LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
chbgv.f
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1 *> \brief \b CHBGV
2 *
3 * =========== DOCUMENTATION ===========
4 *
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17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE CHBGV( 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 * REAL RWORK( * ), W( * )
30 * COMPLEX AB( LDAB, * ), BB( LDBB, * ), WORK( * ),
31 * \$ Z( LDZ, * )
32 * ..
33 *
34 *
35 *> \par Purpose:
36 * =============
37 *>
38 *> \verbatim
39 *>
40 *> CHBGV 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 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 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 CPBSTF.
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 REAL 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 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 array, dimension (N)
148 *> \endverbatim
149 *>
150 *> \param[out] RWORK
151 *> \verbatim
152 *> RWORK is REAL 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 CPBSTF
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 *> \date November 2015
179 *
180 *> \ingroup complexOTHEReigen
181 *
182 * =====================================================================
183  SUBROUTINE chbgv( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
184  \$ ldz, work, rwork, info )
185 *
186 * -- LAPACK driver routine (version 3.6.0) --
187 * -- LAPACK is a software package provided by Univ. of Tennessee, --
188 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
189 * November 2015
190 *
191 * .. Scalar Arguments ..
192  CHARACTER JOBZ, UPLO
193  INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
194 * ..
195 * .. Array Arguments ..
196  REAL RWORK( * ), W( * )
197  COMPLEX AB( ldab, * ), BB( ldbb, * ), WORK( * ),
198  \$ z( ldz, * )
199 * ..
200 *
201 * =====================================================================
202 *
203 * .. Local Scalars ..
204  LOGICAL UPPER, WANTZ
205  CHARACTER VECT
206  INTEGER IINFO, INDE, INDWRK
207 * ..
208 * .. External Functions ..
209  LOGICAL LSAME
210  EXTERNAL lsame
211 * ..
212 * .. External Subroutines ..
213  EXTERNAL chbgst, chbtrd, cpbstf, csteqr, ssterf, xerbla
214 * ..
215 * .. Executable Statements ..
216 *
217 * Test the input parameters.
218 *
219  wantz = lsame( jobz, 'V' )
220  upper = lsame( uplo, 'U' )
221 *
222  info = 0
223  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
224  info = -1
225  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
226  info = -2
227  ELSE IF( n.LT.0 ) THEN
228  info = -3
229  ELSE IF( ka.LT.0 ) THEN
230  info = -4
231  ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
232  info = -5
233  ELSE IF( ldab.LT.ka+1 ) THEN
234  info = -7
235  ELSE IF( ldbb.LT.kb+1 ) THEN
236  info = -9
237  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
238  info = -12
239  END IF
240  IF( info.NE.0 ) THEN
241  CALL xerbla( 'CHBGV ', -info )
242  RETURN
243  END IF
244 *
245 * Quick return if possible
246 *
247  IF( n.EQ.0 )
248  \$ RETURN
249 *
250 * Form a split Cholesky factorization of B.
251 *
252  CALL cpbstf( uplo, n, kb, bb, ldbb, info )
253  IF( info.NE.0 ) THEN
254  info = n + info
255  RETURN
256  END IF
257 *
258 * Transform problem to standard eigenvalue problem.
259 *
260  inde = 1
261  indwrk = inde + n
262  CALL chbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
263  \$ work, rwork( indwrk ), iinfo )
264 *
265 * Reduce to tridiagonal form.
266 *
267  IF( wantz ) THEN
268  vect = 'U'
269  ELSE
270  vect = 'N'
271  END IF
272  CALL chbtrd( vect, uplo, n, ka, ab, ldab, w, rwork( inde ), z,
273  \$ ldz, work, iinfo )
274 *
275 * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR.
276 *
277  IF( .NOT.wantz ) THEN
278  CALL ssterf( n, w, rwork( inde ), info )
279  ELSE
280  CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
281  \$ rwork( indwrk ), info )
282  END IF
283  RETURN
284 *
285 * End of CHBGV
286 *
287  END
subroutine chbgv(JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z, LDZ, WORK, RWORK, INFO)
CHBGV
Definition: chbgv.f:185
subroutine cpbstf(UPLO, N, KD, AB, LDAB, INFO)
CPBSTF
Definition: cpbstf.f:155
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine chbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD
Definition: chbtrd.f:165
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:134
subroutine chbgst(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
CHBGST
Definition: chbgst.f:167
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:88