LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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chbev_2stage.f
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1*> \brief <b> CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2*
3* @generated from zhbev_2stage.f, fortran z -> c, Sat Nov 5 23:18:20 2016
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download CHBEV_2STAGE + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chbev_2stage.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chbev_2stage.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chbev_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE CHBEV_2STAGE( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
24* WORK, LWORK, RWORK, INFO )
25*
26* IMPLICIT NONE
27*
28* .. Scalar Arguments ..
29* CHARACTER JOBZ, UPLO
30* INTEGER INFO, KD, LDAB, LDZ, N, LWORK
31* ..
32* .. Array Arguments ..
33* REAL RWORK( * ), W( * )
34* COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
35* ..
36*
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> CHBEV_2STAGE computes all the eigenvalues and, optionally, eigenvectors of
44*> a complex Hermitian band matrix A using the 2stage technique for
45*> the reduction to tridiagonal.
46*> \endverbatim
47*
48* Arguments:
49* ==========
50*
51*> \param[in] JOBZ
52*> \verbatim
53*> JOBZ is CHARACTER*1
54*> = 'N': Compute eigenvalues only;
55*> = 'V': Compute eigenvalues and eigenvectors.
56*> Not available in this release.
57*> \endverbatim
58*>
59*> \param[in] UPLO
60*> \verbatim
61*> UPLO is CHARACTER*1
62*> = 'U': Upper triangle of A is stored;
63*> = 'L': Lower triangle of A is stored.
64*> \endverbatim
65*>
66*> \param[in] N
67*> \verbatim
68*> N is INTEGER
69*> The order of the matrix A. N >= 0.
70*> \endverbatim
71*>
72*> \param[in] KD
73*> \verbatim
74*> KD is INTEGER
75*> The number of superdiagonals of the matrix A if UPLO = 'U',
76*> or the number of subdiagonals if UPLO = 'L'. KD >= 0.
77*> \endverbatim
78*>
79*> \param[in,out] AB
80*> \verbatim
81*> AB is COMPLEX array, dimension (LDAB, N)
82*> On entry, the upper or lower triangle of the Hermitian band
83*> matrix A, stored in the first KD+1 rows of the array. The
84*> j-th column of A is stored in the j-th column of the array AB
85*> as follows:
86*> if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
87*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd).
88*>
89*> On exit, AB is overwritten by values generated during the
90*> reduction to tridiagonal form. If UPLO = 'U', the first
91*> superdiagonal and the diagonal of the tridiagonal matrix T
92*> are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
93*> the diagonal and first subdiagonal of T are returned in the
94*> first two rows of AB.
95*> \endverbatim
96*>
97*> \param[in] LDAB
98*> \verbatim
99*> LDAB is INTEGER
100*> The leading dimension of the array AB. LDAB >= KD + 1.
101*> \endverbatim
102*>
103*> \param[out] W
104*> \verbatim
105*> W is REAL array, dimension (N)
106*> If INFO = 0, the eigenvalues in ascending order.
107*> \endverbatim
108*>
109*> \param[out] Z
110*> \verbatim
111*> Z is COMPLEX array, dimension (LDZ, N)
112*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
113*> eigenvectors of the matrix A, with the i-th column of Z
114*> holding the eigenvector associated with W(i).
115*> If JOBZ = 'N', then Z is not referenced.
116*> \endverbatim
117*>
118*> \param[in] LDZ
119*> \verbatim
120*> LDZ is INTEGER
121*> The leading dimension of the array Z. LDZ >= 1, and if
122*> JOBZ = 'V', LDZ >= max(1,N).
123*> \endverbatim
124*>
125*> \param[out] WORK
126*> \verbatim
127*> WORK is COMPLEX array, dimension LWORK
128*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
129*> \endverbatim
130*>
131*> \param[in] LWORK
132*> \verbatim
133*> LWORK is INTEGER
134*> The length of the array WORK. LWORK >= 1, when N <= 1;
135*> otherwise
136*> If JOBZ = 'N' and N > 1, LWORK must be queried.
137*> LWORK = MAX(1, dimension) where
138*> dimension = (2KD+1)*N + KD*NTHREADS
139*> where KD is the size of the band.
140*> NTHREADS is the number of threads used when
141*> openMP compilation is enabled, otherwise =1.
142*> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available.
143*>
144*> If LWORK = -1, then a workspace query is assumed; the routine
145*> only calculates the optimal sizes of the WORK, RWORK and
146*> IWORK arrays, returns these values as the first entries of
147*> the WORK, RWORK and IWORK arrays, and no error message
148*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
149*> \endverbatim
150*>
151*> \param[out] RWORK
152*> \verbatim
153*> RWORK is REAL array, dimension (max(1,3*N-2))
154*> \endverbatim
155*>
156*> \param[out] INFO
157*> \verbatim
158*> INFO is INTEGER
159*> = 0: successful exit.
160*> < 0: if INFO = -i, the i-th argument had an illegal value.
161*> > 0: if INFO = i, the algorithm failed to converge; i
162*> off-diagonal elements of an intermediate tridiagonal
163*> form did not converge to zero.
164*> \endverbatim
165*
166* Authors:
167* ========
168*
169*> \author Univ. of Tennessee
170*> \author Univ. of California Berkeley
171*> \author Univ. of Colorado Denver
172*> \author NAG Ltd.
173*
174*> \ingroup complexOTHEReigen
175*
176*> \par Further Details:
177* =====================
178*>
179*> \verbatim
180*>
181*> All details about the 2stage techniques are available in:
182*>
183*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
184*> Parallel reduction to condensed forms for symmetric eigenvalue problems
185*> using aggregated fine-grained and memory-aware kernels. In Proceedings
186*> of 2011 International Conference for High Performance Computing,
187*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
188*> Article 8 , 11 pages.
189*> http://doi.acm.org/10.1145/2063384.2063394
190*>
191*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
192*> An improved parallel singular value algorithm and its implementation
193*> for multicore hardware, In Proceedings of 2013 International Conference
194*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
195*> Denver, Colorado, USA, 2013.
196*> Article 90, 12 pages.
197*> http://doi.acm.org/10.1145/2503210.2503292
198*>
199*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
200*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
201*> calculations based on fine-grained memory aware tasks.
202*> International Journal of High Performance Computing Applications.
203*> Volume 28 Issue 2, Pages 196-209, May 2014.
204*> http://hpc.sagepub.com/content/28/2/196
205*>
206*> \endverbatim
207*
208* =====================================================================
209 SUBROUTINE chbev_2stage( JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ,
210 $ WORK, LWORK, RWORK, INFO )
211*
212 IMPLICIT NONE
213*
214* -- LAPACK driver routine --
215* -- LAPACK is a software package provided by Univ. of Tennessee, --
216* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
217*
218* .. Scalar Arguments ..
219 CHARACTER JOBZ, UPLO
220 INTEGER INFO, KD, LDAB, LDZ, N, LWORK
221* ..
222* .. Array Arguments ..
223 REAL RWORK( * ), W( * )
224 COMPLEX AB( LDAB, * ), WORK( * ), Z( LDZ, * )
225* ..
226*
227* =====================================================================
228*
229* .. Parameters ..
230 REAL ZERO, ONE
231 parameter( zero = 0.0e0, one = 1.0e0 )
232* ..
233* .. Local Scalars ..
234 LOGICAL LOWER, WANTZ, LQUERY
235 INTEGER IINFO, IMAX, INDE, INDWRK, INDRWK, ISCALE,
236 $ llwork, lwmin, lhtrd, lwtrd, ib, indhous
237 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
238 $ smlnum
239* ..
240* .. External Functions ..
241 LOGICAL LSAME
242 INTEGER ILAENV2STAGE
243 REAL SLAMCH, CLANHB
244 EXTERNAL lsame, slamch, clanhb, ilaenv2stage
245* ..
246* .. External Subroutines ..
247 EXTERNAL sscal, ssterf, xerbla, clascl, csteqr,
248 $ chetrd_2stage, chetrd_hb2st
249* ..
250* .. Intrinsic Functions ..
251 INTRINSIC real, sqrt
252* ..
253* .. Executable Statements ..
254*
255* Test the input parameters.
256*
257 wantz = lsame( jobz, 'V' )
258 lower = lsame( uplo, 'L' )
259 lquery = ( lwork.EQ.-1 )
260*
261 info = 0
262 IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
263 info = -1
264 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
265 info = -2
266 ELSE IF( n.LT.0 ) THEN
267 info = -3
268 ELSE IF( kd.LT.0 ) THEN
269 info = -4
270 ELSE IF( ldab.LT.kd+1 ) THEN
271 info = -6
272 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
273 info = -9
274 END IF
275*
276 IF( info.EQ.0 ) THEN
277 IF( n.LE.1 ) THEN
278 lwmin = 1
279 work( 1 ) = lwmin
280 ELSE
281 ib = ilaenv2stage( 2, 'CHETRD_HB2ST', jobz,
282 $ n, kd, -1, -1 )
283 lhtrd = ilaenv2stage( 3, 'CHETRD_HB2ST', jobz,
284 $ n, kd, ib, -1 )
285 lwtrd = ilaenv2stage( 4, 'CHETRD_HB2ST', jobz,
286 $ n, kd, ib, -1 )
287 lwmin = lhtrd + lwtrd
288 work( 1 ) = lwmin
289 ENDIF
290*
291 IF( lwork.LT.lwmin .AND. .NOT.lquery )
292 $ info = -11
293 END IF
294*
295 IF( info.NE.0 ) THEN
296 CALL xerbla( 'CHBEV_2STAGE ', -info )
297 RETURN
298 ELSE IF( lquery ) THEN
299 RETURN
300 END IF
301*
302* Quick return if possible
303*
304 IF( n.EQ.0 )
305 $ RETURN
306*
307 IF( n.EQ.1 ) THEN
308 IF( lower ) THEN
309 w( 1 ) = real( ab( 1, 1 ) )
310 ELSE
311 w( 1 ) = real( ab( kd+1, 1 ) )
312 END IF
313 IF( wantz )
314 $ z( 1, 1 ) = one
315 RETURN
316 END IF
317*
318* Get machine constants.
319*
320 safmin = slamch( 'Safe minimum' )
321 eps = slamch( 'Precision' )
322 smlnum = safmin / eps
323 bignum = one / smlnum
324 rmin = sqrt( smlnum )
325 rmax = sqrt( bignum )
326*
327* Scale matrix to allowable range, if necessary.
328*
329 anrm = clanhb( 'M', uplo, n, kd, ab, ldab, rwork )
330 iscale = 0
331 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
332 iscale = 1
333 sigma = rmin / anrm
334 ELSE IF( anrm.GT.rmax ) THEN
335 iscale = 1
336 sigma = rmax / anrm
337 END IF
338 IF( iscale.EQ.1 ) THEN
339 IF( lower ) THEN
340 CALL clascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
341 ELSE
342 CALL clascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
343 END IF
344 END IF
345*
346* Call CHBTRD_HB2ST to reduce Hermitian band matrix to tridiagonal form.
347*
348 inde = 1
349 indhous = 1
350 indwrk = indhous + lhtrd
351 llwork = lwork - indwrk + 1
352*
353 CALL chetrd_hb2st( "N", jobz, uplo, n, kd, ab, ldab, w,
354 $ rwork( inde ), work( indhous ), lhtrd,
355 $ work( indwrk ), llwork, iinfo )
356*
357* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR.
358*
359 IF( .NOT.wantz ) THEN
360 CALL ssterf( n, w, rwork( inde ), info )
361 ELSE
362 indrwk = inde + n
363 CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
364 $ rwork( indrwk ), info )
365 END IF
366*
367* If matrix was scaled, then rescale eigenvalues appropriately.
368*
369 IF( iscale.EQ.1 ) THEN
370 IF( info.EQ.0 ) THEN
371 imax = n
372 ELSE
373 imax = info - 1
374 END IF
375 CALL sscal( imax, one / sigma, w, 1 )
376 END IF
377*
378* Set WORK(1) to optimal workspace size.
379*
380 work( 1 ) = lwmin
381*
382 RETURN
383*
384* End of CHBEV_2STAGE
385*
386 END
xerbla
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
ssterf
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
chetrd_2stage
subroutine chetrd_2stage(VECT, UPLO, N, A, LDA, D, E, TAU, HOUS2, LHOUS2, WORK, LWORK, INFO)
CHETRD_2STAGE
Definition: chetrd_2stage.f:224
clascl
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
chetrd_hb2st
subroutine chetrd_hb2st(STAGE1, VECT, UPLO, N, KD, AB, LDAB, D, E, HOUS, LHOUS, WORK, LWORK, INFO)
CHETRD_HB2ST reduces a complex Hermitian band matrix A to real symmetric tridiagonal form T
Definition: chetrd_hb2st.F:230
csteqr
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
chbev_2stage
subroutine chbev_2stage(JOBZ, UPLO, N, KD, AB, LDAB, W, Z, LDZ, WORK, LWORK, RWORK, INFO)
CHBEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER m...
Definition: chbev_2stage.f:211
sscal
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79