LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
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 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZHBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
22 * LDZ, WORK, RWORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER JOBZ, UPLO
26 * INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION RWORK( * ), W( * )
30 * COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
31 * $ Z( LDZ, * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
41 *> of a complex generalized Hermitian-definite banded eigenproblem, of
42 *> the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
43 *> and banded, and B is also positive definite.
44 *> \endverbatim
45 *
46 * Arguments:
47 * ==========
48 *
49 *> \param[in] JOBZ
50 *> \verbatim
51 *> JOBZ is CHARACTER*1
52 *> = 'N': Compute eigenvalues only;
53 *> = 'V': Compute eigenvalues and eigenvectors.
54 *> \endverbatim
55 *>
56 *> \param[in] UPLO
57 *> \verbatim
58 *> UPLO is CHARACTER*1
59 *> = 'U': Upper triangles of A and B are stored;
60 *> = 'L': Lower triangles of A and B are stored.
61 *> \endverbatim
62 *>
63 *> \param[in] N
64 *> \verbatim
65 *> N is INTEGER
66 *> The order of the matrices A and B. N >= 0.
67 *> \endverbatim
68 *>
69 *> \param[in] KA
70 *> \verbatim
71 *> KA is INTEGER
72 *> The number of superdiagonals of the matrix A if UPLO = 'U',
73 *> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
74 *> \endverbatim
75 *>
76 *> \param[in] KB
77 *> \verbatim
78 *> KB is INTEGER
79 *> The number of superdiagonals of the matrix B if UPLO = 'U',
80 *> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
81 *> \endverbatim
82 *>
83 *> \param[in,out] AB
84 *> \verbatim
85 *> AB is COMPLEX*16 array, dimension (LDAB, N)
86 *> On entry, the upper or lower triangle of the Hermitian band
87 *> matrix A, stored in the first ka+1 rows of the array. The
88 *> j-th column of A is stored in the j-th column of the array AB
89 *> as follows:
90 *> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
91 *> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
92 *>
93 *> On exit, the contents of AB are destroyed.
94 *> \endverbatim
95 *>
96 *> \param[in] LDAB
97 *> \verbatim
98 *> LDAB is INTEGER
99 *> The leading dimension of the array AB. LDAB >= KA+1.
100 *> \endverbatim
101 *>
102 *> \param[in,out] BB
103 *> \verbatim
104 *> BB is COMPLEX*16 array, dimension (LDBB, N)
105 *> On entry, the upper or lower triangle of the Hermitian band
106 *> matrix B, stored in the first kb+1 rows of the array. The
107 *> j-th column of B is stored in the j-th column of the array BB
108 *> as follows:
109 *> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
110 *> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
111 *>
112 *> On exit, the factor S from the split Cholesky factorization
113 *> B = S**H*S, as returned by ZPBSTF.
114 *> \endverbatim
115 *>
116 *> \param[in] LDBB
117 *> \verbatim
118 *> LDBB is INTEGER
119 *> The leading dimension of the array BB. LDBB >= KB+1.
120 *> \endverbatim
121 *>
122 *> \param[out] W
123 *> \verbatim
124 *> W is DOUBLE PRECISION array, dimension (N)
125 *> If INFO = 0, the eigenvalues in ascending order.
126 *> \endverbatim
127 *>
128 *> \param[out] Z
129 *> \verbatim
130 *> Z is COMPLEX*16 array, dimension (LDZ, N)
131 *> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
132 *> eigenvectors, with the i-th column of Z holding the
133 *> eigenvector associated with W(i). The eigenvectors are
134 *> normalized so that Z**H*B*Z = I.
135 *> If JOBZ = 'N', then Z is not referenced.
136 *> \endverbatim
137 *>
138 *> \param[in] LDZ
139 *> \verbatim
140 *> LDZ is INTEGER
141 *> The leading dimension of the array Z. LDZ >= 1, and if
142 *> JOBZ = 'V', LDZ >= N.
143 *> \endverbatim
144 *>
145 *> \param[out] WORK
146 *> \verbatim
147 *> WORK is COMPLEX*16 array, dimension (N)
148 *> \endverbatim
149 *>
150 *> \param[out] RWORK
151 *> \verbatim
152 *> RWORK is DOUBLE PRECISION array, dimension (3*N)
153 *> \endverbatim
154 *>
155 *> \param[out] INFO
156 *> \verbatim
157 *> INFO is INTEGER
158 *> = 0: successful exit
159 *> < 0: if INFO = -i, the i-th argument had an illegal value
160 *> > 0: if INFO = i, and i is:
161 *> <= N: the algorithm failed to converge:
162 *> i off-diagonal elements of an intermediate
163 *> tridiagonal form did not converge to zero;
164 *> > N: if INFO = N + i, for 1 <= i <= N, then ZPBSTF
165 *> returned INFO = i: B is not positive definite.
166 *> The factorization of B could not be completed and
167 *> no eigenvalues or eigenvectors were computed.
168 *> \endverbatim
169 *
170 * Authors:
171 * ========
172 *
173 *> \author Univ. of Tennessee
174 *> \author Univ. of California Berkeley
175 *> \author Univ. of Colorado Denver
176 *> \author NAG Ltd.
177 *
178 *> \ingroup complex16OTHEReigen
179 *
180 * =====================================================================
181  SUBROUTINE zhbgv( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
182  $ LDZ, WORK, RWORK, INFO )
183 *
184 * -- LAPACK driver routine --
185 * -- LAPACK is a software package provided by Univ. of Tennessee, --
186 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
187 *
188 * .. Scalar Arguments ..
189  CHARACTER JOBZ, UPLO
190  INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
191 * ..
192 * .. Array Arguments ..
193  DOUBLE PRECISION RWORK( * ), W( * )
194  COMPLEX*16 AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
195  $ z( ldz, * )
196 * ..
197 *
198 * =====================================================================
199 *
200 * .. Local Scalars ..
201  LOGICAL UPPER, WANTZ
202  CHARACTER VECT
203  INTEGER IINFO, INDE, INDWRK
204 * ..
205 * .. External Functions ..
206  LOGICAL LSAME
207  EXTERNAL lsame
208 * ..
209 * .. External Subroutines ..
210  EXTERNAL dsterf, xerbla, zhbgst, zhbtrd, zpbstf, 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)
XERBLA
Definition: xerbla.f:60
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:86
subroutine zsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
ZSTEQR
Definition: zsteqr.f:132
subroutine zhbgst(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
ZHBGST
Definition: zhbgst.f:165
subroutine zpbstf(UPLO, N, KD, AB, LDAB, INFO)
ZPBSTF
Definition: zpbstf.f:153
subroutine zhbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
ZHBTRD
Definition: zhbtrd.f:163
subroutine zhbgv(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK, INFO)
ZHBGV
Definition: zhbgv.f:183