LAPACK  3.9.0
LAPACK: Linear Algebra PACKage
zgsvj1.f
Go to the documentation of this file.
1 *> \brief \b ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivots.
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download ZGSVJ1 + dependencies
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgsvj1.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgsvj1.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgsvj1.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZGSVJ1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
22 * EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * DOUBLE PRECISION EPS, SFMIN, TOL
26 * INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
27 * CHARACTER*1 JOBV
28 * ..
29 * .. Array Arguments ..
30 * COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
31 * DOUBLE PRECISION SVA( N )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> ZGSVJ1 is called from ZGESVJ as a pre-processor and that is its main
41 *> purpose. It applies Jacobi rotations in the same way as ZGESVJ does, but
42 *> it targets only particular pivots and it does not check convergence
43 *> (stopping criterion). Few tunning parameters (marked by [TP]) are
44 *> available for the implementer.
45 *>
46 *> Further Details
47 *> ~~~~~~~~~~~~~~~
48 *> ZGSVJ1 applies few sweeps of Jacobi rotations in the column space of
49 *> the input M-by-N matrix A. The pivot pairs are taken from the (1,2)
50 *> off-diagonal block in the corresponding N-by-N Gram matrix A^T * A. The
51 *> block-entries (tiles) of the (1,2) off-diagonal block are marked by the
52 *> [x]'s in the following scheme:
53 *>
54 *> | * * * [x] [x] [x]|
55 *> | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks.
56 *> | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
57 *> |[x] [x] [x] * * * |
58 *> |[x] [x] [x] * * * |
59 *> |[x] [x] [x] * * * |
60 *>
61 *> In terms of the columns of A, the first N1 columns are rotated 'against'
62 *> the remaining N-N1 columns, trying to increase the angle between the
63 *> corresponding subspaces. The off-diagonal block is N1-by(N-N1) and it is
64 *> tiled using quadratic tiles of side KBL. Here, KBL is a tunning parameter.
65 *> The number of sweeps is given in NSWEEP and the orthogonality threshold
66 *> is given in TOL.
67 *> \endverbatim
68 *
69 * Arguments:
70 * ==========
71 *
72 *> \param[in] JOBV
73 *> \verbatim
74 *> JOBV is CHARACTER*1
75 *> Specifies whether the output from this procedure is used
76 *> to compute the matrix V:
77 *> = 'V': the product of the Jacobi rotations is accumulated
78 *> by postmulyiplying the N-by-N array V.
79 *> (See the description of V.)
80 *> = 'A': the product of the Jacobi rotations is accumulated
81 *> by postmulyiplying the MV-by-N array V.
82 *> (See the descriptions of MV and V.)
83 *> = 'N': the Jacobi rotations are not accumulated.
84 *> \endverbatim
85 *>
86 *> \param[in] M
87 *> \verbatim
88 *> M is INTEGER
89 *> The number of rows of the input matrix A. M >= 0.
90 *> \endverbatim
91 *>
92 *> \param[in] N
93 *> \verbatim
94 *> N is INTEGER
95 *> The number of columns of the input matrix A.
96 *> M >= N >= 0.
97 *> \endverbatim
98 *>
99 *> \param[in] N1
100 *> \verbatim
101 *> N1 is INTEGER
102 *> N1 specifies the 2 x 2 block partition, the first N1 columns are
103 *> rotated 'against' the remaining N-N1 columns of A.
104 *> \endverbatim
105 *>
106 *> \param[in,out] A
107 *> \verbatim
108 *> A is COMPLEX*16 array, dimension (LDA,N)
109 *> On entry, M-by-N matrix A, such that A*diag(D) represents
110 *> the input matrix.
111 *> On exit,
112 *> A_onexit * D_onexit represents the input matrix A*diag(D)
113 *> post-multiplied by a sequence of Jacobi rotations, where the
114 *> rotation threshold and the total number of sweeps are given in
115 *> TOL and NSWEEP, respectively.
116 *> (See the descriptions of N1, D, TOL and NSWEEP.)
117 *> \endverbatim
118 *>
119 *> \param[in] LDA
120 *> \verbatim
121 *> LDA is INTEGER
122 *> The leading dimension of the array A. LDA >= max(1,M).
123 *> \endverbatim
124 *>
125 *> \param[in,out] D
126 *> \verbatim
127 *> D is COMPLEX*16 array, dimension (N)
128 *> The array D accumulates the scaling factors from the fast scaled
129 *> Jacobi rotations.
130 *> On entry, A*diag(D) represents the input matrix.
131 *> On exit, A_onexit*diag(D_onexit) represents the input matrix
132 *> post-multiplied by a sequence of Jacobi rotations, where the
133 *> rotation threshold and the total number of sweeps are given in
134 *> TOL and NSWEEP, respectively.
135 *> (See the descriptions of N1, A, TOL and NSWEEP.)
136 *> \endverbatim
137 *>
138 *> \param[in,out] SVA
139 *> \verbatim
140 *> SVA is DOUBLE PRECISION array, dimension (N)
141 *> On entry, SVA contains the Euclidean norms of the columns of
142 *> the matrix A*diag(D).
143 *> On exit, SVA contains the Euclidean norms of the columns of
144 *> the matrix onexit*diag(D_onexit).
145 *> \endverbatim
146 *>
147 *> \param[in] MV
148 *> \verbatim
149 *> MV is INTEGER
150 *> If JOBV = 'A', then MV rows of V are post-multipled by a
151 *> sequence of Jacobi rotations.
152 *> If JOBV = 'N', then MV is not referenced.
153 *> \endverbatim
154 *>
155 *> \param[in,out] V
156 *> \verbatim
157 *> V is COMPLEX*16 array, dimension (LDV,N)
158 *> If JOBV = 'V' then N rows of V are post-multipled by a
159 *> sequence of Jacobi rotations.
160 *> If JOBV = 'A' then MV rows of V are post-multipled by a
161 *> sequence of Jacobi rotations.
162 *> If JOBV = 'N', then V is not referenced.
163 *> \endverbatim
164 *>
165 *> \param[in] LDV
166 *> \verbatim
167 *> LDV is INTEGER
168 *> The leading dimension of the array V, LDV >= 1.
169 *> If JOBV = 'V', LDV >= N.
170 *> If JOBV = 'A', LDV >= MV.
171 *> \endverbatim
172 *>
173 *> \param[in] EPS
174 *> \verbatim
175 *> EPS is DOUBLE PRECISION
176 *> EPS = DLAMCH('Epsilon')
177 *> \endverbatim
178 *>
179 *> \param[in] SFMIN
180 *> \verbatim
181 *> SFMIN is DOUBLE PRECISION
182 *> SFMIN = DLAMCH('Safe Minimum')
183 *> \endverbatim
184 *>
185 *> \param[in] TOL
186 *> \verbatim
187 *> TOL is DOUBLE PRECISION
188 *> TOL is the threshold for Jacobi rotations. For a pair
189 *> A(:,p), A(:,q) of pivot columns, the Jacobi rotation is
190 *> applied only if ABS(COS(angle(A(:,p),A(:,q)))) > TOL.
191 *> \endverbatim
192 *>
193 *> \param[in] NSWEEP
194 *> \verbatim
195 *> NSWEEP is INTEGER
196 *> NSWEEP is the number of sweeps of Jacobi rotations to be
197 *> performed.
198 *> \endverbatim
199 *>
200 *> \param[out] WORK
201 *> \verbatim
202 *> WORK is COMPLEX*16 array, dimension (LWORK)
203 *> \endverbatim
204 *>
205 *> \param[in] LWORK
206 *> \verbatim
207 *> LWORK is INTEGER
208 *> LWORK is the dimension of WORK. LWORK >= M.
209 *> \endverbatim
210 *>
211 *> \param[out] INFO
212 *> \verbatim
213 *> INFO is INTEGER
214 *> = 0: successful exit.
215 *> < 0: if INFO = -i, then the i-th argument had an illegal value
216 *> \endverbatim
217 *
218 * Authors:
219 * ========
220 *
221 *> \author Univ. of Tennessee
222 *> \author Univ. of California Berkeley
223 *> \author Univ. of Colorado Denver
224 *> \author NAG Ltd.
225 *
226 *> \date June 2016
227 *
228 *> \ingroup complex16OTHERcomputational
229 *
230 *> \par Contributor:
231 * ==================
232 *>
233 *> Zlatko Drmac (Zagreb, Croatia)
234 *
235 * =====================================================================
236  SUBROUTINE zgsvj1( JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV,
237  $ EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO )
238 *
239 * -- LAPACK computational routine (version 3.8.0) --
240 * -- LAPACK is a software package provided by Univ. of Tennessee, --
241 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
242 * June 2016
243 *
244  IMPLICIT NONE
245 * .. Scalar Arguments ..
246  DOUBLE PRECISION EPS, SFMIN, TOL
247  INTEGER INFO, LDA, LDV, LWORK, M, MV, N, N1, NSWEEP
248  CHARACTER*1 JOBV
249 * ..
250 * .. Array Arguments ..
251  COMPLEX*16 A( LDA, * ), D( N ), V( LDV, * ), WORK( LWORK )
252  DOUBLE PRECISION SVA( N )
253 * ..
254 *
255 * =====================================================================
256 *
257 * .. Local Parameters ..
258  DOUBLE PRECISION ZERO, HALF, ONE
259  parameter( zero = 0.0d0, half = 0.5d0, one = 1.0d0)
260 * ..
261 * .. Local Scalars ..
262  COMPLEX*16 AAPQ, OMPQ
263  DOUBLE PRECISION AAPP, AAPP0, AAPQ1, AAQQ, APOAQ, AQOAP, BIG,
264  $ bigtheta, cs, mxaapq, mxsinj, rootbig,
265  $ rooteps, rootsfmin, roottol, small, sn, t,
266  $ temp1, theta, thsign
267  INTEGER BLSKIP, EMPTSW, i, ibr, igl, IERR, IJBLSK,
268  $ iswrot, jbc, jgl, kbl, mvl, notrot, nblc, nblr,
269  $ p, pskipped, q, rowskip, swband
270  LOGICAL APPLV, ROTOK, RSVEC
271 * ..
272 * ..
273 * .. Intrinsic Functions ..
274  INTRINSIC abs, conjg, max, dble, min, sign, sqrt
275 * ..
276 * .. External Functions ..
277  DOUBLE PRECISION DZNRM2
278  COMPLEX*16 ZDOTC
279  INTEGER IDAMAX
280  LOGICAL LSAME
281  EXTERNAL idamax, lsame, zdotc, dznrm2
282 * ..
283 * .. External Subroutines ..
284 * .. from BLAS
285  EXTERNAL zcopy, zrot, zswap, zaxpy
286 * .. from LAPACK
287  EXTERNAL zlascl, zlassq, xerbla
288 * ..
289 * .. Executable Statements ..
290 *
291 * Test the input parameters.
292 *
293  applv = lsame( jobv, 'A' )
294  rsvec = lsame( jobv, 'V' )
295  IF( .NOT.( rsvec .OR. applv .OR. lsame( jobv, 'N' ) ) ) THEN
296  info = -1
297  ELSE IF( m.LT.0 ) THEN
298  info = -2
299  ELSE IF( ( n.LT.0 ) .OR. ( n.GT.m ) ) THEN
300  info = -3
301  ELSE IF( n1.LT.0 ) THEN
302  info = -4
303  ELSE IF( lda.LT.m ) THEN
304  info = -6
305  ELSE IF( ( rsvec.OR.applv ) .AND. ( mv.LT.0 ) ) THEN
306  info = -9
307  ELSE IF( ( rsvec.AND.( ldv.LT.n ) ).OR.
308  $ ( applv.AND.( ldv.LT.mv ) ) ) THEN
309  info = -11
310  ELSE IF( tol.LE.eps ) THEN
311  info = -14
312  ELSE IF( nsweep.LT.0 ) THEN
313  info = -15
314  ELSE IF( lwork.LT.m ) THEN
315  info = -17
316  ELSE
317  info = 0
318  END IF
319 *
320 * #:(
321  IF( info.NE.0 ) THEN
322  CALL xerbla( 'ZGSVJ1', -info )
323  RETURN
324  END IF
325 *
326  IF( rsvec ) THEN
327  mvl = n
328  ELSE IF( applv ) THEN
329  mvl = mv
330  END IF
331  rsvec = rsvec .OR. applv
332 
333  rooteps = sqrt( eps )
334  rootsfmin = sqrt( sfmin )
335  small = sfmin / eps
336  big = one / sfmin
337  rootbig = one / rootsfmin
338 * LARGE = BIG / SQRT( DBLE( M*N ) )
339  bigtheta = one / rooteps
340  roottol = sqrt( tol )
341 *
342 * .. Initialize the right singular vector matrix ..
343 *
344 * RSVEC = LSAME( JOBV, 'Y' )
345 *
346  emptsw = n1*( n-n1 )
347  notrot = 0
348 *
349 * .. Row-cyclic pivot strategy with de Rijk's pivoting ..
350 *
351  kbl = min( 8, n )
352  nblr = n1 / kbl
353  IF( ( nblr*kbl ).NE.n1 )nblr = nblr + 1
354 
355 * .. the tiling is nblr-by-nblc [tiles]
356 
357  nblc = ( n-n1 ) / kbl
358  IF( ( nblc*kbl ).NE.( n-n1 ) )nblc = nblc + 1
359  blskip = ( kbl**2 ) + 1
360 *[TP] BLKSKIP is a tuning parameter that depends on SWBAND and KBL.
361 
362  rowskip = min( 5, kbl )
363 *[TP] ROWSKIP is a tuning parameter.
364  swband = 0
365 *[TP] SWBAND is a tuning parameter. It is meaningful and effective
366 * if ZGESVJ is used as a computational routine in the preconditioned
367 * Jacobi SVD algorithm ZGEJSV.
368 *
369 *
370 * | * * * [x] [x] [x]|
371 * | * * * [x] [x] [x]| Row-cycling in the nblr-by-nblc [x] blocks.
372 * | * * * [x] [x] [x]| Row-cyclic pivoting inside each [x] block.
373 * |[x] [x] [x] * * * |
374 * |[x] [x] [x] * * * |
375 * |[x] [x] [x] * * * |
376 *
377 *
378  DO 1993 i = 1, nsweep
379 *
380 * .. go go go ...
381 *
382  mxaapq = zero
383  mxsinj = zero
384  iswrot = 0
385 *
386  notrot = 0
387  pskipped = 0
388 *
389 * Each sweep is unrolled using KBL-by-KBL tiles over the pivot pairs
390 * 1 <= p < q <= N. This is the first step toward a blocked implementation
391 * of the rotations. New implementation, based on block transformations,
392 * is under development.
393 *
394  DO 2000 ibr = 1, nblr
395 *
396  igl = ( ibr-1 )*kbl + 1
397 *
398 
399 *
400 * ... go to the off diagonal blocks
401 *
402  igl = ( ibr-1 )*kbl + 1
403 *
404 * DO 2010 jbc = ibr + 1, NBL
405  DO 2010 jbc = 1, nblc
406 *
407  jgl = ( jbc-1 )*kbl + n1 + 1
408 *
409 * doing the block at ( ibr, jbc )
410 *
411  ijblsk = 0
412  DO 2100 p = igl, min( igl+kbl-1, n1 )
413 *
414  aapp = sva( p )
415  IF( aapp.GT.zero ) THEN
416 *
417  pskipped = 0
418 *
419  DO 2200 q = jgl, min( jgl+kbl-1, n )
420 *
421  aaqq = sva( q )
422  IF( aaqq.GT.zero ) THEN
423  aapp0 = aapp
424 *
425 * .. M x 2 Jacobi SVD ..
426 *
427 * Safe Gram matrix computation
428 *
429  IF( aaqq.GE.one ) THEN
430  IF( aapp.GE.aaqq ) THEN
431  rotok = ( small*aapp ).LE.aaqq
432  ELSE
433  rotok = ( small*aaqq ).LE.aapp
434  END IF
435  IF( aapp.LT.( big / aaqq ) ) THEN
436  aapq = ( zdotc( m, a( 1, p ), 1,
437  $ a( 1, q ), 1 ) / aaqq ) / aapp
438  ELSE
439  CALL zcopy( m, a( 1, p ), 1,
440  $ work, 1 )
441  CALL zlascl( 'G', 0, 0, aapp,
442  $ one, m, 1,
443  $ work, lda, ierr )
444  aapq = zdotc( m, work, 1,
445  $ a( 1, q ), 1 ) / aaqq
446  END IF
447  ELSE
448  IF( aapp.GE.aaqq ) THEN
449  rotok = aapp.LE.( aaqq / small )
450  ELSE
451  rotok = aaqq.LE.( aapp / small )
452  END IF
453  IF( aapp.GT.( small / aaqq ) ) THEN
454  aapq = ( zdotc( m, a( 1, p ), 1,
455  $ a( 1, q ), 1 ) / max(aaqq,aapp) )
456  $ / min(aaqq,aapp)
457  ELSE
458  CALL zcopy( m, a( 1, q ), 1,
459  $ work, 1 )
460  CALL zlascl( 'G', 0, 0, aaqq,
461  $ one, m, 1,
462  $ work, lda, ierr )
463  aapq = zdotc( m, a( 1, p ), 1,
464  $ work, 1 ) / aapp
465  END IF
466  END IF
467 *
468 * AAPQ = AAPQ * CONJG(CWORK(p))*CWORK(q)
469  aapq1 = -abs(aapq)
470  mxaapq = max( mxaapq, -aapq1 )
471 *
472 * TO rotate or NOT to rotate, THAT is the question ...
473 *
474  IF( abs( aapq1 ).GT.tol ) THEN
475  ompq = aapq / abs(aapq)
476  notrot = 0
477 *[RTD] ROTATED = ROTATED + 1
478  pskipped = 0
479  iswrot = iswrot + 1
480 *
481  IF( rotok ) THEN
482 *
483  aqoap = aaqq / aapp
484  apoaq = aapp / aaqq
485  theta = -half*abs( aqoap-apoaq )/ aapq1
486  IF( aaqq.GT.aapp0 )theta = -theta
487 *
488  IF( abs( theta ).GT.bigtheta ) THEN
489  t = half / theta
490  cs = one
491  CALL zrot( m, a(1,p), 1, a(1,q), 1,
492  $ cs, conjg(ompq)*t )
493  IF( rsvec ) THEN
494  CALL zrot( mvl, v(1,p), 1,
495  $ v(1,q), 1, cs, conjg(ompq)*t )
496  END IF
497  sva( q ) = aaqq*sqrt( max( zero,
498  $ one+t*apoaq*aapq1 ) )
499  aapp = aapp*sqrt( max( zero,
500  $ one-t*aqoap*aapq1 ) )
501  mxsinj = max( mxsinj, abs( t ) )
502  ELSE
503 *
504 * .. choose correct signum for THETA and rotate
505 *
506  thsign = -sign( one, aapq1 )
507  IF( aaqq.GT.aapp0 )thsign = -thsign
508  t = one / ( theta+thsign*
509  $ sqrt( one+theta*theta ) )
510  cs = sqrt( one / ( one+t*t ) )
511  sn = t*cs
512  mxsinj = max( mxsinj, abs( sn ) )
513  sva( q ) = aaqq*sqrt( max( zero,
514  $ one+t*apoaq*aapq1 ) )
515  aapp = aapp*sqrt( max( zero,
516  $ one-t*aqoap*aapq1 ) )
517 *
518  CALL zrot( m, a(1,p), 1, a(1,q), 1,
519  $ cs, conjg(ompq)*sn )
520  IF( rsvec ) THEN
521  CALL zrot( mvl, v(1,p), 1,
522  $ v(1,q), 1, cs, conjg(ompq)*sn )
523  END IF
524  END IF
525  d(p) = -d(q) * ompq
526 *
527  ELSE
528 * .. have to use modified Gram-Schmidt like transformation
529  IF( aapp.GT.aaqq ) THEN
530  CALL zcopy( m, a( 1, p ), 1,
531  $ work, 1 )
532  CALL zlascl( 'G', 0, 0, aapp, one,
533  $ m, 1, work,lda,
534  $ ierr )
535  CALL zlascl( 'G', 0, 0, aaqq, one,
536  $ m, 1, a( 1, q ), lda,
537  $ ierr )
538  CALL zaxpy( m, -aapq, work,
539  $ 1, a( 1, q ), 1 )
540  CALL zlascl( 'G', 0, 0, one, aaqq,
541  $ m, 1, a( 1, q ), lda,
542  $ ierr )
543  sva( q ) = aaqq*sqrt( max( zero,
544  $ one-aapq1*aapq1 ) )
545  mxsinj = max( mxsinj, sfmin )
546  ELSE
547  CALL zcopy( m, a( 1, q ), 1,
548  $ work, 1 )
549  CALL zlascl( 'G', 0, 0, aaqq, one,
550  $ m, 1, work,lda,
551  $ ierr )
552  CALL zlascl( 'G', 0, 0, aapp, one,
553  $ m, 1, a( 1, p ), lda,
554  $ ierr )
555  CALL zaxpy( m, -conjg(aapq),
556  $ work, 1, a( 1, p ), 1 )
557  CALL zlascl( 'G', 0, 0, one, aapp,
558  $ m, 1, a( 1, p ), lda,
559  $ ierr )
560  sva( p ) = aapp*sqrt( max( zero,
561  $ one-aapq1*aapq1 ) )
562  mxsinj = max( mxsinj, sfmin )
563  END IF
564  END IF
565 * END IF ROTOK THEN ... ELSE
566 *
567 * In the case of cancellation in updating SVA(q), SVA(p)
568 * .. recompute SVA(q), SVA(p)
569  IF( ( sva( q ) / aaqq )**2.LE.rooteps )
570  $ THEN
571  IF( ( aaqq.LT.rootbig ) .AND.
572  $ ( aaqq.GT.rootsfmin ) ) THEN
573  sva( q ) = dznrm2( m, a( 1, q ), 1)
574  ELSE
575  t = zero
576  aaqq = one
577  CALL zlassq( m, a( 1, q ), 1, t,
578  $ aaqq )
579  sva( q ) = t*sqrt( aaqq )
580  END IF
581  END IF
582  IF( ( aapp / aapp0 )**2.LE.rooteps ) THEN
583  IF( ( aapp.LT.rootbig ) .AND.
584  $ ( aapp.GT.rootsfmin ) ) THEN
585  aapp = dznrm2( m, a( 1, p ), 1 )
586  ELSE
587  t = zero
588  aapp = one
589  CALL zlassq( m, a( 1, p ), 1, t,
590  $ aapp )
591  aapp = t*sqrt( aapp )
592  END IF
593  sva( p ) = aapp
594  END IF
595 * end of OK rotation
596  ELSE
597  notrot = notrot + 1
598 *[RTD] SKIPPED = SKIPPED + 1
599  pskipped = pskipped + 1
600  ijblsk = ijblsk + 1
601  END IF
602  ELSE
603  notrot = notrot + 1
604  pskipped = pskipped + 1
605  ijblsk = ijblsk + 1
606  END IF
607 *
608  IF( ( i.LE.swband ) .AND. ( ijblsk.GE.blskip ) )
609  $ THEN
610  sva( p ) = aapp
611  notrot = 0
612  GO TO 2011
613  END IF
614  IF( ( i.LE.swband ) .AND.
615  $ ( pskipped.GT.rowskip ) ) THEN
616  aapp = -aapp
617  notrot = 0
618  GO TO 2203
619  END IF
620 *
621  2200 CONTINUE
622 * end of the q-loop
623  2203 CONTINUE
624 *
625  sva( p ) = aapp
626 *
627  ELSE
628 *
629  IF( aapp.EQ.zero )notrot = notrot +
630  $ min( jgl+kbl-1, n ) - jgl + 1
631  IF( aapp.LT.zero )notrot = 0
632 *
633  END IF
634 *
635  2100 CONTINUE
636 * end of the p-loop
637  2010 CONTINUE
638 * end of the jbc-loop
639  2011 CONTINUE
640 *2011 bailed out of the jbc-loop
641  DO 2012 p = igl, min( igl+kbl-1, n )
642  sva( p ) = abs( sva( p ) )
643  2012 CONTINUE
644 ***
645  2000 CONTINUE
646 *2000 :: end of the ibr-loop
647 *
648 * .. update SVA(N)
649  IF( ( sva( n ).LT.rootbig ) .AND. ( sva( n ).GT.rootsfmin ) )
650  $ THEN
651  sva( n ) = dznrm2( m, a( 1, n ), 1 )
652  ELSE
653  t = zero
654  aapp = one
655  CALL zlassq( m, a( 1, n ), 1, t, aapp )
656  sva( n ) = t*sqrt( aapp )
657  END IF
658 *
659 * Additional steering devices
660 *
661  IF( ( i.LT.swband ) .AND. ( ( mxaapq.LE.roottol ) .OR.
662  $ ( iswrot.LE.n ) ) )swband = i
663 *
664  IF( ( i.GT.swband+1 ) .AND. ( mxaapq.LT.sqrt( dble( n ) )*
665  $ tol ) .AND. ( dble( n )*mxaapq*mxsinj.LT.tol ) ) THEN
666  GO TO 1994
667  END IF
668 *
669  IF( notrot.GE.emptsw )GO TO 1994
670 *
671  1993 CONTINUE
672 * end i=1:NSWEEP loop
673 *
674 * #:( Reaching this point means that the procedure has not converged.
675  info = nsweep - 1
676  GO TO 1995
677 *
678  1994 CONTINUE
679 * #:) Reaching this point means numerical convergence after the i-th
680 * sweep.
681 *
682  info = 0
683 * #:) INFO = 0 confirms successful iterations.
684  1995 CONTINUE
685 *
686 * Sort the vector SVA() of column norms.
687  DO 5991 p = 1, n - 1
688  q = idamax( n-p+1, sva( p ), 1 ) + p - 1
689  IF( p.NE.q ) THEN
690  temp1 = sva( p )
691  sva( p ) = sva( q )
692  sva( q ) = temp1
693  aapq = d( p )
694  d( p ) = d( q )
695  d( q ) = aapq
696  CALL zswap( m, a( 1, p ), 1, a( 1, q ), 1 )
697  IF( rsvec )CALL zswap( mvl, v( 1, p ), 1, v( 1, q ), 1 )
698  END IF
699  5991 CONTINUE
700 *
701 *
702  RETURN
703 * ..
704 * .. END OF ZGSVJ1
705 * ..
706  END
zaxpy
subroutine zaxpy(N, ZA, ZX, INCX, ZY, INCY)
ZAXPY
Definition: zaxpy.f:90
zlassq
subroutine zlassq(N, X, INCX, SCALE, SUMSQ)
ZLASSQ updates a sum of squares represented in scaled form.
Definition: zlassq.f:108
zcopy
subroutine zcopy(N, ZX, INCX, ZY, INCY)
ZCOPY
Definition: zcopy.f:83
zlascl
subroutine zlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: zlascl.f:145
zgsvj1
subroutine zgsvj1(JOBV, M, N, N1, A, LDA, D, SVA, MV, V, LDV, EPS, SFMIN, TOL, NSWEEP, WORK, LWORK, INFO)
ZGSVJ1 pre-processor for the routine zgesvj, applies Jacobi rotations targeting only particular pivot...
Definition: zgsvj1.f:238
zrot
subroutine zrot(N, CX, INCX, CY, INCY, C, S)
ZROT applies a plane rotation with real cosine and complex sine to a pair of complex vectors.
Definition: zrot.f:105
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
zswap
subroutine zswap(N, ZX, INCX, ZY, INCY)
ZSWAP
Definition: zswap.f:83