1*> \brief <b> SSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
2*
3*  @generated from dsyevx_2stage.f, fortran d -> s, Sat Nov  5 23:55:46 2016
4*
5*  =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8*            http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download SSYEVX_2STAGE + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ssyevx_2stage.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ssyevx_2stage.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ssyevx_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20*  Definition:
21*  ===========
22*
23*       SUBROUTINE SSYEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
24*                                 IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
25*                                 LWORK, IWORK, IFAIL, INFO )
26*
27*       IMPLICIT NONE
28*
29*       .. Scalar Arguments ..
30*       CHARACTER          JOBZ, RANGE, UPLO
31*       INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
32*       REAL               ABSTOL, VL, VU
33*       ..
34*       .. Array Arguments ..
35*       INTEGER            IFAIL( * ), IWORK( * )
36*       REAL               A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
37*       ..
38*
39*
40*> \par Purpose:
41*  =============
42*>
43*> \verbatim
44*>
45*> SSYEVX_2STAGE computes selected eigenvalues and, optionally, eigenvectors
46*> of a real symmetric matrix A using the 2stage technique for
47*> the reduction to tridiagonal.  Eigenvalues and eigenvectors can be
48*> selected by specifying either a range of values or a range of indices
49*> for the desired eigenvalues.
50*> \endverbatim
51*
52*  Arguments:
53*  ==========
54*
55*> \param[in] JOBZ
56*> \verbatim
57*>          JOBZ is CHARACTER*1
58*>          = 'N':  Compute eigenvalues only;
59*>          = 'V':  Compute eigenvalues and eigenvectors.
60*>                  Not available in this release.
61*> \endverbatim
62*>
63*> \param[in] RANGE
64*> \verbatim
65*>          RANGE is CHARACTER*1
66*>          = 'A': all eigenvalues will be found.
67*>          = 'V': all eigenvalues in the half-open interval (VL,VU]
68*>                 will be found.
69*>          = 'I': the IL-th through IU-th eigenvalues will be found.
70*> \endverbatim
71*>
72*> \param[in] UPLO
73*> \verbatim
74*>          UPLO is CHARACTER*1
75*>          = 'U':  Upper triangle of A is stored;
76*>          = 'L':  Lower triangle of A is stored.
77*> \endverbatim
78*>
79*> \param[in] N
80*> \verbatim
81*>          N is INTEGER
82*>          The order of the matrix A.  N >= 0.
83*> \endverbatim
84*>
85*> \param[in,out] A
86*> \verbatim
87*>          A is REAL array, dimension (LDA, N)
88*>          On entry, the symmetric matrix A.  If UPLO = 'U', the
89*>          leading N-by-N upper triangular part of A contains the
90*>          upper triangular part of the matrix A.  If UPLO = 'L',
91*>          the leading N-by-N lower triangular part of A contains
92*>          the lower triangular part of the matrix A.
93*>          On exit, the lower triangle (if UPLO='L') or the upper
94*>          triangle (if UPLO='U') of A, including the diagonal, is
95*>          destroyed.
96*> \endverbatim
97*>
98*> \param[in] LDA
99*> \verbatim
100*>          LDA is INTEGER
101*>          The leading dimension of the array A.  LDA >= max(1,N).
102*> \endverbatim
103*>
104*> \param[in] VL
105*> \verbatim
106*>          VL is REAL
107*>          If RANGE='V', the lower bound of the interval to
108*>          be searched for eigenvalues. VL < VU.
109*>          Not referenced if RANGE = 'A' or 'I'.
110*> \endverbatim
111*>
112*> \param[in] VU
113*> \verbatim
114*>          VU is REAL
115*>          If RANGE='V', the upper bound of the interval to
116*>          be searched for eigenvalues. VL < VU.
117*>          Not referenced if RANGE = 'A' or 'I'.
118*> \endverbatim
119*>
120*> \param[in] IL
121*> \verbatim
122*>          IL is INTEGER
123*>          If RANGE='I', the index of the
124*>          smallest eigenvalue to be returned.
125*>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
126*>          Not referenced if RANGE = 'A' or 'V'.
127*> \endverbatim
128*>
129*> \param[in] IU
130*> \verbatim
131*>          IU is INTEGER
132*>          If RANGE='I', the index of the
133*>          largest eigenvalue to be returned.
134*>          1 <= IL <= IU <= N, if N > 0; IL = 1 and IU = 0 if N = 0.
135*>          Not referenced if RANGE = 'A' or 'V'.
136*> \endverbatim
137*>
138*> \param[in] ABSTOL
139*> \verbatim
140*>          ABSTOL is REAL
141*>          The absolute error tolerance for the eigenvalues.
142*>          An approximate eigenvalue is accepted as converged
143*>          when it is determined to lie in an interval [a,b]
144*>          of width less than or equal to
145*>
146*>                  ABSTOL + EPS *   max( |a|,|b| ) ,
147*>
148*>          where EPS is the machine precision.  If ABSTOL is less than
149*>          or equal to zero, then  EPS*|T|  will be used in its place,
150*>          where |T| is the 1-norm of the tridiagonal matrix obtained
151*>          by reducing A to tridiagonal form.
152*>
153*>          Eigenvalues will be computed most accurately when ABSTOL is
154*>          set to twice the underflow threshold 2*SLAMCH('S'), not zero.
155*>          If this routine returns with INFO>0, indicating that some
156*>          eigenvectors did not converge, try setting ABSTOL to
157*>          2*SLAMCH('S').
158*>
159*>          See "Computing Small Singular Values of Bidiagonal Matrices
160*>          with Guaranteed High Relative Accuracy," by Demmel and
161*>          Kahan, LAPACK Working Note #3.
162*> \endverbatim
163*>
164*> \param[out] M
165*> \verbatim
166*>          M is INTEGER
167*>          The total number of eigenvalues found.  0 <= M <= N.
168*>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
169*> \endverbatim
170*>
171*> \param[out] W
172*> \verbatim
173*>          W is REAL array, dimension (N)
174*>          On normal exit, the first M elements contain the selected
175*>          eigenvalues in ascending order.
176*> \endverbatim
177*>
178*> \param[out] Z
179*> \verbatim
180*>          Z is REAL array, dimension (LDZ, max(1,M))
181*>          If JOBZ = 'V', then if INFO = 0, the first M columns of Z
182*>          contain the orthonormal eigenvectors of the matrix A
183*>          corresponding to the selected eigenvalues, with the i-th
184*>          column of Z holding the eigenvector associated with W(i).
185*>          If an eigenvector fails to converge, then that column of Z
186*>          contains the latest approximation to the eigenvector, and the
187*>          index of the eigenvector is returned in IFAIL.
188*>          If JOBZ = 'N', then Z is not referenced.
189*>          Note: the user must ensure that at least max(1,M) columns are
190*>          supplied in the array Z; if RANGE = 'V', the exact value of M
191*>          is not known in advance and an upper bound must be used.
192*> \endverbatim
193*>
194*> \param[in] LDZ
195*> \verbatim
196*>          LDZ is INTEGER
197*>          The leading dimension of the array Z.  LDZ >= 1, and if
198*>          JOBZ = 'V', LDZ >= max(1,N).
199*> \endverbatim
200*>
201*> \param[out] WORK
202*> \verbatim
203*>          WORK is REAL array, dimension (MAX(1,LWORK))
204*>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
205*> \endverbatim
206*>
207*> \param[in] LWORK
208*> \verbatim
209*>          LWORK is INTEGER
210*>          The length of the array WORK. LWORK >= 1, when N <= 1;
211*>          otherwise
212*>          If JOBZ = 'N' and N > 1, LWORK must be queried.
213*>                                   LWORK = MAX(1, 8*N, dimension) where
214*>                                   dimension = max(stage1,stage2) + (KD+1)*N + 3*N
215*>                                             = N*KD + N*max(KD+1,FACTOPTNB)
216*>                                               + max(2*KD*KD, KD*NTHREADS)
217*>                                               + (KD+1)*N + 3*N
218*>                                   where KD is the blocking size of the reduction,
219*>                                   FACTOPTNB is the blocking used by the QR or LQ
220*>                                   algorithm, usually FACTOPTNB=128 is a good choice
221*>                                   NTHREADS is the number of threads used when
222*>                                   openMP compilation is enabled, otherwise =1.
223*>          If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
224*>
225*>          If LWORK = -1, then a workspace query is assumed; the routine
226*>          only calculates the optimal size of the WORK array, returns
227*>          this value as the first entry of the WORK array, and no error
228*>          message related to LWORK is issued by XERBLA.
229*> \endverbatim
230*>
231*> \param[out] IWORK
232*> \verbatim
233*>          IWORK is INTEGER array, dimension (5*N)
234*> \endverbatim
235*>
236*> \param[out] IFAIL
237*> \verbatim
238*>          IFAIL is INTEGER array, dimension (N)
239*>          If JOBZ = 'V', then if INFO = 0, the first M elements of
240*>          IFAIL are zero.  If INFO > 0, then IFAIL contains the
241*>          indices of the eigenvectors that failed to converge.
242*>          If JOBZ = 'N', then IFAIL is not referenced.
243*> \endverbatim
244*>
245*> \param[out] INFO
246*> \verbatim
247*>          INFO is INTEGER
248*>          = 0:  successful exit
249*>          < 0:  if INFO = -i, the i-th argument had an illegal value
250*>          > 0:  if INFO = i, then i eigenvectors failed to converge.
251*>                Their indices are stored in array IFAIL.
252*> \endverbatim
253*
254*  Authors:
255*  ========
256*
257*> \author Univ. of Tennessee
258*> \author Univ. of California Berkeley
259*> \author Univ. of Colorado Denver
260*> \author NAG Ltd.
261*
262*> \date June 2016
263*
264*> \ingroup realSYeigen
265*
266*> \par Further Details:
267*  =====================
268*>
269*> \verbatim
270*>
271*>  All details about the 2stage techniques are available in:
272*>
273*>  Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
274*>  Parallel reduction to condensed forms for symmetric eigenvalue problems
275*>  using aggregated fine-grained and memory-aware kernels. In Proceedings
276*>  of 2011 International Conference for High Performance Computing,
277*>  Networking, Storage and Analysis (SC '11), New York, NY, USA,
278*>  Article 8 , 11 pages.
279*>  http://doi.acm.org/10.1145/2063384.2063394
280*>
281*>  A. Haidar, J. Kurzak, P. Luszczek, 2013.
282*>  An improved parallel singular value algorithm and its implementation
283*>  for multicore hardware, In Proceedings of 2013 International Conference
284*>  for High Performance Computing, Networking, Storage and Analysis (SC '13).
285*>  Denver, Colorado, USA, 2013.
286*>  Article 90, 12 pages.
287*>  http://doi.acm.org/10.1145/2503210.2503292
288*>
289*>  A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
290*>  A novel hybrid CPU-GPU generalized eigensolver for electronic structure
291*>  calculations based on fine-grained memory aware tasks.
292*>  International Journal of High Performance Computing Applications.
293*>  Volume 28 Issue 2, Pages 196-209, May 2014.
294*>  http://hpc.sagepub.com/content/28/2/196
295*>
296*> \endverbatim
297*
298*  =====================================================================
299      SUBROUTINE SSYEVX_2STAGE( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
300     $                          IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
301     $                          LWORK, IWORK, IFAIL, INFO )
302*
303      IMPLICIT NONE
304*
305*  -- LAPACK driver routine (version 3.8.0) --
306*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
307*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
308*     June 2016
309*
310*     .. Scalar Arguments ..
311      CHARACTER          JOBZ, RANGE, UPLO
312      INTEGER            IL, INFO, IU, LDA, LDZ, LWORK, M, N
313      REAL               ABSTOL, VL, VU
314*     ..
315*     .. Array Arguments ..
316      INTEGER            IFAIL( * ), IWORK( * )
317      REAL               A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
318*     ..
319*
320* =====================================================================
321*
322*     .. Parameters ..
323      REAL               ZERO, ONE
324      PARAMETER          ( ZERO = 0.0E+0, ONE = 1.0E+0 )
325*     ..
326*     .. Local Scalars ..
327      LOGICAL            ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
328     $                   WANTZ
329      CHARACTER          ORDER
330      INTEGER            I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
331     $                   INDISP, INDIWO, INDTAU, INDWKN, INDWRK, ISCALE,
332     $                   ITMP1, J, JJ, LLWORK, LLWRKN,
333     $                   NSPLIT, LWMIN, LHTRD, LWTRD, KD, IB, INDHOUS
334      REAL               ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
335     $                   SIGMA, SMLNUM, TMP1, VLL, VUU
336*     ..
337*     .. External Functions ..
338      LOGICAL            LSAME
339      INTEGER            ILAENV2STAGE
340      REAL               SLAMCH, SLANSY
341      EXTERNAL           LSAME, SLAMCH, SLANSY, ILAENV2STAGE
342*     ..
343*     .. External Subroutines ..
344      EXTERNAL           SCOPY, SLACPY, SORGTR, SORMTR, SSCAL, SSTEBZ,
345     $                   SSTEIN, SSTEQR, SSTERF, SSWAP, XERBLA,
346     $                   SSYTRD_2STAGE
347*     ..
348*     .. Intrinsic Functions ..
349      INTRINSIC          MAX, MIN, SQRT
350*     ..
351*     .. Executable Statements ..
352*
353*     Test the input parameters.
354*
355      LOWER = LSAME( UPLO, 'L' )
356      WANTZ = LSAME( JOBZ, 'V' )
357      ALLEIG = LSAME( RANGE, 'A' )
358      VALEIG = LSAME( RANGE, 'V' )
359      INDEIG = LSAME( RANGE, 'I' )
360      LQUERY = ( LWORK.EQ.-1 )
361*
362      INFO = 0
363      IF( .NOT.( LSAME( JOBZ, 'N' ) ) ) THEN
364         INFO = -1
365      ELSE IF( .NOT.( ALLEIG .OR. VALEIG .OR. INDEIG ) ) THEN
366         INFO = -2
367      ELSE IF( .NOT.( LOWER .OR. LSAME( UPLO, 'U' ) ) ) THEN
368         INFO = -3
369      ELSE IF( N.LT.0 ) THEN
370         INFO = -4
371      ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
372         INFO = -6
373      ELSE
374         IF( VALEIG ) THEN
375            IF( N.GT.0 .AND. VU.LE.VL )
376     $         INFO = -8
377         ELSE IF( INDEIG ) THEN
378            IF( IL.LT.1 .OR. IL.GT.MAX( 1, N ) ) THEN
379               INFO = -9
380            ELSE IF( IU.LT.MIN( N, IL ) .OR. IU.GT.N ) THEN
381               INFO = -10
382            END IF
383         END IF
384      END IF
385      IF( INFO.EQ.0 ) THEN
386         IF( LDZ.LT.1 .OR. ( WANTZ .AND. LDZ.LT.N ) ) THEN
387            INFO = -15
388         END IF
389      END IF
390*
391      IF( INFO.EQ.0 ) THEN
392         IF( N.LE.1 ) THEN
393            LWMIN = 1
394            WORK( 1 ) = LWMIN
395         ELSE
396            KD    = ILAENV2STAGE( 1, 'SSYTRD_2STAGE', JOBZ,
397     $                            N, -1, -1, -1 )
398            IB    = ILAENV2STAGE( 2, 'SSYTRD_2STAGE', JOBZ,
399     $                            N, KD, -1, -1 )
400            LHTRD = ILAENV2STAGE( 3, 'SSYTRD_2STAGE', JOBZ,
401     $                            N, KD, IB, -1 )
402            LWTRD = ILAENV2STAGE( 4, 'SSYTRD_2STAGE', JOBZ,
403     $                            N, KD, IB, -1 )
404            LWMIN = MAX( 8*N, 3*N + LHTRD + LWTRD )
405            WORK( 1 )  = LWMIN
406         END IF
407*
408         IF( LWORK.LT.LWMIN .AND. .NOT.LQUERY )
409     $      INFO = -17
410      END IF
411*
412      IF( INFO.NE.0 ) THEN
413         CALL XERBLA( 'SSYEVX_2STAGE', -INFO )
414         RETURN
415      ELSE IF( LQUERY ) THEN
416         RETURN
417      END IF
418*
419*     Quick return if possible
420*
421      M = 0
422      IF( N.EQ.0 ) THEN
423         RETURN
424      END IF
425*
426      IF( N.EQ.1 ) THEN
427         IF( ALLEIG .OR. INDEIG ) THEN
428            M = 1
429            W( 1 ) = A( 1, 1 )
430         ELSE
431            IF( VL.LT.A( 1, 1 ) .AND. VU.GE.A( 1, 1 ) ) THEN
432               M = 1
433               W( 1 ) = A( 1, 1 )
434            END IF
435         END IF
436         IF( WANTZ )
437     $      Z( 1, 1 ) = ONE
438         RETURN
439      END IF
440*
441*     Get machine constants.
442*
443      SAFMIN = SLAMCH( 'Safe minimum' )
444      EPS    = SLAMCH( 'Precision' )
445      SMLNUM = SAFMIN / EPS
446      BIGNUM = ONE / SMLNUM
447      RMIN   = SQRT( SMLNUM )
448      RMAX   = MIN( SQRT( BIGNUM ), ONE / SQRT( SQRT( SAFMIN ) ) )
449*
450*     Scale matrix to allowable range, if necessary.
451*
452      ISCALE = 0
453      ABSTLL = ABSTOL
454      IF( VALEIG ) THEN
455         VLL = VL
456         VUU = VU
457      END IF
458      ANRM = SLANSY( 'M', UPLO, N, A, LDA, WORK )
459      IF( ANRM.GT.ZERO .AND. ANRM.LT.RMIN ) THEN
460         ISCALE = 1
461         SIGMA = RMIN / ANRM
462      ELSE IF( ANRM.GT.RMAX ) THEN
463         ISCALE = 1
464         SIGMA = RMAX / ANRM
465      END IF
466      IF( ISCALE.EQ.1 ) THEN
467         IF( LOWER ) THEN
468            DO 10 J = 1, N
469               CALL SSCAL( N-J+1, SIGMA, A( J, J ), 1 )
470   10       CONTINUE
471         ELSE
472            DO 20 J = 1, N
473               CALL SSCAL( J, SIGMA, A( 1, J ), 1 )
474   20       CONTINUE
475         END IF
476         IF( ABSTOL.GT.0 )
477     $      ABSTLL = ABSTOL*SIGMA
478         IF( VALEIG ) THEN
479            VLL = VL*SIGMA
480            VUU = VU*SIGMA
481         END IF
482      END IF
483*
484*     Call SSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
485*
486      INDTAU  = 1
487      INDE    = INDTAU + N
488      INDD    = INDE + N
489      INDHOUS = INDD + N
490      INDWRK  = INDHOUS + LHTRD
491      LLWORK  = LWORK - INDWRK + 1
492*
493      CALL SSYTRD_2STAGE( JOBZ, UPLO, N, A, LDA, WORK( INDD ),
494     $                    WORK( INDE ), WORK( INDTAU ), WORK( INDHOUS ),
495     $                    LHTRD, WORK( INDWRK ), LLWORK, IINFO )
496*
497*     If all eigenvalues are desired and ABSTOL is less than or equal to
498*     zero, then call SSTERF or SORGTR and SSTEQR.  If this fails for
499*     some eigenvalue, then try SSTEBZ.
500*
501      TEST = .FALSE.
502      IF( INDEIG ) THEN
503         IF( IL.EQ.1 .AND. IU.EQ.N ) THEN
504            TEST = .TRUE.
505         END IF
506      END IF
507      IF( ( ALLEIG .OR. TEST ) .AND. ( ABSTOL.LE.ZERO ) ) THEN
508         CALL SCOPY( N, WORK( INDD ), 1, W, 1 )
509         INDEE = INDWRK + 2*N
510         IF( .NOT.WANTZ ) THEN
511            CALL SCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
512            CALL SSTERF( N, W, WORK( INDEE ), INFO )
513         ELSE
514            CALL SLACPY( 'A', N, N, A, LDA, Z, LDZ )
515            CALL SORGTR( UPLO, N, Z, LDZ, WORK( INDTAU ),
516     $                   WORK( INDWRK ), LLWORK, IINFO )
517            CALL SCOPY( N-1, WORK( INDE ), 1, WORK( INDEE ), 1 )
518            CALL SSTEQR( JOBZ, N, W, WORK( INDEE ), Z, LDZ,
519     $                   WORK( INDWRK ), INFO )
520            IF( INFO.EQ.0 ) THEN
521               DO 30 I = 1, N
522                  IFAIL( I ) = 0
523   30          CONTINUE
524            END IF
525         END IF
526         IF( INFO.EQ.0 ) THEN
527            M = N
528            GO TO 40
529         END IF
530         INFO = 0
531      END IF
532*
533*     Otherwise, call SSTEBZ and, if eigenvectors are desired, SSTEIN.
534*
535      IF( WANTZ ) THEN
536         ORDER = 'B'
537      ELSE
538         ORDER = 'E'
539      END IF
540      INDIBL = 1
541      INDISP = INDIBL + N
542      INDIWO = INDISP + N
543      CALL SSTEBZ( RANGE, ORDER, N, VLL, VUU, IL, IU, ABSTLL,
544     $             WORK( INDD ), WORK( INDE ), M, NSPLIT, W,
545     $             IWORK( INDIBL ), IWORK( INDISP ), WORK( INDWRK ),
546     $             IWORK( INDIWO ), INFO )
547*
548      IF( WANTZ ) THEN
549         CALL SSTEIN( N, WORK( INDD ), WORK( INDE ), M, W,
550     $                IWORK( INDIBL ), IWORK( INDISP ), Z, LDZ,
551     $                WORK( INDWRK ), IWORK( INDIWO ), IFAIL, INFO )
552*
553*        Apply orthogonal matrix used in reduction to tridiagonal
554*        form to eigenvectors returned by SSTEIN.
555*
556         INDWKN = INDE
557         LLWRKN = LWORK - INDWKN + 1
558         CALL SORMTR( 'L', UPLO, 'N', N, M, A, LDA, WORK( INDTAU ), Z,
559     $                LDZ, WORK( INDWKN ), LLWRKN, IINFO )
560      END IF
561*
562*     If matrix was scaled, then rescale eigenvalues appropriately.
563*
564   40 CONTINUE
565      IF( ISCALE.EQ.1 ) THEN
566         IF( INFO.EQ.0 ) THEN
567            IMAX = M
568         ELSE
569            IMAX = INFO - 1
570         END IF
571         CALL SSCAL( IMAX, ONE / SIGMA, W, 1 )
572      END IF
573*
574*     If eigenvalues are not in order, then sort them, along with
575*     eigenvectors.
576*
577      IF( WANTZ ) THEN
578         DO 60 J = 1, M - 1
579            I = 0
580            TMP1 = W( J )
581            DO 50 JJ = J + 1, M
582               IF( W( JJ ).LT.TMP1 ) THEN
583                  I = JJ
584                  TMP1 = W( JJ )
585               END IF
586   50       CONTINUE
587*
588            IF( I.NE.0 ) THEN
589               ITMP1 = IWORK( INDIBL+I-1 )
590               W( I ) = W( J )
591               IWORK( INDIBL+I-1 ) = IWORK( INDIBL+J-1 )
592               W( J ) = TMP1
593               IWORK( INDIBL+J-1 ) = ITMP1
594               CALL SSWAP( N, Z( 1, I ), 1, Z( 1, J ), 1 )
595               IF( INFO.NE.0 ) THEN
596                  ITMP1 = IFAIL( I )
597                  IFAIL( I ) = IFAIL( J )
598                  IFAIL( J ) = ITMP1
599               END IF
600            END IF
601   60    CONTINUE
602      END IF
603*
604*     Set WORK(1) to optimal workspace size.
605*
606      WORK( 1 ) = LWMIN
607*
608      RETURN
609*
610*     End of SSYEVX_2STAGE
611*
612      END
613