LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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dsbgv.f
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1*> \brief \b DSBGV
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/dsbgv.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsbgv.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsbgv.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DSBGV( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
22* LDZ, WORK, 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 AB( LDAB, * ), BB( LDBB, * ), W( * ),
30* \$ WORK( * ), Z( LDZ, * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> DSBGV computes all the eigenvalues, and optionally, the eigenvectors
40*> of a real generalized symmetric-definite banded eigenproblem, of
41*> the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
42*> and banded, and B is also positive definite.
43*> \endverbatim
44*
45* Arguments:
46* ==========
47*
48*> \param[in] JOBZ
49*> \verbatim
50*> JOBZ is CHARACTER*1
51*> = 'N': Compute eigenvalues only;
52*> = 'V': Compute eigenvalues and eigenvectors.
53*> \endverbatim
54*>
55*> \param[in] UPLO
56*> \verbatim
57*> UPLO is CHARACTER*1
58*> = 'U': Upper triangles of A and B are stored;
59*> = 'L': Lower triangles of A and B are stored.
60*> \endverbatim
61*>
62*> \param[in] N
63*> \verbatim
64*> N is INTEGER
65*> The order of the matrices A and B. N >= 0.
66*> \endverbatim
67*>
68*> \param[in] KA
69*> \verbatim
70*> KA is INTEGER
71*> The number of superdiagonals of the matrix A if UPLO = 'U',
72*> or the number of subdiagonals if UPLO = 'L'. KA >= 0.
73*> \endverbatim
74*>
75*> \param[in] KB
76*> \verbatim
77*> KB is INTEGER
78*> The number of superdiagonals of the matrix B if UPLO = 'U',
79*> or the number of subdiagonals if UPLO = 'L'. KB >= 0.
80*> \endverbatim
81*>
82*> \param[in,out] AB
83*> \verbatim
84*> AB is DOUBLE PRECISION array, dimension (LDAB, N)
85*> On entry, the upper or lower triangle of the symmetric band
86*> matrix A, stored in the first ka+1 rows of the array. The
87*> j-th column of A is stored in the j-th column of the array AB
88*> as follows:
89*> if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j;
90*> if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka).
91*>
92*> On exit, the contents of AB are destroyed.
93*> \endverbatim
94*>
95*> \param[in] LDAB
96*> \verbatim
97*> LDAB is INTEGER
98*> The leading dimension of the array AB. LDAB >= KA+1.
99*> \endverbatim
100*>
101*> \param[in,out] BB
102*> \verbatim
103*> BB is DOUBLE PRECISION array, dimension (LDBB, N)
104*> On entry, the upper or lower triangle of the symmetric band
105*> matrix B, stored in the first kb+1 rows of the array. The
106*> j-th column of B is stored in the j-th column of the array BB
107*> as follows:
108*> if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j;
109*> if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb).
110*>
111*> On exit, the factor S from the split Cholesky factorization
112*> B = S**T*S, as returned by DPBSTF.
113*> \endverbatim
114*>
115*> \param[in] LDBB
116*> \verbatim
117*> LDBB is INTEGER
118*> The leading dimension of the array BB. LDBB >= KB+1.
119*> \endverbatim
120*>
121*> \param[out] W
122*> \verbatim
123*> W is DOUBLE PRECISION array, dimension (N)
124*> If INFO = 0, the eigenvalues in ascending order.
125*> \endverbatim
126*>
127*> \param[out] Z
128*> \verbatim
129*> Z is DOUBLE PRECISION array, dimension (LDZ, N)
130*> If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of
131*> eigenvectors, with the i-th column of Z holding the
132*> eigenvector associated with W(i). The eigenvectors are
133*> normalized so that Z**T*B*Z = I.
134*> If JOBZ = 'N', then Z is not referenced.
135*> \endverbatim
136*>
137*> \param[in] LDZ
138*> \verbatim
139*> LDZ is INTEGER
140*> The leading dimension of the array Z. LDZ >= 1, and if
141*> JOBZ = 'V', LDZ >= N.
142*> \endverbatim
143*>
144*> \param[out] WORK
145*> \verbatim
146*> WORK is DOUBLE PRECISION array, dimension (3*N)
147*> \endverbatim
148*>
149*> \param[out] INFO
150*> \verbatim
151*> INFO is INTEGER
152*> = 0: successful exit
153*> < 0: if INFO = -i, the i-th argument had an illegal value
154*> > 0: if INFO = i, and i is:
155*> <= N: the algorithm failed to converge:
156*> i off-diagonal elements of an intermediate
157*> tridiagonal form did not converge to zero;
158*> > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF
159*> returned INFO = i: B is not positive definite.
160*> The factorization of B could not be completed and
161*> no eigenvalues or eigenvectors were computed.
162*> \endverbatim
163*
164* Authors:
165* ========
166*
167*> \author Univ. of Tennessee
168*> \author Univ. of California Berkeley
169*> \author Univ. of Colorado Denver
170*> \author NAG Ltd.
171*
172*> \ingroup hbgv
173*
174* =====================================================================
175 SUBROUTINE dsbgv( JOBZ, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, W, Z,
176 \$ LDZ, WORK, INFO )
177*
178* -- LAPACK driver routine --
179* -- LAPACK is a software package provided by Univ. of Tennessee, --
180* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
181*
182* .. Scalar Arguments ..
183 CHARACTER JOBZ, UPLO
184 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, N
185* ..
186* .. Array Arguments ..
187 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
188 \$ work( * ), z( ldz, * )
189* ..
190*
191* =====================================================================
192*
193* .. Local Scalars ..
194 LOGICAL UPPER, WANTZ
195 CHARACTER VECT
196 INTEGER IINFO, INDE, INDWRK
197* ..
198* .. External Functions ..
199 LOGICAL LSAME
200 EXTERNAL lsame
201* ..
202* .. External Subroutines ..
203 EXTERNAL dpbstf, dsbgst, dsbtrd, dsteqr, dsterf, xerbla
204* ..
205* .. Executable Statements ..
206*
207* Test the input parameters.
208*
209 wantz = lsame( jobz, 'V' )
210 upper = lsame( uplo, 'U' )
211*
212 info = 0
213 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
214 info = -1
215 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
216 info = -2
217 ELSE IF( n.LT.0 ) THEN
218 info = -3
219 ELSE IF( ka.LT.0 ) THEN
220 info = -4
221 ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
222 info = -5
223 ELSE IF( ldab.LT.ka+1 ) THEN
224 info = -7
225 ELSE IF( ldbb.LT.kb+1 ) THEN
226 info = -9
227 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
228 info = -12
229 END IF
230 IF( info.NE.0 ) THEN
231 CALL xerbla( 'DSBGV', -info )
232 RETURN
233 END IF
234*
235* Quick return if possible
236*
237 IF( n.EQ.0 )
238 \$ RETURN
239*
240* Form a split Cholesky factorization of B.
241*
242 CALL dpbstf( uplo, n, kb, bb, ldbb, info )
243 IF( info.NE.0 ) THEN
244 info = n + info
245 RETURN
246 END IF
247*
248* Transform problem to standard eigenvalue problem.
249*
250 inde = 1
251 indwrk = inde + n
252 CALL dsbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
253 \$ work( indwrk ), iinfo )
254*
255* Reduce to tridiagonal form.
256*
257 IF( wantz ) THEN
258 vect = 'U'
259 ELSE
260 vect = 'N'
261 END IF
262 CALL dsbtrd( vect, uplo, n, ka, ab, ldab, w, work( inde ), z, ldz,
263 \$ work( indwrk ), iinfo )
264*
265* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
266*
267 IF( .NOT.wantz ) THEN
268 CALL dsterf( n, w, work( inde ), info )
269 ELSE
270 CALL dsteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
271 \$ info )
272 END IF
273 RETURN
274*
275* End of DSBGV
276*
277 END
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine dsbgst(vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
DSBGST
Definition dsbgst.f:159
subroutine dsbgv(jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, w, z, ldz, work, info)
DSBGV
Definition dsbgv.f:177
subroutine dsbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD
Definition dsbtrd.f:163
subroutine dpbstf(uplo, n, kd, ab, ldab, info)
DPBSTF
Definition dpbstf.f:152
subroutine dsteqr(compz, n, d, e, z, ldz, work, info)
DSTEQR
Definition dsteqr.f:131
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:86