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,
342: $ DSTEIN, DSTEQR, DSTERF, DSWAP, XERBLA,
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
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