LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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zhbgv.f
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1*> \brief \b ZHBGV
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> Download ZHBGV + dependencies
9*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zhbgv.f">
10*> [TGZ]</a>
11*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zhbgv.f">
12*> [ZIP]</a>
13*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zhbgv.f">
14*> [TXT]</a>
15*
16* Definition:
17* ===========
18*
19* SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
20* LDZ, WORK, RWORK, INFO )
21*
22* .. Scalar Arguments ..
23* CHARACTER JOBZ, UPLO
24* INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
25* ..
26* .. Array Arguments ..
27* DOUBLE PRECISION RWORK( * ), W( * )
28* COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
29* $ Z( LDZ, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
39*> of a complex generalized Hermitian-definite banded eigenproblem, of
40*> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
41*> and banded, and B is also positive definite.
42*> \endverbatim
43*
44* Arguments:
45* ==========
46*
47*> \param[in] JOBZ
48*> \verbatim
49*> JOBZ is CHARACTER*1
50*> = 'N': Compute eigenvalues only;
51*> = 'V': Compute eigenvalues and eigenvectors.
52*> \endverbatim
53*>
54*> \param[in] UPLO
55*> \verbatim
56*> UPLO is CHARACTER*1
57*> = 'U': Upper triangles of A and B are stored;
58*> = 'L': Lower triangles of A and B are stored.
59*> \endverbatim
60*>
61*> \param[in] N
62*> \verbatim
63*> N is INTEGER
64*> The order of the matrices A and B. N >= 0.
65*> \endverbatim
66*>
67*> \param[in] KA
68*> \verbatim
69*> KA is INTEGER
70*> The number of superdiagonals of the matrix A if UPLO = 'U',
71*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
72*> \endverbatim
73*>
74*> \param[in] KB
75*> \verbatim
76*> KB is INTEGER
77*> The number of superdiagonals of the matrix B if UPLO = 'U',
78*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
79*> \endverbatim
80*>
81*> \param[in,out] AB
82*> \verbatim
83*> AB is COMPLEX*16 array, dimension (LDAB, N)
84*> On entry, the upper or lower triangle of the Hermitian band
85*> matrix A, stored in the first ka+1 rows of the array. The
86*> j-th column of A is stored in the j-th column of the array AB
87*> as follows:
88*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
89*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
90*>
91*> On exit, the contents of AB are destroyed.
92*> \endverbatim
93*>
94*> \param[in] LDAB
95*> \verbatim
96*> LDAB is INTEGER
97*> The leading dimension of the array AB. LDAB >= KA+1.
98*> \endverbatim
99*>
100*> \param[in,out] BB
101*> \verbatim
102*> BB is COMPLEX*16 array, dimension (LDBB, N)
103*> On entry, the upper or lower triangle of the Hermitian band
104*> matrix B, stored in the first kb+1 rows of the array. The
105*> j-th column of B is stored in the j-th column of the array BB
106*> as follows:
107*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
108*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
109*>
110*> On exit, the factor S from the split Cholesky factorization
111*> B = S**H*S, as returned by ZPBSTF.
112*> \endverbatim
113*>
114*> \param[in] LDBB
115*> \verbatim
116*> LDBB is INTEGER
117*> The leading dimension of the array BB. LDBB >= KB+1.
118*> \endverbatim
119*>
120*> \param[out] W
121*> \verbatim
122*> W is DOUBLE PRECISION array, dimension (N)
123*> If INFO = 0, the eigenvalues in ascending order.
124*> \endverbatim
125*>
126*> \param[out] Z
127*> \verbatim
128*> Z is COMPLEX*16 array, dimension (LDZ, N)
129*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
130*> eigenvectors, with the i-th column of Z holding the
131*> eigenvector associated with W(i). The eigenvectors are
132*> normalized so that Z**H*B*Z = I.
133*> If JOBZ = 'N', then Z is not referenced.
134*> \endverbatim
135*>
136*> \param[in] LDZ
137*> \verbatim
138*> LDZ is INTEGER
139*> The leading dimension of the array Z. LDZ >= 1, and if
140*> JOBZ = 'V', LDZ >= N.
141*> \endverbatim
142*>
143*> \param[out] WORK
144*> \verbatim
145*> WORK is COMPLEX*16 array, dimension (N)
146*> \endverbatim
147*>
148*> \param[out] RWORK
149*> \verbatim
150*> RWORK is DOUBLE PRECISION array, dimension (3*N)
151*> \endverbatim
152*>
153*> \param[out] INFO
154*> \verbatim
155*> INFO is INTEGER
156*> = 0: successful exit
157*> < 0: if INFO = -i, the i-th argument had an illegal value
158*> > 0: if INFO = i, and i is:
159*> <= N: the algorithm failed to converge:
160*> i off-diagonal elements of an intermediate
161*> tridiagonal form did not converge to zero;
162*> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
163*> returned INFO = i: B is not positive definite.
164*> The factorization of B could not be completed and
165*> no eigenvalues or eigenvectors were computed.
166*> \endverbatim
167*
168* Authors:
169* ========
170*
171*> \author Univ. of Tennessee
172*> \author Univ. of California Berkeley
173*> \author Univ. of Colorado Denver
174*> \author NAG Ltd.
175*
176*> \ingroup hbgv
177*
178* =====================================================================
179 SUBROUTINE zhbgv( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W,
180 $ Z,
181 $ LDZ, WORK, RWORK, INFO )
182*
183* -- LAPACK driver routine --
184* -- LAPACK is a software package provided by Univ. of Tennessee, --
185* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
186*
187* .. Scalar Arguments ..
188 CHARACTER JOBZ, UPLO
189 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
190* ..
191* .. Array Arguments ..
192 DOUBLE PRECISION RWORK( * ), W( * )
193 COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
194 $ z( ldz, * )
195* ..
196*
197* =====================================================================
198*
199* .. Local Scalars ..
200 LOGICAL UPPER, WANTZ
201 CHARACTER VECT
202 INTEGER IINFO, INDE, INDWRK
203* ..
204* .. External Functions ..
205 LOGICAL LSAME
206 EXTERNAL LSAME
207* ..
208* .. External Subroutines ..
209 EXTERNAL dsterf, xerbla, zhbgst, zhbtrd, zpbstf,
210 $ zsteqr
211* ..
212* .. Executable Statements ..
213*
214* Test the input parameters.
215*
216 wantz = lsame( jobz, 'V' )
217 upper = lsame( uplo, 'U' )
218*
219 info = 0
220 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
221 info = -1
222 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
223 info = -2
224 ELSE IF( n.LT.0 ) THEN
225 info = -3
226 ELSE IF( ka.LT.0 ) THEN
227 info = -4
228 ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
229 info = -5
230 ELSE IF( ldab.LT.ka+1 ) THEN
231 info = -7
232 ELSE IF( ldbb.LT.kb+1 ) THEN
233 info = -9
234 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
235 info = -12
236 END IF
237 IF( info.NE.0 ) THEN
238 CALL xerbla( 'ZHBGV', -info )
239 RETURN
240 END IF
241*
242* Quick return if possible
243*
244 IF( n.EQ.0 )
245 $ RETURN
246*
247* Form a split Cholesky factorization of B.
248*
249 CALL zpbstf( uplo, n, kb, bb, ldbb, info )
250 IF( info.NE.0 ) THEN
251 info = n + info
252 RETURN
253 END IF
254*
255* Transform problem to standard eigenvalue problem.
256*
257 inde = 1
258 indwrk = inde + n
259 CALL zhbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
260 $ work, rwork( indwrk ), iinfo )
261*
262* Reduce to tridiagonal form.
263*
264 IF( wantz ) THEN
265 vect = 'U'
266 ELSE
267 vect = 'N'
268 END IF
269 CALL zhbtrd( vect, uplo, n, ka, ab, ldab, w, rwork( inde ), z,
270 $ ldz, work, iinfo )
271*
272* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
273*
274 IF( .NOT.wantz ) THEN
275 CALL dsterf( n, w, rwork( inde ), info )
276 ELSE
277 CALL zsteqr( jobz, n, w, rwork( inde ), z, ldz,
278 $ rwork( indwrk ), info )
279 END IF
280 RETURN
281*
282* End of ZHBGV
283*
284 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zhbgst(vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, rwork, info)
ZHBGST
Definition zhbgst.f:164
subroutine zhbgv(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, rwork, info)
ZHBGV
Definition zhbgv.f:182
subroutine zhbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
ZHBTRD
Definition zhbtrd.f:161
subroutine zpbstf(uplo, n, kd, ab, ldab, info)
ZPBSTF
Definition zpbstf.f:151
subroutine zsteqr(compz, n, d, e, z, ldz, work, info)
ZSTEQR
Definition zsteqr.f:130
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:84