LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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chegv_2stage.f
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1*> \brief \b CHEGV_2STAGE
2*
3* @generated from zhegv_2stage.f, fortran z -> c, Sun Nov 6 13:09:52 2016
4*
5* =========== DOCUMENTATION ===========
6*
7* Online html documentation available at
8* http://www.netlib.org/lapack/explore-html/
9*
10*> \htmlonly
11*> Download CHEGV_2STAGE + dependencies
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chegv_2stage.f">
13*> [TGZ]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chegv_2stage.f">
15*> [ZIP]</a>
16*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chegv_2stage.f">
17*> [TXT]</a>
18*> \endhtmlonly
19*
20* Definition:
21* ===========
22*
23* SUBROUTINE CHEGV_2STAGE( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
24* WORK, LWORK, RWORK, INFO )
25*
26* IMPLICIT NONE
27*
28* .. Scalar Arguments ..
29* CHARACTER JOBZ, UPLO
30* INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
31* ..
32* .. Array Arguments ..
33* REAL RWORK( * ), W( * )
34* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
35* ..
36*
37*
38*> \par Purpose:
39* =============
40*>
41*> \verbatim
42*>
43*> CHEGV_2STAGE computes all the eigenvalues, and optionally, the eigenvectors
44*> of a complex generalized Hermitian-definite eigenproblem, of the form
45*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x.
46*> Here A and B are assumed to be Hermitian and B is also
47*> positive definite.
48*> This routine use the 2stage technique for the reduction to tridiagonal
49*> which showed higher performance on recent architecture and for large
50*> sizes N>2000.
51*> \endverbatim
52*
53* Arguments:
54* ==========
55*
56*> \param[in] ITYPE
57*> \verbatim
58*> ITYPE is INTEGER
59*> Specifies the problem type to be solved:
60*> = 1: A*x = (lambda)*B*x
61*> = 2: A*B*x = (lambda)*x
62*> = 3: B*A*x = (lambda)*x
63*> \endverbatim
64*>
65*> \param[in] JOBZ
66*> \verbatim
67*> JOBZ is CHARACTER*1
68*> = 'N': Compute eigenvalues only;
69*> = 'V': Compute eigenvalues and eigenvectors.
70*> Not available in this release.
71*> \endverbatim
72*>
73*> \param[in] UPLO
74*> \verbatim
75*> UPLO is CHARACTER*1
76*> = 'U': Upper triangles of A and B are stored;
77*> = 'L': Lower triangles of A and B are stored.
78*> \endverbatim
79*>
80*> \param[in] N
81*> \verbatim
82*> N is INTEGER
83*> The order of the matrices A and B. N >= 0.
84*> \endverbatim
85*>
86*> \param[in,out] A
87*> \verbatim
88*> A is COMPLEX array, dimension (LDA, N)
89*> On entry, the Hermitian matrix A. If UPLO = 'U', the
90*> leading N-by-N upper triangular part of A contains the
91*> upper triangular part of the matrix A. If UPLO = 'L',
92*> the leading N-by-N lower triangular part of A contains
93*> the lower triangular part of the matrix A.
94*>
95*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
96*> matrix Z of eigenvectors. The eigenvectors are normalized
97*> as follows:
98*> if ITYPE = 1 or 2, Z**H*B*Z = I;
99*> if ITYPE = 3, Z**H*inv(B)*Z = I.
100*> If JOBZ = 'N', then on exit the upper triangle (if UPLO='U')
101*> or the lower triangle (if UPLO='L') of A, including the
102*> diagonal, is destroyed.
103*> \endverbatim
104*>
105*> \param[in] LDA
106*> \verbatim
107*> LDA is INTEGER
108*> The leading dimension of the array A. LDA >= max(1,N).
109*> \endverbatim
110*>
111*> \param[in,out] B
112*> \verbatim
113*> B is COMPLEX array, dimension (LDB, N)
114*> On entry, the Hermitian positive definite matrix B.
115*> If UPLO = 'U', the leading N-by-N upper triangular part of B
116*> contains the upper triangular part of the matrix B.
117*> If UPLO = 'L', the leading N-by-N lower triangular part of B
118*> contains the lower triangular part of the matrix B.
119*>
120*> On exit, if INFO <= N, the part of B containing the matrix is
121*> overwritten by the triangular factor U or L from the Cholesky
122*> factorization B = U**H*U or B = L*L**H.
123*> \endverbatim
124*>
125*> \param[in] LDB
126*> \verbatim
127*> LDB is INTEGER
128*> The leading dimension of the array B. LDB >= max(1,N).
129*> \endverbatim
130*>
131*> \param[out] W
132*> \verbatim
133*> W is REAL array, dimension (N)
134*> If INFO = 0, the eigenvalues in ascending order.
135*> \endverbatim
136*>
137*> \param[out] WORK
138*> \verbatim
139*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
140*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
141*> \endverbatim
142*>
143*> \param[in] LWORK
144*> \verbatim
145*> LWORK is INTEGER
146*> The length of the array WORK. LWORK >= 1, when N <= 1;
147*> otherwise
148*> If JOBZ = 'N' and N > 1, LWORK must be queried.
149*> LWORK = MAX(1, dimension) where
150*> dimension = max(stage1,stage2) + (KD+1)*N + N
151*> = N*KD + N*max(KD+1,FACTOPTNB)
152*> + max(2*KD*KD, KD*NTHREADS)
153*> + (KD+1)*N + N
154*> where KD is the blocking size of the reduction,
155*> FACTOPTNB is the blocking used by the QR or LQ
156*> algorithm, usually FACTOPTNB=128 is a good choice
157*> NTHREADS is the number of threads used when
158*> openMP compilation is enabled, otherwise =1.
159*> If JOBZ = 'V' and N > 1, LWORK must be queried. Not yet available
160*>
161*> If LWORK = -1, then a workspace query is assumed; the routine
162*> only calculates the optimal size of the WORK array, returns
163*> this value as the first entry of the WORK array, and no error
164*> message related to LWORK is issued by XERBLA.
165*> \endverbatim
166*>
167*> \param[out] RWORK
168*> \verbatim
169*> RWORK is REAL array, dimension (max(1, 3*N-2))
170*> \endverbatim
171*>
172*> \param[out] INFO
173*> \verbatim
174*> INFO is INTEGER
175*> = 0: successful exit
176*> < 0: if INFO = -i, the i-th argument had an illegal value
177*> > 0: CPOTRF or CHEEV returned an error code:
178*> <= N: if INFO = i, CHEEV failed to converge;
179*> i off-diagonal elements of an intermediate
180*> tridiagonal form did not converge to zero;
181*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
182*> minor of order i of B is not positive definite.
183*> The factorization of B could not be completed and
184*> no eigenvalues or eigenvectors were computed.
185*> \endverbatim
186*
187* Authors:
188* ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup complexHEeigen
196*
197*> \par Further Details:
198* =====================
199*>
200*> \verbatim
201*>
202*> All details about the 2stage techniques are available in:
203*>
204*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
205*> Parallel reduction to condensed forms for symmetric eigenvalue problems
206*> using aggregated fine-grained and memory-aware kernels. In Proceedings
207*> of 2011 International Conference for High Performance Computing,
208*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
209*> Article 8 , 11 pages.
210*> http://doi.acm.org/10.1145/2063384.2063394
211*>
212*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
213*> An improved parallel singular value algorithm and its implementation
214*> for multicore hardware, In Proceedings of 2013 International Conference
215*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
216*> Denver, Colorado, USA, 2013.
217*> Article 90, 12 pages.
218*> http://doi.acm.org/10.1145/2503210.2503292
219*>
220*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
221*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
222*> calculations based on fine-grained memory aware tasks.
223*> International Journal of High Performance Computing Applications.
224*> Volume 28 Issue 2, Pages 196-209, May 2014.
225*> http://hpc.sagepub.com/content/28/2/196
226*>
227*> \endverbatim
228*
229* =====================================================================
230 SUBROUTINE chegv_2stage( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W,
231 $ WORK, LWORK, RWORK, INFO )
232*
233 IMPLICIT NONE
234*
235* -- LAPACK driver routine --
236* -- LAPACK is a software package provided by Univ. of Tennessee, --
237* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
238*
239* .. Scalar Arguments ..
240 CHARACTER JOBZ, UPLO
241 INTEGER INFO, ITYPE, LDA, LDB, LWORK, N
242* ..
243* .. Array Arguments ..
244 REAL RWORK( * ), W( * )
245 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
246* ..
247*
248* =====================================================================
249*
250* .. Parameters ..
251 COMPLEX ONE
252 parameter( one = ( 1.0e+0, 0.0e+0 ) )
253* ..
254* .. Local Scalars ..
255 LOGICAL LQUERY, UPPER, WANTZ
256 CHARACTER TRANS
257 INTEGER NEIG, LWMIN, LHTRD, LWTRD, KD, IB
258* ..
259* .. External Functions ..
260 LOGICAL LSAME
261 INTEGER ILAENV2STAGE
262 EXTERNAL lsame, ilaenv2stage
263* ..
264* .. External Subroutines ..
265 EXTERNAL xerbla, chegst, cpotrf, ctrmm, ctrsm,
267* ..
268* .. Intrinsic Functions ..
269 INTRINSIC max
270* ..
271* .. Executable Statements ..
272*
273* Test the input parameters.
274*
275 wantz = lsame( jobz, 'V' )
276 upper = lsame( uplo, 'U' )
277 lquery = ( lwork.EQ.-1 )
278*
279 info = 0
280 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
281 info = -1
282 ELSE IF( .NOT.( lsame( jobz, 'N' ) ) ) THEN
283 info = -2
284 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
285 info = -3
286 ELSE IF( n.LT.0 ) THEN
287 info = -4
288 ELSE IF( lda.LT.max( 1, n ) ) THEN
289 info = -6
290 ELSE IF( ldb.LT.max( 1, n ) ) THEN
291 info = -8
292 END IF
293*
294 IF( info.EQ.0 ) THEN
295 kd = ilaenv2stage( 1, 'CHETRD_2STAGE', jobz, n, -1, -1, -1 )
296 ib = ilaenv2stage( 2, 'CHETRD_2STAGE', jobz, n, kd, -1, -1 )
297 lhtrd = ilaenv2stage( 3, 'CHETRD_2STAGE', jobz, n, kd, ib, -1 )
298 lwtrd = ilaenv2stage( 4, 'CHETRD_2STAGE', jobz, n, kd, ib, -1 )
299 lwmin = n + lhtrd + lwtrd
300 work( 1 ) = lwmin
301*
302 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
303 info = -11
304 END IF
305 END IF
306*
307 IF( info.NE.0 ) THEN
308 CALL xerbla( 'CHEGV_2STAGE ', -info )
309 RETURN
310 ELSE IF( lquery ) THEN
311 RETURN
312 END IF
313*
314* Quick return if possible
315*
316 IF( n.EQ.0 )
317 $ RETURN
318*
319* Form a Cholesky factorization of B.
320*
321 CALL cpotrf( uplo, n, b, ldb, info )
322 IF( info.NE.0 ) THEN
323 info = n + info
324 RETURN
325 END IF
326*
327* Transform problem to standard eigenvalue problem and solve.
328*
329 CALL chegst( itype, uplo, n, a, lda, b, ldb, info )
330 CALL cheev_2stage( jobz, uplo, n, a, lda, w,
331 $ work, lwork, rwork, info )
332*
333 IF( wantz ) THEN
334*
335* Backtransform eigenvectors to the original problem.
336*
337 neig = n
338 IF( info.GT.0 )
339 $ neig = info - 1
340 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
341*
342* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
343* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
344*
345 IF( upper ) THEN
346 trans = 'N'
347 ELSE
348 trans = 'C'
349 END IF
350*
351 CALL ctrsm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
352 $ b, ldb, a, lda )
353*
354 ELSE IF( itype.EQ.3 ) THEN
355*
356* For B*A*x=(lambda)*x;
357* backtransform eigenvectors: x = L*y or U**H *y
358*
359 IF( upper ) THEN
360 trans = 'C'
361 ELSE
362 trans = 'N'
363 END IF
364*
365 CALL ctrmm( 'Left', uplo, trans, 'Non-unit', n, neig, one,
366 $ b, ldb, a, lda )
367 END IF
368 END IF
369*
370 work( 1 ) = lwmin
371*
372 RETURN
373*
374* End of CHEGV_2STAGE
375*
376 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ctrmm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRMM
Definition: ctrmm.f:177
subroutine ctrsm(SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, LDA, B, LDB)
CTRSM
Definition: ctrsm.f:180
subroutine chegst(ITYPE, UPLO, N, A, LDA, B, LDB, INFO)
CHEGST
Definition: chegst.f:128
subroutine chegv_2stage(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, INFO)
CHEGV_2STAGE
Definition: chegv_2stage.f:232
subroutine cheev_2stage(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)
CHEEV_2STAGE computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matr...
Definition: cheev_2stage.f:189
subroutine cpotrf(UPLO, N, A, LDA, INFO)
CPOTRF
Definition: cpotrf.f:107