatim
112*>
113*> \param[in] T
114*> \verbatim
115*> T is COMPLEX*16 array,
116*> dimension (LDT, N * NIRB)
117*> where NIRB = Number_of_input_row_blocks
118*> = MAX( 1, CEIL((M-N)/(MB-N)) )
119*> Let NICB = Number_of_input_col_blocks
120*> = CEIL(N/NB)
121*>
122*> The upper-triangular block reflectors used to define the
123*> input matrices Q_in(k), k=(1:NIRB*NICB). The block
124*> reflectors are stored in compact form in NIRB block
125*> reflector sequences. Each of the NIRB block reflector
126*> sequences is stored in a larger NB-by-N column block of T
127*> and consists of NICB smaller NB-by-NB upper-triangular
128*> column blocks. See ZLATSQR for more details on the format
129*> of T.
130*> \endverbatim
131*>
132*> \param[in] LDT
133*> \verbatim
134*> LDT is INTEGER
135*> The leading dimension of the array T.
136*> LDT >= max(1,min(NB,N)).
137*> \endverbatim
138*>
139*> \param[out] WORK
140*> \verbatim
141*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
142*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
143*> \endverbatim
144*>
145*> \param[in] LWORK
146*> \verbatim
147*> The dimension of the array WORK.
148*> LWORK >= NBLOCAL * MAX(NBLOCAL,(N-NBLOCAL)),
149*> where NBLOCAL=MIN(NB,N).
150*> If LWORK = -1, then a workspace query is assumed.
151*> The routine only calculates the optimal size of the WORK
152*> array, returns this value as the first entry of the WORK
153*> array, and no error message related to LWORK is issued
154*> by XERBLA.
155*> \endverbatim
156*>
157*> \param[out] INFO
158*> \verbatim
159*> INFO is INTEGER
160*> = 0: successful exit
161*> < 0: if INFO = -i, the i-th argument had an illegal value
162*> \endverbatim
163*>
164* Authors:
165* ========
166*
167*> \author Univ. of Tennessee
168*> \author Univ. of California Berkeley
169*> \author Univ. of Colorado Denver
170*> \author NAG Ltd.
171*
172*> \ingroup complex16OTHERcomputational
173*
174*> \par Contributors:
175* ==================
176*>
177*> \verbatim
178*>
179*> November 2020, Igor Kozachenko,
180*> Computer Science Division,
181*> University of California, Berkeley
182*>
183*> \endverbatim
184*>
185* =====================================================================
186 SUBROUTINE zungtsqr_row( M, N, MB, NB, A, LDA, T, LDT, WORK,
187 $ LWORK, INFO )
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*16 A( LDA, * ), T( LDT, * ), WORK( * )
199* ..
200*
201* =====================================================================
202*
203* .. Parameters ..
204 COMPLEX*16 CONE, CZERO
205 parameter( cone = ( 1.0d+0, 0.0d+0 ),
206 $ czero = ( 0.0d+0, 0.0d+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*16 DUMMY( 1, 1 )
216* ..
217* .. External Subroutines ..
218 EXTERNAL zlarfb_gett, zlaset, xerbla
219* ..
220* .. Intrinsic Functions ..
221 INTRINSIC dcmplx, 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( 'ZUNGTSQR_ROW', -info )
257 RETURN
258 ELSE IF ( lquery ) THEN
259 work( 1 ) = dcmplx( lworkopt )
260 RETURN
261 END IF
262*
263* Quick return if possible
264*
265 IF( min( m, n ).EQ.0 ) THEN
266 work( 1 ) = dcmplx( 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 zlaset('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 zlarfb_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 zlarfb_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 zlarfb_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 ) = dcmplx( lworkopt )
376 RETURN
377*
378* End of ZUNGTSQR_ROW
379*
380 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine zlarfb_gett(IDENT, M, N, K, T, LDT, A, LDA, B, LDB, WORK, LDWORK)
ZLARFB_GETT
Definition: zlarfb_gett.f:392
subroutine zlaset(UPLO, M, N, ALPHA, BETA, A, LDA)
ZLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition: zlaset.f:106
subroutine zungtsqr_row(M, N, MB, NB, A, LDA, T, LDT, WORK, LWORK, INFO)
ZUNGTSQR_ROW
Definition: zungtsqr_row.f:188