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cgesvd.f
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1*> \brief <b> CGESVD computes the singular value decomposition (SVD) for GE matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download CGESVD + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgesvd.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgesvd.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgesvd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CGESVD( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
22* WORK, LWORK, RWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBU, JOBVT
26* INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
27* ..
28* .. Array Arguments ..
29* REAL RWORK( * ), S( * )
30* COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ),
31* $ WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> CGESVD computes the singular value decomposition (SVD) of a complex
41*> M-by-N matrix A, optionally computing the left and/or right singular
42*> vectors. The SVD is written
43*>
44*> A = U * SIGMA * conjugate-transpose(V)
45*>
46*> where SIGMA is an M-by-N matrix which is zero except for its
47*> min(m,n) diagonal elements, U is an M-by-M unitary matrix, and
48*> V is an N-by-N unitary matrix. The diagonal elements of SIGMA
49*> are the singular values of A; they are real and non-negative, and
50*> are returned in descending order. The first min(m,n) columns of
51*> U and V are the left and right singular vectors of A.
52*>
53*> Note that the routine returns V**H, not V.
54*> \endverbatim
55*
56* Arguments:
57* ==========
58*
59*> \param[in] JOBU
60*> \verbatim
61*> JOBU is CHARACTER*1
62*> Specifies options for computing all or part of the matrix U:
63*> = 'A': all M columns of U are returned in array U:
64*> = 'S': the first min(m,n) columns of U (the left singular
65*> vectors) are returned in the array U;
66*> = 'O': the first min(m,n) columns of U (the left singular
67*> vectors) are overwritten on the array A;
68*> = 'N': no columns of U (no left singular vectors) are
69*> computed.
70*> \endverbatim
71*>
72*> \param[in] JOBVT
73*> \verbatim
74*> JOBVT is CHARACTER*1
75*> Specifies options for computing all or part of the matrix
76*> V**H:
77*> = 'A': all N rows of V**H are returned in the array VT;
78*> = 'S': the first min(m,n) rows of V**H (the right singular
79*> vectors) are returned in the array VT;
80*> = 'O': the first min(m,n) rows of V**H (the right singular
81*> vectors) are overwritten on the array A;
82*> = 'N': no rows of V**H (no right singular vectors) are
83*> computed.
84*>
85*> JOBVT and JOBU cannot both be 'O'.
86*> \endverbatim
87*>
88*> \param[in] M
89*> \verbatim
90*> M is INTEGER
91*> The number of rows of the input matrix A. M >= 0.
92*> \endverbatim
93*>
94*> \param[in] N
95*> \verbatim
96*> N is INTEGER
97*> The number of columns of the input matrix A. N >= 0.
98*> \endverbatim
99*>
100*> \param[in,out] A
101*> \verbatim
102*> A is COMPLEX array, dimension (LDA,N)
103*> On entry, the M-by-N matrix A.
104*> On exit,
105*> if JOBU = 'O', A is overwritten with the first min(m,n)
106*> columns of U (the left singular vectors,
107*> stored columnwise);
108*> if JOBVT = 'O', A is overwritten with the first min(m,n)
109*> rows of V**H (the right singular vectors,
110*> stored rowwise);
111*> if JOBU .ne. 'O' and JOBVT .ne. 'O', the contents of A
112*> are destroyed.
113*> \endverbatim
114*>
115*> \param[in] LDA
116*> \verbatim
117*> LDA is INTEGER
118*> The leading dimension of the array A. LDA >= max(1,M).
119*> \endverbatim
120*>
121*> \param[out] S
122*> \verbatim
123*> S is REAL array, dimension (min(M,N))
124*> The singular values of A, sorted so that S(i) >= S(i+1).
125*> \endverbatim
126*>
127*> \param[out] U
128*> \verbatim
129*> U is COMPLEX array, dimension (LDU,UCOL)
130*> (LDU,M) if JOBU = 'A' or (LDU,min(M,N)) if JOBU = 'S'.
131*> If JOBU = 'A', U contains the M-by-M unitary matrix U;
132*> if JOBU = 'S', U contains the first min(m,n) columns of U
133*> (the left singular vectors, stored columnwise);
134*> if JOBU = 'N' or 'O', U is not referenced.
135*> \endverbatim
136*>
137*> \param[in] LDU
138*> \verbatim
139*> LDU is INTEGER
140*> The leading dimension of the array U. LDU >= 1; if
141*> JOBU = 'S' or 'A', LDU >= M.
142*> \endverbatim
143*>
144*> \param[out] VT
145*> \verbatim
146*> VT is COMPLEX array, dimension (LDVT,N)
147*> If JOBVT = 'A', VT contains the N-by-N unitary matrix
148*> V**H;
149*> if JOBVT = 'S', VT contains the first min(m,n) rows of
150*> V**H (the right singular vectors, stored rowwise);
151*> if JOBVT = 'N' or 'O', VT is not referenced.
152*> \endverbatim
153*>
154*> \param[in] LDVT
155*> \verbatim
156*> LDVT is INTEGER
157*> The leading dimension of the array VT. LDVT >= 1; if
158*> JOBVT = 'A', LDVT >= N; if JOBVT = 'S', LDVT >= min(M,N).
159*> \endverbatim
160*>
161*> \param[out] WORK
162*> \verbatim
163*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
164*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
165*> \endverbatim
166*>
167*> \param[in] LWORK
168*> \verbatim
169*> LWORK is INTEGER
170*> The dimension of the array WORK.
171*> LWORK >= MAX(1,2*MIN(M,N)+MAX(M,N)).
172*> For good performance, LWORK should generally be larger.
173*>
174*> If LWORK = -1, then a workspace query is assumed; the routine
175*> only calculates the optimal size of the WORK array, returns
176*> this value as the first entry of the WORK array, and no error
177*> message related to LWORK is issued by XERBLA.
178*> \endverbatim
179*>
180*> \param[out] RWORK
181*> \verbatim
182*> RWORK is REAL array, dimension (5*min(M,N))
183*> On exit, if INFO > 0, RWORK(1:MIN(M,N)-1) contains the
184*> unconverged superdiagonal elements of an upper bidiagonal
185*> matrix B whose diagonal is in S (not necessarily sorted).
186*> B satisfies A = U * B * VT, so it has the same singular
187*> values as A, and singular vectors related by U and VT.
188*> \endverbatim
189*>
190*> \param[out] INFO
191*> \verbatim
192*> INFO is INTEGER
193*> = 0: successful exit.
194*> < 0: if INFO = -i, the i-th argument had an illegal value.
195*> > 0: if CBDSQR did not converge, INFO specifies how many
196*> superdiagonals of an intermediate bidiagonal form B
197*> did not converge to zero. See the description of RWORK
198*> above for details.
199*> \endverbatim
200*
201* Authors:
202* ========
203*
204*> \author Univ. of Tennessee
205*> \author Univ. of California Berkeley
206*> \author Univ. of Colorado Denver
207*> \author NAG Ltd.
208*
209*> \ingroup complexGEsing
210*
211* =====================================================================
212 SUBROUTINE cgesvd( JOBU, JOBVT, M, N, A, LDA, S, U, LDU, VT, LDVT,
213 $ WORK, LWORK, RWORK, INFO )
214*
215* -- LAPACK driver routine --
216* -- LAPACK is a software package provided by Univ. of Tennessee, --
217* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
218*
219* .. Scalar Arguments ..
220 CHARACTER JOBU, JOBVT
221 INTEGER INFO, LDA, LDU, LDVT, LWORK, M, N
222* ..
223* .. Array Arguments ..
224 REAL RWORK( * ), S( * )
225 COMPLEX A( LDA, * ), U( LDU, * ), VT( LDVT, * ),
226 $ work( * )
227* ..
228*
229* =====================================================================
230*
231* .. Parameters ..
232 COMPLEX CZERO, CONE
233 parameter( czero = ( 0.0e0, 0.0e0 ),
234 $ cone = ( 1.0e0, 0.0e0 ) )
235 REAL ZERO, ONE
236 parameter( zero = 0.0e0, one = 1.0e0 )
237* ..
238* .. Local Scalars ..
239 LOGICAL LQUERY, WNTUA, WNTUAS, WNTUN, WNTUO, WNTUS,
240 $ wntva, wntvas, wntvn, wntvo, wntvs
241 INTEGER BLK, CHUNK, I, IE, IERR, IR, IRWORK, ISCL,
242 $ itau, itaup, itauq, iu, iwork, ldwrkr, ldwrku,
243 $ maxwrk, minmn, minwrk, mnthr, ncu, ncvt, nru,
244 $ nrvt, wrkbl
245 INTEGER LWORK_CGEQRF, LWORK_CUNGQR_N, LWORK_CUNGQR_M,
246 $ lwork_cgebrd, lwork_cungbr_p, lwork_cungbr_q,
247 $ lwork_cgelqf, lwork_cunglq_n, lwork_cunglq_m
248 REAL ANRM, BIGNUM, EPS, SMLNUM
249* ..
250* .. Local Arrays ..
251 REAL DUM( 1 )
252 COMPLEX CDUM( 1 )
253* ..
254* .. External Subroutines ..
255 EXTERNAL cbdsqr, cgebrd, cgelqf, cgemm, cgeqrf, clacpy,
256 $ clascl, claset, cungbr, cunglq, cungqr, cunmbr,
257 $ slascl, xerbla
258* ..
259* .. External Functions ..
260 LOGICAL LSAME
261 INTEGER ILAENV
262 REAL CLANGE, SLAMCH
263 EXTERNAL lsame, ilaenv, clange, slamch
264* ..
265* .. Intrinsic Functions ..
266 INTRINSIC max, min, sqrt
267* ..
268* .. Executable Statements ..
269*
270* Test the input arguments
271*
272 info = 0
273 minmn = min( m, n )
274 wntua = lsame( jobu, 'A' )
275 wntus = lsame( jobu, 'S' )
276 wntuas = wntua .OR. wntus
277 wntuo = lsame( jobu, 'O' )
278 wntun = lsame( jobu, 'N' )
279 wntva = lsame( jobvt, 'A' )
280 wntvs = lsame( jobvt, 'S' )
281 wntvas = wntva .OR. wntvs
282 wntvo = lsame( jobvt, 'O' )
283 wntvn = lsame( jobvt, 'N' )
284 lquery = ( lwork.EQ.-1 )
285*
286 IF( .NOT.( wntua .OR. wntus .OR. wntuo .OR. wntun ) ) THEN
287 info = -1
288 ELSE IF( .NOT.( wntva .OR. wntvs .OR. wntvo .OR. wntvn ) .OR.
289 $ ( wntvo .AND. wntuo ) ) THEN
290 info = -2
291 ELSE IF( m.LT.0 ) THEN
292 info = -3
293 ELSE IF( n.LT.0 ) THEN
294 info = -4
295 ELSE IF( lda.LT.max( 1, m ) ) THEN
296 info = -6
297 ELSE IF( ldu.LT.1 .OR. ( wntuas .AND. ldu.LT.m ) ) THEN
298 info = -9
299 ELSE IF( ldvt.LT.1 .OR. ( wntva .AND. ldvt.LT.n ) .OR.
300 $ ( wntvs .AND. ldvt.LT.minmn ) ) THEN
301 info = -11
302 END IF
303*
304* Compute workspace
305* (Note: Comments in the code beginning "Workspace:" describe the
306* minimal amount of workspace needed at that point in the code,
307* as well as the preferred amount for good performance.
308* CWorkspace refers to complex workspace, and RWorkspace to
309* real workspace. NB refers to the optimal block size for the
310* immediately following subroutine, as returned by ILAENV.)
311*
312 IF( info.EQ.0 ) THEN
313 minwrk = 1
314 maxwrk = 1
315 IF( m.GE.n .AND. minmn.GT.0 ) THEN
316*
317* Space needed for ZBDSQR is BDSPAC = 5*N
318*
319 mnthr = ilaenv( 6, 'CGESVD', jobu // jobvt, m, n, 0, 0 )
320* Compute space needed for CGEQRF
321 CALL cgeqrf( m, n, a, lda, cdum(1), cdum(1), -1, ierr )
322 lwork_cgeqrf = int( cdum(1) )
323* Compute space needed for CUNGQR
324 CALL cungqr( m, n, n, a, lda, cdum(1), cdum(1), -1, ierr )
325 lwork_cungqr_n = int( cdum(1) )
326 CALL cungqr( m, m, n, a, lda, cdum(1), cdum(1), -1, ierr )
327 lwork_cungqr_m = int( cdum(1) )
328* Compute space needed for CGEBRD
329 CALL cgebrd( n, n, a, lda, s, dum(1), cdum(1),
330 $ cdum(1), cdum(1), -1, ierr )
331 lwork_cgebrd = int( cdum(1) )
332* Compute space needed for CUNGBR
333 CALL cungbr( 'P', n, n, n, a, lda, cdum(1),
334 $ cdum(1), -1, ierr )
335 lwork_cungbr_p = int( cdum(1) )
336 CALL cungbr( 'Q', n, n, n, a, lda, cdum(1),
337 $ cdum(1), -1, ierr )
338 lwork_cungbr_q = int( cdum(1) )
339*
340 mnthr = ilaenv( 6, 'CGESVD', jobu // jobvt, m, n, 0, 0 )
341 IF( m.GE.mnthr ) THEN
342 IF( wntun ) THEN
343*
344* Path 1 (M much larger than N, JOBU='N')
345*
346 maxwrk = n + lwork_cgeqrf
347 maxwrk = max( maxwrk, 2*n+lwork_cgebrd )
348 IF( wntvo .OR. wntvas )
349 $ maxwrk = max( maxwrk, 2*n+lwork_cungbr_p )
350 minwrk = 3*n
351 ELSE IF( wntuo .AND. wntvn ) THEN
352*
353* Path 2 (M much larger than N, JOBU='O', JOBVT='N')
354*
355 wrkbl = n + lwork_cgeqrf
356 wrkbl = max( wrkbl, n+lwork_cungqr_n )
357 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
358 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
359 maxwrk = max( n*n+wrkbl, n*n+m*n )
360 minwrk = 2*n + m
361 ELSE IF( wntuo .AND. wntvas ) THEN
362*
363* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or
364* 'A')
365*
366 wrkbl = n + lwork_cgeqrf
367 wrkbl = max( wrkbl, n+lwork_cungqr_n )
368 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
369 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
370 wrkbl = max( wrkbl, 2*n+lwork_cungbr_p )
371 maxwrk = max( n*n+wrkbl, n*n+m*n )
372 minwrk = 2*n + m
373 ELSE IF( wntus .AND. wntvn ) THEN
374*
375* Path 4 (M much larger than N, JOBU='S', JOBVT='N')
376*
377 wrkbl = n + lwork_cgeqrf
378 wrkbl = max( wrkbl, n+lwork_cungqr_n )
379 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
380 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
381 maxwrk = n*n + wrkbl
382 minwrk = 2*n + m
383 ELSE IF( wntus .AND. wntvo ) THEN
384*
385* Path 5 (M much larger than N, JOBU='S', JOBVT='O')
386*
387 wrkbl = n + lwork_cgeqrf
388 wrkbl = max( wrkbl, n+lwork_cungqr_n )
389 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
390 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
391 wrkbl = max( wrkbl, 2*n+lwork_cungbr_p )
392 maxwrk = 2*n*n + wrkbl
393 minwrk = 2*n + m
394 ELSE IF( wntus .AND. wntvas ) THEN
395*
396* Path 6 (M much larger than N, JOBU='S', JOBVT='S' or
397* 'A')
398*
399 wrkbl = n + lwork_cgeqrf
400 wrkbl = max( wrkbl, n+lwork_cungqr_n )
401 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
402 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
403 wrkbl = max( wrkbl, 2*n+lwork_cungbr_p )
404 maxwrk = n*n + wrkbl
405 minwrk = 2*n + m
406 ELSE IF( wntua .AND. wntvn ) THEN
407*
408* Path 7 (M much larger than N, JOBU='A', JOBVT='N')
409*
410 wrkbl = n + lwork_cgeqrf
411 wrkbl = max( wrkbl, n+lwork_cungqr_m )
412 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
413 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
414 maxwrk = n*n + wrkbl
415 minwrk = 2*n + m
416 ELSE IF( wntua .AND. wntvo ) THEN
417*
418* Path 8 (M much larger than N, JOBU='A', JOBVT='O')
419*
420 wrkbl = n + lwork_cgeqrf
421 wrkbl = max( wrkbl, n+lwork_cungqr_m )
422 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
423 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
424 wrkbl = max( wrkbl, 2*n+lwork_cungbr_p )
425 maxwrk = 2*n*n + wrkbl
426 minwrk = 2*n + m
427 ELSE IF( wntua .AND. wntvas ) THEN
428*
429* Path 9 (M much larger than N, JOBU='A', JOBVT='S' or
430* 'A')
431*
432 wrkbl = n + lwork_cgeqrf
433 wrkbl = max( wrkbl, n+lwork_cungqr_m )
434 wrkbl = max( wrkbl, 2*n+lwork_cgebrd )
435 wrkbl = max( wrkbl, 2*n+lwork_cungbr_q )
436 wrkbl = max( wrkbl, 2*n+lwork_cungbr_p )
437 maxwrk = n*n + wrkbl
438 minwrk = 2*n + m
439 END IF
440 ELSE
441*
442* Path 10 (M at least N, but not much larger)
443*
444 CALL cgebrd( m, n, a, lda, s, dum(1), cdum(1),
445 $ cdum(1), cdum(1), -1, ierr )
446 lwork_cgebrd = int( cdum(1) )
447 maxwrk = 2*n + lwork_cgebrd
448 IF( wntus .OR. wntuo ) THEN
449 CALL cungbr( 'Q', m, n, n, a, lda, cdum(1),
450 $ cdum(1), -1, ierr )
451 lwork_cungbr_q = int( cdum(1) )
452 maxwrk = max( maxwrk, 2*n+lwork_cungbr_q )
453 END IF
454 IF( wntua ) THEN
455 CALL cungbr( 'Q', m, m, n, a, lda, cdum(1),
456 $ cdum(1), -1, ierr )
457 lwork_cungbr_q = int( cdum(1) )
458 maxwrk = max( maxwrk, 2*n+lwork_cungbr_q )
459 END IF
460 IF( .NOT.wntvn ) THEN
461 maxwrk = max( maxwrk, 2*n+lwork_cungbr_p )
462 END IF
463 minwrk = 2*n + m
464 END IF
465 ELSE IF( minmn.GT.0 ) THEN
466*
467* Space needed for CBDSQR is BDSPAC = 5*M
468*
469 mnthr = ilaenv( 6, 'CGESVD', jobu // jobvt, m, n, 0, 0 )
470* Compute space needed for CGELQF
471 CALL cgelqf( m, n, a, lda, cdum(1), cdum(1), -1, ierr )
472 lwork_cgelqf = int( cdum(1) )
473* Compute space needed for CUNGLQ
474 CALL cunglq( n, n, m, cdum(1), n, cdum(1), cdum(1), -1,
475 $ ierr )
476 lwork_cunglq_n = int( cdum(1) )
477 CALL cunglq( m, n, m, a, lda, cdum(1), cdum(1), -1, ierr )
478 lwork_cunglq_m = int( cdum(1) )
479* Compute space needed for CGEBRD
480 CALL cgebrd( m, m, a, lda, s, dum(1), cdum(1),
481 $ cdum(1), cdum(1), -1, ierr )
482 lwork_cgebrd = int( cdum(1) )
483* Compute space needed for CUNGBR P
484 CALL cungbr( 'P', m, m, m, a, n, cdum(1),
485 $ cdum(1), -1, ierr )
486 lwork_cungbr_p = int( cdum(1) )
487* Compute space needed for CUNGBR Q
488 CALL cungbr( 'Q', m, m, m, a, n, cdum(1),
489 $ cdum(1), -1, ierr )
490 lwork_cungbr_q = int( cdum(1) )
491 IF( n.GE.mnthr ) THEN
492 IF( wntvn ) THEN
493*
494* Path 1t(N much larger than M, JOBVT='N')
495*
496 maxwrk = m + lwork_cgelqf
497 maxwrk = max( maxwrk, 2*m+lwork_cgebrd )
498 IF( wntuo .OR. wntuas )
499 $ maxwrk = max( maxwrk, 2*m+lwork_cungbr_q )
500 minwrk = 3*m
501 ELSE IF( wntvo .AND. wntun ) THEN
502*
503* Path 2t(N much larger than M, JOBU='N', JOBVT='O')
504*
505 wrkbl = m + lwork_cgelqf
506 wrkbl = max( wrkbl, m+lwork_cunglq_m )
507 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
508 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
509 maxwrk = max( m*m+wrkbl, m*m+m*n )
510 minwrk = 2*m + n
511 ELSE IF( wntvo .AND. wntuas ) THEN
512*
513* Path 3t(N much larger than M, JOBU='S' or 'A',
514* JOBVT='O')
515*
516 wrkbl = m + lwork_cgelqf
517 wrkbl = max( wrkbl, m+lwork_cunglq_m )
518 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
519 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
520 wrkbl = max( wrkbl, 2*m+lwork_cungbr_q )
521 maxwrk = max( m*m+wrkbl, m*m+m*n )
522 minwrk = 2*m + n
523 ELSE IF( wntvs .AND. wntun ) THEN
524*
525* Path 4t(N much larger than M, JOBU='N', JOBVT='S')
526*
527 wrkbl = m + lwork_cgelqf
528 wrkbl = max( wrkbl, m+lwork_cunglq_m )
529 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
530 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
531 maxwrk = m*m + wrkbl
532 minwrk = 2*m + n
533 ELSE IF( wntvs .AND. wntuo ) THEN
534*
535* Path 5t(N much larger than M, JOBU='O', JOBVT='S')
536*
537 wrkbl = m + lwork_cgelqf
538 wrkbl = max( wrkbl, m+lwork_cunglq_m )
539 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
540 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
541 wrkbl = max( wrkbl, 2*m+lwork_cungbr_q )
542 maxwrk = 2*m*m + wrkbl
543 minwrk = 2*m + n
544 ELSE IF( wntvs .AND. wntuas ) THEN
545*
546* Path 6t(N much larger than M, JOBU='S' or 'A',
547* JOBVT='S')
548*
549 wrkbl = m + lwork_cgelqf
550 wrkbl = max( wrkbl, m+lwork_cunglq_m )
551 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
552 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
553 wrkbl = max( wrkbl, 2*m+lwork_cungbr_q )
554 maxwrk = m*m + wrkbl
555 minwrk = 2*m + n
556 ELSE IF( wntva .AND. wntun ) THEN
557*
558* Path 7t(N much larger than M, JOBU='N', JOBVT='A')
559*
560 wrkbl = m + lwork_cgelqf
561 wrkbl = max( wrkbl, m+lwork_cunglq_n )
562 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
563 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
564 maxwrk = m*m + wrkbl
565 minwrk = 2*m + n
566 ELSE IF( wntva .AND. wntuo ) THEN
567*
568* Path 8t(N much larger than M, JOBU='O', JOBVT='A')
569*
570 wrkbl = m + lwork_cgelqf
571 wrkbl = max( wrkbl, m+lwork_cunglq_n )
572 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
573 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
574 wrkbl = max( wrkbl, 2*m+lwork_cungbr_q )
575 maxwrk = 2*m*m + wrkbl
576 minwrk = 2*m + n
577 ELSE IF( wntva .AND. wntuas ) THEN
578*
579* Path 9t(N much larger than M, JOBU='S' or 'A',
580* JOBVT='A')
581*
582 wrkbl = m + lwork_cgelqf
583 wrkbl = max( wrkbl, m+lwork_cunglq_n )
584 wrkbl = max( wrkbl, 2*m+lwork_cgebrd )
585 wrkbl = max( wrkbl, 2*m+lwork_cungbr_p )
586 wrkbl = max( wrkbl, 2*m+lwork_cungbr_q )
587 maxwrk = m*m + wrkbl
588 minwrk = 2*m + n
589 END IF
590 ELSE
591*
592* Path 10t(N greater than M, but not much larger)
593*
594 CALL cgebrd( m, n, a, lda, s, dum(1), cdum(1),
595 $ cdum(1), cdum(1), -1, ierr )
596 lwork_cgebrd = int( cdum(1) )
597 maxwrk = 2*m + lwork_cgebrd
598 IF( wntvs .OR. wntvo ) THEN
599* Compute space needed for CUNGBR P
600 CALL cungbr( 'P', m, n, m, a, n, cdum(1),
601 $ cdum(1), -1, ierr )
602 lwork_cungbr_p = int( cdum(1) )
603 maxwrk = max( maxwrk, 2*m+lwork_cungbr_p )
604 END IF
605 IF( wntva ) THEN
606 CALL cungbr( 'P', n, n, m, a, n, cdum(1),
607 $ cdum(1), -1, ierr )
608 lwork_cungbr_p = int( cdum(1) )
609 maxwrk = max( maxwrk, 2*m+lwork_cungbr_p )
610 END IF
611 IF( .NOT.wntun ) THEN
612 maxwrk = max( maxwrk, 2*m+lwork_cungbr_q )
613 END IF
614 minwrk = 2*m + n
615 END IF
616 END IF
617 maxwrk = max( minwrk, maxwrk )
618 work( 1 ) = maxwrk
619*
620 IF( lwork.LT.minwrk .AND. .NOT.lquery ) THEN
621 info = -13
622 END IF
623 END IF
624*
625 IF( info.NE.0 ) THEN
626 CALL xerbla( 'CGESVD', -info )
627 RETURN
628 ELSE IF( lquery ) THEN
629 RETURN
630 END IF
631*
632* Quick return if possible
633*
634 IF( m.EQ.0 .OR. n.EQ.0 ) THEN
635 RETURN
636 END IF
637*
638* Get machine constants
639*
640 eps = slamch( 'P' )
641 smlnum = sqrt( slamch( 'S' ) ) / eps
642 bignum = one / smlnum
643*
644* Scale A if max element outside range [SMLNUM,BIGNUM]
645*
646 anrm = clange( 'M', m, n, a, lda, dum )
647 iscl = 0
648 IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
649 iscl = 1
650 CALL clascl( 'G', 0, 0, anrm, smlnum, m, n, a, lda, ierr )
651 ELSE IF( anrm.GT.bignum ) THEN
652 iscl = 1
653 CALL clascl( 'G', 0, 0, anrm, bignum, m, n, a, lda, ierr )
654 END IF
655*
656 IF( m.GE.n ) THEN
657*
658* A has at least as many rows as columns. If A has sufficiently
659* more rows than columns, first reduce using the QR
660* decomposition (if sufficient workspace available)
661*
662 IF( m.GE.mnthr ) THEN
663*
664 IF( wntun ) THEN
665*
666* Path 1 (M much larger than N, JOBU='N')
667* No left singular vectors to be computed
668*
669 itau = 1
670 iwork = itau + n
671*
672* Compute A=Q*R
673* (CWorkspace: need 2*N, prefer N+N*NB)
674* (RWorkspace: need 0)
675*
676 CALL cgeqrf( m, n, a, lda, work( itau ), work( iwork ),
677 $ lwork-iwork+1, ierr )
678*
679* Zero out below R
680*
681 IF( n .GT. 1 ) THEN
682 CALL claset( 'L', n-1, n-1, czero, czero, a( 2, 1 ),
683 $ lda )
684 END IF
685 ie = 1
686 itauq = 1
687 itaup = itauq + n
688 iwork = itaup + n
689*
690* Bidiagonalize R in A
691* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
692* (RWorkspace: need N)
693*
694 CALL cgebrd( n, n, a, lda, s, rwork( ie ), work( itauq ),
695 $ work( itaup ), work( iwork ), lwork-iwork+1,
696 $ ierr )
697 ncvt = 0
698 IF( wntvo .OR. wntvas ) THEN
699*
700* If right singular vectors desired, generate P'.
701* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
702* (RWorkspace: 0)
703*
704 CALL cungbr( 'P', n, n, n, a, lda, work( itaup ),
705 $ work( iwork ), lwork-iwork+1, ierr )
706 ncvt = n
707 END IF
708 irwork = ie + n
709*
710* Perform bidiagonal QR iteration, computing right
711* singular vectors of A in A if desired
712* (CWorkspace: 0)
713* (RWorkspace: need BDSPAC)
714*
715 CALL cbdsqr( 'U', n, ncvt, 0, 0, s, rwork( ie ), a, lda,
716 $ cdum, 1, cdum, 1, rwork( irwork ), info )
717*
718* If right singular vectors desired in VT, copy them there
719*
720 IF( wntvas )
721 $ CALL clacpy( 'F', n, n, a, lda, vt, ldvt )
722*
723 ELSE IF( wntuo .AND. wntvn ) THEN
724*
725* Path 2 (M much larger than N, JOBU='O', JOBVT='N')
726* N left singular vectors to be overwritten on A and
727* no right singular vectors to be computed
728*
729 IF( lwork.GE.n*n+3*n ) THEN
730*
731* Sufficient workspace for a fast algorithm
732*
733 ir = 1
734 IF( lwork.GE.max( wrkbl, lda*n )+lda*n ) THEN
735*
736* WORK(IU) is LDA by N, WORK(IR) is LDA by N
737*
738 ldwrku = lda
739 ldwrkr = lda
740 ELSE IF( lwork.GE.max( wrkbl, lda*n )+n*n ) THEN
741*
742* WORK(IU) is LDA by N, WORK(IR) is N by N
743*
744 ldwrku = lda
745 ldwrkr = n
746 ELSE
747*
748* WORK(IU) is LDWRKU by N, WORK(IR) is N by N
749*
750 ldwrku = ( lwork-n*n ) / n
751 ldwrkr = n
752 END IF
753 itau = ir + ldwrkr*n
754 iwork = itau + n
755*
756* Compute A=Q*R
757* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
758* (RWorkspace: 0)
759*
760 CALL cgeqrf( m, n, a, lda, work( itau ),
761 $ work( iwork ), lwork-iwork+1, ierr )
762*
763* Copy R to WORK(IR) and zero out below it
764*
765 CALL clacpy( 'U', n, n, a, lda, work( ir ), ldwrkr )
766 CALL claset( 'L', n-1, n-1, czero, czero,
767 $ work( ir+1 ), ldwrkr )
768*
769* Generate Q in A
770* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
771* (RWorkspace: 0)
772*
773 CALL cungqr( m, n, n, a, lda, work( itau ),
774 $ work( iwork ), lwork-iwork+1, ierr )
775 ie = 1
776 itauq = itau
777 itaup = itauq + n
778 iwork = itaup + n
779*
780* Bidiagonalize R in WORK(IR)
781* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
782* (RWorkspace: need N)
783*
784 CALL cgebrd( n, n, work( ir ), ldwrkr, s, rwork( ie ),
785 $ work( itauq ), work( itaup ),
786 $ work( iwork ), lwork-iwork+1, ierr )
787*
788* Generate left vectors bidiagonalizing R
789* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
790* (RWorkspace: need 0)
791*
792 CALL cungbr( 'Q', n, n, n, work( ir ), ldwrkr,
793 $ work( itauq ), work( iwork ),
794 $ lwork-iwork+1, ierr )
795 irwork = ie + n
796*
797* Perform bidiagonal QR iteration, computing left
798* singular vectors of R in WORK(IR)
799* (CWorkspace: need N*N)
800* (RWorkspace: need BDSPAC)
801*
802 CALL cbdsqr( 'U', n, 0, n, 0, s, rwork( ie ), cdum, 1,
803 $ work( ir ), ldwrkr, cdum, 1,
804 $ rwork( irwork ), info )
805 iu = itauq
806*
807* Multiply Q in A by left singular vectors of R in
808* WORK(IR), storing result in WORK(IU) and copying to A
809* (CWorkspace: need N*N+N, prefer N*N+M*N)
810* (RWorkspace: 0)
811*
812 DO 10 i = 1, m, ldwrku
813 chunk = min( m-i+1, ldwrku )
814 CALL cgemm( 'N', 'N', chunk, n, n, cone, a( i, 1 ),
815 $ lda, work( ir ), ldwrkr, czero,
816 $ work( iu ), ldwrku )
817 CALL clacpy( 'F', chunk, n, work( iu ), ldwrku,
818 $ a( i, 1 ), lda )
819 10 CONTINUE
820*
821 ELSE
822*
823* Insufficient workspace for a fast algorithm
824*
825 ie = 1
826 itauq = 1
827 itaup = itauq + n
828 iwork = itaup + n
829*
830* Bidiagonalize A
831* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
832* (RWorkspace: N)
833*
834 CALL cgebrd( m, n, a, lda, s, rwork( ie ),
835 $ work( itauq ), work( itaup ),
836 $ work( iwork ), lwork-iwork+1, ierr )
837*
838* Generate left vectors bidiagonalizing A
839* (CWorkspace: need 3*N, prefer 2*N+N*NB)
840* (RWorkspace: 0)
841*
842 CALL cungbr( 'Q', m, n, n, a, lda, work( itauq ),
843 $ work( iwork ), lwork-iwork+1, ierr )
844 irwork = ie + n
845*
846* Perform bidiagonal QR iteration, computing left
847* singular vectors of A in A
848* (CWorkspace: need 0)
849* (RWorkspace: need BDSPAC)
850*
851 CALL cbdsqr( 'U', n, 0, m, 0, s, rwork( ie ), cdum, 1,
852 $ a, lda, cdum, 1, rwork( irwork ), info )
853*
854 END IF
855*
856 ELSE IF( wntuo .AND. wntvas ) THEN
857*
858* Path 3 (M much larger than N, JOBU='O', JOBVT='S' or 'A')
859* N left singular vectors to be overwritten on A and
860* N right singular vectors to be computed in VT
861*
862 IF( lwork.GE.n*n+3*n ) THEN
863*
864* Sufficient workspace for a fast algorithm
865*
866 ir = 1
867 IF( lwork.GE.max( wrkbl, lda*n )+lda*n ) THEN
868*
869* WORK(IU) is LDA by N and WORK(IR) is LDA by N
870*
871 ldwrku = lda
872 ldwrkr = lda
873 ELSE IF( lwork.GE.max( wrkbl, lda*n )+n*n ) THEN
874*
875* WORK(IU) is LDA by N and WORK(IR) is N by N
876*
877 ldwrku = lda
878 ldwrkr = n
879 ELSE
880*
881* WORK(IU) is LDWRKU by N and WORK(IR) is N by N
882*
883 ldwrku = ( lwork-n*n ) / n
884 ldwrkr = n
885 END IF
886 itau = ir + ldwrkr*n
887 iwork = itau + n
888*
889* Compute A=Q*R
890* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
891* (RWorkspace: 0)
892*
893 CALL cgeqrf( m, n, a, lda, work( itau ),
894 $ work( iwork ), lwork-iwork+1, ierr )
895*
896* Copy R to VT, zeroing out below it
897*
898 CALL clacpy( 'U', n, n, a, lda, vt, ldvt )
899 IF( n.GT.1 )
900 $ CALL claset( 'L', n-1, n-1, czero, czero,
901 $ vt( 2, 1 ), ldvt )
902*
903* Generate Q in A
904* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
905* (RWorkspace: 0)
906*
907 CALL cungqr( m, n, n, a, lda, work( itau ),
908 $ work( iwork ), lwork-iwork+1, ierr )
909 ie = 1
910 itauq = itau
911 itaup = itauq + n
912 iwork = itaup + n
913*
914* Bidiagonalize R in VT, copying result to WORK(IR)
915* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
916* (RWorkspace: need N)
917*
918 CALL cgebrd( n, n, vt, ldvt, s, rwork( ie ),
919 $ work( itauq ), work( itaup ),
920 $ work( iwork ), lwork-iwork+1, ierr )
921 CALL clacpy( 'L', n, n, vt, ldvt, work( ir ), ldwrkr )
922*
923* Generate left vectors bidiagonalizing R in WORK(IR)
924* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
925* (RWorkspace: 0)
926*
927 CALL cungbr( 'Q', n, n, n, work( ir ), ldwrkr,
928 $ work( itauq ), work( iwork ),
929 $ lwork-iwork+1, ierr )
930*
931* Generate right vectors bidiagonalizing R in VT
932* (CWorkspace: need N*N+3*N-1, prefer N*N+2*N+(N-1)*NB)
933* (RWorkspace: 0)
934*
935 CALL cungbr( 'P', n, n, n, vt, ldvt, work( itaup ),
936 $ work( iwork ), lwork-iwork+1, ierr )
937 irwork = ie + n
938*
939* Perform bidiagonal QR iteration, computing left
940* singular vectors of R in WORK(IR) and computing right
941* singular vectors of R in VT
942* (CWorkspace: need N*N)
943* (RWorkspace: need BDSPAC)
944*
945 CALL cbdsqr( 'U', n, n, n, 0, s, rwork( ie ), vt,
946 $ ldvt, work( ir ), ldwrkr, cdum, 1,
947 $ rwork( irwork ), info )
948 iu = itauq
949*
950* Multiply Q in A by left singular vectors of R in
951* WORK(IR), storing result in WORK(IU) and copying to A
952* (CWorkspace: need N*N+N, prefer N*N+M*N)
953* (RWorkspace: 0)
954*
955 DO 20 i = 1, m, ldwrku
956 chunk = min( m-i+1, ldwrku )
957 CALL cgemm( 'N', 'N', chunk, n, n, cone, a( i, 1 ),
958 $ lda, work( ir ), ldwrkr, czero,
959 $ work( iu ), ldwrku )
960 CALL clacpy( 'F', chunk, n, work( iu ), ldwrku,
961 $ a( i, 1 ), lda )
962 20 CONTINUE
963*
964 ELSE
965*
966* Insufficient workspace for a fast algorithm
967*
968 itau = 1
969 iwork = itau + n
970*
971* Compute A=Q*R
972* (CWorkspace: need 2*N, prefer N+N*NB)
973* (RWorkspace: 0)
974*
975 CALL cgeqrf( m, n, a, lda, work( itau ),
976 $ work( iwork ), lwork-iwork+1, ierr )
977*
978* Copy R to VT, zeroing out below it
979*
980 CALL clacpy( 'U', n, n, a, lda, vt, ldvt )
981 IF( n.GT.1 )
982 $ CALL claset( 'L', n-1, n-1, czero, czero,
983 $ vt( 2, 1 ), ldvt )
984*
985* Generate Q in A
986* (CWorkspace: need 2*N, prefer N+N*NB)
987* (RWorkspace: 0)
988*
989 CALL cungqr( m, n, n, a, lda, work( itau ),
990 $ work( iwork ), lwork-iwork+1, ierr )
991 ie = 1
992 itauq = itau
993 itaup = itauq + n
994 iwork = itaup + n
995*
996* Bidiagonalize R in VT
997* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
998* (RWorkspace: N)
999*
1000 CALL cgebrd( n, n, vt, ldvt, s, rwork( ie ),
1001 $ work( itauq ), work( itaup ),
1002 $ work( iwork ), lwork-iwork+1, ierr )
1003*
1004* Multiply Q in A by left vectors bidiagonalizing R
1005* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1006* (RWorkspace: 0)
1007*
1008 CALL cunmbr( 'Q', 'r', 'n', M, N, N, VT, LDVT,
1009 $ WORK( ITAUQ ), A, LDA, WORK( IWORK ),
1010 $ LWORK-IWORK+1, IERR )
1011*
1012* Generate right vectors bidiagonalizing R in VT
1013* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
1014* (RWorkspace: 0)
1015*
1016 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
1017 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1018 IRWORK = IE + N
1019*
1020* Perform bidiagonal QR iteration, computing left
1021* singular vectors of A in A and computing right
1022* singular vectors of A in VT
1023* (CWorkspace: 0)
1024* (RWorkspace: need BDSPAC)
1025*
1026 CALL CBDSQR( 'u', N, N, M, 0, S, RWORK( IE ), VT,
1027 $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ),
1028 $ INFO )
1029*
1030 END IF
1031*
1032 ELSE IF( WNTUS ) THEN
1033*
1034 IF( WNTVN ) THEN
1035*
1036* Path 4 (M much larger than N, JOBU='S', JOBVT='N')
1037* N left singular vectors to be computed in U and
1038* no right singular vectors to be computed
1039*
1040.GE. IF( LWORKN*N+3*N ) THEN
1041*
1042* Sufficient workspace for a fast algorithm
1043*
1044 IR = 1
1045.GE. IF( LWORKWRKBL+LDA*N ) THEN
1046*
1047* WORK(IR) is LDA by N
1048*
1049 LDWRKR = LDA
1050 ELSE
1051*
1052* WORK(IR) is N by N
1053*
1054 LDWRKR = N
1055 END IF
1056 ITAU = IR + LDWRKR*N
1057 IWORK = ITAU + N
1058*
1059* Compute A=Q*R
1060* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1061* (RWorkspace: 0)
1062*
1063 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1064 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1065*
1066* Copy R to WORK(IR), zeroing out below it
1067*
1068 CALL CLACPY( 'u', N, N, A, LDA, WORK( IR ),
1069 $ LDWRKR )
1070 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1071 $ WORK( IR+1 ), LDWRKR )
1072*
1073* Generate Q in A
1074* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1075* (RWorkspace: 0)
1076*
1077 CALL CUNGQR( M, N, N, A, LDA, WORK( ITAU ),
1078 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1079 IE = 1
1080 ITAUQ = ITAU
1081 ITAUP = ITAUQ + N
1082 IWORK = ITAUP + N
1083*
1084* Bidiagonalize R in WORK(IR)
1085* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
1086* (RWorkspace: need N)
1087*
1088 CALL CGEBRD( N, N, WORK( IR ), LDWRKR, S,
1089 $ RWORK( IE ), WORK( ITAUQ ),
1090 $ WORK( ITAUP ), WORK( IWORK ),
1091 $ LWORK-IWORK+1, IERR )
1092*
1093* Generate left vectors bidiagonalizing R in WORK(IR)
1094* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
1095* (RWorkspace: 0)
1096*
1097 CALL CUNGBR( 'q', N, N, N, WORK( IR ), LDWRKR,
1098 $ WORK( ITAUQ ), WORK( IWORK ),
1099 $ LWORK-IWORK+1, IERR )
1100 IRWORK = IE + N
1101*
1102* Perform bidiagonal QR iteration, computing left
1103* singular vectors of R in WORK(IR)
1104* (CWorkspace: need N*N)
1105* (RWorkspace: need BDSPAC)
1106*
1107 CALL CBDSQR( 'u', N, 0, N, 0, S, RWORK( IE ), CDUM,
1108 $ 1, WORK( IR ), LDWRKR, CDUM, 1,
1109 $ RWORK( IRWORK ), INFO )
1110*
1111* Multiply Q in A by left singular vectors of R in
1112* WORK(IR), storing result in U
1113* (CWorkspace: need N*N)
1114* (RWorkspace: 0)
1115*
1116 CALL CGEMM( 'n', 'n', M, N, N, CONE, A, LDA,
1117 $ WORK( IR ), LDWRKR, CZERO, U, LDU )
1118*
1119 ELSE
1120*
1121* Insufficient workspace for a fast algorithm
1122*
1123 ITAU = 1
1124 IWORK = ITAU + N
1125*
1126* Compute A=Q*R, copying result to U
1127* (CWorkspace: need 2*N, prefer N+N*NB)
1128* (RWorkspace: 0)
1129*
1130 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1131 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1132 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1133*
1134* Generate Q in U
1135* (CWorkspace: need 2*N, prefer N+N*NB)
1136* (RWorkspace: 0)
1137*
1138 CALL CUNGQR( M, N, N, U, LDU, WORK( ITAU ),
1139 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1140 IE = 1
1141 ITAUQ = ITAU
1142 ITAUP = ITAUQ + N
1143 IWORK = ITAUP + N
1144*
1145* Zero out below R in A
1146*
1147.GT. IF( N 1 ) THEN
1148 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1149 $ A( 2, 1 ), LDA )
1150 END IF
1151*
1152* Bidiagonalize R in A
1153* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
1154* (RWorkspace: need N)
1155*
1156 CALL CGEBRD( N, N, A, LDA, S, RWORK( IE ),
1157 $ WORK( ITAUQ ), WORK( ITAUP ),
1158 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1159*
1160* Multiply Q in U by left vectors bidiagonalizing R
1161* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1162* (RWorkspace: 0)
1163*
1164 CALL CUNMBR( 'q', 'r', 'n', M, N, N, A, LDA,
1165 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
1166 $ LWORK-IWORK+1, IERR )
1167 IRWORK = IE + N
1168*
1169* Perform bidiagonal QR iteration, computing left
1170* singular vectors of A in U
1171* (CWorkspace: 0)
1172* (RWorkspace: need BDSPAC)
1173*
1174 CALL CBDSQR( 'u', N, 0, M, 0, S, RWORK( IE ), CDUM,
1175 $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ),
1176 $ INFO )
1177*
1178 END IF
1179*
1180 ELSE IF( WNTVO ) THEN
1181*
1182* Path 5 (M much larger than N, JOBU='S', JOBVT='O')
1183* N left singular vectors to be computed in U and
1184* N right singular vectors to be overwritten on A
1185*
1186.GE. IF( LWORK2*N*N+3*N ) THEN
1187*
1188* Sufficient workspace for a fast algorithm
1189*
1190 IU = 1
1191.GE. IF( LWORKWRKBL+2*LDA*N ) THEN
1192*
1193* WORK(IU) is LDA by N and WORK(IR) is LDA by N
1194*
1195 LDWRKU = LDA
1196 IR = IU + LDWRKU*N
1197 LDWRKR = LDA
1198.GE. ELSE IF( LWORKWRKBL+( LDA+N )*N ) THEN
1199*
1200* WORK(IU) is LDA by N and WORK(IR) is N by N
1201*
1202 LDWRKU = LDA
1203 IR = IU + LDWRKU*N
1204 LDWRKR = N
1205 ELSE
1206*
1207* WORK(IU) is N by N and WORK(IR) is N by N
1208*
1209 LDWRKU = N
1210 IR = IU + LDWRKU*N
1211 LDWRKR = N
1212 END IF
1213 ITAU = IR + LDWRKR*N
1214 IWORK = ITAU + N
1215*
1216* Compute A=Q*R
1217* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
1218* (RWorkspace: 0)
1219*
1220 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1221 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1222*
1223* Copy R to WORK(IU), zeroing out below it
1224*
1225 CALL CLACPY( 'u', N, N, A, LDA, WORK( IU ),
1226 $ LDWRKU )
1227 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1228 $ WORK( IU+1 ), LDWRKU )
1229*
1230* Generate Q in A
1231* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
1232* (RWorkspace: 0)
1233*
1234 CALL CUNGQR( M, N, N, A, LDA, WORK( ITAU ),
1235 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1236 IE = 1
1237 ITAUQ = ITAU
1238 ITAUP = ITAUQ + N
1239 IWORK = ITAUP + N
1240*
1241* Bidiagonalize R in WORK(IU), copying result to
1242* WORK(IR)
1243* (CWorkspace: need 2*N*N+3*N,
1244* prefer 2*N*N+2*N+2*N*NB)
1245* (RWorkspace: need N)
1246*
1247 CALL CGEBRD( N, N, WORK( IU ), LDWRKU, S,
1248 $ RWORK( IE ), WORK( ITAUQ ),
1249 $ WORK( ITAUP ), WORK( IWORK ),
1250 $ LWORK-IWORK+1, IERR )
1251 CALL CLACPY( 'u', N, N, WORK( IU ), LDWRKU,
1252 $ WORK( IR ), LDWRKR )
1253*
1254* Generate left bidiagonalizing vectors in WORK(IU)
1255* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB)
1256* (RWorkspace: 0)
1257*
1258 CALL CUNGBR( 'q', N, N, N, WORK( IU ), LDWRKU,
1259 $ WORK( ITAUQ ), WORK( IWORK ),
1260 $ LWORK-IWORK+1, IERR )
1261*
1262* Generate right bidiagonalizing vectors in WORK(IR)
1263* (CWorkspace: need 2*N*N+3*N-1,
1264* prefer 2*N*N+2*N+(N-1)*NB)
1265* (RWorkspace: 0)
1266*
1267 CALL CUNGBR( 'p', N, N, N, WORK( IR ), LDWRKR,
1268 $ WORK( ITAUP ), WORK( IWORK ),
1269 $ LWORK-IWORK+1, IERR )
1270 IRWORK = IE + N
1271*
1272* Perform bidiagonal QR iteration, computing left
1273* singular vectors of R in WORK(IU) and computing
1274* right singular vectors of R in WORK(IR)
1275* (CWorkspace: need 2*N*N)
1276* (RWorkspace: need BDSPAC)
1277*
1278 CALL CBDSQR( 'u', N, N, N, 0, S, RWORK( IE ),
1279 $ WORK( IR ), LDWRKR, WORK( IU ),
1280 $ LDWRKU, CDUM, 1, RWORK( IRWORK ),
1281 $ INFO )
1282*
1283* Multiply Q in A by left singular vectors of R in
1284* WORK(IU), storing result in U
1285* (CWorkspace: need N*N)
1286* (RWorkspace: 0)
1287*
1288 CALL CGEMM( 'n', 'n', M, N, N, CONE, A, LDA,
1289 $ WORK( IU ), LDWRKU, CZERO, U, LDU )
1290*
1291* Copy right singular vectors of R to A
1292* (CWorkspace: need N*N)
1293* (RWorkspace: 0)
1294*
1295 CALL CLACPY( 'f', N, N, WORK( IR ), LDWRKR, A,
1296 $ LDA )
1297*
1298 ELSE
1299*
1300* Insufficient workspace for a fast algorithm
1301*
1302 ITAU = 1
1303 IWORK = ITAU + N
1304*
1305* Compute A=Q*R, copying result to U
1306* (CWorkspace: need 2*N, prefer N+N*NB)
1307* (RWorkspace: 0)
1308*
1309 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1310 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1311 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1312*
1313* Generate Q in U
1314* (CWorkspace: need 2*N, prefer N+N*NB)
1315* (RWorkspace: 0)
1316*
1317 CALL CUNGQR( M, N, N, U, LDU, WORK( ITAU ),
1318 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1319 IE = 1
1320 ITAUQ = ITAU
1321 ITAUP = ITAUQ + N
1322 IWORK = ITAUP + N
1323*
1324* Zero out below R in A
1325*
1326.GT. IF( N 1 ) THEN
1327 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1328 $ A( 2, 1 ), LDA )
1329 END IF
1330*
1331* Bidiagonalize R in A
1332* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
1333* (RWorkspace: need N)
1334*
1335 CALL CGEBRD( N, N, A, LDA, S, RWORK( IE ),
1336 $ WORK( ITAUQ ), WORK( ITAUP ),
1337 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1338*
1339* Multiply Q in U by left vectors bidiagonalizing R
1340* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1341* (RWorkspace: 0)
1342*
1343 CALL CUNMBR( 'q', 'r', 'n', M, N, N, A, LDA,
1344 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
1345 $ LWORK-IWORK+1, IERR )
1346*
1347* Generate right vectors bidiagonalizing R in A
1348* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
1349* (RWorkspace: 0)
1350*
1351 CALL CUNGBR( 'p', N, N, N, A, LDA, WORK( ITAUP ),
1352 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1353 IRWORK = IE + N
1354*
1355* Perform bidiagonal QR iteration, computing left
1356* singular vectors of A in U and computing right
1357* singular vectors of A in A
1358* (CWorkspace: 0)
1359* (RWorkspace: need BDSPAC)
1360*
1361 CALL CBDSQR( 'u', N, N, M, 0, S, RWORK( IE ), A,
1362 $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ),
1363 $ INFO )
1364*
1365 END IF
1366*
1367 ELSE IF( WNTVAS ) THEN
1368*
1369* Path 6 (M much larger than N, JOBU='S', JOBVT='S'
1370* or 'A')
1371* N left singular vectors to be computed in U and
1372* N right singular vectors to be computed in VT
1373*
1374.GE. IF( LWORKN*N+3*N ) THEN
1375*
1376* Sufficient workspace for a fast algorithm
1377*
1378 IU = 1
1379.GE. IF( LWORKWRKBL+LDA*N ) THEN
1380*
1381* WORK(IU) is LDA by N
1382*
1383 LDWRKU = LDA
1384 ELSE
1385*
1386* WORK(IU) is N by N
1387*
1388 LDWRKU = N
1389 END IF
1390 ITAU = IU + LDWRKU*N
1391 IWORK = ITAU + N
1392*
1393* Compute A=Q*R
1394* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1395* (RWorkspace: 0)
1396*
1397 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1398 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1399*
1400* Copy R to WORK(IU), zeroing out below it
1401*
1402 CALL CLACPY( 'u', N, N, A, LDA, WORK( IU ),
1403 $ LDWRKU )
1404 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1405 $ WORK( IU+1 ), LDWRKU )
1406*
1407* Generate Q in A
1408* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1409* (RWorkspace: 0)
1410*
1411 CALL CUNGQR( M, N, N, A, LDA, WORK( ITAU ),
1412 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1413 IE = 1
1414 ITAUQ = ITAU
1415 ITAUP = ITAUQ + N
1416 IWORK = ITAUP + N
1417*
1418* Bidiagonalize R in WORK(IU), copying result to VT
1419* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
1420* (RWorkspace: need N)
1421*
1422 CALL CGEBRD( N, N, WORK( IU ), LDWRKU, S,
1423 $ RWORK( IE ), WORK( ITAUQ ),
1424 $ WORK( ITAUP ), WORK( IWORK ),
1425 $ LWORK-IWORK+1, IERR )
1426 CALL CLACPY( 'u', N, N, WORK( IU ), LDWRKU, VT,
1427 $ LDVT )
1428*
1429* Generate left bidiagonalizing vectors in WORK(IU)
1430* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
1431* (RWorkspace: 0)
1432*
1433 CALL CUNGBR( 'q', N, N, N, WORK( IU ), LDWRKU,
1434 $ WORK( ITAUQ ), WORK( IWORK ),
1435 $ LWORK-IWORK+1, IERR )
1436*
1437* Generate right bidiagonalizing vectors in VT
1438* (CWorkspace: need N*N+3*N-1,
1439* prefer N*N+2*N+(N-1)*NB)
1440* (RWorkspace: 0)
1441*
1442 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
1443 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1444 IRWORK = IE + N
1445*
1446* Perform bidiagonal QR iteration, computing left
1447* singular vectors of R in WORK(IU) and computing
1448* right singular vectors of R in VT
1449* (CWorkspace: need N*N)
1450* (RWorkspace: need BDSPAC)
1451*
1452 CALL CBDSQR( 'u', N, N, N, 0, S, RWORK( IE ), VT,
1453 $ LDVT, WORK( IU ), LDWRKU, CDUM, 1,
1454 $ RWORK( IRWORK ), INFO )
1455*
1456* Multiply Q in A by left singular vectors of R in
1457* WORK(IU), storing result in U
1458* (CWorkspace: need N*N)
1459* (RWorkspace: 0)
1460*
1461 CALL CGEMM( 'n', 'n', M, N, N, CONE, A, LDA,
1462 $ WORK( IU ), LDWRKU, CZERO, U, LDU )
1463*
1464 ELSE
1465*
1466* Insufficient workspace for a fast algorithm
1467*
1468 ITAU = 1
1469 IWORK = ITAU + N
1470*
1471* Compute A=Q*R, copying result to U
1472* (CWorkspace: need 2*N, prefer N+N*NB)
1473* (RWorkspace: 0)
1474*
1475 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1476 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1477 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1478*
1479* Generate Q in U
1480* (CWorkspace: need 2*N, prefer N+N*NB)
1481* (RWorkspace: 0)
1482*
1483 CALL CUNGQR( M, N, N, U, LDU, WORK( ITAU ),
1484 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1485*
1486* Copy R to VT, zeroing out below it
1487*
1488 CALL CLACPY( 'u', N, N, A, LDA, VT, LDVT )
1489.GT. IF( N1 )
1490 $ CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1491 $ VT( 2, 1 ), LDVT )
1492 IE = 1
1493 ITAUQ = ITAU
1494 ITAUP = ITAUQ + N
1495 IWORK = ITAUP + N
1496*
1497* Bidiagonalize R in VT
1498* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
1499* (RWorkspace: need N)
1500*
1501 CALL CGEBRD( N, N, VT, LDVT, S, RWORK( IE ),
1502 $ WORK( ITAUQ ), WORK( ITAUP ),
1503 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1504*
1505* Multiply Q in U by left bidiagonalizing vectors
1506* in VT
1507* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1508* (RWorkspace: 0)
1509*
1510 CALL CUNMBR( 'q', 'r', 'n', M, N, N, VT, LDVT,
1511 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
1512 $ LWORK-IWORK+1, IERR )
1513*
1514* Generate right bidiagonalizing vectors in VT
1515* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
1516* (RWorkspace: 0)
1517*
1518 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
1519 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1520 IRWORK = IE + N
1521*
1522* Perform bidiagonal QR iteration, computing left
1523* singular vectors of A in U and computing right
1524* singular vectors of A in VT
1525* (CWorkspace: 0)
1526* (RWorkspace: need BDSPAC)
1527*
1528 CALL CBDSQR( 'u', N, N, M, 0, S, RWORK( IE ), VT,
1529 $ LDVT, U, LDU, CDUM, 1,
1530 $ RWORK( IRWORK ), INFO )
1531*
1532 END IF
1533*
1534 END IF
1535*
1536 ELSE IF( WNTUA ) THEN
1537*
1538 IF( WNTVN ) THEN
1539*
1540* Path 7 (M much larger than N, JOBU='A', JOBVT='N')
1541* M left singular vectors to be computed in U and
1542* no right singular vectors to be computed
1543*
1544.GE. IF( LWORKN*N+MAX( N+M, 3*N ) ) THEN
1545*
1546* Sufficient workspace for a fast algorithm
1547*
1548 IR = 1
1549.GE. IF( LWORKWRKBL+LDA*N ) THEN
1550*
1551* WORK(IR) is LDA by N
1552*
1553 LDWRKR = LDA
1554 ELSE
1555*
1556* WORK(IR) is N by N
1557*
1558 LDWRKR = N
1559 END IF
1560 ITAU = IR + LDWRKR*N
1561 IWORK = ITAU + N
1562*
1563* Compute A=Q*R, copying result to U
1564* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1565* (RWorkspace: 0)
1566*
1567 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1568 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1569 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1570*
1571* Copy R to WORK(IR), zeroing out below it
1572*
1573 CALL CLACPY( 'u', N, N, A, LDA, WORK( IR ),
1574 $ LDWRKR )
1575 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1576 $ WORK( IR+1 ), LDWRKR )
1577*
1578* Generate Q in U
1579* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB)
1580* (RWorkspace: 0)
1581*
1582 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
1583 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1584 IE = 1
1585 ITAUQ = ITAU
1586 ITAUP = ITAUQ + N
1587 IWORK = ITAUP + N
1588*
1589* Bidiagonalize R in WORK(IR)
1590* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
1591* (RWorkspace: need N)
1592*
1593 CALL CGEBRD( N, N, WORK( IR ), LDWRKR, S,
1594 $ RWORK( IE ), WORK( ITAUQ ),
1595 $ WORK( ITAUP ), WORK( IWORK ),
1596 $ LWORK-IWORK+1, IERR )
1597*
1598* Generate left bidiagonalizing vectors in WORK(IR)
1599* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
1600* (RWorkspace: 0)
1601*
1602 CALL CUNGBR( 'q', N, N, N, WORK( IR ), LDWRKR,
1603 $ WORK( ITAUQ ), WORK( IWORK ),
1604 $ LWORK-IWORK+1, IERR )
1605 IRWORK = IE + N
1606*
1607* Perform bidiagonal QR iteration, computing left
1608* singular vectors of R in WORK(IR)
1609* (CWorkspace: need N*N)
1610* (RWorkspace: need BDSPAC)
1611*
1612 CALL CBDSQR( 'u', N, 0, N, 0, S, RWORK( IE ), CDUM,
1613 $ 1, WORK( IR ), LDWRKR, CDUM, 1,
1614 $ RWORK( IRWORK ), INFO )
1615*
1616* Multiply Q in U by left singular vectors of R in
1617* WORK(IR), storing result in A
1618* (CWorkspace: need N*N)
1619* (RWorkspace: 0)
1620*
1621 CALL CGEMM( 'n', 'n', M, N, N, CONE, U, LDU,
1622 $ WORK( IR ), LDWRKR, CZERO, A, LDA )
1623*
1624* Copy left singular vectors of A from A to U
1625*
1626 CALL CLACPY( 'f', M, N, A, LDA, U, LDU )
1627*
1628 ELSE
1629*
1630* Insufficient workspace for a fast algorithm
1631*
1632 ITAU = 1
1633 IWORK = ITAU + N
1634*
1635* Compute A=Q*R, copying result to U
1636* (CWorkspace: need 2*N, prefer N+N*NB)
1637* (RWorkspace: 0)
1638*
1639 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1640 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1641 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1642*
1643* Generate Q in U
1644* (CWorkspace: need N+M, prefer N+M*NB)
1645* (RWorkspace: 0)
1646*
1647 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
1648 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1649 IE = 1
1650 ITAUQ = ITAU
1651 ITAUP = ITAUQ + N
1652 IWORK = ITAUP + N
1653*
1654* Zero out below R in A
1655*
1656.GT. IF( N 1 ) THEN
1657 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1658 $ A( 2, 1 ), LDA )
1659 END IF
1660*
1661* Bidiagonalize R in A
1662* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
1663* (RWorkspace: need N)
1664*
1665 CALL CGEBRD( N, N, A, LDA, S, RWORK( IE ),
1666 $ WORK( ITAUQ ), WORK( ITAUP ),
1667 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1668*
1669* Multiply Q in U by left bidiagonalizing vectors
1670* in A
1671* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1672* (RWorkspace: 0)
1673*
1674 CALL CUNMBR( 'q', 'r', 'n', M, N, N, A, LDA,
1675 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
1676 $ LWORK-IWORK+1, IERR )
1677 IRWORK = IE + N
1678*
1679* Perform bidiagonal QR iteration, computing left
1680* singular vectors of A in U
1681* (CWorkspace: 0)
1682* (RWorkspace: need BDSPAC)
1683*
1684 CALL CBDSQR( 'u', N, 0, M, 0, S, RWORK( IE ), CDUM,
1685 $ 1, U, LDU, CDUM, 1, RWORK( IRWORK ),
1686 $ INFO )
1687*
1688 END IF
1689*
1690 ELSE IF( WNTVO ) THEN
1691*
1692* Path 8 (M much larger than N, JOBU='A', JOBVT='O')
1693* M left singular vectors to be computed in U and
1694* N right singular vectors to be overwritten on A
1695*
1696.GE. IF( LWORK2*N*N+MAX( N+M, 3*N ) ) THEN
1697*
1698* Sufficient workspace for a fast algorithm
1699*
1700 IU = 1
1701.GE. IF( LWORKWRKBL+2*LDA*N ) THEN
1702*
1703* WORK(IU) is LDA by N and WORK(IR) is LDA by N
1704*
1705 LDWRKU = LDA
1706 IR = IU + LDWRKU*N
1707 LDWRKR = LDA
1708.GE. ELSE IF( LWORKWRKBL+( LDA+N )*N ) THEN
1709*
1710* WORK(IU) is LDA by N and WORK(IR) is N by N
1711*
1712 LDWRKU = LDA
1713 IR = IU + LDWRKU*N
1714 LDWRKR = N
1715 ELSE
1716*
1717* WORK(IU) is N by N and WORK(IR) is N by N
1718*
1719 LDWRKU = N
1720 IR = IU + LDWRKU*N
1721 LDWRKR = N
1722 END IF
1723 ITAU = IR + LDWRKR*N
1724 IWORK = ITAU + N
1725*
1726* Compute A=Q*R, copying result to U
1727* (CWorkspace: need 2*N*N+2*N, prefer 2*N*N+N+N*NB)
1728* (RWorkspace: 0)
1729*
1730 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1731 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1732 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1733*
1734* Generate Q in U
1735* (CWorkspace: need 2*N*N+N+M, prefer 2*N*N+N+M*NB)
1736* (RWorkspace: 0)
1737*
1738 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
1739 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1740*
1741* Copy R to WORK(IU), zeroing out below it
1742*
1743 CALL CLACPY( 'u', N, N, A, LDA, WORK( IU ),
1744 $ LDWRKU )
1745 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1746 $ WORK( IU+1 ), LDWRKU )
1747 IE = 1
1748 ITAUQ = ITAU
1749 ITAUP = ITAUQ + N
1750 IWORK = ITAUP + N
1751*
1752* Bidiagonalize R in WORK(IU), copying result to
1753* WORK(IR)
1754* (CWorkspace: need 2*N*N+3*N,
1755* prefer 2*N*N+2*N+2*N*NB)
1756* (RWorkspace: need N)
1757*
1758 CALL CGEBRD( N, N, WORK( IU ), LDWRKU, S,
1759 $ RWORK( IE ), WORK( ITAUQ ),
1760 $ WORK( ITAUP ), WORK( IWORK ),
1761 $ LWORK-IWORK+1, IERR )
1762 CALL CLACPY( 'u', N, N, WORK( IU ), LDWRKU,
1763 $ WORK( IR ), LDWRKR )
1764*
1765* Generate left bidiagonalizing vectors in WORK(IU)
1766* (CWorkspace: need 2*N*N+3*N, prefer 2*N*N+2*N+N*NB)
1767* (RWorkspace: 0)
1768*
1769 CALL CUNGBR( 'q', N, N, N, WORK( IU ), LDWRKU,
1770 $ WORK( ITAUQ ), WORK( IWORK ),
1771 $ LWORK-IWORK+1, IERR )
1772*
1773* Generate right bidiagonalizing vectors in WORK(IR)
1774* (CWorkspace: need 2*N*N+3*N-1,
1775* prefer 2*N*N+2*N+(N-1)*NB)
1776* (RWorkspace: 0)
1777*
1778 CALL CUNGBR( 'p', N, N, N, WORK( IR ), LDWRKR,
1779 $ WORK( ITAUP ), WORK( IWORK ),
1780 $ LWORK-IWORK+1, IERR )
1781 IRWORK = IE + N
1782*
1783* Perform bidiagonal QR iteration, computing left
1784* singular vectors of R in WORK(IU) and computing
1785* right singular vectors of R in WORK(IR)
1786* (CWorkspace: need 2*N*N)
1787* (RWorkspace: need BDSPAC)
1788*
1789 CALL CBDSQR( 'u', N, N, N, 0, S, RWORK( IE ),
1790 $ WORK( IR ), LDWRKR, WORK( IU ),
1791 $ LDWRKU, CDUM, 1, RWORK( IRWORK ),
1792 $ INFO )
1793*
1794* Multiply Q in U by left singular vectors of R in
1795* WORK(IU), storing result in A
1796* (CWorkspace: need N*N)
1797* (RWorkspace: 0)
1798*
1799 CALL CGEMM( 'n', 'n', M, N, N, CONE, U, LDU,
1800 $ WORK( IU ), LDWRKU, CZERO, A, LDA )
1801*
1802* Copy left singular vectors of A from A to U
1803*
1804 CALL CLACPY( 'f', M, N, A, LDA, U, LDU )
1805*
1806* Copy right singular vectors of R from WORK(IR) to A
1807*
1808 CALL CLACPY( 'f', N, N, WORK( IR ), LDWRKR, A,
1809 $ LDA )
1810*
1811 ELSE
1812*
1813* Insufficient workspace for a fast algorithm
1814*
1815 ITAU = 1
1816 IWORK = ITAU + N
1817*
1818* Compute A=Q*R, copying result to U
1819* (CWorkspace: need 2*N, prefer N+N*NB)
1820* (RWorkspace: 0)
1821*
1822 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1823 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1824 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1825*
1826* Generate Q in U
1827* (CWorkspace: need N+M, prefer N+M*NB)
1828* (RWorkspace: 0)
1829*
1830 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
1831 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1832 IE = 1
1833 ITAUQ = ITAU
1834 ITAUP = ITAUQ + N
1835 IWORK = ITAUP + N
1836*
1837* Zero out below R in A
1838*
1839.GT. IF( N 1 ) THEN
1840 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1841 $ A( 2, 1 ), LDA )
1842 END IF
1843*
1844* Bidiagonalize R in A
1845* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
1846* (RWorkspace: need N)
1847*
1848 CALL CGEBRD( N, N, A, LDA, S, RWORK( IE ),
1849 $ WORK( ITAUQ ), WORK( ITAUP ),
1850 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1851*
1852* Multiply Q in U by left bidiagonalizing vectors
1853* in A
1854* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
1855* (RWorkspace: 0)
1856*
1857 CALL CUNMBR( 'q', 'r', 'n', M, N, N, A, LDA,
1858 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
1859 $ LWORK-IWORK+1, IERR )
1860*
1861* Generate right bidiagonalizing vectors in A
1862* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
1863* (RWorkspace: 0)
1864*
1865 CALL CUNGBR( 'p', N, N, N, A, LDA, WORK( ITAUP ),
1866 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1867 IRWORK = IE + N
1868*
1869* Perform bidiagonal QR iteration, computing left
1870* singular vectors of A in U and computing right
1871* singular vectors of A in A
1872* (CWorkspace: 0)
1873* (RWorkspace: need BDSPAC)
1874*
1875 CALL CBDSQR( 'u', N, N, M, 0, S, RWORK( IE ), A,
1876 $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ),
1877 $ INFO )
1878*
1879 END IF
1880*
1881 ELSE IF( WNTVAS ) THEN
1882*
1883* Path 9 (M much larger than N, JOBU='A', JOBVT='S'
1884* or 'A')
1885* M left singular vectors to be computed in U and
1886* N right singular vectors to be computed in VT
1887*
1888.GE. IF( LWORKN*N+MAX( N+M, 3*N ) ) THEN
1889*
1890* Sufficient workspace for a fast algorithm
1891*
1892 IU = 1
1893.GE. IF( LWORKWRKBL+LDA*N ) THEN
1894*
1895* WORK(IU) is LDA by N
1896*
1897 LDWRKU = LDA
1898 ELSE
1899*
1900* WORK(IU) is N by N
1901*
1902 LDWRKU = N
1903 END IF
1904 ITAU = IU + LDWRKU*N
1905 IWORK = ITAU + N
1906*
1907* Compute A=Q*R, copying result to U
1908* (CWorkspace: need N*N+2*N, prefer N*N+N+N*NB)
1909* (RWorkspace: 0)
1910*
1911 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1912 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1913 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1914*
1915* Generate Q in U
1916* (CWorkspace: need N*N+N+M, prefer N*N+N+M*NB)
1917* (RWorkspace: 0)
1918*
1919 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
1920 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1921*
1922* Copy R to WORK(IU), zeroing out below it
1923*
1924 CALL CLACPY( 'u', N, N, A, LDA, WORK( IU ),
1925 $ LDWRKU )
1926 CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
1927 $ WORK( IU+1 ), LDWRKU )
1928 IE = 1
1929 ITAUQ = ITAU
1930 ITAUP = ITAUQ + N
1931 IWORK = ITAUP + N
1932*
1933* Bidiagonalize R in WORK(IU), copying result to VT
1934* (CWorkspace: need N*N+3*N, prefer N*N+2*N+2*N*NB)
1935* (RWorkspace: need N)
1936*
1937 CALL CGEBRD( N, N, WORK( IU ), LDWRKU, S,
1938 $ RWORK( IE ), WORK( ITAUQ ),
1939 $ WORK( ITAUP ), WORK( IWORK ),
1940 $ LWORK-IWORK+1, IERR )
1941 CALL CLACPY( 'u', N, N, WORK( IU ), LDWRKU, VT,
1942 $ LDVT )
1943*
1944* Generate left bidiagonalizing vectors in WORK(IU)
1945* (CWorkspace: need N*N+3*N, prefer N*N+2*N+N*NB)
1946* (RWorkspace: 0)
1947*
1948 CALL CUNGBR( 'q', N, N, N, WORK( IU ), LDWRKU,
1949 $ WORK( ITAUQ ), WORK( IWORK ),
1950 $ LWORK-IWORK+1, IERR )
1951*
1952* Generate right bidiagonalizing vectors in VT
1953* (CWorkspace: need N*N+3*N-1,
1954* prefer N*N+2*N+(N-1)*NB)
1955* (RWorkspace: need 0)
1956*
1957 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
1958 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1959 IRWORK = IE + N
1960*
1961* Perform bidiagonal QR iteration, computing left
1962* singular vectors of R in WORK(IU) and computing
1963* right singular vectors of R in VT
1964* (CWorkspace: need N*N)
1965* (RWorkspace: need BDSPAC)
1966*
1967 CALL CBDSQR( 'u', N, N, N, 0, S, RWORK( IE ), VT,
1968 $ LDVT, WORK( IU ), LDWRKU, CDUM, 1,
1969 $ RWORK( IRWORK ), INFO )
1970*
1971* Multiply Q in U by left singular vectors of R in
1972* WORK(IU), storing result in A
1973* (CWorkspace: need N*N)
1974* (RWorkspace: 0)
1975*
1976 CALL CGEMM( 'n', 'n', M, N, N, CONE, U, LDU,
1977 $ WORK( IU ), LDWRKU, CZERO, A, LDA )
1978*
1979* Copy left singular vectors of A from A to U
1980*
1981 CALL CLACPY( 'f', M, N, A, LDA, U, LDU )
1982*
1983 ELSE
1984*
1985* Insufficient workspace for a fast algorithm
1986*
1987 ITAU = 1
1988 IWORK = ITAU + N
1989*
1990* Compute A=Q*R, copying result to U
1991* (CWorkspace: need 2*N, prefer N+N*NB)
1992* (RWorkspace: 0)
1993*
1994 CALL CGEQRF( M, N, A, LDA, WORK( ITAU ),
1995 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
1996 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
1997*
1998* Generate Q in U
1999* (CWorkspace: need N+M, prefer N+M*NB)
2000* (RWorkspace: 0)
2001*
2002 CALL CUNGQR( M, M, N, U, LDU, WORK( ITAU ),
2003 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2004*
2005* Copy R from A to VT, zeroing out below it
2006*
2007 CALL CLACPY( 'u', N, N, A, LDA, VT, LDVT )
2008.GT. IF( N1 )
2009 $ CALL CLASET( 'l', N-1, N-1, CZERO, CZERO,
2010 $ VT( 2, 1 ), LDVT )
2011 IE = 1
2012 ITAUQ = ITAU
2013 ITAUP = ITAUQ + N
2014 IWORK = ITAUP + N
2015*
2016* Bidiagonalize R in VT
2017* (CWorkspace: need 3*N, prefer 2*N+2*N*NB)
2018* (RWorkspace: need N)
2019*
2020 CALL CGEBRD( N, N, VT, LDVT, S, RWORK( IE ),
2021 $ WORK( ITAUQ ), WORK( ITAUP ),
2022 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2023*
2024* Multiply Q in U by left bidiagonalizing vectors
2025* in VT
2026* (CWorkspace: need 2*N+M, prefer 2*N+M*NB)
2027* (RWorkspace: 0)
2028*
2029 CALL CUNMBR( 'q', 'r', 'n', M, N, N, VT, LDVT,
2030 $ WORK( ITAUQ ), U, LDU, WORK( IWORK ),
2031 $ LWORK-IWORK+1, IERR )
2032*
2033* Generate right bidiagonalizing vectors in VT
2034* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
2035* (RWorkspace: 0)
2036*
2037 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
2038 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2039 IRWORK = IE + N
2040*
2041* Perform bidiagonal QR iteration, computing left
2042* singular vectors of A in U and computing right
2043* singular vectors of A in VT
2044* (CWorkspace: 0)
2045* (RWorkspace: need BDSPAC)
2046*
2047 CALL CBDSQR( 'u', N, N, M, 0, S, RWORK( IE ), VT,
2048 $ LDVT, U, LDU, CDUM, 1,
2049 $ RWORK( IRWORK ), INFO )
2050*
2051 END IF
2052*
2053 END IF
2054*
2055 END IF
2056*
2057 ELSE
2058*
2059* M .LT. MNTHR
2060*
2061* Path 10 (M at least N, but not much larger)
2062* Reduce to bidiagonal form without QR decomposition
2063*
2064 IE = 1
2065 ITAUQ = 1
2066 ITAUP = ITAUQ + N
2067 IWORK = ITAUP + N
2068*
2069* Bidiagonalize A
2070* (CWorkspace: need 2*N+M, prefer 2*N+(M+N)*NB)
2071* (RWorkspace: need N)
2072*
2073 CALL CGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
2074 $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
2075 $ IERR )
2076 IF( WNTUAS ) THEN
2077*
2078* If left singular vectors desired in U, copy result to U
2079* and generate left bidiagonalizing vectors in U
2080* (CWorkspace: need 2*N+NCU, prefer 2*N+NCU*NB)
2081* (RWorkspace: 0)
2082*
2083 CALL CLACPY( 'l', M, N, A, LDA, U, LDU )
2084 IF( WNTUS )
2085 $ NCU = N
2086 IF( WNTUA )
2087 $ NCU = M
2088 CALL CUNGBR( 'q', M, NCU, N, U, LDU, WORK( ITAUQ ),
2089 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2090 END IF
2091 IF( WNTVAS ) THEN
2092*
2093* If right singular vectors desired in VT, copy result to
2094* VT and generate right bidiagonalizing vectors in VT
2095* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
2096* (RWorkspace: 0)
2097*
2098 CALL CLACPY( 'u', N, N, A, LDA, VT, LDVT )
2099 CALL CUNGBR( 'p', N, N, N, VT, LDVT, WORK( ITAUP ),
2100 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2101 END IF
2102 IF( WNTUO ) THEN
2103*
2104* If left singular vectors desired in A, generate left
2105* bidiagonalizing vectors in A
2106* (CWorkspace: need 3*N, prefer 2*N+N*NB)
2107* (RWorkspace: 0)
2108*
2109 CALL CUNGBR( 'q', M, N, N, A, LDA, WORK( ITAUQ ),
2110 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2111 END IF
2112 IF( WNTVO ) THEN
2113*
2114* If right singular vectors desired in A, generate right
2115* bidiagonalizing vectors in A
2116* (CWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
2117* (RWorkspace: 0)
2118*
2119 CALL CUNGBR( 'p', N, N, N, A, LDA, WORK( ITAUP ),
2120 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2121 END IF
2122 IRWORK = IE + N
2123.OR. IF( WNTUAS WNTUO )
2124 $ NRU = M
2125 IF( WNTUN )
2126 $ NRU = 0
2127.OR. IF( WNTVAS WNTVO )
2128 $ NCVT = N
2129 IF( WNTVN )
2130 $ NCVT = 0
2131.NOT..AND..NOT. IF( ( WNTUO ) ( WNTVO ) ) THEN
2132*
2133* Perform bidiagonal QR iteration, if desired, computing
2134* left singular vectors in U and computing right singular
2135* vectors in VT
2136* (CWorkspace: 0)
2137* (RWorkspace: need BDSPAC)
2138*
2139 CALL CBDSQR( 'u', N, NCVT, NRU, 0, S, RWORK( IE ), VT,
2140 $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ),
2141 $ INFO )
2142.NOT..AND. ELSE IF( ( WNTUO ) WNTVO ) THEN
2143*
2144* Perform bidiagonal QR iteration, if desired, computing
2145* left singular vectors in U and computing right singular
2146* vectors in A
2147* (CWorkspace: 0)
2148* (RWorkspace: need BDSPAC)
2149*
2150 CALL CBDSQR( 'u', N, NCVT, NRU, 0, S, RWORK( IE ), A,
2151 $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ),
2152 $ INFO )
2153 ELSE
2154*
2155* Perform bidiagonal QR iteration, if desired, computing
2156* left singular vectors in A and computing right singular
2157* vectors in VT
2158* (CWorkspace: 0)
2159* (RWorkspace: need BDSPAC)
2160*
2161 CALL CBDSQR( 'u', N, NCVT, NRU, 0, S, RWORK( IE ), VT,
2162 $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ),
2163 $ INFO )
2164 END IF
2165*
2166 END IF
2167*
2168 ELSE
2169*
2170* A has more columns than rows. If A has sufficiently more
2171* columns than rows, first reduce using the LQ decomposition (if
2172* sufficient workspace available)
2173*
2174.GE. IF( NMNTHR ) THEN
2175*
2176 IF( WNTVN ) THEN
2177*
2178* Path 1t(N much larger than M, JOBVT='N')
2179* No right singular vectors to be computed
2180*
2181 ITAU = 1
2182 IWORK = ITAU + M
2183*
2184* Compute A=L*Q
2185* (CWorkspace: need 2*M, prefer M+M*NB)
2186* (RWorkspace: 0)
2187*
2188 CALL CGELQF( M, N, A, LDA, WORK( ITAU ), WORK( IWORK ),
2189 $ LWORK-IWORK+1, IERR )
2190*
2191* Zero out above L
2192*
2193 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO, A( 1, 2 ),
2194 $ LDA )
2195 IE = 1
2196 ITAUQ = 1
2197 ITAUP = ITAUQ + M
2198 IWORK = ITAUP + M
2199*
2200* Bidiagonalize L in A
2201* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
2202* (RWorkspace: need M)
2203*
2204 CALL CGEBRD( M, M, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
2205 $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
2206 $ IERR )
2207.OR. IF( WNTUO WNTUAS ) THEN
2208*
2209* If left singular vectors desired, generate Q
2210* (CWorkspace: need 3*M, prefer 2*M+M*NB)
2211* (RWorkspace: 0)
2212*
2213 CALL CUNGBR( 'q', M, M, M, A, LDA, WORK( ITAUQ ),
2214 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2215 END IF
2216 IRWORK = IE + M
2217 NRU = 0
2218.OR. IF( WNTUO WNTUAS )
2219 $ NRU = M
2220*
2221* Perform bidiagonal QR iteration, computing left singular
2222* vectors of A in A if desired
2223* (CWorkspace: 0)
2224* (RWorkspace: need BDSPAC)
2225*
2226 CALL CBDSQR( 'u', M, 0, NRU, 0, S, RWORK( IE ), CDUM, 1,
2227 $ A, LDA, CDUM, 1, RWORK( IRWORK ), INFO )
2228*
2229* If left singular vectors desired in U, copy them there
2230*
2231 IF( WNTUAS )
2232 $ CALL CLACPY( 'f', M, M, A, LDA, U, LDU )
2233*
2234.AND. ELSE IF( WNTVO WNTUN ) THEN
2235*
2236* Path 2t(N much larger than M, JOBU='N', JOBVT='O')
2237* M right singular vectors to be overwritten on A and
2238* no left singular vectors to be computed
2239*
2240.GE. IF( LWORKM*M+3*M ) THEN
2241*
2242* Sufficient workspace for a fast algorithm
2243*
2244 IR = 1
2245.GE. IF( LWORKMAX( WRKBL, LDA*N )+LDA*M ) THEN
2246*
2247* WORK(IU) is LDA by N and WORK(IR) is LDA by M
2248*
2249 LDWRKU = LDA
2250 CHUNK = N
2251 LDWRKR = LDA
2252.GE. ELSE IF( LWORKMAX( WRKBL, LDA*N )+M*M ) THEN
2253*
2254* WORK(IU) is LDA by N and WORK(IR) is M by M
2255*
2256 LDWRKU = LDA
2257 CHUNK = N
2258 LDWRKR = M
2259 ELSE
2260*
2261* WORK(IU) is M by CHUNK and WORK(IR) is M by M
2262*
2263 LDWRKU = M
2264 CHUNK = ( LWORK-M*M ) / M
2265 LDWRKR = M
2266 END IF
2267 ITAU = IR + LDWRKR*M
2268 IWORK = ITAU + M
2269*
2270* Compute A=L*Q
2271* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2272* (RWorkspace: 0)
2273*
2274 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2275 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2276*
2277* Copy L to WORK(IR) and zero out above it
2278*
2279 CALL CLACPY( 'l', M, M, A, LDA, WORK( IR ), LDWRKR )
2280 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
2281 $ WORK( IR+LDWRKR ), LDWRKR )
2282*
2283* Generate Q in A
2284* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2285* (RWorkspace: 0)
2286*
2287 CALL CUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
2288 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2289 IE = 1
2290 ITAUQ = ITAU
2291 ITAUP = ITAUQ + M
2292 IWORK = ITAUP + M
2293*
2294* Bidiagonalize L in WORK(IR)
2295* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
2296* (RWorkspace: need M)
2297*
2298 CALL CGEBRD( M, M, WORK( IR ), LDWRKR, S, RWORK( IE ),
2299 $ WORK( ITAUQ ), WORK( ITAUP ),
2300 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2301*
2302* Generate right vectors bidiagonalizing L
2303* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB)
2304* (RWorkspace: 0)
2305*
2306 CALL CUNGBR( 'p', M, M, M, WORK( IR ), LDWRKR,
2307 $ WORK( ITAUP ), WORK( IWORK ),
2308 $ LWORK-IWORK+1, IERR )
2309 IRWORK = IE + M
2310*
2311* Perform bidiagonal QR iteration, computing right
2312* singular vectors of L in WORK(IR)
2313* (CWorkspace: need M*M)
2314* (RWorkspace: need BDSPAC)
2315*
2316 CALL CBDSQR( 'u', M, M, 0, 0, S, RWORK( IE ),
2317 $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1,
2318 $ RWORK( IRWORK ), INFO )
2319 IU = ITAUQ
2320*
2321* Multiply right singular vectors of L in WORK(IR) by Q
2322* in A, storing result in WORK(IU) and copying to A
2323* (CWorkspace: need M*M+M, prefer M*M+M*N)
2324* (RWorkspace: 0)
2325*
2326 DO 30 I = 1, N, CHUNK
2327 BLK = MIN( N-I+1, CHUNK )
2328 CALL CGEMM( 'n', 'n', M, BLK, M, CONE, WORK( IR ),
2329 $ LDWRKR, A( 1, I ), LDA, CZERO,
2330 $ WORK( IU ), LDWRKU )
2331 CALL CLACPY( 'f', M, BLK, WORK( IU ), LDWRKU,
2332 $ A( 1, I ), LDA )
2333 30 CONTINUE
2334*
2335 ELSE
2336*
2337* Insufficient workspace for a fast algorithm
2338*
2339 IE = 1
2340 ITAUQ = 1
2341 ITAUP = ITAUQ + M
2342 IWORK = ITAUP + M
2343*
2344* Bidiagonalize A
2345* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
2346* (RWorkspace: need M)
2347*
2348 CALL CGEBRD( M, N, A, LDA, S, RWORK( IE ),
2349 $ WORK( ITAUQ ), WORK( ITAUP ),
2350 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2351*
2352* Generate right vectors bidiagonalizing A
2353* (CWorkspace: need 3*M, prefer 2*M+M*NB)
2354* (RWorkspace: 0)
2355*
2356 CALL CUNGBR( 'p', M, N, M, A, LDA, WORK( ITAUP ),
2357 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2358 IRWORK = IE + M
2359*
2360* Perform bidiagonal QR iteration, computing right
2361* singular vectors of A in A
2362* (CWorkspace: 0)
2363* (RWorkspace: need BDSPAC)
2364*
2365 CALL CBDSQR( 'l', M, N, 0, 0, S, RWORK( IE ), A, LDA,
2366 $ CDUM, 1, CDUM, 1, RWORK( IRWORK ), INFO )
2367*
2368 END IF
2369*
2370.AND. ELSE IF( WNTVO WNTUAS ) THEN
2371*
2372* Path 3t(N much larger than M, JOBU='S' or 'A', JOBVT='O')
2373* M right singular vectors to be overwritten on A and
2374* M left singular vectors to be computed in U
2375*
2376.GE. IF( LWORKM*M+3*M ) THEN
2377*
2378* Sufficient workspace for a fast algorithm
2379*
2380 IR = 1
2381.GE. IF( LWORKMAX( WRKBL, LDA*N )+LDA*M ) THEN
2382*
2383* WORK(IU) is LDA by N and WORK(IR) is LDA by M
2384*
2385 LDWRKU = LDA
2386 CHUNK = N
2387 LDWRKR = LDA
2388.GE. ELSE IF( LWORKMAX( WRKBL, LDA*N )+M*M ) THEN
2389*
2390* WORK(IU) is LDA by N and WORK(IR) is M by M
2391*
2392 LDWRKU = LDA
2393 CHUNK = N
2394 LDWRKR = M
2395 ELSE
2396*
2397* WORK(IU) is M by CHUNK and WORK(IR) is M by M
2398*
2399 LDWRKU = M
2400 CHUNK = ( LWORK-M*M ) / M
2401 LDWRKR = M
2402 END IF
2403 ITAU = IR + LDWRKR*M
2404 IWORK = ITAU + M
2405*
2406* Compute A=L*Q
2407* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2408* (RWorkspace: 0)
2409*
2410 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2411 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2412*
2413* Copy L to U, zeroing about above it
2414*
2415 CALL CLACPY( 'l', M, M, A, LDA, U, LDU )
2416 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO, U( 1, 2 ),
2417 $ LDU )
2418*
2419* Generate Q in A
2420* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2421* (RWorkspace: 0)
2422*
2423 CALL CUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
2424 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2425 IE = 1
2426 ITAUQ = ITAU
2427 ITAUP = ITAUQ + M
2428 IWORK = ITAUP + M
2429*
2430* Bidiagonalize L in U, copying result to WORK(IR)
2431* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
2432* (RWorkspace: need M)
2433*
2434 CALL CGEBRD( M, M, U, LDU, S, RWORK( IE ),
2435 $ WORK( ITAUQ ), WORK( ITAUP ),
2436 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2437 CALL CLACPY( 'u', M, M, U, LDU, WORK( IR ), LDWRKR )
2438*
2439* Generate right vectors bidiagonalizing L in WORK(IR)
2440* (CWorkspace: need M*M+3*M-1, prefer M*M+2*M+(M-1)*NB)
2441* (RWorkspace: 0)
2442*
2443 CALL CUNGBR( 'p', M, M, M, WORK( IR ), LDWRKR,
2444 $ WORK( ITAUP ), WORK( IWORK ),
2445 $ LWORK-IWORK+1, IERR )
2446*
2447* Generate left vectors bidiagonalizing L in U
2448* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
2449* (RWorkspace: 0)
2450*
2451 CALL CUNGBR( 'q', M, M, M, U, LDU, WORK( ITAUQ ),
2452 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2453 IRWORK = IE + M
2454*
2455* Perform bidiagonal QR iteration, computing left
2456* singular vectors of L in U, and computing right
2457* singular vectors of L in WORK(IR)
2458* (CWorkspace: need M*M)
2459* (RWorkspace: need BDSPAC)
2460*
2461 CALL CBDSQR( 'u', M, M, M, 0, S, RWORK( IE ),
2462 $ WORK( IR ), LDWRKR, U, LDU, CDUM, 1,
2463 $ RWORK( IRWORK ), INFO )
2464 IU = ITAUQ
2465*
2466* Multiply right singular vectors of L in WORK(IR) by Q
2467* in A, storing result in WORK(IU) and copying to A
2468* (CWorkspace: need M*M+M, prefer M*M+M*N))
2469* (RWorkspace: 0)
2470*
2471 DO 40 I = 1, N, CHUNK
2472 BLK = MIN( N-I+1, CHUNK )
2473 CALL CGEMM( 'n', 'n', M, BLK, M, CONE, WORK( IR ),
2474 $ LDWRKR, A( 1, I ), LDA, CZERO,
2475 $ WORK( IU ), LDWRKU )
2476 CALL CLACPY( 'f', M, BLK, WORK( IU ), LDWRKU,
2477 $ A( 1, I ), LDA )
2478 40 CONTINUE
2479*
2480 ELSE
2481*
2482* Insufficient workspace for a fast algorithm
2483*
2484 ITAU = 1
2485 IWORK = ITAU + M
2486*
2487* Compute A=L*Q
2488* (CWorkspace: need 2*M, prefer M+M*NB)
2489* (RWorkspace: 0)
2490*
2491 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2492 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2493*
2494* Copy L to U, zeroing out above it
2495*
2496 CALL CLACPY( 'l', M, M, A, LDA, U, LDU )
2497 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO, U( 1, 2 ),
2498 $ LDU )
2499*
2500* Generate Q in A
2501* (CWorkspace: need 2*M, prefer M+M*NB)
2502* (RWorkspace: 0)
2503*
2504 CALL CUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
2505 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2506 IE = 1
2507 ITAUQ = ITAU
2508 ITAUP = ITAUQ + M
2509 IWORK = ITAUP + M
2510*
2511* Bidiagonalize L in U
2512* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
2513* (RWorkspace: need M)
2514*
2515 CALL CGEBRD( M, M, U, LDU, S, RWORK( IE ),
2516 $ WORK( ITAUQ ), WORK( ITAUP ),
2517 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2518*
2519* Multiply right vectors bidiagonalizing L by Q in A
2520* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
2521* (RWorkspace: 0)
2522*
2523 CALL CUNMBR( 'p', 'l', 'c', M, N, M, U, LDU,
2524 $ WORK( ITAUP ), A, LDA, WORK( IWORK ),
2525 $ LWORK-IWORK+1, IERR )
2526*
2527* Generate left vectors bidiagonalizing L in U
2528* (CWorkspace: need 3*M, prefer 2*M+M*NB)
2529* (RWorkspace: 0)
2530*
2531 CALL CUNGBR( 'q', M, M, M, U, LDU, WORK( ITAUQ ),
2532 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2533 IRWORK = IE + M
2534*
2535* Perform bidiagonal QR iteration, computing left
2536* singular vectors of A in U and computing right
2537* singular vectors of A in A
2538* (CWorkspace: 0)
2539* (RWorkspace: need BDSPAC)
2540*
2541 CALL CBDSQR( 'u', M, N, M, 0, S, RWORK( IE ), A, LDA,
2542 $ U, LDU, CDUM, 1, RWORK( IRWORK ), INFO )
2543*
2544 END IF
2545*
2546 ELSE IF( WNTVS ) THEN
2547*
2548 IF( WNTUN ) THEN
2549*
2550* Path 4t(N much larger than M, JOBU='N', JOBVT='S')
2551* M right singular vectors to be computed in VT and
2552* no left singular vectors to be computed
2553*
2554.GE. IF( LWORKM*M+3*M ) THEN
2555*
2556* Sufficient workspace for a fast algorithm
2557*
2558 IR = 1
2559.GE. IF( LWORKWRKBL+LDA*M ) THEN
2560*
2561* WORK(IR) is LDA by M
2562*
2563 LDWRKR = LDA
2564 ELSE
2565*
2566* WORK(IR) is M by M
2567*
2568 LDWRKR = M
2569 END IF
2570 ITAU = IR + LDWRKR*M
2571 IWORK = ITAU + M
2572*
2573* Compute A=L*Q
2574* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2575* (RWorkspace: 0)
2576*
2577 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2578 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2579*
2580* Copy L to WORK(IR), zeroing out above it
2581*
2582 CALL CLACPY( 'l', M, M, A, LDA, WORK( IR ),
2583 $ LDWRKR )
2584 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
2585 $ WORK( IR+LDWRKR ), LDWRKR )
2586*
2587* Generate Q in A
2588* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2589* (RWorkspace: 0)
2590*
2591 CALL CUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
2592 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2593 IE = 1
2594 ITAUQ = ITAU
2595 ITAUP = ITAUQ + M
2596 IWORK = ITAUP + M
2597*
2598* Bidiagonalize L in WORK(IR)
2599* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
2600* (RWorkspace: need M)
2601*
2602 CALL CGEBRD( M, M, WORK( IR ), LDWRKR, S,
2603 $ RWORK( IE ), WORK( ITAUQ ),
2604 $ WORK( ITAUP ), WORK( IWORK ),
2605 $ LWORK-IWORK+1, IERR )
2606*
2607* Generate right vectors bidiagonalizing L in
2608* WORK(IR)
2609* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB)
2610* (RWorkspace: 0)
2611*
2612 CALL CUNGBR( 'p', M, M, M, WORK( IR ), LDWRKR,
2613 $ WORK( ITAUP ), WORK( IWORK ),
2614 $ LWORK-IWORK+1, IERR )
2615 IRWORK = IE + M
2616*
2617* Perform bidiagonal QR iteration, computing right
2618* singular vectors of L in WORK(IR)
2619* (CWorkspace: need M*M)
2620* (RWorkspace: need BDSPAC)
2621*
2622 CALL CBDSQR( 'u', M, M, 0, 0, S, RWORK( IE ),
2623 $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1,
2624 $ RWORK( IRWORK ), INFO )
2625*
2626* Multiply right singular vectors of L in WORK(IR) by
2627* Q in A, storing result in VT
2628* (CWorkspace: need M*M)
2629* (RWorkspace: 0)
2630*
2631 CALL CGEMM( 'n', 'n', M, N, M, CONE, WORK( IR ),
2632 $ LDWRKR, A, LDA, CZERO, VT, LDVT )
2633*
2634 ELSE
2635*
2636* Insufficient workspace for a fast algorithm
2637*
2638 ITAU = 1
2639 IWORK = ITAU + M
2640*
2641* Compute A=L*Q
2642* (CWorkspace: need 2*M, prefer M+M*NB)
2643* (RWorkspace: 0)
2644*
2645 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2646 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2647*
2648* Copy result to VT
2649*
2650 CALL CLACPY( 'u', M, N, A, LDA, VT, LDVT )
2651*
2652* Generate Q in VT
2653* (CWorkspace: need 2*M, prefer M+M*NB)
2654* (RWorkspace: 0)
2655*
2656 CALL CUNGLQ( M, N, M, VT, LDVT, WORK( ITAU ),
2657 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2658 IE = 1
2659 ITAUQ = ITAU
2660 ITAUP = ITAUQ + M
2661 IWORK = ITAUP + M
2662*
2663* Zero out above L in A
2664*
2665 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
2666 $ A( 1, 2 ), LDA )
2667*
2668* Bidiagonalize L in A
2669* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
2670* (RWorkspace: need M)
2671*
2672 CALL CGEBRD( M, M, A, LDA, S, RWORK( IE ),
2673 $ WORK( ITAUQ ), WORK( ITAUP ),
2674 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2675*
2676* Multiply right vectors bidiagonalizing L by Q in VT
2677* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
2678* (RWorkspace: 0)
2679*
2680 CALL CUNMBR( 'p', 'l', 'c', M, N, M, A, LDA,
2681 $ WORK( ITAUP ), VT, LDVT,
2682 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2683 IRWORK = IE + M
2684*
2685* Perform bidiagonal QR iteration, computing right
2686* singular vectors of A in VT
2687* (CWorkspace: 0)
2688* (RWorkspace: need BDSPAC)
2689*
2690 CALL CBDSQR( 'u', M, N, 0, 0, S, RWORK( IE ), VT,
2691 $ LDVT, CDUM, 1, CDUM, 1,
2692 $ RWORK( IRWORK ), INFO )
2693*
2694 END IF
2695*
2696 ELSE IF( WNTUO ) THEN
2697*
2698* Path 5t(N much larger than M, JOBU='O', JOBVT='S')
2699* M right singular vectors to be computed in VT and
2700* M left singular vectors to be overwritten on A
2701*
2702.GE. IF( LWORK2*M*M+3*M ) THEN
2703*
2704* Sufficient workspace for a fast algorithm
2705*
2706 IU = 1
2707.GE. IF( LWORKWRKBL+2*LDA*M ) THEN
2708*
2709* WORK(IU) is LDA by M and WORK(IR) is LDA by M
2710*
2711 LDWRKU = LDA
2712 IR = IU + LDWRKU*M
2713 LDWRKR = LDA
2714.GE. ELSE IF( LWORKWRKBL+( LDA+M )*M ) THEN
2715*
2716* WORK(IU) is LDA by M and WORK(IR) is M by M
2717*
2718 LDWRKU = LDA
2719 IR = IU + LDWRKU*M
2720 LDWRKR = M
2721 ELSE
2722*
2723* WORK(IU) is M by M and WORK(IR) is M by M
2724*
2725 LDWRKU = M
2726 IR = IU + LDWRKU*M
2727 LDWRKR = M
2728 END IF
2729 ITAU = IR + LDWRKR*M
2730 IWORK = ITAU + M
2731*
2732* Compute A=L*Q
2733* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
2734* (RWorkspace: 0)
2735*
2736 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
2737 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2738*
2739* Copy L to WORK(IU), zeroing out below it
2740*
2741 CALL CLACPY( 'l', M, M, A, LDA, WORK( IU ),
2742 $ LDWRKU )
2743 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
2744 $ WORK( IU+LDWRKU ), LDWRKU )
2745*
2746* Generate Q in A
2747* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
2748* (RWorkspace: 0)
2749*
2750 CALL CUNGLQ( M, N, M, A, LDA, WORK( ITAU ),
2751 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
2752 IE = 1
2753 ITAUQ = ITAU
2754 ITAUP = ITAUQ + M
2755 IWORK = ITAUP + M
2756*
2757* Bidiagonalize L in WORK(IU), copying result to
2758* WORK(IR)
2759* (CWorkspace: need 2*M*M+3*M,
2760* prefer 2*M*M+2*M+2*M*NB)
2761* (RWorkspace: need M)
2762*
2763 CALL CGEBRD( M, M, WORK( IU ), LDWRKU, S,
2764 $ RWORK( IE ), WORK( ITAUQ ),
2765 $ WORK( ITAUP ), WORK( IWORK ),
2766 $ LWORK-IWORK+1, IERR )
2767 CALL CLACPY( 'l', M, M, WORK( IU ), LDWRKU,
2768 $ WORK( IR ), LDWRKR )
2769*
2770* Generate right bidiagonalizing vectors in WORK(IU)
2771* (CWorkspace: need 2*M*M+3*M-1,
2772* prefer 2*M*M+2*M+(M-1)*NB)
2773* (RWorkspace: 0)
2774*
2775 CALL CUNGBR( 'p', M, M, M, WORK( IU ), LDWRKU,
2776 $ WORK( ITAUP ), WORK( IWORK ),
2777 $ LWORK-IWORK+1, IERR )
2778*
2779* Generate left bidiagonalizing vectors in WORK(IR)
2780* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB)
2781* (RWorkspace: 0)
2782*
2783 CALL CUNGBR( 'q', M, M, M, WORK( IR ), LDWRKR,
2784 $ WORK( ITAUQ ), WORK( IWORK ),
2785 $ LWORK-IWORK+1, IERR )
2786 IRWORK = IE + M
2787*
2788* Perform bidiagonal QR iteration, computing left
2789* singular vectors of L in WORK(IR) and computing
2790* right singular vectors of L in WORK(IU)
2791* (CWorkspace: need 2*M*M)
2792* (RWorkspace: need BDSPAC)
2793*
2794 CALL CBDSQR( 'u', M, M, M, 0, S, RWORK( IE ),
2795 $ WORK( IU ), LDWRKU, WORK( IR ),
2796 $ LDWRKR, CDUM, 1, RWORK( IRWORK ),
2797 $ INFO )
2798*
2799* Multiply right singular vectors of L in WORK(IU) by
2800* Q in A, storing result in VT
2801* (CWorkspace: need M*M)
2802* (RWorkspace: 0)
2803*
2804 CALL CGEMM( 'n', 'n', M, N, M, CONE, WORK( IU ),
2805 $ LDWRKU, A, LDA, CZERO, VT, LDVT )
2806*
2807* Copy left singular vectors of L to A
2808* (CWorkspace: need M*M)
2809* (RWorkspace: 0)
2810*
2811 CALL CLACPY( 'f', m, m, work( ir ), ldwrkr, a,
2812 $ lda )
2813*
2814 ELSE
2815*
2816* Insufficient workspace for a fast algorithm
2817*
2818 itau = 1
2819 iwork = itau + m
2820*
2821* Compute A=L*Q, copying result to VT
2822* (CWorkspace: need 2*M, prefer M+M*NB)
2823* (RWorkspace: 0)
2824*
2825 CALL cgelqf( m, n, a, lda, work( itau ),
2826 $ work( iwork ), lwork-iwork+1, ierr )
2827 CALL clacpy( 'U', m, n, a, lda, vt, ldvt )
2828*
2829* Generate Q in VT
2830* (CWorkspace: need 2*M, prefer M+M*NB)
2831* (RWorkspace: 0)
2832*
2833 CALL cunglq( m, n, m, vt, ldvt, work( itau ),
2834 $ work( iwork ), lwork-iwork+1, ierr )
2835 ie = 1
2836 itauq = itau
2837 itaup = itauq + m
2838 iwork = itaup + m
2839*
2840* Zero out above L in A
2841*
2842 CALL claset( 'U', m-1, m-1, czero, czero,
2843 $ a( 1, 2 ), lda )
2844*
2845* Bidiagonalize L in A
2846* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
2847* (RWorkspace: need M)
2848*
2849 CALL cgebrd( m, m, a, lda, s, rwork( ie ),
2850 $ work( itauq ), work( itaup ),
2851 $ work( iwork ), lwork-iwork+1, ierr )
2852*
2853* Multiply right vectors bidiagonalizing L by Q in VT
2854* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
2855* (RWorkspace: 0)
2856*
2857 CALL cunmbr( 'P', 'L', 'C', m, n, m, a, lda,
2858 $ work( itaup ), vt, ldvt,
2859 $ work( iwork ), lwork-iwork+1, ierr )
2860*
2861* Generate left bidiagonalizing vectors of L in A
2862* (CWorkspace: need 3*M, prefer 2*M+M*NB)
2863* (RWorkspace: 0)
2864*
2865 CALL cungbr( 'Q', m, m, m, a, lda, work( itauq ),
2866 $ work( iwork ), lwork-iwork+1, ierr )
2867 irwork = ie + m
2868*
2869* Perform bidiagonal QR iteration, computing left
2870* singular vectors of A in A and computing right
2871* singular vectors of A in VT
2872* (CWorkspace: 0)
2873* (RWorkspace: need BDSPAC)
2874*
2875 CALL cbdsqr( 'U', m, n, m, 0, s, rwork( ie ), vt,
2876 $ ldvt, a, lda, cdum, 1,
2877 $ rwork( irwork ), info )
2878*
2879 END IF
2880*
2881 ELSE IF( wntuas ) THEN
2882*
2883* Path 6t(N much larger than M, JOBU='S' or 'A',
2884* JOBVT='S')
2885* M right singular vectors to be computed in VT and
2886* M left singular vectors to be computed in U
2887*
2888 IF( lwork.GE.m*m+3*m ) THEN
2889*
2890* Sufficient workspace for a fast algorithm
2891*
2892 iu = 1
2893 IF( lwork.GE.wrkbl+lda*m ) THEN
2894*
2895* WORK(IU) is LDA by N
2896*
2897 ldwrku = lda
2898 ELSE
2899*
2900* WORK(IU) is LDA by M
2901*
2902 ldwrku = m
2903 END IF
2904 itau = iu + ldwrku*m
2905 iwork = itau + m
2906*
2907* Compute A=L*Q
2908* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2909* (RWorkspace: 0)
2910*
2911 CALL cgelqf( m, n, a, lda, work( itau ),
2912 $ work( iwork ), lwork-iwork+1, ierr )
2913*
2914* Copy L to WORK(IU), zeroing out above it
2915*
2916 CALL clacpy( 'L', m, m, a, lda, work( iu ),
2917 $ ldwrku )
2918 CALL claset( 'U', m-1, m-1, czero, czero,
2919 $ work( iu+ldwrku ), ldwrku )
2920*
2921* Generate Q in A
2922* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
2923* (RWorkspace: 0)
2924*
2925 CALL cunglq( m, n, m, a, lda, work( itau ),
2926 $ work( iwork ), lwork-iwork+1, ierr )
2927 ie = 1
2928 itauq = itau
2929 itaup = itauq + m
2930 iwork = itaup + m
2931*
2932* Bidiagonalize L in WORK(IU), copying result to U
2933* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
2934* (RWorkspace: need M)
2935*
2936 CALL cgebrd( m, m, work( iu ), ldwrku, s,
2937 $ rwork( ie ), work( itauq ),
2938 $ work( itaup ), work( iwork ),
2939 $ lwork-iwork+1, ierr )
2940 CALL clacpy( 'L', m, m, work( iu ), ldwrku, u,
2941 $ ldu )
2942*
2943* Generate right bidiagonalizing vectors in WORK(IU)
2944* (CWorkspace: need M*M+3*M-1,
2945* prefer M*M+2*M+(M-1)*NB)
2946* (RWorkspace: 0)
2947*
2948 CALL cungbr( 'P', m, m, m, work( iu ), ldwrku,
2949 $ work( itaup ), work( iwork ),
2950 $ lwork-iwork+1, ierr )
2951*
2952* Generate left bidiagonalizing vectors in U
2953* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
2954* (RWorkspace: 0)
2955*
2956 CALL cungbr( 'Q', m, m, m, u, ldu, work( itauq ),
2957 $ work( iwork ), lwork-iwork+1, ierr )
2958 irwork = ie + m
2959*
2960* Perform bidiagonal QR iteration, computing left
2961* singular vectors of L in U and computing right
2962* singular vectors of L in WORK(IU)
2963* (CWorkspace: need M*M)
2964* (RWorkspace: need BDSPAC)
2965*
2966 CALL cbdsqr( 'U', m, m, m, 0, s, rwork( ie ),
2967 $ work( iu ), ldwrku, u, ldu, cdum, 1,
2968 $ rwork( irwork ), info )
2969*
2970* Multiply right singular vectors of L in WORK(IU) by
2971* Q in A, storing result in VT
2972* (CWorkspace: need M*M)
2973* (RWorkspace: 0)
2974*
2975 CALL cgemm( 'N', 'N', m, n, m, cone, work( iu ),
2976 $ ldwrku, a, lda, czero, vt, ldvt )
2977*
2978 ELSE
2979*
2980* Insufficient workspace for a fast algorithm
2981*
2982 itau = 1
2983 iwork = itau + m
2984*
2985* Compute A=L*Q, copying result to VT
2986* (CWorkspace: need 2*M, prefer M+M*NB)
2987* (RWorkspace: 0)
2988*
2989 CALL cgelqf( m, n, a, lda, work( itau ),
2990 $ work( iwork ), lwork-iwork+1, ierr )
2991 CALL clacpy( 'U', m, n, a, lda, vt, ldvt )
2992*
2993* Generate Q in VT
2994* (CWorkspace: need 2*M, prefer M+M*NB)
2995* (RWorkspace: 0)
2996*
2997 CALL cunglq( m, n, m, vt, ldvt, work( itau ),
2998 $ work( iwork ), lwork-iwork+1, ierr )
2999*
3000* Copy L to U, zeroing out above it
3001*
3002 CALL clacpy( 'L', m, m, a, lda, u, ldu )
3003 CALL claset( 'u', M-1, M-1, CZERO, CZERO,
3004 $ U( 1, 2 ), LDU )
3005 IE = 1
3006 ITAUQ = ITAU
3007 ITAUP = ITAUQ + M
3008 IWORK = ITAUP + M
3009*
3010* Bidiagonalize L in U
3011* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
3012* (RWorkspace: need M)
3013*
3014 CALL CGEBRD( M, M, U, LDU, S, RWORK( IE ),
3015 $ WORK( ITAUQ ), WORK( ITAUP ),
3016 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3017*
3018* Multiply right bidiagonalizing vectors in U by Q
3019* in VT
3020* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
3021* (RWorkspace: 0)
3022*
3023 CALL CUNMBR( 'p', 'l', 'c', M, N, M, U, LDU,
3024 $ WORK( ITAUP ), VT, LDVT,
3025 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3026*
3027* Generate left bidiagonalizing vectors in U
3028* (CWorkspace: need 3*M, prefer 2*M+M*NB)
3029* (RWorkspace: 0)
3030*
3031 CALL CUNGBR( 'q', M, M, M, U, LDU, WORK( ITAUQ ),
3032 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3033 IRWORK = IE + M
3034*
3035* Perform bidiagonal QR iteration, computing left
3036* singular vectors of A in U and computing right
3037* singular vectors of A in VT
3038* (CWorkspace: 0)
3039* (RWorkspace: need BDSPAC)
3040*
3041 CALL CBDSQR( 'u', M, N, M, 0, S, RWORK( IE ), VT,
3042 $ LDVT, U, LDU, CDUM, 1,
3043 $ RWORK( IRWORK ), INFO )
3044*
3045 END IF
3046*
3047 END IF
3048*
3049 ELSE IF( WNTVA ) THEN
3050*
3051 IF( WNTUN ) THEN
3052*
3053* Path 7t(N much larger than M, JOBU='N', JOBVT='A')
3054* N right singular vectors to be computed in VT and
3055* no left singular vectors to be computed
3056*
3057.GE. IF( LWORKM*M+MAX( N+M, 3*M ) ) THEN
3058*
3059* Sufficient workspace for a fast algorithm
3060*
3061 IR = 1
3062.GE. IF( LWORKWRKBL+LDA*M ) THEN
3063*
3064* WORK(IR) is LDA by M
3065*
3066 LDWRKR = LDA
3067 ELSE
3068*
3069* WORK(IR) is M by M
3070*
3071 LDWRKR = M
3072 END IF
3073 ITAU = IR + LDWRKR*M
3074 IWORK = ITAU + M
3075*
3076* Compute A=L*Q, copying result to VT
3077* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
3078* (RWorkspace: 0)
3079*
3080 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
3081 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3082 CALL CLACPY( 'u', M, N, A, LDA, VT, LDVT )
3083*
3084* Copy L to WORK(IR), zeroing out above it
3085*
3086 CALL CLACPY( 'l', M, M, A, LDA, WORK( IR ),
3087 $ LDWRKR )
3088 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
3089 $ WORK( IR+LDWRKR ), LDWRKR )
3090*
3091* Generate Q in VT
3092* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB)
3093* (RWorkspace: 0)
3094*
3095 CALL CUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
3096 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3097 IE = 1
3098 ITAUQ = ITAU
3099 ITAUP = ITAUQ + M
3100 IWORK = ITAUP + M
3101*
3102* Bidiagonalize L in WORK(IR)
3103* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
3104* (RWorkspace: need M)
3105*
3106 CALL CGEBRD( M, M, WORK( IR ), LDWRKR, S,
3107 $ RWORK( IE ), WORK( ITAUQ ),
3108 $ WORK( ITAUP ), WORK( IWORK ),
3109 $ LWORK-IWORK+1, IERR )
3110*
3111* Generate right bidiagonalizing vectors in WORK(IR)
3112* (CWorkspace: need M*M+3*M-1,
3113* prefer M*M+2*M+(M-1)*NB)
3114* (RWorkspace: 0)
3115*
3116 CALL CUNGBR( 'p', M, M, M, WORK( IR ), LDWRKR,
3117 $ WORK( ITAUP ), WORK( IWORK ),
3118 $ LWORK-IWORK+1, IERR )
3119 IRWORK = IE + M
3120*
3121* Perform bidiagonal QR iteration, computing right
3122* singular vectors of L in WORK(IR)
3123* (CWorkspace: need M*M)
3124* (RWorkspace: need BDSPAC)
3125*
3126 CALL CBDSQR( 'u', M, M, 0, 0, S, RWORK( IE ),
3127 $ WORK( IR ), LDWRKR, CDUM, 1, CDUM, 1,
3128 $ RWORK( IRWORK ), INFO )
3129*
3130* Multiply right singular vectors of L in WORK(IR) by
3131* Q in VT, storing result in A
3132* (CWorkspace: need M*M)
3133* (RWorkspace: 0)
3134*
3135 CALL CGEMM( 'n', 'n', M, N, M, CONE, WORK( IR ),
3136 $ LDWRKR, VT, LDVT, CZERO, A, LDA )
3137*
3138* Copy right singular vectors of A from A to VT
3139*
3140 CALL CLACPY( 'f', m, n, a, lda, vt, ldvt )
3141*
3142 ELSE
3143*
3144* Insufficient workspace for a fast algorithm
3145*
3146 itau = 1
3147 iwork = itau + m
3148*
3149* Compute A=L*Q, copying result to VT
3150* (CWorkspace: need 2*M, prefer M+M*NB)
3151* (RWorkspace: 0)
3152*
3153 CALL cgelqf( m, n, a, lda, work( itau ),
3154 $ work( iwork ), lwork-iwork+1, ierr )
3155 CALL clacpy( 'U', m, n, a, lda, vt, ldvt )
3156*
3157* Generate Q in VT
3158* (CWorkspace: need M+N, prefer M+N*NB)
3159* (RWorkspace: 0)
3160*
3161 CALL cunglq( n, n, m, vt, ldvt, work( itau ),
3162 $ work( iwork ), lwork-iwork+1, ierr )
3163 ie = 1
3164 itauq = itau
3165 itaup = itauq + m
3166 iwork = itaup + m
3167*
3168* Zero out above L in A
3169*
3170 CALL claset( 'U', m-1, m-1, czero, czero,
3171 $ a( 1, 2 ), lda )
3172*
3173* Bidiagonalize L in A
3174* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
3175* (RWorkspace: need M)
3176*
3177 CALL cgebrd( m, m, a, lda, s, rwork( ie ),
3178 $ work( itauq ), work( itaup ),
3179 $ work( iwork ), lwork-iwork+1, ierr )
3180*
3181* Multiply right bidiagonalizing vectors in A by Q
3182* in VT
3183* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
3184* (RWorkspace: 0)
3185*
3186 CALL cunmbr( 'P', 'L', 'C', m, n, m, a, lda,
3187 $ work( itaup ), vt, ldvt,
3188 $ work( iwork ), lwork-iwork+1, ierr )
3189 irwork = ie + m
3190*
3191* Perform bidiagonal QR iteration, computing right
3192* singular vectors of A in VT
3193* (CWorkspace: 0)
3194* (RWorkspace: need BDSPAC)
3195*
3196 CALL cbdsqr( 'U', m, n, 0, 0, s, rwork( ie ), vt,
3197 $ ldvt, cdum, 1, cdum, 1,
3198 $ rwork( irwork ), info )
3199*
3200 END IF
3201*
3202 ELSE IF( wntuo ) THEN
3203*
3204* Path 8t(N much larger than M, JOBU='O', JOBVT='A')
3205* N right singular vectors to be computed in VT and
3206* M left singular vectors to be overwritten on A
3207*
3208 IF( lwork.GE.2*m*m+max( n+m, 3*m ) ) THEN
3209*
3210* Sufficient workspace for a fast algorithm
3211*
3212 iu = 1
3213 IF( lwork.GE.wrkbl+2*lda*m ) THEN
3214*
3215* WORK(IU) is LDA by M and WORK(IR) is LDA by M
3216*
3217 ldwrku = lda
3218 ir = iu + ldwrku*m
3219 ldwrkr = lda
3220 ELSE IF( lwork.GE.wrkbl+( lda+m )*m ) THEN
3221*
3222* WORK(IU) is LDA by M and WORK(IR) is M by M
3223*
3224 ldwrku = lda
3225 ir = iu + ldwrku*m
3226 ldwrkr = m
3227 ELSE
3228*
3229* WORK(IU) is M by M and WORK(IR) is M by M
3230*
3231 ldwrku = m
3232 ir = iu + ldwrku*m
3233 ldwrkr = m
3234 END IF
3235 itau = ir + ldwrkr*m
3236 iwork = itau + m
3237*
3238* Compute A=L*Q, copying result to VT
3239* (CWorkspace: need 2*M*M+2*M, prefer 2*M*M+M+M*NB)
3240* (RWorkspace: 0)
3241*
3242 CALL cgelqf( m, n, a, lda, work( itau ),
3243 $ work( iwork ), lwork-iwork+1, ierr )
3244 CALL clacpy( 'U', m, n, a, lda, vt, ldvt )
3245*
3246* Generate Q in VT
3247* (CWorkspace: need 2*M*M+M+N, prefer 2*M*M+M+N*NB)
3248* (RWorkspace: 0)
3249*
3250 CALL cunglq( n, n, m, vt, ldvt, work( itau ),
3251 $ work( iwork ), lwork-iwork+1, ierr )
3252*
3253* Copy L to WORK(IU), zeroing out above it
3254*
3255 CALL clacpy( 'L', m, m, a, lda, work( iu ),
3256 $ ldwrku )
3257 CALL claset( 'U', m-1, m-1, czero, czero,
3258 $ work( iu+ldwrku ), ldwrku )
3259 ie = 1
3260 itauq = itau
3261 itaup = itauq + m
3262 iwork = itaup + m
3263*
3264* Bidiagonalize L in WORK(IU), copying result to
3265* WORK(IR)
3266* (CWorkspace: need 2*M*M+3*M,
3267* prefer 2*M*M+2*M+2*M*NB)
3268* (RWorkspace: need M)
3269*
3270 CALL cgebrd( m, m, work( iu ), ldwrku, s,
3271 $ rwork( ie ), work( itauq ),
3272 $ work( itaup ), work( iwork ),
3273 $ lwork-iwork+1, ierr )
3274 CALL clacpy( 'L', m, m, work( iu ), ldwrku,
3275 $ work( ir ), ldwrkr )
3276*
3277* Generate right bidiagonalizing vectors in WORK(IU)
3278* (CWorkspace: need 2*M*M+3*M-1,
3279* prefer 2*M*M+2*M+(M-1)*NB)
3280* (RWorkspace: 0)
3281*
3282 CALL cungbr( 'P', m, m, m, work( iu ), ldwrku,
3283 $ work( itaup ), work( iwork ),
3284 $ lwork-iwork+1, ierr )
3285*
3286* Generate left bidiagonalizing vectors in WORK(IR)
3287* (CWorkspace: need 2*M*M+3*M, prefer 2*M*M+2*M+M*NB)
3288* (RWorkspace: 0)
3289*
3290 CALL cungbr( 'Q', m, m, m, work( ir ), ldwrkr,
3291 $ work( itauq ), work( iwork ),
3292 $ lwork-iwork+1, ierr )
3293 irwork = ie + m
3294*
3295* Perform bidiagonal QR iteration, computing left
3296* singular vectors of L in WORK(IR) and computing
3297* right singular vectors of L in WORK(IU)
3298* (CWorkspace: need 2*M*M)
3299* (RWorkspace: need BDSPAC)
3300*
3301 CALL cbdsqr( 'U', m, m, m, 0, s, rwork( ie ),
3302 $ work( iu ), ldwrku, work( ir ),
3303 $ ldwrkr, cdum, 1, rwork( irwork ),
3304 $ info )
3305*
3306* Multiply right singular vectors of L in WORK(IU) by
3307* Q in VT, storing result in A
3308* (CWorkspace: need M*M)
3309* (RWorkspace: 0)
3310*
3311 CALL cgemm( 'N', 'N', m, n, m, cone, work( iu ),
3312 $ ldwrku, vt, ldvt, czero, a, lda )
3313*
3314* Copy right singular vectors of A from A to VT
3315*
3316 CALL clacpy( 'F', m, n, a, lda, vt, ldvt )
3317*
3318* Copy left singular vectors of A from WORK(IR) to A
3319*
3320 CALL clacpy( 'F', m, m, work( ir ), ldwrkr, a,
3321 $ lda )
3322*
3323 ELSE
3324*
3325* Insufficient workspace for a fast algorithm
3326*
3327 itau = 1
3328 iwork = itau + m
3329*
3330* Compute A=L*Q, copying result to VT
3331* (CWorkspace: need 2*M, prefer M+M*NB)
3332* (RWorkspace: 0)
3333*
3334 CALL cgelqf( m, n, a, lda, work( itau ),
3335 $ work( iwork ), lwork-iwork+1, ierr )
3336 CALL clacpy( 'U', m, n, a, lda, vt, ldvt )
3337*
3338* Generate Q in VT
3339* (CWorkspace: need M+N, prefer M+N*NB)
3340* (RWorkspace: 0)
3341*
3342 CALL cunglq( n, n, m, vt, ldvt, work( itau ),
3343 $ work( iwork ), lwork-iwork+1, ierr )
3344 ie = 1
3345 itauq = itau
3346 itaup = itauq + m
3347 iwork = itaup + m
3348*
3349* Zero out above L in A
3350*
3351 CALL claset( 'U', m-1, m-1, czero, czero,
3352 $ a( 1, 2 ), lda )
3353*
3354* Bidiagonalize L in A
3355* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
3356* (RWorkspace: need M)
3357*
3358 CALL cgebrd( m, m, a, lda, s, rwork( ie ),
3359 $ work( itauq ), work( itaup ),
3360 $ work( iwork ), lwork-iwork+1, ierr )
3361*
3362* Multiply right bidiagonalizing vectors in A by Q
3363* in VT
3364* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
3365* (RWorkspace: 0)
3366*
3367 CALL cunmbr( 'p', 'l', 'c', M, N, M, A, LDA,
3368 $ WORK( ITAUP ), VT, LDVT,
3369 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3370*
3371* Generate left bidiagonalizing vectors in A
3372* (CWorkspace: need 3*M, prefer 2*M+M*NB)
3373* (RWorkspace: 0)
3374*
3375 CALL CUNGBR( 'q', M, M, M, A, LDA, WORK( ITAUQ ),
3376 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3377 IRWORK = IE + M
3378*
3379* Perform bidiagonal QR iteration, computing left
3380* singular vectors of A in A and computing right
3381* singular vectors of A in VT
3382* (CWorkspace: 0)
3383* (RWorkspace: need BDSPAC)
3384*
3385 CALL CBDSQR( 'u', M, N, M, 0, S, RWORK( IE ), VT,
3386 $ LDVT, A, LDA, CDUM, 1,
3387 $ RWORK( IRWORK ), INFO )
3388*
3389 END IF
3390*
3391 ELSE IF( WNTUAS ) THEN
3392*
3393* Path 9t(N much larger than M, JOBU='S' or 'A',
3394* JOBVT='A')
3395* N right singular vectors to be computed in VT and
3396* M left singular vectors to be computed in U
3397*
3398.GE. IF( LWORKM*M+MAX( N+M, 3*M ) ) THEN
3399*
3400* Sufficient workspace for a fast algorithm
3401*
3402 IU = 1
3403.GE. IF( LWORKWRKBL+LDA*M ) THEN
3404*
3405* WORK(IU) is LDA by M
3406*
3407 LDWRKU = LDA
3408 ELSE
3409*
3410* WORK(IU) is M by M
3411*
3412 LDWRKU = M
3413 END IF
3414 ITAU = IU + LDWRKU*M
3415 IWORK = ITAU + M
3416*
3417* Compute A=L*Q, copying result to VT
3418* (CWorkspace: need M*M+2*M, prefer M*M+M+M*NB)
3419* (RWorkspace: 0)
3420*
3421 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
3422 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3423 CALL CLACPY( 'u', M, N, A, LDA, VT, LDVT )
3424*
3425* Generate Q in VT
3426* (CWorkspace: need M*M+M+N, prefer M*M+M+N*NB)
3427* (RWorkspace: 0)
3428*
3429 CALL CUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
3430 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3431*
3432* Copy L to WORK(IU), zeroing out above it
3433*
3434 CALL CLACPY( 'l', M, M, A, LDA, WORK( IU ),
3435 $ LDWRKU )
3436 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
3437 $ WORK( IU+LDWRKU ), LDWRKU )
3438 IE = 1
3439 ITAUQ = ITAU
3440 ITAUP = ITAUQ + M
3441 IWORK = ITAUP + M
3442*
3443* Bidiagonalize L in WORK(IU), copying result to U
3444* (CWorkspace: need M*M+3*M, prefer M*M+2*M+2*M*NB)
3445* (RWorkspace: need M)
3446*
3447 CALL CGEBRD( M, M, WORK( IU ), LDWRKU, S,
3448 $ RWORK( IE ), WORK( ITAUQ ),
3449 $ WORK( ITAUP ), WORK( IWORK ),
3450 $ LWORK-IWORK+1, IERR )
3451 CALL CLACPY( 'l', M, M, WORK( IU ), LDWRKU, U,
3452 $ LDU )
3453*
3454* Generate right bidiagonalizing vectors in WORK(IU)
3455* (CWorkspace: need M*M+3*M, prefer M*M+2*M+(M-1)*NB)
3456* (RWorkspace: 0)
3457*
3458 CALL CUNGBR( 'p', M, M, M, WORK( IU ), LDWRKU,
3459 $ WORK( ITAUP ), WORK( IWORK ),
3460 $ LWORK-IWORK+1, IERR )
3461*
3462* Generate left bidiagonalizing vectors in U
3463* (CWorkspace: need M*M+3*M, prefer M*M+2*M+M*NB)
3464* (RWorkspace: 0)
3465*
3466 CALL CUNGBR( 'q', M, M, M, U, LDU, WORK( ITAUQ ),
3467 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3468 IRWORK = IE + M
3469*
3470* Perform bidiagonal QR iteration, computing left
3471* singular vectors of L in U and computing right
3472* singular vectors of L in WORK(IU)
3473* (CWorkspace: need M*M)
3474* (RWorkspace: need BDSPAC)
3475*
3476 CALL CBDSQR( 'u', M, M, M, 0, S, RWORK( IE ),
3477 $ WORK( IU ), LDWRKU, U, LDU, CDUM, 1,
3478 $ RWORK( IRWORK ), INFO )
3479*
3480* Multiply right singular vectors of L in WORK(IU) by
3481* Q in VT, storing result in A
3482* (CWorkspace: need M*M)
3483* (RWorkspace: 0)
3484*
3485 CALL CGEMM( 'n', 'n', M, N, M, CONE, WORK( IU ),
3486 $ LDWRKU, VT, LDVT, CZERO, A, LDA )
3487*
3488* Copy right singular vectors of A from A to VT
3489*
3490 CALL CLACPY( 'f', M, N, A, LDA, VT, LDVT )
3491*
3492 ELSE
3493*
3494* Insufficient workspace for a fast algorithm
3495*
3496 ITAU = 1
3497 IWORK = ITAU + M
3498*
3499* Compute A=L*Q, copying result to VT
3500* (CWorkspace: need 2*M, prefer M+M*NB)
3501* (RWorkspace: 0)
3502*
3503 CALL CGELQF( M, N, A, LDA, WORK( ITAU ),
3504 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3505 CALL CLACPY( 'u', M, N, A, LDA, VT, LDVT )
3506*
3507* Generate Q in VT
3508* (CWorkspace: need M+N, prefer M+N*NB)
3509* (RWorkspace: 0)
3510*
3511 CALL CUNGLQ( N, N, M, VT, LDVT, WORK( ITAU ),
3512 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3513*
3514* Copy L to U, zeroing out above it
3515*
3516 CALL CLACPY( 'l', M, M, A, LDA, U, LDU )
3517 CALL CLASET( 'u', M-1, M-1, CZERO, CZERO,
3518 $ U( 1, 2 ), LDU )
3519 IE = 1
3520 ITAUQ = ITAU
3521 ITAUP = ITAUQ + M
3522 IWORK = ITAUP + M
3523*
3524* Bidiagonalize L in U
3525* (CWorkspace: need 3*M, prefer 2*M+2*M*NB)
3526* (RWorkspace: need M)
3527*
3528 CALL CGEBRD( M, M, U, LDU, S, RWORK( IE ),
3529 $ WORK( ITAUQ ), WORK( ITAUP ),
3530 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3531*
3532* Multiply right bidiagonalizing vectors in U by Q
3533* in VT
3534* (CWorkspace: need 2*M+N, prefer 2*M+N*NB)
3535* (RWorkspace: 0)
3536*
3537 CALL CUNMBR( 'p', 'l', 'c', M, N, M, U, LDU,
3538 $ WORK( ITAUP ), VT, LDVT,
3539 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3540*
3541* Generate left bidiagonalizing vectors in U
3542* (CWorkspace: need 3*M, prefer 2*M+M*NB)
3543* (RWorkspace: 0)
3544*
3545 CALL CUNGBR( 'q', M, M, M, U, LDU, WORK( ITAUQ ),
3546 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3547 IRWORK = IE + M
3548*
3549* Perform bidiagonal QR iteration, computing left
3550* singular vectors of A in U and computing right
3551* singular vectors of A in VT
3552* (CWorkspace: 0)
3553* (RWorkspace: need BDSPAC)
3554*
3555 CALL CBDSQR( 'u', M, N, M, 0, S, RWORK( IE ), VT,
3556 $ LDVT, U, LDU, CDUM, 1,
3557 $ RWORK( IRWORK ), INFO )
3558*
3559 END IF
3560*
3561 END IF
3562*
3563 END IF
3564*
3565 ELSE
3566*
3567* N .LT. MNTHR
3568*
3569* Path 10t(N greater than M, but not much larger)
3570* Reduce to bidiagonal form without LQ decomposition
3571*
3572 IE = 1
3573 ITAUQ = 1
3574 ITAUP = ITAUQ + M
3575 IWORK = ITAUP + M
3576*
3577* Bidiagonalize A
3578* (CWorkspace: need 2*M+N, prefer 2*M+(M+N)*NB)
3579* (RWorkspace: M)
3580*
3581 CALL CGEBRD( M, N, A, LDA, S, RWORK( IE ), WORK( ITAUQ ),
3582 $ WORK( ITAUP ), WORK( IWORK ), LWORK-IWORK+1,
3583 $ IERR )
3584 IF( WNTUAS ) THEN
3585*
3586* If left singular vectors desired in U, copy result to U
3587* and generate left bidiagonalizing vectors in U
3588* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB)
3589* (RWorkspace: 0)
3590*
3591 CALL CLACPY( 'l', M, M, A, LDA, U, LDU )
3592 CALL CUNGBR( 'q', M, M, N, U, LDU, WORK( ITAUQ ),
3593 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3594 END IF
3595 IF( WNTVAS ) THEN
3596*
3597* If right singular vectors desired in VT, copy result to
3598* VT and generate right bidiagonalizing vectors in VT
3599* (CWorkspace: need 2*M+NRVT, prefer 2*M+NRVT*NB)
3600* (RWorkspace: 0)
3601*
3602 CALL CLACPY( 'u', M, N, A, LDA, VT, LDVT )
3603 IF( WNTVA )
3604 $ NRVT = N
3605 IF( WNTVS )
3606 $ NRVT = M
3607 CALL CUNGBR( 'p', NRVT, N, M, VT, LDVT, WORK( ITAUP ),
3608 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3609 END IF
3610 IF( WNTUO ) THEN
3611*
3612* If left singular vectors desired in A, generate left
3613* bidiagonalizing vectors in A
3614* (CWorkspace: need 3*M-1, prefer 2*M+(M-1)*NB)
3615* (RWorkspace: 0)
3616*
3617 CALL CUNGBR( 'q', M, M, N, A, LDA, WORK( ITAUQ ),
3618 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3619 END IF
3620 IF( WNTVO ) THEN
3621*
3622* If right singular vectors desired in A, generate right
3623* bidiagonalizing vectors in A
3624* (CWorkspace: need 3*M, prefer 2*M+M*NB)
3625* (RWorkspace: 0)
3626*
3627 CALL CUNGBR( 'p', M, N, M, A, LDA, WORK( ITAUP ),
3628 $ WORK( IWORK ), LWORK-IWORK+1, IERR )
3629 END IF
3630 IRWORK = IE + M
3631.OR. IF( WNTUAS WNTUO )
3632 $ NRU = M
3633 IF( WNTUN )
3634 $ NRU = 0
3635.OR. IF( WNTVAS WNTVO )
3636 $ NCVT = N
3637 IF( WNTVN )
3638 $ NCVT = 0
3639.NOT..AND..NOT. IF( ( WNTUO ) ( WNTVO ) ) THEN
3640*
3641* Perform bidiagonal QR iteration, if desired, computing
3642* left singular vectors in U and computing right singular
3643* vectors in VT
3644* (CWorkspace: 0)
3645* (RWorkspace: need BDSPAC)
3646*
3647 CALL CBDSQR( 'l', M, NCVT, NRU, 0, S, RWORK( IE ), VT,
3648 $ LDVT, U, LDU, CDUM, 1, RWORK( IRWORK ),
3649 $ INFO )
3650.NOT..AND. ELSE IF( ( WNTUO ) WNTVO ) THEN
3651*
3652* Perform bidiagonal QR iteration, if desired, computing
3653* left singular vectors in U and computing right singular
3654* vectors in A
3655* (CWorkspace: 0)
3656* (RWorkspace: need BDSPAC)
3657*
3658 CALL CBDSQR( 'l', M, NCVT, NRU, 0, S, RWORK( IE ), A,
3659 $ LDA, U, LDU, CDUM, 1, RWORK( IRWORK ),
3660 $ INFO )
3661 ELSE
3662*
3663* Perform bidiagonal QR iteration, if desired, computing
3664* left singular vectors in A and computing right singular
3665* vectors in VT
3666* (CWorkspace: 0)
3667* (RWorkspace: need BDSPAC)
3668*
3669 CALL CBDSQR( 'l', M, NCVT, NRU, 0, S, RWORK( IE ), VT,
3670 $ LDVT, A, LDA, CDUM, 1, RWORK( IRWORK ),
3671 $ INFO )
3672 END IF
3673*
3674 END IF
3675*
3676 END IF
3677*
3678* Undo scaling if necessary
3679*
3680.EQ. IF( ISCL1 ) THEN
3681.GT. IF( ANRMBIGNUM )
3682 $ CALL SLASCL( 'g', 0, 0, BIGNUM, ANRM, MINMN, 1, S, MINMN,
3683 $ IERR )
3684.NE..AND..GT. IF( INFO0 ANRMBIGNUM )
3685 $ CALL SLASCL( 'g', 0, 0, BIGNUM, ANRM, MINMN-1, 1,
3686 $ RWORK( IE ), MINMN, IERR )
3687.LT. IF( ANRMSMLNUM )
3688 $ CALL SLASCL( 'g', 0, 0, SMLNUM, ANRM, MINMN, 1, S, MINMN,
3689 $ IERR )
3690.NE..AND..LT. IF( INFO0 ANRMSMLNUM )
3691 $ CALL SLASCL( 'g', 0, 0, SMLNUM, ANRM, MINMN-1, 1,
3692 $ RWORK( IE ), MINMN, IERR )
3693 END IF
3694*
3695* Return optimal workspace in WORK(1)
3696*
3697 WORK( 1 ) = MAXWRK
3698*
3699 RETURN
3700*
3701* End of CGESVD
3702*
3703 END
slascl
subroutine slascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition slascl.f:143
xerbla
subroutine xerbla(srname, info)
XERBLA
Definition xerbla.f:60
cungbr
subroutine cungbr(vect, m, n, k, a, lda, tau, work, lwork, info)
CUNGBR
Definition cungbr.f:157
cgeqrf
subroutine cgeqrf(m, n, a, lda, tau, work, lwork, info)
CGEQRF
Definition cgeqrf.f:146
cgebrd
subroutine cgebrd(m, n, a, lda, d, e, tauq, taup, work, lwork, info)
CGEBRD
Definition cgebrd.f:206
cgelqf
subroutine cgelqf(m, n, a, lda, tau, work, lwork, info)
CGELQF
Definition cgelqf.f:143
cgesvd
subroutine cgesvd(jobu, jobvt, m, n, a, lda, s, u, ldu, vt, ldvt, work, lwork, rwork, info)
CGESVD computes the singular value decomposition (SVD) for GE matrices
Definition cgesvd.f:214
clascl
subroutine clascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition clascl.f:143
clacpy
subroutine clacpy(uplo, m, n, a, lda, b, ldb)
CLACPY copies all or part of one two-dimensional array to another.
Definition clacpy.f:103
claset
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
cunglq
subroutine cunglq(m, n, k, a, lda, tau, work, lwork, info)
CUNGLQ
Definition cunglq.f:127
cbdsqr
subroutine cbdsqr(uplo, n, ncvt, nru, ncc, d, e, vt, ldvt, u, ldu, c, ldc, rwork, info)
CBDSQR
Definition cbdsqr.f:222
cungqr
subroutine cungqr(m, n, k, a, lda, tau, work, lwork, info)
CUNGQR
Definition cungqr.f:128
cunmbr
subroutine cunmbr(vect, side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
CUNMBR
Definition cunmbr.f:197
cgemm
subroutine cgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
CGEMM
Definition cgemm.f:187
min
#define min(a, b)
Definition macros.h:20
max
#define max(a, b)
Definition macros.h:21