LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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chegvd.f
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1*> \brief \b CHEGVD
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/chegvd.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/chegvd.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chegvd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHEGVD( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
22* LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
27* ..
28* .. Array Arguments ..
29* INTEGER IWORK( * )
30* REAL RWORK( * ), W( * )
31* COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> CHEGVD computes all the eigenvalues, and optionally, the eigenvectors
41*> of a complex generalized Hermitian-definite eigenproblem, of the form
42*> A*x=(lambda)*B*x, A*Bx=(lambda)*x, or B*A*x=(lambda)*x. Here A and
43*> B are assumed to be Hermitian and B is also positive definite.
44*> If eigenvectors are desired, it uses a divide and conquer algorithm.
45*>
46*> The divide and conquer algorithm makes very mild assumptions about
47*> floating point arithmetic. It will work on machines with a guard
48*> digit in add/subtract, or on those binary machines without guard
49*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
50*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
51*> without guard digits, but we know of none.
52*> \endverbatim
53*
54* Arguments:
55* ==========
56*
57*> \param[in] ITYPE
58*> \verbatim
59*> ITYPE is INTEGER
60*> Specifies the problem type to be solved:
61*> = 1: A*x = (lambda)*B*x
62*> = 2: A*B*x = (lambda)*x
63*> = 3: B*A*x = (lambda)*x
64*> \endverbatim
65*>
66*> \param[in] JOBZ
67*> \verbatim
68*> JOBZ is CHARACTER*1
69*> = 'N': Compute eigenvalues only;
70*> = 'V': Compute eigenvalues and eigenvectors.
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 matrix B. If UPLO = 'U', the
115*> leading N-by-N upper triangular part of B contains the
116*> upper triangular part of the matrix B. If UPLO = 'L',
117*> the leading N-by-N lower triangular part of B contains
118*> 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.
147*> If N <= 1, LWORK >= 1.
148*> If JOBZ = 'N' and N > 1, LWORK >= N + 1.
149*> If JOBZ = 'V' and N > 1, LWORK >= 2*N + N**2.
150*>
151*> If LWORK = -1, then a workspace query is assumed; the routine
152*> only calculates the optimal sizes of the WORK, RWORK and
153*> IWORK arrays, returns these values as the first entries of
154*> the WORK, RWORK and IWORK arrays, and no error message
155*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
156*> \endverbatim
157*>
158*> \param[out] RWORK
159*> \verbatim
160*> RWORK is REAL array, dimension (MAX(1,LRWORK))
161*> On exit, if INFO = 0, RWORK(1) returns the optimal LRWORK.
162*> \endverbatim
163*>
164*> \param[in] LRWORK
165*> \verbatim
166*> LRWORK is INTEGER
167*> The dimension of the array RWORK.
168*> If N <= 1, LRWORK >= 1.
169*> If JOBZ = 'N' and N > 1, LRWORK >= N.
170*> If JOBZ = 'V' and N > 1, LRWORK >= 1 + 5*N + 2*N**2.
171*>
172*> If LRWORK = -1, then a workspace query is assumed; the
173*> routine only calculates the optimal sizes of the WORK, RWORK
174*> and IWORK arrays, returns these values as the first entries
175*> of the WORK, RWORK and IWORK arrays, and no error message
176*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
177*> \endverbatim
178*>
179*> \param[out] IWORK
180*> \verbatim
181*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
182*> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
183*> \endverbatim
184*>
185*> \param[in] LIWORK
186*> \verbatim
187*> LIWORK is INTEGER
188*> The dimension of the array IWORK.
189*> If N <= 1, LIWORK >= 1.
190*> If JOBZ = 'N' and N > 1, LIWORK >= 1.
191*> If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N.
192*>
193*> If LIWORK = -1, then a workspace query is assumed; the
194*> routine only calculates the optimal sizes of the WORK, RWORK
195*> and IWORK arrays, returns these values as the first entries
196*> of the WORK, RWORK and IWORK arrays, and no error message
197*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
198*> \endverbatim
199*>
200*> \param[out] INFO
201*> \verbatim
202*> INFO is INTEGER
203*> = 0: successful exit
204*> < 0: if INFO = -i, the i-th argument had an illegal value
205*> > 0: CPOTRF or CHEEVD returned an error code:
206*> <= N: if INFO = i and JOBZ = 'N', then the algorithm
207*> failed to converge; i off-diagonal elements of an
208*> intermediate tridiagonal form did not converge to
209*> zero;
210*> if INFO = i and JOBZ = 'V', then the algorithm
211*> failed to compute an eigenvalue while working on
212*> the submatrix lying in rows and columns INFO/(N+1)
213*> through mod(INFO,N+1);
214*> > N: if INFO = N + i, for 1 <= i <= N, then the leading
215*> minor of order i of B is not positive definite.
216*> The factorization of B could not be completed and
217*> no eigenvalues or eigenvectors were computed.
218*> \endverbatim
219*
220* Authors:
221* ========
222*
223*> \author Univ. of Tennessee
224*> \author Univ. of California Berkeley
225*> \author Univ. of Colorado Denver
226*> \author NAG Ltd.
227*
228*> \ingroup complexHEeigen
229*
230*> \par Further Details:
231* =====================
232*>
233*> \verbatim
234*>
235*> Modified so that no backsubstitution is performed if CHEEVD fails to
236*> converge (NEIG in old code could be greater than N causing out of
237*> bounds reference to A - reported by Ralf Meyer). Also corrected the
238*> description of INFO and the test on ITYPE. Sven, 16 Feb 05.
239*> \endverbatim
240*
241*> \par Contributors:
242* ==================
243*>
244*> Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA
245*>
246* =====================================================================
247 SUBROUTINE chegvd( ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK,
248 \$ LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO )
249*
250* -- LAPACK driver routine --
251* -- LAPACK is a software package provided by Univ. of Tennessee, --
252* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
253*
254* .. Scalar Arguments ..
255 CHARACTER JOBZ, UPLO
256 INTEGER INFO, ITYPE, LDA, LDB, LIWORK, LRWORK, LWORK, N
257* ..
258* .. Array Arguments ..
259 INTEGER IWORK( * )
260 REAL RWORK( * ), W( * )
261 COMPLEX A( LDA, * ), B( LDB, * ), WORK( * )
262* ..
263*
264* =====================================================================
265*
266* .. Parameters ..
267 COMPLEX CONE
268 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
269* ..
270* .. Local Scalars ..
271 LOGICAL LQUERY, UPPER, WANTZ
272 CHARACTER TRANS
273 INTEGER LIOPT, LIWMIN, LOPT, LROPT, LRWMIN, LWMIN
274* ..
275* .. External Functions ..
276 LOGICAL LSAME
277 EXTERNAL lsame
278* ..
279* .. External Subroutines ..
280 EXTERNAL cheevd, chegst, cpotrf, ctrmm, ctrsm, xerbla
281* ..
282* .. Intrinsic Functions ..
283 INTRINSIC max, real
284* ..
285* .. Executable Statements ..
286*
287* Test the input parameters.
288*
289 wantz = lsame( jobz, 'V' )
290 upper = lsame( uplo, 'U' )
291 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
292*
293 info = 0
294 IF( n.LE.1 ) THEN
295 lwmin = 1
296 lrwmin = 1
297 liwmin = 1
298 ELSE IF( wantz ) THEN
299 lwmin = 2*n + n*n
300 lrwmin = 1 + 5*n + 2*n*n
301 liwmin = 3 + 5*n
302 ELSE
303 lwmin = n + 1
304 lrwmin = n
305 liwmin = 1
306 END IF
307 lopt = lwmin
308 lropt = lrwmin
309 liopt = liwmin
310 IF( itype.LT.1 .OR. itype.GT.3 ) THEN
311 info = -1
312 ELSE IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
313 info = -2
314 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
315 info = -3
316 ELSE IF( n.LT.0 ) THEN
317 info = -4
318 ELSE IF( lda.LT.max( 1, n ) ) THEN
319 info = -6
320 ELSE IF( ldb.LT.max( 1, n ) ) THEN
321 info = -8
322 END IF
323*
324 IF( info.EQ.0 ) THEN
325 work( 1 ) = lopt
326 rwork( 1 ) = lropt
327 iwork( 1 ) = liopt
328*
329 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
330 info = -11
331 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
332 info = -13
333 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
334 info = -15
335 END IF
336 END IF
337*
338 IF( info.NE.0 ) THEN
339 CALL xerbla( 'CHEGVD', -info )
340 RETURN
341 ELSE IF( lquery ) THEN
342 RETURN
343 END IF
344*
345* Quick return if possible
346*
347 IF( n.EQ.0 )
348 \$ RETURN
349*
350* Form a Cholesky factorization of B.
351*
352 CALL cpotrf( uplo, n, b, ldb, info )
353 IF( info.NE.0 ) THEN
354 info = n + info
355 RETURN
356 END IF
357*
358* Transform problem to standard eigenvalue problem and solve.
359*
360 CALL chegst( itype, uplo, n, a, lda, b, ldb, info )
361 CALL cheevd( jobz, uplo, n, a, lda, w, work, lwork, rwork, lrwork,
362 \$ iwork, liwork, info )
363 lopt = int( max( real( lopt ), real( work( 1 ) ) ) )
364 lropt = int( max( real( lropt ), real( rwork( 1 ) ) ) )
365 liopt = int( max( real( liopt ), real( iwork( 1 ) ) ) )
366*
367 IF( wantz .AND. info.EQ.0 ) THEN
368*
369* Backtransform eigenvectors to the original problem.
370*
371 IF( itype.EQ.1 .OR. itype.EQ.2 ) THEN
372*
373* For A*x=(lambda)*B*x and A*B*x=(lambda)*x;
374* backtransform eigenvectors: x = inv(L)**H *y or inv(U)*y
375*
376 IF( upper ) THEN
377 trans = 'N'
378 ELSE
379 trans = 'C'
380 END IF
381*
382 CALL ctrsm( 'Left', uplo, trans, 'Non-unit', n, n, cone,
383 \$ b, ldb, a, lda )
384*
385 ELSE IF( itype.EQ.3 ) THEN
386*
387* For B*A*x=(lambda)*x;
388* backtransform eigenvectors: x = L*y or U**H *y
389*
390 IF( upper ) THEN
391 trans = 'C'
392 ELSE
393 trans = 'N'
394 END IF
395*
396 CALL ctrmm( 'Left', uplo, trans, 'Non-unit', n, n, cone,
397 \$ b, ldb, a, lda )
398 END IF
399 END IF
400*
401 work( 1 ) = lopt
402 rwork( 1 ) = lropt
403 iwork( 1 ) = liopt
404*
405 RETURN
406*
407* End of CHEGVD
408*
409 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 chegvd(ITYPE, JOBZ, UPLO, N, A, LDA, B, LDB, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHEGVD
Definition: chegvd.f:249
subroutine cheevd(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHEEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: cheevd.f:205
subroutine cpotrf(UPLO, N, A, LDA, INFO)
CPOTRF
Definition: cpotrf.f:107