LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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dgeesx.f
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1*> \brief <b> DGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors 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
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeesx.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DGEESX( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM,
22* WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK,
23* IWORK, LIWORK, BWORK, INFO )
24*
25* .. Scalar Arguments ..
26* CHARACTER JOBVS, SENSE, SORT
27* INTEGER INFO, LDA, LDVS, LIWORK, LWORK, N, SDIM
28* DOUBLE PRECISION RCONDE, RCONDV
29* ..
30* .. Array Arguments ..
31* LOGICAL BWORK( * )
32* INTEGER IWORK( * )
33* DOUBLE PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ),
34* \$ WR( * )
35* ..
36* .. Function Arguments ..
37* LOGICAL SELECT
38* EXTERNAL SELECT
39* ..
40*
41*
42*> \par Purpose:
43* =============
44*>
45*> \verbatim
46*>
47*> DGEESX computes for an N-by-N real nonsymmetric matrix A, the
48*> eigenvalues, the real Schur form T, and, optionally, the matrix of
49*> Schur vectors Z. This gives the Schur factorization A = Z*T*(Z**T).
50*>
51*> Optionally, it also orders the eigenvalues on the diagonal of the
52*> real Schur form so that selected eigenvalues are at the top left;
53*> computes a reciprocal condition number for the average of the
54*> selected eigenvalues (RCONDE); and computes a reciprocal condition
55*> number for the right invariant subspace corresponding to the
56*> selected eigenvalues (RCONDV). The leading columns of Z form an
57*> orthonormal basis for this invariant subspace.
58*>
59*> For further explanation of the reciprocal condition numbers RCONDE
60*> and RCONDV, see Section 4.10 of the LAPACK Users' Guide (where
61*> these quantities are called s and sep respectively).
62*>
63*> A real matrix is in real Schur form if it is upper quasi-triangular
64*> with 1-by-1 and 2-by-2 blocks. 2-by-2 blocks will be standardized in
65*> the form
66*> [ a b ]
67*> [ c a ]
68*>
69*> where b*c < 0. The eigenvalues of such a block are a +- sqrt(bc).
70*> \endverbatim
71*
72* Arguments:
73* ==========
74*
75*> \param[in] JOBVS
76*> \verbatim
77*> JOBVS is CHARACTER*1
78*> = 'N': Schur vectors are not computed;
79*> = 'V': Schur vectors are computed.
80*> \endverbatim
81*>
82*> \param[in] SORT
83*> \verbatim
84*> SORT is CHARACTER*1
85*> Specifies whether or not to order the eigenvalues on the
86*> diagonal of the Schur form.
87*> = 'N': Eigenvalues are not ordered;
88*> = 'S': Eigenvalues are ordered (see SELECT).
89*> \endverbatim
90*>
91*> \param[in] SELECT
92*> \verbatim
93*> SELECT is a LOGICAL FUNCTION of two DOUBLE PRECISION arguments
94*> SELECT must be declared EXTERNAL in the calling subroutine.
95*> If SORT = 'S', SELECT is used to select eigenvalues to sort
96*> to the top left of the Schur form.
97*> If SORT = 'N', SELECT is not referenced.
98*> An eigenvalue WR(j)+sqrt(-1)*WI(j) is selected if
99*> SELECT(WR(j),WI(j)) is true; i.e., if either one of a
100*> complex conjugate pair of eigenvalues is selected, then both
101*> are. Note that a selected complex eigenvalue may no longer
102*> satisfy SELECT(WR(j),WI(j)) = .TRUE. after ordering, since
103*> ordering may change the value of complex eigenvalues
104*> (especially if the eigenvalue is ill-conditioned); in this
105*> case INFO may be set to N+3 (see INFO below).
106*> \endverbatim
107*>
108*> \param[in] SENSE
109*> \verbatim
110*> SENSE is CHARACTER*1
111*> Determines which reciprocal condition numbers are computed.
112*> = 'N': None are computed;
113*> = 'E': Computed for average of selected eigenvalues only;
114*> = 'V': Computed for selected right invariant subspace only;
115*> = 'B': Computed for both.
116*> If SENSE = 'E', 'V' or 'B', SORT must equal 'S'.
117*> \endverbatim
118*>
119*> \param[in] N
120*> \verbatim
121*> N is INTEGER
122*> The order of the matrix A. N >= 0.
123*> \endverbatim
124*>
125*> \param[in,out] A
126*> \verbatim
127*> A is DOUBLE PRECISION array, dimension (LDA, N)
128*> On entry, the N-by-N matrix A.
129*> On exit, A is overwritten by its real Schur form T.
130*> \endverbatim
131*>
132*> \param[in] LDA
133*> \verbatim
134*> LDA is INTEGER
135*> The leading dimension of the array A. LDA >= max(1,N).
136*> \endverbatim
137*>
138*> \param[out] SDIM
139*> \verbatim
140*> SDIM is INTEGER
141*> If SORT = 'N', SDIM = 0.
142*> If SORT = 'S', SDIM = number of eigenvalues (after sorting)
143*> for which SELECT is true. (Complex conjugate
144*> pairs for which SELECT is true for either
145*> eigenvalue count as 2.)
146*> \endverbatim
147*>
148*> \param[out] WR
149*> \verbatim
150*> WR is DOUBLE PRECISION array, dimension (N)
151*> \endverbatim
152*>
153*> \param[out] WI
154*> \verbatim
155*> WI is DOUBLE PRECISION array, dimension (N)
156*> WR and WI contain the real and imaginary parts, respectively,
157*> of the computed eigenvalues, in the same order that they
158*> appear on the diagonal of the output Schur form T. Complex
159*> conjugate pairs of eigenvalues appear consecutively with the
160*> eigenvalue having the positive imaginary part first.
161*> \endverbatim
162*>
163*> \param[out] VS
164*> \verbatim
165*> VS is DOUBLE PRECISION array, dimension (LDVS,N)
166*> If JOBVS = 'V', VS contains the orthogonal matrix Z of Schur
167*> vectors.
168*> If JOBVS = 'N', VS is not referenced.
169*> \endverbatim
170*>
171*> \param[in] LDVS
172*> \verbatim
173*> LDVS is INTEGER
174*> The leading dimension of the array VS. LDVS >= 1, and if
175*> JOBVS = 'V', LDVS >= N.
176*> \endverbatim
177*>
178*> \param[out] RCONDE
179*> \verbatim
180*> RCONDE is DOUBLE PRECISION
181*> If SENSE = 'E' or 'B', RCONDE contains the reciprocal
182*> condition number for the average of the selected eigenvalues.
183*> Not referenced if SENSE = 'N' or 'V'.
184*> \endverbatim
185*>
186*> \param[out] RCONDV
187*> \verbatim
188*> RCONDV is DOUBLE PRECISION
189*> If SENSE = 'V' or 'B', RCONDV contains the reciprocal
190*> condition number for the selected right invariant subspace.
191*> Not referenced if SENSE = 'N' or 'E'.
192*> \endverbatim
193*>
194*> \param[out] WORK
195*> \verbatim
196*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
197*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
198*> \endverbatim
199*>
200*> \param[in] LWORK
201*> \verbatim
202*> LWORK is INTEGER
203*> The dimension of the array WORK. LWORK >= max(1,3*N).
204*> Also, if SENSE = 'E' or 'V' or 'B',
205*> LWORK >= N+2*SDIM*(N-SDIM), where SDIM is the number of
206*> selected eigenvalues computed by this routine. Note that
207*> N+2*SDIM*(N-SDIM) <= N+N*N/2. Note also that an error is only
208*> returned if LWORK < max(1,3*N), but if SENSE = 'E' or 'V' or
209*> 'B' this may not be large enough.
210*> For good performance, LWORK must generally be larger.
211*>
212*> If LWORK = -1, then a workspace query is assumed; the routine
213*> only calculates upper bounds on the optimal sizes of the
214*> arrays WORK and IWORK, returns these values as the first
215*> entries of the WORK and IWORK arrays, and no error messages
216*> related to LWORK or LIWORK are issued by XERBLA.
217*> \endverbatim
218*>
219*> \param[out] IWORK
220*> \verbatim
221*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
222*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
223*> \endverbatim
224*>
225*> \param[in] LIWORK
226*> \verbatim
227*> LIWORK is INTEGER
228*> The dimension of the array IWORK.
229*> LIWORK >= 1; if SENSE = 'V' or 'B', LIWORK >= SDIM*(N-SDIM).
230*> Note that SDIM*(N-SDIM) <= N*N/4. Note also that an error is
231*> only returned if LIWORK < 1, but if SENSE = 'V' or 'B' this
232*> may not be large enough.
233*>
234*> If LIWORK = -1, then a workspace query is assumed; the
235*> routine only calculates upper bounds on the optimal sizes of
236*> the arrays WORK and IWORK, returns these values as the first
237*> entries of the WORK and IWORK arrays, and no error messages
238*> related to LWORK or LIWORK are issued by XERBLA.
239*> \endverbatim
240*>
241*> \param[out] BWORK
242*> \verbatim
243*> BWORK is LOGICAL array, dimension (N)
244*> Not referenced if SORT = 'N'.
245*> \endverbatim
246*>
247*> \param[out] INFO
248*> \verbatim
249*> INFO is INTEGER
250*> = 0: successful exit
251*> < 0: if INFO = -i, the i-th argument had an illegal value.
252*> > 0: if INFO = i, and i is
253*> <= N: the QR algorithm failed to compute all the
254*> eigenvalues; elements 1:ILO-1 and i+1:N of WR and WI
255*> contain those eigenvalues which have converged; if
256*> JOBVS = 'V', VS contains the transformation which
257*> reduces A to its partially converged Schur form.
258*> = N+1: the eigenvalues could not be reordered because some
259*> eigenvalues were too close to separate (the problem
260*> is very ill-conditioned);
261*> = N+2: after reordering, roundoff changed values of some
262*> complex eigenvalues so that leading eigenvalues in
263*> the Schur form no longer satisfy SELECT=.TRUE. This
264*> could also be caused by underflow due to scaling.
265*> \endverbatim
266*
267* Authors:
268* ========
269*
270*> \author Univ. of Tennessee
271*> \author Univ. of California Berkeley
272*> \author Univ. of Colorado Denver
273*> \author NAG Ltd.
274*
275*> \ingroup doubleGEeigen
276*
277* =====================================================================
278 SUBROUTINE dgeesx( JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM,
279 \$ WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK,
280 \$ IWORK, LIWORK, BWORK, INFO )
281*
282* -- LAPACK driver routine --
283* -- LAPACK is a software package provided by Univ. of Tennessee, --
284* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
285*
286* .. Scalar Arguments ..
287 CHARACTER JOBVS, SENSE, SORT
288 INTEGER INFO, LDA, LDVS, LIWORK, LWORK, N, SDIM
289 DOUBLE PRECISION RCONDE, RCONDV
290* ..
291* .. Array Arguments ..
292 LOGICAL BWORK( * )
293 INTEGER IWORK( * )
294 DOUBLE PRECISION A( LDA, * ), VS( LDVS, * ), WI( * ), WORK( * ),
295 \$ wr( * )
296* ..
297* .. Function Arguments ..
298 LOGICAL SELECT
299 EXTERNAL SELECT
300* ..
301*
302* =====================================================================
303*
304* .. Parameters ..
305 DOUBLE PRECISION ZERO, ONE
306 PARAMETER ( ZERO = 0.0d0, one = 1.0d0 )
307* ..
308* .. Local Scalars ..
309 LOGICAL CURSL, LASTSL, LQUERY, LST2SL, SCALEA, WANTSB,
310 \$ WANTSE, WANTSN, WANTST, WANTSV, WANTVS
311 INTEGER HSWORK, I, I1, I2, IBAL, ICOND, IERR, IEVAL,
312 \$ IHI, ILO, INXT, IP, ITAU, IWRK, LIWRK, LWRK,
313 \$ maxwrk, minwrk
314 DOUBLE PRECISION ANRM, BIGNUM, CSCALE, EPS, SMLNUM
315* ..
316* .. Local Arrays ..
317 DOUBLE PRECISION DUM( 1 )
318* ..
319* .. External Subroutines ..
320 EXTERNAL dcopy, dgebak, dgebal, dgehrd, dhseqr, dlacpy,
322* ..
323* .. External Functions ..
324 LOGICAL LSAME
325 INTEGER ILAENV
326 DOUBLE PRECISION DLAMCH, DLANGE
327 EXTERNAL lsame, ilaenv, dlabad, dlamch, dlange
328* ..
329* .. Intrinsic Functions ..
330 INTRINSIC max, sqrt
331* ..
332* .. Executable Statements ..
333*
334* Test the input arguments
335*
336 info = 0
337 wantvs = lsame( jobvs, 'V' )
338 wantst = lsame( sort, 'S' )
339 wantsn = lsame( sense, 'N' )
340 wantse = lsame( sense, 'E' )
341 wantsv = lsame( sense, 'V' )
342 wantsb = lsame( sense, 'B' )
343 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
344*
345 IF( ( .NOT.wantvs ) .AND. ( .NOT.lsame( jobvs, 'N' ) ) ) THEN
346 info = -1
347 ELSE IF( ( .NOT.wantst ) .AND. ( .NOT.lsame( sort, 'N' ) ) ) THEN
348 info = -2
349 ELSE IF( .NOT.( wantsn .OR. wantse .OR. wantsv .OR. wantsb ) .OR.
350 \$ ( .NOT.wantst .AND. .NOT.wantsn ) ) THEN
351 info = -4
352 ELSE IF( n.LT.0 ) THEN
353 info = -5
354 ELSE IF( lda.LT.max( 1, n ) ) THEN
355 info = -7
356 ELSE IF( ldvs.LT.1 .OR. ( wantvs .AND. ldvs.LT.n ) ) THEN
357 info = -12
358 END IF
359*
360* Compute workspace
361* (Note: Comments in the code beginning "RWorkspace:" describe the
362* minimal amount of real workspace needed at that point in the
363* code, as well as the preferred amount for good performance.
364* IWorkspace refers to integer workspace.
365* NB refers to the optimal block size for the immediately
366* following subroutine, as returned by ILAENV.
367* HSWORK refers to the workspace preferred by DHSEQR, as
368* calculated below. HSWORK is computed assuming ILO=1 and IHI=N,
369* the worst case.
370* If SENSE = 'E', 'V' or 'B', then the amount of workspace needed
371* depends on SDIM, which is computed by the routine DTRSEN later
372* in the code.)
373*
374 IF( info.EQ.0 ) THEN
375 liwrk = 1
376 IF( n.EQ.0 ) THEN
377 minwrk = 1
378 lwrk = 1
379 ELSE
380 maxwrk = 2*n + n*ilaenv( 1, 'DGEHRD', ' ', n, 1, n, 0 )
381 minwrk = 3*n
382*
383 CALL dhseqr( 'S', jobvs, n, 1, n, a, lda, wr, wi, vs, ldvs,
384 \$ work, -1, ieval )
385 hswork = int( work( 1 ) )
386*
387 IF( .NOT.wantvs ) THEN
388 maxwrk = max( maxwrk, n + hswork )
389 ELSE
390 maxwrk = max( maxwrk, 2*n + ( n - 1 )*ilaenv( 1,
391 \$ 'DORGHR', ' ', n, 1, n, -1 ) )
392 maxwrk = max( maxwrk, n + hswork )
393 END IF
394 lwrk = maxwrk
395 IF( .NOT.wantsn )
396 \$ lwrk = max( lwrk, n + ( n*n )/2 )
397 IF( wantsv .OR. wantsb )
398 \$ liwrk = ( n*n )/4
399 END IF
400 iwork( 1 ) = liwrk
401 work( 1 ) = lwrk
402*
403 IF( lwork.LT.minwrk .AND. .NOT.lquery ) THEN
404 info = -16
405 ELSE IF( liwork.LT.1 .AND. .NOT.lquery ) THEN
406 info = -18
407 END IF
408 END IF
409*
410 IF( info.NE.0 ) THEN
411 CALL xerbla( 'DGEESX', -info )
412 RETURN
413 ELSE IF( lquery ) THEN
414 RETURN
415 END IF
416*
417* Quick return if possible
418*
419 IF( n.EQ.0 ) THEN
420 sdim = 0
421 RETURN
422 END IF
423*
424* Get machine constants
425*
426 eps = dlamch( 'P' )
427 smlnum = dlamch( 'S' )
428 bignum = one / smlnum
429 CALL dlabad( smlnum, bignum )
430 smlnum = sqrt( smlnum ) / eps
431 bignum = one / smlnum
432*
433* Scale A if max element outside range [SMLNUM,BIGNUM]
434*
435 anrm = dlange( 'M', n, n, a, lda, dum )
436 scalea = .false.
437 IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
438 scalea = .true.
439 cscale = smlnum
440 ELSE IF( anrm.GT.bignum ) THEN
441 scalea = .true.
442 cscale = bignum
443 END IF
444 IF( scalea )
445 \$ CALL dlascl( 'G', 0, 0, anrm, cscale, n, n, a, lda, ierr )
446*
447* Permute the matrix to make it more nearly triangular
448* (RWorkspace: need N)
449*
450 ibal = 1
451 CALL dgebal( 'P', n, a, lda, ilo, ihi, work( ibal ), ierr )
452*
453* Reduce to upper Hessenberg form
454* (RWorkspace: need 3*N, prefer 2*N+N*NB)
455*
456 itau = n + ibal
457 iwrk = n + itau
458 CALL dgehrd( n, ilo, ihi, a, lda, work( itau ), work( iwrk ),
459 \$ lwork-iwrk+1, ierr )
460*
461 IF( wantvs ) THEN
462*
463* Copy Householder vectors to VS
464*
465 CALL dlacpy( 'L', n, n, a, lda, vs, ldvs )
466*
467* Generate orthogonal matrix in VS
468* (RWorkspace: need 3*N-1, prefer 2*N+(N-1)*NB)
469*
470 CALL dorghr( n, ilo, ihi, vs, ldvs, work( itau ), work( iwrk ),
471 \$ lwork-iwrk+1, ierr )
472 END IF
473*
474 sdim = 0
475*
476* Perform QR iteration, accumulating Schur vectors in VS if desired
477* (RWorkspace: need N+1, prefer N+HSWORK (see comments) )
478*
479 iwrk = itau
480 CALL dhseqr( 'S', jobvs, n, ilo, ihi, a, lda, wr, wi, vs, ldvs,
481 \$ work( iwrk ), lwork-iwrk+1, ieval )
482 IF( ieval.GT.0 )
483 \$ info = ieval
484*
485* Sort eigenvalues if desired
486*
487 IF( wantst .AND. info.EQ.0 ) THEN
488 IF( scalea ) THEN
489 CALL dlascl( 'G', 0, 0, cscale, anrm, n, 1, wr, n, ierr )
490 CALL dlascl( 'G', 0, 0, cscale, anrm, n, 1, wi, n, ierr )
491 END IF
492 DO 10 i = 1, n
493 bwork( i ) = SELECT( wr( i ), wi( i ) )
494 10 CONTINUE
495*
496* Reorder eigenvalues, transform Schur vectors, and compute
497* reciprocal condition numbers
498* (RWorkspace: if SENSE is not 'N', need N+2*SDIM*(N-SDIM)
499* otherwise, need N )
500* (IWorkspace: if SENSE is 'V' or 'B', need SDIM*(N-SDIM)
501* otherwise, need 0 )
502*
503 CALL dtrsen( sense, jobvs, bwork, n, a, lda, vs, ldvs, wr, wi,
504 \$ sdim, rconde, rcondv, work( iwrk ), lwork-iwrk+1,
505 \$ iwork, liwork, icond )
506 IF( .NOT.wantsn )
507 \$ maxwrk = max( maxwrk, n+2*sdim*( n-sdim ) )
508 IF( icond.EQ.-15 ) THEN
509*
510* Not enough real workspace
511*
512 info = -16
513 ELSE IF( icond.EQ.-17 ) THEN
514*
515* Not enough integer workspace
516*
517 info = -18
518 ELSE IF( icond.GT.0 ) THEN
519*
520* DTRSEN failed to reorder or to restore standard Schur form
521*
522 info = icond + n
523 END IF
524 END IF
525*
526 IF( wantvs ) THEN
527*
528* Undo balancing
529* (RWorkspace: need N)
530*
531 CALL dgebak( 'P', 'R', n, ilo, ihi, work( ibal ), n, vs, ldvs,
532 \$ ierr )
533 END IF
534*
535 IF( scalea ) THEN
536*
537* Undo scaling for the Schur form of A
538*
539 CALL dlascl( 'H', 0, 0, cscale, anrm, n, n, a, lda, ierr )
540 CALL dcopy( n, a, lda+1, wr, 1 )
541 IF( ( wantsv .OR. wantsb ) .AND. info.EQ.0 ) THEN
542 dum( 1 ) = rcondv
543 CALL dlascl( 'G', 0, 0, cscale, anrm, 1, 1, dum, 1, ierr )
544 rcondv = dum( 1 )
545 END IF
546 IF( cscale.EQ.smlnum ) THEN
547*
548* If scaling back towards underflow, adjust WI if an
549* offdiagonal element of a 2-by-2 block in the Schur form
550* underflows.
551*
552 IF( ieval.GT.0 ) THEN
553 i1 = ieval + 1
554 i2 = ihi - 1
555 CALL dlascl( 'G', 0, 0, cscale, anrm, ilo-1, 1, wi, n,
556 \$ ierr )
557 ELSE IF( wantst ) THEN
558 i1 = 1
559 i2 = n - 1
560 ELSE
561 i1 = ilo
562 i2 = ihi - 1
563 END IF
564 inxt = i1 - 1
565 DO 20 i = i1, i2
566 IF( i.LT.inxt )
567 \$ GO TO 20
568 IF( wi( i ).EQ.zero ) THEN
569 inxt = i + 1
570 ELSE
571 IF( a( i+1, i ).EQ.zero ) THEN
572 wi( i ) = zero
573 wi( i+1 ) = zero
574 ELSE IF( a( i+1, i ).NE.zero .AND. a( i, i+1 ).EQ.
575 \$ zero ) THEN
576 wi( i ) = zero
577 wi( i+1 ) = zero
578 IF( i.GT.1 )
579 \$ CALL dswap( i-1, a( 1, i ), 1, a( 1, i+1 ), 1 )
580 IF( n.GT.i+1 )
581 \$ CALL dswap( n-i-1, a( i, i+2 ), lda,
582 \$ a( i+1, i+2 ), lda )
583 IF( wantvs ) THEN
584 CALL dswap( n, vs( 1, i ), 1, vs( 1, i+1 ), 1 )
585 END IF
586 a( i, i+1 ) = a( i+1, i )
587 a( i+1, i ) = zero
588 END IF
589 inxt = i + 2
590 END IF
591 20 CONTINUE
592 END IF
593 CALL dlascl( 'G', 0, 0, cscale, anrm, n-ieval, 1,
594 \$ wi( ieval+1 ), max( n-ieval, 1 ), ierr )
595 END IF
596*
597 IF( wantst .AND. info.EQ.0 ) THEN
598*
599* Check if reordering successful
600*
601 lastsl = .true.
602 lst2sl = .true.
603 sdim = 0
604 ip = 0
605 DO 30 i = 1, n
606 cursl = SELECT( wr( i ), wi( i ) )
607 IF( wi( i ).EQ.zero ) THEN
608 IF( cursl )
609 \$ sdim = sdim + 1
610 ip = 0
611 IF( cursl .AND. .NOT.lastsl )
612 \$ info = n + 2
613 ELSE
614 IF( ip.EQ.1 ) THEN
615*
616* Last eigenvalue of conjugate pair
617*
618 cursl = cursl .OR. lastsl
619 lastsl = cursl
620 IF( cursl )
621 \$ sdim = sdim + 2
622 ip = -1
623 IF( cursl .AND. .NOT.lst2sl )
624 \$ info = n + 2
625 ELSE
626*
627* First eigenvalue of conjugate pair
628*
629 ip = 1
630 END IF
631 END IF
632 lst2sl = lastsl
633 lastsl = cursl
634 30 CONTINUE
635 END IF
636*
637 work( 1 ) = maxwrk
638 IF( wantsv .OR. wantsb ) THEN
639 iwork( 1 ) = max( 1, sdim*( n-sdim ) )
640 ELSE
641 iwork( 1 ) = 1
642 END IF
643*
644 RETURN
645*
646* End of DGEESX
647*
648 END
subroutine dlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: dlascl.f:143
subroutine dlacpy(UPLO, M, N, A, LDA, B, LDB)
DLACPY copies all or part of one two-dimensional array to another.
Definition: dlacpy.f:103
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dgehrd(N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
DGEHRD
Definition: dgehrd.f:167
subroutine dgebal(JOB, N, A, LDA, ILO, IHI, SCALE, INFO)
DGEBAL
Definition: dgebal.f:160
subroutine dgebak(JOB, SIDE, N, ILO, IHI, SCALE, M, V, LDV, INFO)
DGEBAK
Definition: dgebak.f:130
subroutine dgeesx(JOBVS, SORT, SELECT, SENSE, N, A, LDA, SDIM, WR, WI, VS, LDVS, RCONDE, RCONDV, WORK, LWORK, IWORK, LIWORK, BWORK, INFO)
DGEESX computes the eigenvalues, the Schur form, and, optionally, the matrix of Schur vectors for GE ...
Definition: dgeesx.f:281
subroutine dhseqr(JOB, COMPZ, N, ILO, IHI, H, LDH, WR, WI, Z, LDZ, WORK, LWORK, INFO)
DHSEQR
Definition: dhseqr.f:316
subroutine dorghr(N, ILO, IHI, A, LDA, TAU, WORK, LWORK, INFO)
DORGHR
Definition: dorghr.f:126
subroutine dtrsen(JOB, COMPQ, SELECT, N, T, LDT, Q, LDQ, WR, WI, M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO)
DTRSEN
Definition: dtrsen.f:313