LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
cheevd_2stage.f
Go to the documentation of this file.
1*> \brief <b> CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
2*
3* @generated from zheevd_2stage.f, fortran z -> c, Sat Nov 5 23:18:14 2016
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download CHEEVD_2STAGE + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheevd_2stage.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheevd_2stage.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheevd_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE CHEEVD_2STAGE( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
24* RWORK, LRWORK, IWORK, LIWORK, INFO )
25*
26* IMPLICIT NONE
27*
28* .. Scalar Arguments ..
29* CHARACTER JOBZ, UPLO
30* INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
31* ..
32* .. Array Arguments ..
33* INTEGER IWORK( * )
34* REAL RWORK( * ), W( * )
35* COMPLEX A( LDA, * ), WORK( * )
36* ..
37*
38*
39*> \par Purpose:
40* =============
41*>
42*> \verbatim
43*>
44*> CHEEVD_2STAGE computes all eigenvalues and, optionally, eigenvectors of a
45*> complex Hermitian matrix A using the 2stage technique for
46*> the reduction to tridiagonal. If eigenvectors are desired, it uses a
47*> divide and conquer algorithm.
48*>
49*> The divide and conquer algorithm makes very mild assumptions about
50*> floating point arithmetic. It will work on machines with a guard
51*> digit in add/subtract, or on those binary machines without guard
52*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
53*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
54*> without guard digits, but we know of none.
55*> \endverbatim
56*
57* Arguments:
58* ==========
59*
60*> \param[in] JOBZ
61*> \verbatim
62*> JOBZ is CHARACTER*1
63*> = 'N': Compute eigenvalues only;
64*> = 'V': Compute eigenvalues and eigenvectors.
65*> Not available in this release.
66*> \endverbatim
67*>
68*> \param[in] UPLO
69*> \verbatim
70*> UPLO is CHARACTER*1
71*> = 'U': Upper triangle of A is stored;
72*> = 'L': Lower triangle of A is stored.
73*> \endverbatim
74*>
75*> \param[in] N
76*> \verbatim
77*> N is INTEGER
78*> The order of the matrix A. N >= 0.
79*> \endverbatim
80*>
81*> \param[in,out] A
82*> \verbatim
83*> A is COMPLEX array, dimension (LDA, N)
84*> On entry, the Hermitian matrix A. If UPLO = 'U', the
85*> leading N-by-N upper triangular part of A contains the
86*> upper triangular part of the matrix A. If UPLO = 'L',
87*> the leading N-by-N lower triangular part of A contains
88*> the lower triangular part of the matrix A.
89*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
90*> orthonormal eigenvectors of the matrix A.
91*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
92*> or the upper triangle (if UPLO='U') of A, including the
93*> diagonal, is destroyed.
94*> \endverbatim
95*>
96*> \param[in] LDA
97*> \verbatim
98*> LDA is INTEGER
99*> The leading dimension of the array A. LDA >= max(1,N).
100*> \endverbatim
101*>
102*> \param[out] W
103*> \verbatim
104*> W is REAL array, dimension (N)
105*> If INFO = 0, the eigenvalues in ascending order.
106*> \endverbatim
107*>
108*> \param[out] WORK
109*> \verbatim
110*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
111*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
112*> \endverbatim
113*>
114*> \param[in] LWORK
115*> \verbatim
116*> LWORK is INTEGER
117*> The dimension of the array WORK.
118*> If N <= 1, LWORK must be at least 1.
119*> If JOBZ = 'N' and N > 1, LWORK must be queried.
120*> LWORK = MAX(1, dimension) where
121*> dimension = max(stage1,stage2) + (KD+1)*N + N+1
122*> = N*KD + N*max(KD+1,FACTOPTNB)
123*> + max(2*KD*KD, KD*NTHREADS)
124*> + (KD+1)*N + N+1
125*> where KD is the blocking size of the reduction,
126*> FACTOPTNB is the blocking used by the QR or LQ
127*> algorithm, usually FACTOPTNB=128 is a good choice
128*> NTHREADS is the number of threads used when
129*> openMP compilation is enabled, otherwise =1.
130*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N + N**2
131*>
132*> If LWORK = -1, then a workspace query is assumed; the routine
133*> only calculates the optimal sizes of the WORK, RWORK and
134*> IWORK arrays, returns these values as the first entries of
135*> the WORK, RWORK and IWORK arrays, and no error message
136*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
137*> \endverbatim
138*>
139*> \param[out] RWORK
140*> \verbatim
141*> RWORK is REAL array,
142*> dimension (LRWORK)
143*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
144*> \endverbatim
145*>
146*> \param[in] LRWORK
147*> \verbatim
148*> LRWORK is INTEGER
149*> The dimension of the array RWORK.
150*> If N <= 1, LRWORK must be at least 1.
151*> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
152*> If JOBZ = 'V' and N > 1, LRWORK must be at least
153*> 1 + 5*N + 2*N**2.
154*>
155*> If LRWORK = -1, then a workspace query is assumed; the
156*> routine only calculates the optimal sizes of the WORK, RWORK
157*> and IWORK arrays, returns these values as the first entries
158*> of the WORK, RWORK and IWORK arrays, and no error message
159*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
160*> \endverbatim
161*>
162*> \param[out] IWORK
163*> \verbatim
164*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
165*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
166*> \endverbatim
167*>
168*> \param[in] LIWORK
169*> \verbatim
170*> LIWORK is INTEGER
171*> The dimension of the array IWORK.
172*> If N <= 1, LIWORK must be at least 1.
173*> If JOBZ = 'N' and N > 1, LIWORK must be at least 1.
174*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
175*>
176*> If LIWORK = -1, then a workspace query is assumed; the
177*> routine only calculates the optimal sizes of the WORK, RWORK
178*> and IWORK arrays, returns these values as the first entries
179*> of the WORK, RWORK and IWORK arrays, and no error message
180*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
181*> \endverbatim
182*>
183*> \param[out] INFO
184*> \verbatim
185*> INFO is INTEGER
186*> = 0: successful exit
187*> < 0: if INFO = -i, the i-th argument had an illegal value
188*> > 0: if INFO = i and JOBZ = 'N', then the algorithm failed
189*> to converge; i off-diagonal elements of an intermediate
190*> tridiagonal form did not converge to zero;
191*> if INFO = i and JOBZ = 'V', then the algorithm failed
192*> to compute an eigenvalue while working on the submatrix
193*> lying in rows and columns INFO/(N+1) through
194*> mod(INFO,N+1).
195*> \endverbatim
196*
197* Authors:
198* ========
199*
200*> \author Univ. of Tennessee
201*> \author Univ. of California Berkeley
202*> \author Univ. of Colorado Denver
203*> \author NAG Ltd.
204*
205*> \ingroup complexHEeigen
206*
207*> \par Further Details:
208* =====================
209*>
210*> Modified description of INFO. Sven, 16 Feb 05.
211*
212*> \par Contributors:
213* ==================
214*>
215*> Jeff Rutter, Computer Science Division, University of California
216*> at Berkeley, USA
217*>
218*> \par Further Details:
219* =====================
220*>
221*> \verbatim
222*>
223*> All details about the 2stage techniques are available in:
224*>
225*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
226*> Parallel reduction to condensed forms for symmetric eigenvalue problems
227*> using aggregated fine-grained and memory-aware kernels. In Proceedings
228*> of 2011 International Conference for High Performance Computing,
229*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
230*> Article 8 , 11 pages.
231*> http://doi.acm.org/10.1145/2063384.2063394
232*>
233*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
234*> An improved parallel singular value algorithm and its implementation
235*> for multicore hardware, In Proceedings of 2013 International Conference
236*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
237*> Denver, Colorado, USA, 2013.
238*> Article 90, 12 pages.
239*> http://doi.acm.org/10.1145/2503210.2503292
240*>
241*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
242*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
243*> calculations based on fine-grained memory aware tasks.
244*> International Journal of High Performance Computing Applications.
245*> Volume 28 Issue 2, Pages 196-209, May 2014.
246*> http://hpc.sagepub.com/content/28/2/196
247*>
248*> \endverbatim
249*
250* =====================================================================
251 SUBROUTINE cheevd_2stage( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK,
252 $ RWORK, LRWORK, IWORK, LIWORK, INFO )
253*
254 IMPLICIT NONE
255*
256* -- LAPACK driver routine --
257* -- LAPACK is a software package provided by Univ. of Tennessee, --
258* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
259*
260* .. Scalar Arguments ..
261 CHARACTER JOBZ, UPLO
262 INTEGER INFO, LDA, LIWORK, LRWORK, LWORK, N
263* ..
264* .. Array Arguments ..
265 INTEGER IWORK( * )
266 REAL RWORK( * ), W( * )
267 COMPLEX A( LDA, * ), WORK( * )
268* ..
269*
270* =====================================================================
271*
272* .. Parameters ..
273 REAL ZERO, ONE
274 parameter( zero = 0.0e0, one = 1.0e0 )
275 COMPLEX CONE
276 parameter( cone = ( 1.0e0, 0.0e0 ) )
277* ..
278* .. Local Scalars ..
279 LOGICAL LOWER, LQUERY, WANTZ
280 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWK2,
281 $ indwrk, iscale, liwmin, llrwk, llwork,
282 $ llwrk2, lrwmin, lwmin,
283 $ lhtrd, lwtrd, kd, ib, indhous
284
285
286 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
287 $ smlnum
288* ..
289* .. External Functions ..
290 LOGICAL LSAME
291 INTEGER ILAENV2STAGE
292 REAL SLAMCH, CLANHE
293 EXTERNAL lsame, slamch, clanhe, ilaenv2stage
294* ..
295* .. External Subroutines ..
296 EXTERNAL sscal, ssterf, xerbla, clacpy, clascl,
298* ..
299* .. Intrinsic Functions ..
300 INTRINSIC real, max, sqrt
301* ..
302* .. Executable Statements ..
303*
304* Test the input parameters.
305*
306 wantz = lsame( jobz, 'V' )
307 lower = lsame( uplo, 'L' )
308 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
309*
310 info = 0
311 IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
312 info = -1
313 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
314 info = -2
315 ELSE IF( n.LT.0 ) THEN
316 info = -3
317 ELSE IF( lda.LT.max( 1, n ) ) THEN
318 info = -5
319 END IF
320*
321 IF( info.EQ.0 ) THEN
322 IF( n.LE.1 ) THEN
323 lwmin = 1
324 lrwmin = 1
325 liwmin = 1
326 ELSE
327 kd = ilaenv2stage( 1, 'CHETRD_2STAGE', jobz,
328 $ n, -1, -1, -1 )
329 ib = ilaenv2stage( 2, 'CHETRD_2STAGE', jobz,
330 $ n, kd, -1, -1 )
331 lhtrd = ilaenv2stage( 3, 'CHETRD_2STAGE', jobz,
332 $ n, kd, ib, -1 )
333 lwtrd = ilaenv2stage( 4, 'CHETRD_2STAGE', jobz,
334 $ n, kd, ib, -1 )
335 IF( wantz ) THEN
336 lwmin = 2*n + n*n
337 lrwmin = 1 + 5*n + 2*n**2
338 liwmin = 3 + 5*n
339 ELSE
340 lwmin = n + 1 + lhtrd + lwtrd
341 lrwmin = n
342 liwmin = 1
343 END IF
344 END IF
345 work( 1 ) = lwmin
346 rwork( 1 ) = lrwmin
347 iwork( 1 ) = liwmin
348*
349 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
350 info = -8
351 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
352 info = -10
353 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
354 info = -12
355 END IF
356 END IF
357*
358 IF( info.NE.0 ) THEN
359 CALL xerbla( 'CHEEVD_2STAGE', -info )
360 RETURN
361 ELSE IF( lquery ) THEN
362 RETURN
363 END IF
364*
365* Quick return if possible
366*
367 IF( n.EQ.0 )
368 $ RETURN
369*
370 IF( n.EQ.1 ) THEN
371 w( 1 ) = real( a( 1, 1 ) )
372 IF( wantz )
373 $ a( 1, 1 ) = cone
374 RETURN
375 END IF
376*
377* Get machine constants.
378*
379 safmin = slamch( 'Safe minimum' )
380 eps = slamch( 'Precision' )
381 smlnum = safmin / eps
382 bignum = one / smlnum
383 rmin = sqrt( smlnum )
384 rmax = sqrt( bignum )
385*
386* Scale matrix to allowable range, if necessary.
387*
388 anrm = clanhe( 'M', uplo, n, a, lda, rwork )
389 iscale = 0
390 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
391 iscale = 1
392 sigma = rmin / anrm
393 ELSE IF( anrm.GT.rmax ) THEN
394 iscale = 1
395 sigma = rmax / anrm
396 END IF
397 IF( iscale.EQ.1 )
398 $ CALL clascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
399*
400* Call CHETRD_2STAGE to reduce Hermitian matrix to tridiagonal form.
401*
402 inde = 1
403 indrwk = inde + n
404 llrwk = lrwork - indrwk + 1
405 indtau = 1
406 indhous = indtau + n
407 indwrk = indhous + lhtrd
408 llwork = lwork - indwrk + 1
409 indwk2 = indwrk + n*n
410 llwrk2 = lwork - indwk2 + 1
411*
412 CALL chetrd_2stage( jobz, uplo, n, a, lda, w, rwork( inde ),
413 $ work( indtau ), work( indhous ), lhtrd,
414 $ work( indwrk ), llwork, iinfo )
415*
416* For eigenvalues only, call SSTERF. For eigenvectors, first call
417* CSTEDC to generate the eigenvector matrix, WORK(INDWRK), of the
418* tridiagonal matrix, then call CUNMTR to multiply it to the
419* Householder transformations represented as Householder vectors in
420* A.
421*
422 IF( .NOT.wantz ) THEN
423 CALL ssterf( n, w, rwork( inde ), info )
424 ELSE
425 CALL cstedc( 'I', n, w, rwork( inde ), work( indwrk ), n,
426 $ work( indwk2 ), llwrk2, rwork( indrwk ), llrwk,
427 $ iwork, liwork, info )
428 CALL cunmtr( 'L', uplo, 'N', n, n, a, lda, work( indtau ),
429 $ work( indwrk ), n, work( indwk2 ), llwrk2, iinfo )
430 CALL clacpy( 'A', n, n, work( indwrk ), n, a, lda )
431 END IF
432*
433* If matrix was scaled, then rescale eigenvalues appropriately.
434*
435 IF( iscale.EQ.1 ) THEN
436 IF( info.EQ.0 ) THEN
437 imax = n
438 ELSE
439 imax = info - 1
440 END IF
441 CALL sscal( imax, one / sigma, w, 1 )
442 END IF
443*
444 work( 1 ) = lwmin
445 rwork( 1 ) = lrwmin
446 iwork( 1 ) = liwmin
447*
448 RETURN
449*
450* End of CHEEVD_2STAGE
451*
452 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine chetrd_2stage(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO)
CHETRD_2STAGE
subroutine cheevd_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHEEVD_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE mat...
subroutine clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:143
subroutine clacpy(UPLO, M, N, A, LDA, B, LDB)
CLACPY copies all or part of one two-dimensional array to another.
Definition: clacpy.f:103
subroutine cunmtr(SIDE, UPLO, TRANS, M, N, A, LDA, TAU, C, LDC, WORK, LWORK, INFO)
CUNMTR
Definition: cunmtr.f:172
subroutine cstedc(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CSTEDC
Definition: cstedc.f:212
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79