LAPACK  3.10.1
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

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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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 175 of file dsbgv.f.

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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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 dsbgst(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, INFO)
DSBGST
Definition: dsbgst.f:159
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