LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dsyevx_2stage.f
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1 *> \brief <b> DSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY matrices</b>
2 *
3 * @precisions fortran d -> s
4 *
5 * =========== DOCUMENTATION ===========
6 *
7 * Online html documentation available at
8 * http://www.netlib.org/lapack/explore-html/
9 *
10 *> \htmlonly
11 *> Download DSYEVX_2STAGE + dependencies
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsyevx_2stage.f">
13 *> [TGZ]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsyevx_2stage.f">
15 *> [ZIP]</a>
16 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsyevx_2stage.f">
17 *> [TXT]</a>
18 *> \endhtmlonly
19 *
20 * Definition:
21 * ===========
22 *
23 * SUBROUTINE DSYEVX_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 * DOUBLE PRECISION ABSTOL, VL, VU
33 * ..
34 * .. Array Arguments ..
35 * INTEGER IFAIL( * ), IWORK( * )
36 * DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
37 * ..
38 *
39 *
40 *> \par Purpose:
41 * =============
42 *>
43 *> \verbatim
44 *>
45 *> DSYEVX_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 DOUBLE PRECISION 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 DOUBLE PRECISION
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 DOUBLE PRECISION
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 DOUBLE PRECISION
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*DLAMCH('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*DLAMCH('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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 *> \ingroup doubleSYeigen
263 *
264 *> \par Further Details:
265 * =====================
266 *>
267 *> \verbatim
268 *>
269 *> All details about the 2stage techniques are available in:
270 *>
271 *> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
272 *> Parallel reduction to condensed forms for symmetric eigenvalue problems
273 *> using aggregated fine-grained and memory-aware kernels. In Proceedings
274 *> of 2011 International Conference for High Performance Computing,
275 *> Networking, Storage and Analysis (SC '11), New York, NY, USA,
276 *> Article 8 , 11 pages.
277 *> http://doi.acm.org/10.1145/2063384.2063394
278 *>
279 *> A. Haidar, J. Kurzak, P. Luszczek, 2013.
280 *> An improved parallel singular value algorithm and its implementation
281 *> for multicore hardware, In Proceedings of 2013 International Conference
282 *> for High Performance Computing, Networking, Storage and Analysis (SC '13).
283 *> Denver, Colorado, USA, 2013.
284 *> Article 90, 12 pages.
285 *> http://doi.acm.org/10.1145/2503210.2503292
286 *>
287 *> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
288 *> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
289 *> calculations based on fine-grained memory aware tasks.
290 *> International Journal of High Performance Computing Applications.
291 *> Volume 28 Issue 2, Pages 196-209, May 2014.
292 *> http://hpc.sagepub.com/content/28/2/196
293 *>
294 *> \endverbatim
295 *
296 * =====================================================================
297  SUBROUTINE dsyevx_2stage( JOBZ, RANGE, UPLO, N, A, LDA, VL, VU,
298  $ IL, IU, ABSTOL, M, W, Z, LDZ, WORK,
299  $ LWORK, IWORK, IFAIL, INFO )
300 *
301  IMPLICIT NONE
302 *
303 * -- LAPACK driver routine --
304 * -- LAPACK is a software package provided by Univ. of Tennessee, --
305 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
306 *
307 * .. Scalar Arguments ..
308  CHARACTER JOBZ, RANGE, UPLO
309  INTEGER IL, INFO, IU, LDA, LDZ, LWORK, M, N
310  DOUBLE PRECISION ABSTOL, VL, VU
311 * ..
312 * .. Array Arguments ..
313  INTEGER IFAIL( * ), IWORK( * )
314  DOUBLE PRECISION A( LDA, * ), W( * ), WORK( * ), Z( LDZ, * )
315 * ..
316 *
317 * =====================================================================
318 *
319 * .. Parameters ..
320  DOUBLE PRECISION ZERO, ONE
321  PARAMETER ( ZERO = 0.0d+0, one = 1.0d+0 )
322 * ..
323 * .. Local Scalars ..
324  LOGICAL ALLEIG, INDEIG, LOWER, LQUERY, TEST, VALEIG,
325  $ WANTZ
326  CHARACTER ORDER
327  INTEGER I, IINFO, IMAX, INDD, INDE, INDEE, INDIBL,
328  $ indisp, indiwo, indtau, indwkn, indwrk, iscale,
329  $ itmp1, j, jj, llwork, llwrkn,
330  $ nsplit, lwmin, lhtrd, lwtrd, kd, ib, indhous
331  DOUBLE PRECISION ABSTLL, ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN,
332  $ SIGMA, SMLNUM, TMP1, VLL, VUU
333 * ..
334 * .. External Functions ..
335  LOGICAL LSAME
336  INTEGER ILAENV2STAGE
337  DOUBLE PRECISION DLAMCH, DLANSY
338  EXTERNAL lsame, dlamch, dlansy, ilaenv2stage
339 * ..
340 * .. External Subroutines ..
341  EXTERNAL dcopy, dlacpy, dorgtr, dormtr, dscal, dstebz,
343  $ dsytrd_2stage
344 * ..
345 * .. Intrinsic Functions ..
346  INTRINSIC max, min, sqrt
347 * ..
348 * .. Executable Statements ..
349 *
350 * Test the input parameters.
351 *
352  lower = lsame( uplo, 'L' )
353  wantz = lsame( jobz, 'V' )
354  alleig = lsame( range, 'A' )
355  valeig = lsame( range, 'V' )
356  indeig = lsame( range, 'I' )
357  lquery = ( lwork.EQ.-1 )
358 *
359  info = 0
360  IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
361  info = -1
362  ELSE IF( .NOT.( alleig .OR. valeig .OR. indeig ) ) THEN
363  info = -2
364  ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
365  info = -3
366  ELSE IF( n.LT.0 ) THEN
367  info = -4
368  ELSE IF( lda.LT.max( 1, n ) ) THEN
369  info = -6
370  ELSE
371  IF( valeig ) THEN
372  IF( n.GT.0 .AND. vu.LE.vl )
373  $ info = -8
374  ELSE IF( indeig ) THEN
375  IF( il.LT.1 .OR. il.GT.max( 1, n ) ) THEN
376  info = -9
377  ELSE IF( iu.LT.min( n, il ) .OR. iu.GT.n ) THEN
378  info = -10
379  END IF
380  END IF
381  END IF
382  IF( info.EQ.0 ) THEN
383  IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
384  info = -15
385  END IF
386  END IF
387 *
388  IF( info.EQ.0 ) THEN
389  IF( n.LE.1 ) THEN
390  lwmin = 1
391  work( 1 ) = lwmin
392  ELSE
393  kd = ilaenv2stage( 1, 'DSYTRD_2STAGE', jobz,
394  $ n, -1, -1, -1 )
395  ib = ilaenv2stage( 2, 'DSYTRD_2STAGE', jobz,
396  $ n, kd, -1, -1 )
397  lhtrd = ilaenv2stage( 3, 'DSYTRD_2STAGE', jobz,
398  $ n, kd, ib, -1 )
399  lwtrd = ilaenv2stage( 4, 'DSYTRD_2STAGE', jobz,
400  $ n, kd, ib, -1 )
401  lwmin = max( 8*n, 3*n + lhtrd + lwtrd )
402  work( 1 ) = lwmin
403  END IF
404 *
405  IF( lwork.LT.lwmin .AND. .NOT.lquery )
406  $ info = -17
407  END IF
408 *
409  IF( info.NE.0 ) THEN
410  CALL xerbla( 'DSYEVX_2STAGE', -info )
411  RETURN
412  ELSE IF( lquery ) THEN
413  RETURN
414  END IF
415 *
416 * Quick return if possible
417 *
418  m = 0
419  IF( n.EQ.0 ) THEN
420  RETURN
421  END IF
422 *
423  IF( n.EQ.1 ) THEN
424  IF( alleig .OR. indeig ) THEN
425  m = 1
426  w( 1 ) = a( 1, 1 )
427  ELSE
428  IF( vl.LT.a( 1, 1 ) .AND. vu.GE.a( 1, 1 ) ) THEN
429  m = 1
430  w( 1 ) = a( 1, 1 )
431  END IF
432  END IF
433  IF( wantz )
434  $ z( 1, 1 ) = one
435  RETURN
436  END IF
437 *
438 * Get machine constants.
439 *
440  safmin = dlamch( 'Safe minimum' )
441  eps = dlamch( 'Precision' )
442  smlnum = safmin / eps
443  bignum = one / smlnum
444  rmin = sqrt( smlnum )
445  rmax = min( sqrt( bignum ), one / sqrt( sqrt( safmin ) ) )
446 *
447 * Scale matrix to allowable range, if necessary.
448 *
449  iscale = 0
450  abstll = abstol
451  IF( valeig ) THEN
452  vll = vl
453  vuu = vu
454  END IF
455  anrm = dlansy( 'M', uplo, n, a, lda, work )
456  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
457  iscale = 1
458  sigma = rmin / anrm
459  ELSE IF( anrm.GT.rmax ) THEN
460  iscale = 1
461  sigma = rmax / anrm
462  END IF
463  IF( iscale.EQ.1 ) THEN
464  IF( lower ) THEN
465  DO 10 j = 1, n
466  CALL dscal( n-j+1, sigma, a( j, j ), 1 )
467  10 CONTINUE
468  ELSE
469  DO 20 j = 1, n
470  CALL dscal( j, sigma, a( 1, j ), 1 )
471  20 CONTINUE
472  END IF
473  IF( abstol.GT.0 )
474  $ abstll = abstol*sigma
475  IF( valeig ) THEN
476  vll = vl*sigma
477  vuu = vu*sigma
478  END IF
479  END IF
480 *
481 * Call DSYTRD_2STAGE to reduce symmetric matrix to tridiagonal form.
482 *
483  indtau = 1
484  inde = indtau + n
485  indd = inde + n
486  indhous = indd + n
487  indwrk = indhous + lhtrd
488  llwork = lwork - indwrk + 1
489 *
490  CALL dsytrd_2stage( jobz, uplo, n, a, lda, work( indd ),
491  $ work( inde ), work( indtau ), work( indhous ),
492  $ lhtrd, work( indwrk ), llwork, iinfo )
493 *
494 * If all eigenvalues are desired and ABSTOL is less than or equal to
495 * zero, then call DSTERF or DORGTR and SSTEQR. If this fails for
496 * some eigenvalue, then try DSTEBZ.
497 *
498  test = .false.
499  IF( indeig ) THEN
500  IF( il.EQ.1 .AND. iu.EQ.n ) THEN
501  test = .true.
502  END IF
503  END IF
504  IF( ( alleig .OR. test ) .AND. ( abstol.LE.zero ) ) THEN
505  CALL dcopy( n, work( indd ), 1, w, 1 )
506  indee = indwrk + 2*n
507  IF( .NOT.wantz ) THEN
508  CALL dcopy( n-1, work( inde ), 1, work( indee ), 1 )
509  CALL dsterf( n, w, work( indee ), info )
510  ELSE
511  CALL dlacpy( 'A', n, n, a, lda, z, ldz )
512  CALL dorgtr( uplo, n, z, ldz, work( indtau ),
513  $ work( indwrk ), llwork, iinfo )
514  CALL dcopy( n-1, work( inde ), 1, work( indee ), 1 )
515  CALL dsteqr( jobz, n, w, work( indee ), z, ldz,
516  $ work( indwrk ), info )
517  IF( info.EQ.0 ) THEN
518  DO 30 i = 1, n
519  ifail( i ) = 0
520  30 CONTINUE
521  END IF
522  END IF
523  IF( info.EQ.0 ) THEN
524  m = n
525  GO TO 40
526  END IF
527  info = 0
528  END IF
529 *
530 * Otherwise, call DSTEBZ and, if eigenvectors are desired, SSTEIN.
531 *
532  IF( wantz ) THEN
533  order = 'B'
534  ELSE
535  order = 'E'
536  END IF
537  indibl = 1
538  indisp = indibl + n
539  indiwo = indisp + n
540  CALL dstebz( range, order, n, vll, vuu, il, iu, abstll,
541  $ work( indd ), work( inde ), m, nsplit, w,
542  $ iwork( indibl ), iwork( indisp ), work( indwrk ),
543  $ iwork( indiwo ), info )
544 *
545  IF( wantz ) THEN
546  CALL dstein( n, work( indd ), work( inde ), m, w,
547  $ iwork( indibl ), iwork( indisp ), z, ldz,
548  $ work( indwrk ), iwork( indiwo ), ifail, info )
549 *
550 * Apply orthogonal matrix used in reduction to tridiagonal
551 * form to eigenvectors returned by DSTEIN.
552 *
553  indwkn = inde
554  llwrkn = lwork - indwkn + 1
555  CALL dormtr( 'L', uplo, 'N', n, m, a, lda, work( indtau ), z,
556  $ ldz, work( indwkn ), llwrkn, iinfo )
557  END IF
558 *
559 * If matrix was scaled, then rescale eigenvalues appropriately.
560 *
561  40 CONTINUE
562  IF( iscale.EQ.1 ) THEN
563  IF( info.EQ.0 ) THEN
564  imax = m
565  ELSE
566  imax = info - 1
567  END IF
568  CALL dscal( imax, one / sigma, w, 1 )
569  END IF
570 *
571 * If eigenvalues are not in order, then sort them, along with
572 * eigenvectors.
573 *
574  IF( wantz ) THEN
575  DO 60 j = 1, m - 1
576  i = 0
577  tmp1 = w( j )
578  DO 50 jj = j + 1, m
579  IF( w( jj ).LT.tmp1 ) THEN
580  i = jj
581  tmp1 = w( jj )
582  END IF
583  50 CONTINUE
584 *
585  IF( i.NE.0 ) THEN
586  itmp1 = iwork( indibl+i-1 )
587  w( i ) = w( j )
588  iwork( indibl+i-1 ) = iwork( indibl+j-1 )
589  w( j ) = tmp1
590  iwork( indibl+j-1 ) = itmp1
591  CALL dswap( n, z( 1, i ), 1, z( 1, j ), 1 )
592  IF( info.NE.0 ) THEN
593  itmp1 = ifail( i )
594  ifail( i ) = ifail( j )
595  ifail( j ) = itmp1
596  END IF
597  END IF
598  60 CONTINUE
599  END IF
600 *
601 * Set WORK(1) to optimal workspace size.
602 *
603  work( 1 ) = lwmin
604 *
605  RETURN
606 *
607 * End of DSYEVX_2STAGE
608 *
609  END
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 dstebz(RANGE, ORDER, N, VL, VU, IL, IU, ABSTOL, D, E, M, NSPLIT, W, IBLOCK, ISPLIT, WORK, IWORK, INFO)
DSTEBZ
Definition: dstebz.f:273
subroutine dsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR
Definition: dsteqr.f:131
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:86
subroutine dcopy(N, DX, INCX, DY, INCY)
DCOPY
Definition: dcopy.f:82
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
subroutine dswap(N, DX, INCX, DY, INCY)
DSWAP
Definition: dswap.f:82
subroutine dstein(N, D, E, M, W, IBLOCK, ISPLIT, Z, LDZ, WORK, IWORK, IFAIL, INFO)
DSTEIN
Definition: dstein.f:174
subroutine dormtr(SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
DORMTR
Definition: dormtr.f:171
subroutine dorgtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
DORGTR
Definition: dorgtr.f:123
subroutine dsytrd_2stage(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO)
DSYTRD_2STAGE
subroutine dsyevx_2stage(JOBZ, RANGE, UPLO, N, A, LDA, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, WORK, LWORK, IWORK, IFAIL, INFO)
DSYEVX_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for SY mat...