LAPACK  3.8.0 LAPACK: Linear Algebra PACKage

## ◆ dsbgv()

 subroutine dsbgv ( character JOBZ, character UPLO, integer N, integer KA, integer KB, double precision, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( ldbb, * ) BB, integer LDBB, double precision, dimension( * ) W, double precision, dimension( ldz, * ) Z, integer LDZ, double precision, dimension( * ) WORK, integer INFO )

DSBGV

Purpose:
``` DSBGV computes all the eigenvalues, and optionally, the eigenvectors
of a real generalized symmetric-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric
and banded, and B is also positive definite.```
Parameters
 [in] JOBZ ``` JOBZ is CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors.``` [in] UPLO ``` UPLO is CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored.``` [in] N ``` N is INTEGER The order of the matrices A and B. N >= 0.``` [in] KA ``` KA is INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0.``` [in] KB ``` KB is INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0.``` [in,out] AB ``` AB is DOUBLE PRECISION array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed.``` [in] LDAB ``` LDAB is INTEGER The leading dimension of the array AB. LDAB >= KA+1.``` [in,out] BB ``` BB is DOUBLE PRECISION array, dimension (LDBB, N) On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by DPBSTF.``` [in] LDBB ``` LDBB is INTEGER The leading dimension of the array BB. LDBB >= KB+1.``` [out] W ``` W is DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] Z ``` Z is DOUBLE PRECISION array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced.``` [in] LDZ ``` LDZ is INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N.``` [out] WORK ` WORK is DOUBLE PRECISION array, dimension (3*N)` [out] INFO ``` INFO is INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is: <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then DPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```
Date
December 2016

Definition at line 179 of file dsbgv.f.

179 *
180 * -- LAPACK driver routine (version 3.7.0) --
181 * -- LAPACK is a software package provided by Univ. of Tennessee, --
182 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
183 * December 2016
184 *
185 * .. Scalar Arguments ..
186  CHARACTER jobz, uplo
187  INTEGER info, ka, kb, ldab, ldbb, ldz, n
188 * ..
189 * .. Array Arguments ..
190  DOUBLE PRECISION ab( ldab, * ), bb( ldbb, * ), w( * ),
191  \$ work( * ), z( ldz, * )
192 * ..
193 *
194 * =====================================================================
195 *
196 * .. Local Scalars ..
197  LOGICAL upper, wantz
198  CHARACTER vect
199  INTEGER iinfo, inde, indwrk
200 * ..
201 * .. External Functions ..
202  LOGICAL lsame
203  EXTERNAL lsame
204 * ..
205 * .. External Subroutines ..
206  EXTERNAL dpbstf, dsbgst, dsbtrd, dsteqr, dsterf, xerbla
207 * ..
208 * .. Executable Statements ..
209 *
210 * Test the input parameters.
211 *
212  wantz = lsame( jobz, 'V' )
213  upper = lsame( uplo, 'U' )
214 *
215  info = 0
216  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
217  info = -1
218  ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
219  info = -2
220  ELSE IF( n.LT.0 ) THEN
221  info = -3
222  ELSE IF( ka.LT.0 ) THEN
223  info = -4
224  ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
225  info = -5
226  ELSE IF( ldab.LT.ka+1 ) THEN
227  info = -7
228  ELSE IF( ldbb.LT.kb+1 ) THEN
229  info = -9
230  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
231  info = -12
232  END IF
233  IF( info.NE.0 ) THEN
234  CALL xerbla( 'DSBGV ', -info )
235  RETURN
236  END IF
237 *
238 * Quick return if possible
239 *
240  IF( n.EQ.0 )
241  \$ RETURN
242 *
243 * Form a split Cholesky factorization of B.
244 *
245  CALL dpbstf( uplo, n, kb, bb, ldbb, info )
246  IF( info.NE.0 ) THEN
247  info = n + info
248  RETURN
249  END IF
250 *
251 * Transform problem to standard eigenvalue problem.
252 *
253  inde = 1
254  indwrk = inde + n
255  CALL dsbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
256  \$ work( indwrk ), iinfo )
257 *
258 * Reduce to tridiagonal form.
259 *
260  IF( wantz ) THEN
261  vect = 'U'
262  ELSE
263  vect = 'N'
264  END IF
265  CALL dsbtrd( vect, uplo, n, ka, ab, ldab, w, work( inde ), z, ldz,
266  \$ work( indwrk ), iinfo )
267 *
268 * For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
269 *
270  IF( .NOT.wantz ) THEN
271  CALL dsterf( n, w, work( inde ), info )
272  ELSE
273  CALL dsteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
274  \$ info )
275  END IF
276  RETURN
277 *
278 * End of DSBGV
279 *
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:88
subroutine dsbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
DSBTRD
Definition: dsbtrd.f:165
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
subroutine dpbstf(UPLO, N, KD, AB, LDAB, INFO)
DPBSTF
Definition: dpbstf.f:154
subroutine dsbgst(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO)
DSBGST
Definition: dsbgst.f:161
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine dsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
DSTEQR
Definition: dsteqr.f:133
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