LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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sggev3.f
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1*> \brief <b> SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (blocked algorithm)</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download SGGEV3 + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sggev3.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sggev3.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sggev3.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE SGGEV3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR,
22* $ ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK,
23* $ INFO )
24*
25* .. Scalar Arguments ..
26* CHARACTER JOBVL, JOBVR
27* INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
28* ..
29* .. Array Arguments ..
30* REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
31* $ B( LDB, * ), BETA( * ), VL( LDVL, * ),
32* $ VR( LDVR, * ), WORK( * )
33* ..
34*
35*
36*> \par Purpose:
37* =============
38*>
39*> \verbatim
40*>
41*> SGGEV3 computes for a pair of N-by-N real nonsymmetric matrices (A,B)
42*> the generalized eigenvalues, and optionally, the left and/or right
43*> generalized eigenvectors.
44*>
45*> A generalized eigenvalue for a pair of matrices (A,B) is a scalar
46*> lambda or a ratio alpha/beta = lambda, such that A - lambda*B is
47*> singular. It is usually represented as the pair (alpha,beta), as
48*> there is a reasonable interpretation for beta=0, and even for both
49*> being zero.
50*>
51*> The right eigenvector v(j) corresponding to the eigenvalue lambda(j)
52*> of (A,B) satisfies
53*>
54*> A * v(j) = lambda(j) * B * v(j).
55*>
56*> The left eigenvector u(j) corresponding to the eigenvalue lambda(j)
57*> of (A,B) satisfies
58*>
59*> u(j)**H * A = lambda(j) * u(j)**H * B .
60*>
61*> where u(j)**H is the conjugate-transpose of u(j).
62*>
63*> \endverbatim
64*
65* Arguments:
66* ==========
67*
68*> \param[in] JOBVL
69*> \verbatim
70*> JOBVL is CHARACTER*1
71*> = 'N': do not compute the left generalized eigenvectors;
72*> = 'V': compute the left generalized eigenvectors.
73*> \endverbatim
74*>
75*> \param[in] JOBVR
76*> \verbatim
77*> JOBVR is CHARACTER*1
78*> = 'N': do not compute the right generalized eigenvectors;
79*> = 'V': compute the right generalized eigenvectors.
80*> \endverbatim
81*>
82*> \param[in] N
83*> \verbatim
84*> N is INTEGER
85*> The order of the matrices A, B, VL, and VR. N >= 0.
86*> \endverbatim
87*>
88*> \param[in,out] A
89*> \verbatim
90*> A is REAL array, dimension (LDA, N)
91*> On entry, the matrix A in the pair (A,B).
92*> On exit, A has been overwritten.
93*> \endverbatim
94*>
95*> \param[in] LDA
96*> \verbatim
97*> LDA is INTEGER
98*> The leading dimension of A. LDA >= max(1,N).
99*> \endverbatim
100*>
101*> \param[in,out] B
102*> \verbatim
103*> B is REAL array, dimension (LDB, N)
104*> On entry, the matrix B in the pair (A,B).
105*> On exit, B has been overwritten.
106*> \endverbatim
107*>
108*> \param[in] LDB
109*> \verbatim
110*> LDB is INTEGER
111*> The leading dimension of B. LDB >= max(1,N).
112*> \endverbatim
113*>
114*> \param[out] ALPHAR
115*> \verbatim
116*> ALPHAR is REAL array, dimension (N)
117*> \endverbatim
118*>
119*> \param[out] ALPHAI
120*> \verbatim
121*> ALPHAI is REAL array, dimension (N)
122*> \endverbatim
123*>
124*> \param[out] BETA
125*> \verbatim
126*> BETA is REAL array, dimension (N)
127*> On exit, (ALPHAR(j) + ALPHAI(j)*i)/BETA(j), j=1,...,N, will
128*> be the generalized eigenvalues. If ALPHAI(j) is zero, then
129*> the j-th eigenvalue is real; if positive, then the j-th and
130*> (j+1)-st eigenvalues are a complex conjugate pair, with
131*> ALPHAI(j+1) negative.
132*>
133*> Note: the quotients ALPHAR(j)/BETA(j) and ALPHAI(j)/BETA(j)
134*> may easily over- or underflow, and BETA(j) may even be zero.
135*> Thus, the user should avoid naively computing the ratio
136*> alpha/beta. However, ALPHAR and ALPHAI will be always less
137*> than and usually comparable with norm(A) in magnitude, and
138*> BETA always less than and usually comparable with norm(B).
139*> \endverbatim
140*>
141*> \param[out] VL
142*> \verbatim
143*> VL is REAL array, dimension (LDVL,N)
144*> If JOBVL = 'V', the left eigenvectors u(j) are stored one
145*> after another in the columns of VL, in the same order as
146*> their eigenvalues. If the j-th eigenvalue is real, then
147*> u(j) = VL(:,j), the j-th column of VL. If the j-th and
148*> (j+1)-th eigenvalues form a complex conjugate pair, then
149*> u(j) = VL(:,j)+i*VL(:,j+1) and u(j+1) = VL(:,j)-i*VL(:,j+1).
150*> Each eigenvector is scaled so the largest component has
151*> abs(real part)+abs(imag. part)=1.
152*> Not referenced if JOBVL = 'N'.
153*> \endverbatim
154*>
155*> \param[in] LDVL
156*> \verbatim
157*> LDVL is INTEGER
158*> The leading dimension of the matrix VL. LDVL >= 1, and
159*> if JOBVL = 'V', LDVL >= N.
160*> \endverbatim
161*>
162*> \param[out] VR
163*> \verbatim
164*> VR is REAL array, dimension (LDVR,N)
165*> If JOBVR = 'V', the right eigenvectors v(j) are stored one
166*> after another in the columns of VR, in the same order as
167*> their eigenvalues. If the j-th eigenvalue is real, then
168*> v(j) = VR(:,j), the j-th column of VR. If the j-th and
169*> (j+1)-th eigenvalues form a complex conjugate pair, then
170*> v(j) = VR(:,j)+i*VR(:,j+1) and v(j+1) = VR(:,j)-i*VR(:,j+1).
171*> Each eigenvector is scaled so the largest component has
172*> abs(real part)+abs(imag. part)=1.
173*> Not referenced if JOBVR = 'N'.
174*> \endverbatim
175*>
176*> \param[in] LDVR
177*> \verbatim
178*> LDVR is INTEGER
179*> The leading dimension of the matrix VR. LDVR >= 1, and
180*> if JOBVR = 'V', LDVR >= N.
181*> \endverbatim
182*>
183*> \param[out] WORK
184*> \verbatim
185*> WORK is REAL array, dimension (MAX(1,LWORK))
186*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
187*> \endverbatim
188*>
189*> \param[in] LWORK
190*> \verbatim
191*> LWORK is INTEGER
192*>
193*> If LWORK = -1, then a workspace query is assumed; the routine
194*> only calculates the optimal size of the WORK array, returns
195*> this value as the first entry of the WORK array, and no error
196*> message related to LWORK is issued by XERBLA.
197*> \endverbatim
198*>
199*> \param[out] INFO
200*> \verbatim
201*> INFO is INTEGER
202*> = 0: successful exit
203*> < 0: if INFO = -i, the i-th argument had an illegal value.
204*> = 1,...,N:
205*> The QZ iteration failed. No eigenvectors have been
206*> calculated, but ALPHAR(j), ALPHAI(j), and BETA(j)
207*> should be correct for j=INFO+1,...,N.
208*> > N: =N+1: other than QZ iteration failed in SLAQZ0.
209*> =N+2: error return from STGEVC.
210*> \endverbatim
211*
212* Authors:
213* ========
214*
215*> \author Univ. of Tennessee
216*> \author Univ. of California Berkeley
217*> \author Univ. of Colorado Denver
218*> \author NAG Ltd.
219*
220*> \ingroup ggev3
221*
222* =====================================================================
223 SUBROUTINE sggev3( JOBVL, JOBVR, N, A, LDA, B, LDB, ALPHAR,
224 $ ALPHAI, BETA, VL, LDVL, VR, LDVR, WORK, LWORK,
225 $ INFO )
226*
227* -- LAPACK driver routine --
228* -- LAPACK is a software package provided by Univ. of Tennessee, --
229* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
230*
231* .. Scalar Arguments ..
232 CHARACTER JOBVL, JOBVR
233 INTEGER INFO, LDA, LDB, LDVL, LDVR, LWORK, N
234* ..
235* .. Array Arguments ..
236 REAL A( LDA, * ), ALPHAI( * ), ALPHAR( * ),
237 $ B( LDB, * ), BETA( * ), VL( LDVL, * ),
238 $ vr( ldvr, * ), work( * )
239* ..
240*
241* =====================================================================
242*
243* .. Parameters ..
244 REAL ZERO, ONE
245 PARAMETER ( ZERO = 0.0e+0, one = 1.0e+0 )
246* ..
247* .. Local Scalars ..
248 LOGICAL ILASCL, ILBSCL, ILV, ILVL, ILVR, LQUERY
249 CHARACTER CHTEMP
250 INTEGER ICOLS, IERR, IHI, IJOBVL, IJOBVR, ILEFT, ILO,
251 $ in, iright, irows, itau, iwrk, jc, jr, lwkopt
252 REAL ANRM, ANRMTO, BIGNUM, BNRM, BNRMTO, EPS,
253 $ SMLNUM, TEMP
254* ..
255* .. Local Arrays ..
256 LOGICAL LDUMMA( 1 )
257* ..
258* .. External Subroutines ..
259 EXTERNAL sgeqrf, sggbak, sggbal, sgghd3, slaqz0, slacpy,
261* ..
262* .. External Functions ..
263 LOGICAL LSAME
264 REAL SLAMCH, SLANGE, SROUNDUP_LWORK
265 EXTERNAL lsame, slamch, slange, sroundup_lwork
266* ..
267* .. Intrinsic Functions ..
268 INTRINSIC abs, max, sqrt
269* ..
270* .. Executable Statements ..
271*
272* Decode the input arguments
273*
274 IF( lsame( jobvl, 'N' ) ) THEN
275 ijobvl = 1
276 ilvl = .false.
277 ELSE IF( lsame( jobvl, 'V' ) ) THEN
278 ijobvl = 2
279 ilvl = .true.
280 ELSE
281 ijobvl = -1
282 ilvl = .false.
283 END IF
284*
285 IF( lsame( jobvr, 'N' ) ) THEN
286 ijobvr = 1
287 ilvr = .false.
288 ELSE IF( lsame( jobvr, 'V' ) ) THEN
289 ijobvr = 2
290 ilvr = .true.
291 ELSE
292 ijobvr = -1
293 ilvr = .false.
294 END IF
295 ilv = ilvl .OR. ilvr
296*
297* Test the input arguments
298*
299 info = 0
300 lquery = ( lwork.EQ.-1 )
301 IF( ijobvl.LE.0 ) THEN
302 info = -1
303 ELSE IF( ijobvr.LE.0 ) THEN
304 info = -2
305 ELSE IF( n.LT.0 ) THEN
306 info = -3
307 ELSE IF( lda.LT.max( 1, n ) ) THEN
308 info = -5
309 ELSE IF( ldb.LT.max( 1, n ) ) THEN
310 info = -7
311 ELSE IF( ldvl.LT.1 .OR. ( ilvl .AND. ldvl.LT.n ) ) THEN
312 info = -12
313 ELSE IF( ldvr.LT.1 .OR. ( ilvr .AND. ldvr.LT.n ) ) THEN
314 info = -14
315 ELSE IF( lwork.LT.max( 1, 8*n ) .AND. .NOT.lquery ) THEN
316 info = -16
317 END IF
318*
319* Compute workspace
320*
321 IF( info.EQ.0 ) THEN
322 CALL sgeqrf( n, n, b, ldb, work, work, -1, ierr )
323 lwkopt = max( 1, 8*n, 3*n+int( work( 1 ) ) )
324 CALL sormqr( 'L', 'T', n, n, n, b, ldb, work, a, lda, work,
325 $ -1, ierr )
326 lwkopt = max( lwkopt, 3*n+int( work( 1 ) ) )
327 CALL sgghd3( jobvl, jobvr, n, 1, n, a, lda, b, ldb, vl, ldvl,
328 $ vr, ldvr, work, -1, ierr )
329 lwkopt = max( lwkopt, 3*n+int( work( 1 ) ) )
330 IF( ilvl ) THEN
331 CALL sorgqr( n, n, n, vl, ldvl, work, work, -1, ierr )
332 lwkopt = max( lwkopt, 3*n+int( work( 1 ) ) )
333 CALL slaqz0( 'S', jobvl, jobvr, n, 1, n, a, lda, b, ldb,
334 $ alphar, alphai, beta, vl, ldvl, vr, ldvr,
335 $ work, -1, 0, ierr )
336 lwkopt = max( lwkopt, 2*n+int( work( 1 ) ) )
337 ELSE
338 CALL slaqz0( 'E', jobvl, jobvr, n, 1, n, a, lda, b, ldb,
339 $ alphar, alphai, beta, vl, ldvl, vr, ldvr,
340 $ work, -1, 0, ierr )
341 lwkopt = max( lwkopt, 2*n+int( work( 1 ) ) )
342 END IF
343 work( 1 ) = sroundup_lwork( lwkopt )
344*
345 END IF
346*
347 IF( info.NE.0 ) THEN
348 CALL xerbla( 'SGGEV3 ', -info )
349 RETURN
350 ELSE IF( lquery ) THEN
351 RETURN
352 END IF
353*
354* Quick return if possible
355*
356 IF( n.EQ.0 )
357 $ RETURN
358*
359* Get machine constants
360*
361 eps = slamch( 'P' )
362 smlnum = slamch( 'S' )
363 bignum = one / smlnum
364 smlnum = sqrt( smlnum ) / eps
365 bignum = one / smlnum
366*
367* Scale A if max element outside range [SMLNUM,BIGNUM]
368*
369 anrm = slange( 'M', n, n, a, lda, work )
370 ilascl = .false.
371 IF( anrm.GT.zero .AND. anrm.LT.smlnum ) THEN
372 anrmto = smlnum
373 ilascl = .true.
374 ELSE IF( anrm.GT.bignum ) THEN
375 anrmto = bignum
376 ilascl = .true.
377 END IF
378 IF( ilascl )
379 $ CALL slascl( 'G', 0, 0, anrm, anrmto, n, n, a, lda, ierr )
380*
381* Scale B if max element outside range [SMLNUM,BIGNUM]
382*
383 bnrm = slange( 'M', n, n, b, ldb, work )
384 ilbscl = .false.
385 IF( bnrm.GT.zero .AND. bnrm.LT.smlnum ) THEN
386 bnrmto = smlnum
387 ilbscl = .true.
388 ELSE IF( bnrm.GT.bignum ) THEN
389 bnrmto = bignum
390 ilbscl = .true.
391 END IF
392 IF( ilbscl )
393 $ CALL slascl( 'G', 0, 0, bnrm, bnrmto, n, n, b, ldb, ierr )
394*
395* Permute the matrices A, B to isolate eigenvalues if possible
396*
397 ileft = 1
398 iright = n + 1
399 iwrk = iright + n
400 CALL sggbal( 'P', n, a, lda, b, ldb, ilo, ihi, work( ileft ),
401 $ work( iright ), work( iwrk ), ierr )
402*
403* Reduce B to triangular form (QR decomposition of B)
404*
405 irows = ihi + 1 - ilo
406 IF( ilv ) THEN
407 icols = n + 1 - ilo
408 ELSE
409 icols = irows
410 END IF
411 itau = iwrk
412 iwrk = itau + irows
413 CALL sgeqrf( irows, icols, b( ilo, ilo ), ldb, work( itau ),
414 $ work( iwrk ), lwork+1-iwrk, ierr )
415*
416* Apply the orthogonal transformation to matrix A
417*
418 CALL sormqr( 'L', 'T', irows, icols, irows, b( ilo, ilo ), ldb,
419 $ work( itau ), a( ilo, ilo ), lda, work( iwrk ),
420 $ lwork+1-iwrk, ierr )
421*
422* Initialize VL
423*
424 IF( ilvl ) THEN
425 CALL slaset( 'Full', n, n, zero, one, vl, ldvl )
426 IF( irows.GT.1 ) THEN
427 CALL slacpy( 'L', irows-1, irows-1, b( ilo+1, ilo ), ldb,
428 $ vl( ilo+1, ilo ), ldvl )
429 END IF
430 CALL sorgqr( irows, irows, irows, vl( ilo, ilo ), ldvl,
431 $ work( itau ), work( iwrk ), lwork+1-iwrk, ierr )
432 END IF
433*
434* Initialize VR
435*
436 IF( ilvr )
437 $ CALL slaset( 'Full', n, n, zero, one, vr, ldvr )
438*
439* Reduce to generalized Hessenberg form
440*
441 IF( ilv ) THEN
442*
443* Eigenvectors requested -- work on whole matrix.
444*
445 CALL sgghd3( jobvl, jobvr, n, ilo, ihi, a, lda, b, ldb, vl,
446 $ ldvl, vr, ldvr, work( iwrk ), lwork+1-iwrk, ierr )
447 ELSE
448 CALL sgghd3( 'N', 'N', irows, 1, irows, a( ilo, ilo ), lda,
449 $ b( ilo, ilo ), ldb, vl, ldvl, vr, ldvr,
450 $ work( iwrk ), lwork+1-iwrk, ierr )
451 END IF
452*
453* Perform QZ algorithm (Compute eigenvalues, and optionally, the
454* Schur forms and Schur vectors)
455*
456 iwrk = itau
457 IF( ilv ) THEN
458 chtemp = 'S'
459 ELSE
460 chtemp = 'E'
461 END IF
462 CALL slaqz0( chtemp, jobvl, jobvr, n, ilo, ihi, a, lda, b, ldb,
463 $ alphar, alphai, beta, vl, ldvl, vr, ldvr,
464 $ work( iwrk ), lwork+1-iwrk, 0, ierr )
465 IF( ierr.NE.0 ) THEN
466 IF( ierr.GT.0 .AND. ierr.LE.n ) THEN
467 info = ierr
468 ELSE IF( ierr.GT.n .AND. ierr.LE.2*n ) THEN
469 info = ierr - n
470 ELSE
471 info = n + 1
472 END IF
473 GO TO 110
474 END IF
475*
476* Compute Eigenvectors
477*
478 IF( ilv ) THEN
479 IF( ilvl ) THEN
480 IF( ilvr ) THEN
481 chtemp = 'B'
482 ELSE
483 chtemp = 'L'
484 END IF
485 ELSE
486 chtemp = 'R'
487 END IF
488 CALL stgevc( chtemp, 'B', ldumma, n, a, lda, b, ldb, vl, ldvl,
489 $ vr, ldvr, n, in, work( iwrk ), ierr )
490 IF( ierr.NE.0 ) THEN
491 info = n + 2
492 GO TO 110
493 END IF
494*
495* Undo balancing on VL and VR and normalization
496*
497 IF( ilvl ) THEN
498 CALL sggbak( 'P', 'L', n, ilo, ihi, work( ileft ),
499 $ work( iright ), n, vl, ldvl, ierr )
500 DO 50 jc = 1, n
501 IF( alphai( jc ).LT.zero )
502 $ GO TO 50
503 temp = zero
504 IF( alphai( jc ).EQ.zero ) THEN
505 DO 10 jr = 1, n
506 temp = max( temp, abs( vl( jr, jc ) ) )
507 10 CONTINUE
508 ELSE
509 DO 20 jr = 1, n
510 temp = max( temp, abs( vl( jr, jc ) )+
511 $ abs( vl( jr, jc+1 ) ) )
512 20 CONTINUE
513 END IF
514 IF( temp.LT.smlnum )
515 $ GO TO 50
516 temp = one / temp
517 IF( alphai( jc ).EQ.zero ) THEN
518 DO 30 jr = 1, n
519 vl( jr, jc ) = vl( jr, jc )*temp
520 30 CONTINUE
521 ELSE
522 DO 40 jr = 1, n
523 vl( jr, jc ) = vl( jr, jc )*temp
524 vl( jr, jc+1 ) = vl( jr, jc+1 )*temp
525 40 CONTINUE
526 END IF
527 50 CONTINUE
528 END IF
529 IF( ilvr ) THEN
530 CALL sggbak( 'P', 'R', n, ilo, ihi, work( ileft ),
531 $ work( iright ), n, vr, ldvr, ierr )
532 DO 100 jc = 1, n
533 IF( alphai( jc ).LT.zero )
534 $ GO TO 100
535 temp = zero
536 IF( alphai( jc ).EQ.zero ) THEN
537 DO 60 jr = 1, n
538 temp = max( temp, abs( vr( jr, jc ) ) )
539 60 CONTINUE
540 ELSE
541 DO 70 jr = 1, n
542 temp = max( temp, abs( vr( jr, jc ) )+
543 $ abs( vr( jr, jc+1 ) ) )
544 70 CONTINUE
545 END IF
546 IF( temp.LT.smlnum )
547 $ GO TO 100
548 temp = one / temp
549 IF( alphai( jc ).EQ.zero ) THEN
550 DO 80 jr = 1, n
551 vr( jr, jc ) = vr( jr, jc )*temp
552 80 CONTINUE
553 ELSE
554 DO 90 jr = 1, n
555 vr( jr, jc ) = vr( jr, jc )*temp
556 vr( jr, jc+1 ) = vr( jr, jc+1 )*temp
557 90 CONTINUE
558 END IF
559 100 CONTINUE
560 END IF
561*
562* End of eigenvector calculation
563*
564 END IF
565*
566* Undo scaling if necessary
567*
568 110 CONTINUE
569*
570 IF( ilascl ) THEN
571 CALL slascl( 'G', 0, 0, anrmto, anrm, n, 1, alphar, n, ierr )
572 CALL slascl( 'G', 0, 0, anrmto, anrm, n, 1, alphai, n, ierr )
573 END IF
574*
575 IF( ilbscl ) THEN
576 CALL slascl( 'G', 0, 0, bnrmto, bnrm, n, 1, beta, n, ierr )
577 END IF
578*
579 work( 1 ) = sroundup_lwork( lwkopt )
580 RETURN
581*
582* End of SGGEV3
583*
584 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine sgeqrf(m, n, a, lda, tau, work, lwork, info)
SGEQRF
Definition sgeqrf.f:146
subroutine sggbak(job, side, n, ilo, ihi, lscale, rscale, m, v, ldv, info)
SGGBAK
Definition sggbak.f:147
subroutine sggbal(job, n, a, lda, b, ldb, ilo, ihi, lscale, rscale, work, info)
SGGBAL
Definition sggbal.f:177
subroutine sggev3(jobvl, jobvr, n, a, lda, b, ldb, alphar, alphai, beta, vl, ldvl, vr, ldvr, work, lwork, info)
SGGEV3 computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices (...
Definition sggev3.f:226
subroutine sgghd3(compq, compz, n, ilo, ihi, a, lda, b, ldb, q, ldq, z, ldz, work, lwork, info)
SGGHD3
Definition sgghd3.f:230
subroutine slacpy(uplo, m, n, a, lda, b, ldb)
SLACPY copies all or part of one two-dimensional array to another.
Definition slacpy.f:103
recursive subroutine slaqz0(wants, wantq, wantz, n, ilo, ihi, a, lda, b, ldb, alphar, alphai, beta, q, ldq, z, ldz, work, lwork, rec, info)
SLAQZ0
Definition slaqz0.f:304
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
subroutine slaset(uplo, m, n, alpha, beta, a, lda)
SLASET initializes the off-diagonal elements and the diagonal elements of a matrix to given values.
Definition slaset.f:110
subroutine stgevc(side, howmny, select, n, s, lds, p, ldp, vl, ldvl, vr, ldvr, mm, m, work, info)
STGEVC
Definition stgevc.f:295
subroutine sorgqr(m, n, k, a, lda, tau, work, lwork, info)
SORGQR
Definition sorgqr.f:128
subroutine sormqr(side, trans, m, n, k, a, lda, tau, c, ldc, work, lwork, info)
SORMQR
Definition sormqr.f:168