LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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◆ chbgv()

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

CHBGV

Download CHBGV + dependencies [TGZ] [ZIP] [TXT]

Purpose:
 CHBGV 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 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 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 CPBSTF.
[in]LDBB
          LDBB is INTEGER
          The leading dimension of the array BB.  LDBB >= KB+1.
[out]W
          W is REAL array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order.
[out]Z
          Z is COMPLEX 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 array, dimension (N)
[out]RWORK
          RWORK is REAL 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 CPBSTF
                    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 181 of file chbgv.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 REAL RWORK( * ), W( * )
194 COMPLEX 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 chbgst, chbtrd, cpbstf, csteqr, ssterf, xerbla
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( 'CHBGV ', -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 cpbstf( 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 chbgst( 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 chbtrd( vect, uplo, n, ka, ab, ldab, w, rwork( inde ), z,
270 $ ldz, work, iinfo )
271*
272* For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR.
273*
274 IF( .NOT.wantz ) THEN
275 CALL ssterf( n, w, rwork( inde ), info )
276 ELSE
277 CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
278 $ rwork( indwrk ), info )
279 END IF
280 RETURN
281*
282* End of CHBGV
283*
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine cpbstf(UPLO, N, KD, AB, LDAB, INFO)
CPBSTF
Definition: cpbstf.f:153
subroutine chbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD
Definition: chbtrd.f:163
subroutine chbgst(VECT, UPLO, N, KA, KB, AB, LDAB, BB, LDBB, X, LDX, WORK, RWORK, INFO)
CHBGST
Definition: chbgst.f:165
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
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