LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dsbgvd()

subroutine dsbgvd ( 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 lwork,
integer, dimension( * ) iwork,
integer liwork,
integer info )

DSBGVD

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

Purpose:
!>
!> DSBGVD 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.  If eigenvectors are
!> desired, it uses a divide and conquer algorithm.
!>
!>
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(ka+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 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 >= max(1,N).
!>
[out]WORK
!>          WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK))
!>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
!>
[in]LWORK
!>          LWORK is INTEGER
!>          The dimension of the array WORK.
!>          If N <= 1,               LWORK >= 1.
!>          If JOBZ = 'N' and N > 1, LWORK >= 2*N.
!>          If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2.
!>
!>          If LWORK = -1, then a workspace query is assumed; the routine
!>          only calculates the optimal sizes of the WORK and IWORK
!>          arrays, returns these values as the first entries of the WORK
!>          and IWORK arrays, and no error message related to LWORK or
!>          LIWORK is issued by XERBLA.
!>
[out]IWORK
!>          IWORK is INTEGER array, dimension (MAX(1,LIWORK))
!>          On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK.
!>
[in]LIWORK
!>          LIWORK is INTEGER
!>          The dimension of the array IWORK.
!>          If JOBZ  = 'N' or N <= 1, LIWORK >= 1.
!>          If JOBZ  = 'V' and N > 1, LIWORK >= 3 + 5*N.
!>
!>          If LIWORK = -1, then a workspace query is assumed; the
!>          routine only calculates the optimal sizes of the WORK and
!>          IWORK arrays, returns these values as the first entries of
!>          the WORK and IWORK arrays, and no error message related to
!>          LWORK or LIWORK is issued by XERBLA.
!>
[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.
Contributors:
Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA

Definition at line 217 of file dsbgvd.f.

220*
221* -- LAPACK driver routine --
222* -- LAPACK is a software package provided by Univ. of Tennessee, --
223* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
224*
225* .. Scalar Arguments ..
226 CHARACTER JOBZ, UPLO
227 INTEGER INFO, KA, KB, LDAB, LDBB, LDZ, LIWORK, LWORK, N
228* ..
229* .. Array Arguments ..
230 INTEGER IWORK( * )
231 DOUBLE PRECISION AB( LDAB, * ), BB( LDBB, * ), W( * ),
232 $ WORK( * ), Z( LDZ, * )
233* ..
234*
235* =====================================================================
236*
237* .. Parameters ..
238 DOUBLE PRECISION ONE, ZERO
239 parameter( one = 1.0d+0, zero = 0.0d+0 )
240* ..
241* .. Local Scalars ..
242 LOGICAL LQUERY, UPPER, WANTZ
243 CHARACTER VECT
244 INTEGER IINFO, INDE, INDWK2, INDWRK, LIWMIN, LLWRK2,
245 $ LWMIN
246* ..
247* .. External Functions ..
248 LOGICAL LSAME
249 EXTERNAL lsame
250* ..
251* .. External Subroutines ..
252 EXTERNAL dgemm, dlacpy, dpbstf, dsbgst, dsbtrd,
253 $ dstedc,
254 $ dsterf, xerbla
255* ..
256* .. Executable Statements ..
257*
258* Test the input parameters.
259*
260 wantz = lsame( jobz, 'V' )
261 upper = lsame( uplo, 'U' )
262 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
263*
264 info = 0
265 IF( n.LE.1 ) THEN
266 liwmin = 1
267 lwmin = 1
268 ELSE IF( wantz ) THEN
269 liwmin = 3 + 5*n
270 lwmin = 1 + 5*n + 2*n**2
271 ELSE
272 liwmin = 1
273 lwmin = 2*n
274 END IF
275*
276 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
277 info = -1
278 ELSE IF( .NOT.( upper .OR. lsame( uplo, 'L' ) ) ) THEN
279 info = -2
280 ELSE IF( n.LT.0 ) THEN
281 info = -3
282 ELSE IF( ka.LT.0 ) THEN
283 info = -4
284 ELSE IF( kb.LT.0 .OR. kb.GT.ka ) THEN
285 info = -5
286 ELSE IF( ldab.LT.ka+1 ) THEN
287 info = -7
288 ELSE IF( ldbb.LT.kb+1 ) THEN
289 info = -9
290 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
291 info = -12
292 END IF
293*
294 IF( info.EQ.0 ) THEN
295 work( 1 ) = lwmin
296 iwork( 1 ) = liwmin
297*
298 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
299 info = -14
300 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
301 info = -16
302 END IF
303 END IF
304*
305 IF( info.NE.0 ) THEN
306 CALL xerbla( 'DSBGVD', -info )
307 RETURN
308 ELSE IF( lquery ) THEN
309 RETURN
310 END IF
311*
312* Quick return if possible
313*
314 IF( n.EQ.0 )
315 $ RETURN
316*
317* Form a split Cholesky factorization of B.
318*
319 CALL dpbstf( uplo, n, kb, bb, ldbb, info )
320 IF( info.NE.0 ) THEN
321 info = n + info
322 RETURN
323 END IF
324*
325* Transform problem to standard eigenvalue problem.
326*
327 inde = 1
328 indwrk = inde + n
329 indwk2 = indwrk + n*n
330 llwrk2 = lwork - indwk2 + 1
331 CALL dsbgst( jobz, uplo, n, ka, kb, ab, ldab, bb, ldbb, z, ldz,
332 $ work, iinfo )
333*
334* Reduce to tridiagonal form.
335*
336 IF( wantz ) THEN
337 vect = 'U'
338 ELSE
339 vect = 'N'
340 END IF
341 CALL dsbtrd( vect, uplo, n, ka, ab, ldab, w, work( inde ), z,
342 $ ldz,
343 $ work( indwrk ), iinfo )
344*
345* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
346*
347 IF( .NOT.wantz ) THEN
348 CALL dsterf( n, w, work( inde ), info )
349 ELSE
350 CALL dstedc( 'I', n, w, work( inde ), work( indwrk ), n,
351 $ work( indwk2 ), llwrk2, iwork, liwork, info )
352 CALL dgemm( 'N', 'N', n, n, n, one, z, ldz, work( indwrk ),
353 $ n,
354 $ zero, work( indwk2 ), n )
355 CALL dlacpy( 'A', n, n, work( indwk2 ), n, z, ldz )
356 END IF
357*
358 work( 1 ) = lwmin
359 iwork( 1 ) = liwmin
360*
361 RETURN
362*
363* End of DSBGVD
364*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dgemm
subroutine dgemm(transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc)
DGEMM
Definition dgemm.f:188
dsbgst
subroutine dsbgst(vect, uplo, n, ka, kb, ab, ldab, bb, ldbb, x, ldx, work, info)
DSBGST
Definition dsbgst.f:158
dsbtrd
subroutine dsbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD
Definition dsbtrd.f:161
dlacpy
subroutine dlacpy(uplo, m, n, a, lda, b, ldb)
DLACPY copies all or part of one two-dimensional array to another.
Definition dlacpy.f:101
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dpbstf
subroutine dpbstf(uplo, n, kd, ab, ldab, info)
DPBSTF
Definition dpbstf.f:150
dstedc
subroutine dstedc(compz, n, d, e, z, ldz, work, lwork, iwork, liwork, info)
DSTEDC
Definition dstedc.f:180
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:84
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