 LAPACK  3.10.1 LAPACK: Linear Algebra PACKage

## ◆ zhbgv()

 subroutine zhbgv ( character JOBZ, character UPLO, integer N, integer KA, integer KB, complex*16, dimension( ldab, * ) AB, integer LDAB, complex*16, dimension( ldbb, * ) BB, integer LDBB, double precision, dimension( * ) W, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO )

ZHBGV

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Purpose:
``` ZHBGV computes all the eigenvalues, and optionally, the eigenvectors
of a complex generalized Hermitian-definite banded eigenproblem, of
the form A*x=(lambda)*B*x. Here A and B are assumed to be Hermitian
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 COMPLEX*16 array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian 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 COMPLEX*16 array, dimension (LDBB, N) On entry, the upper or lower triangle of the Hermitian 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**H*S, as returned by ZPBSTF.``` [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 COMPLEX*16 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**H*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 COMPLEX*16 array, dimension (N)` [out] RWORK ` RWORK 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 ZPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed.```

Definition at line 181 of file zhbgv.f.

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 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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