LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ ssbgv()

 subroutine ssbgv ( character jobz, character uplo, integer n, integer ka, integer kb, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldbb, * ) bb, integer ldbb, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info )

SSBGV

Purpose:
``` SSBGV 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 REAL 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 REAL 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 SPBSTF.``` [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 REAL 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 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 SPBSTF 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 175 of file ssbgv.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 REAL 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 spbstf, ssbgst, ssbtrd, ssteqr, ssterf, 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( 'SSBGV', -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 spbstf( 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 ssbgst( 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 ssbtrd( vect, uplo, n, ka, ab, ldab, w, work( inde ), z, ldz,
263 \$ work( indwrk ), iinfo )
264*
265* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR.
266*
267 IF( .NOT.wantz ) THEN
268 CALL ssterf( n, w, work( inde ), info )
269 ELSE
270 CALL ssteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
271 \$ info )
272 END IF
273 RETURN
274*
275* End of SSBGV
276*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssbgst(vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
SSBGST
Definition ssbgst.f:159
subroutine ssbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
SSBTRD
Definition ssbtrd.f:163
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine spbstf(uplo, n, kd, ab, ldab, info)
SPBSTF
Definition spbstf.f:152
subroutine ssteqr(compz, n, d, e, z, ldz, work, info)
SSTEQR
Definition ssteqr.f:131
subroutine ssterf(n, d, e, info)
SSTERF
Definition ssterf.f:86
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