LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dsbevd()

subroutine dsbevd ( character jobz,
character uplo,
integer n,
integer kd,
double precision, dimension( ldab, * ) ab,
integer ldab,
double precision, dimension( * ) w,
double precision, dimension( ldz, * ) z,
integer ldz,
double precision, dimension( * ) work,
integer lwork,
integer, dimension( * ) iwork,
integer liwork,
integer info )

DSBEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices

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

Purpose:
!>
!> DSBEVD computes all the eigenvalues and, optionally, eigenvectors of
!> a real symmetric band matrix A. 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 triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
[in]N
!>          N is INTEGER
!>          The order of the matrix A.  N >= 0.
!>
[in]KD
!>          KD is INTEGER
!>          The number of superdiagonals of the matrix A if UPLO = 'U',
!>          or the number of subdiagonals if UPLO = 'L'.  KD >= 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 KD+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(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j;
!>          if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(n,j+kd).
!>
!>          On exit, AB is overwritten by values generated during the
!>          reduction to tridiagonal form.  If UPLO = 'U', the first
!>          superdiagonal and the diagonal of the tridiagonal matrix T
!>          are returned in rows KD and KD+1 of AB, and if UPLO = 'L',
!>          the diagonal and first subdiagonal of T are returned in the
!>          first two rows of AB.
!>
[in]LDAB
!>          LDAB is INTEGER
!>          The leading dimension of the array AB.  LDAB >= KD + 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 orthonormal
!>          eigenvectors of the matrix A, with the i-th column of Z
!>          holding the eigenvector associated with W(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 (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 must be at least 1.
!>          If JOBZ  = 'N' and N > 2, LWORK must be at least 2*N.
!>          If JOBZ  = 'V' and N > 2, LWORK must be at least
!>                         ( 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 INFO = 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 must be at least 1.
!>          If JOBZ  = 'V' and N > 2, LIWORK must be at least 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, the algorithm failed to converge; i
!>                off-diagonal elements of an intermediate tridiagonal
!>                form did not converge to zero.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 183 of file dsbevd.f.

186*
187* -- LAPACK driver routine --
188* -- LAPACK is a software package provided by Univ. of Tennessee, --
189* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
190*
191* .. Scalar Arguments ..
192 CHARACTER JOBZ, UPLO
193 INTEGER INFO, KD, LDAB, LDZ, LIWORK, LWORK, N
194* ..
195* .. Array Arguments ..
196 INTEGER IWORK( * )
197 DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
198* ..
199*
200* =====================================================================
201*
202* .. Parameters ..
203 DOUBLE PRECISION ZERO, ONE
204 parameter( zero = 0.0d+0, one = 1.0d+0 )
205* ..
206* .. Local Scalars ..
207 LOGICAL LOWER, LQUERY, WANTZ
208 INTEGER IINFO, INDE, INDWK2, INDWRK, ISCALE, LIWMIN,
209 $ LLWRK2, LWMIN
210 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
211 $ SMLNUM
212* ..
213* .. External Functions ..
214 LOGICAL LSAME
215 DOUBLE PRECISION DLAMCH, DLANSB
216 EXTERNAL lsame, dlamch, dlansb
217* ..
218* .. External Subroutines ..
219 EXTERNAL dgemm, dlacpy, dlascl, dsbtrd, dscal,
220 $ dstedc,
221 $ dsterf, xerbla
222* ..
223* .. Intrinsic Functions ..
224 INTRINSIC sqrt
225* ..
226* .. Executable Statements ..
227*
228* Test the input parameters.
229*
230 wantz = lsame( jobz, 'V' )
231 lower = lsame( uplo, 'L' )
232 lquery = ( lwork.EQ.-1 .OR. liwork.EQ.-1 )
233*
234 info = 0
235 IF( n.LE.1 ) THEN
236 liwmin = 1
237 lwmin = 1
238 ELSE
239 IF( wantz ) THEN
240 liwmin = 3 + 5*n
241 lwmin = 1 + 5*n + 2*n**2
242 ELSE
243 liwmin = 1
244 lwmin = 2*n
245 END IF
246 END IF
247 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
248 info = -1
249 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
250 info = -2
251 ELSE IF( n.LT.0 ) THEN
252 info = -3
253 ELSE IF( kd.LT.0 ) THEN
254 info = -4
255 ELSE IF( ldab.LT.kd+1 ) THEN
256 info = -6
257 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
258 info = -9
259 END IF
260*
261 IF( info.EQ.0 ) THEN
262 work( 1 ) = lwmin
263 iwork( 1 ) = liwmin
264*
265 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
266 info = -11
267 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
268 info = -13
269 END IF
270 END IF
271*
272 IF( info.NE.0 ) THEN
273 CALL xerbla( 'DSBEVD', -info )
274 RETURN
275 ELSE IF( lquery ) THEN
276 RETURN
277 END IF
278*
279* Quick return if possible
280*
281 IF( n.EQ.0 )
282 $ RETURN
283*
284 IF( n.EQ.1 ) THEN
285 w( 1 ) = ab( 1, 1 )
286 IF( wantz )
287 $ z( 1, 1 ) = one
288 RETURN
289 END IF
290*
291* Get machine constants.
292*
293 safmin = dlamch( 'Safe minimum' )
294 eps = dlamch( 'Precision' )
295 smlnum = safmin / eps
296 bignum = one / smlnum
297 rmin = sqrt( smlnum )
298 rmax = sqrt( bignum )
299*
300* Scale matrix to allowable range, if necessary.
301*
302 anrm = dlansb( 'M', uplo, n, kd, ab, ldab, work )
303 iscale = 0
304 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
305 iscale = 1
306 sigma = rmin / anrm
307 ELSE IF( anrm.GT.rmax ) THEN
308 iscale = 1
309 sigma = rmax / anrm
310 END IF
311 IF( iscale.EQ.1 ) THEN
312 IF( lower ) THEN
313 CALL dlascl( 'B', kd, kd, one, sigma, n, n, ab, ldab,
314 $ info )
315 ELSE
316 CALL dlascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab,
317 $ info )
318 END IF
319 END IF
320*
321* Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
322*
323 inde = 1
324 indwrk = inde + n
325 indwk2 = indwrk + n*n
326 llwrk2 = lwork - indwk2 + 1
327 CALL dsbtrd( jobz, uplo, n, kd, ab, ldab, w, work( inde ), z,
328 $ ldz,
329 $ work( indwrk ), iinfo )
330*
331* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEDC.
332*
333 IF( .NOT.wantz ) THEN
334 CALL dsterf( n, w, work( inde ), info )
335 ELSE
336 CALL dstedc( 'I', n, w, work( inde ), work( indwrk ), n,
337 $ work( indwk2 ), llwrk2, iwork, liwork, info )
338 CALL dgemm( 'N', 'N', n, n, n, one, z, ldz, work( indwrk ),
339 $ n,
340 $ zero, work( indwk2 ), n )
341 CALL dlacpy( 'A', n, n, work( indwk2 ), n, z, ldz )
342 END IF
343*
344* If matrix was scaled, then rescale eigenvalues appropriately.
345*
346 IF( iscale.EQ.1 )
347 $ CALL dscal( n, one / sigma, w, 1 )
348*
349 work( 1 ) = lwmin
350 iwork( 1 ) = liwmin
351 RETURN
352*
353* End of DSBEVD
354*
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
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
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
dlansb
double precision function dlansb(norm, uplo, n, k, ab, ldab, work)
DLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition dlansb.f:127
dlascl
subroutine dlascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
DLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition dlascl.f:142
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
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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