LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ dsbev()

subroutine dsbev ( 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  info 
)

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

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

Purpose:
 DSBEV computes all the eigenvalues and, optionally, eigenvectors of
 a real symmetric band matrix A.
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 (max(1,3*N-2))
[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 144 of file dsbev.f.

146*
147* -- LAPACK driver routine --
148* -- LAPACK is a software package provided by Univ. of Tennessee, --
149* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
150*
151* .. Scalar Arguments ..
152 CHARACTER JOBZ, UPLO
153 INTEGER INFO, KD, LDAB, LDZ, N
154* ..
155* .. Array Arguments ..
156 DOUBLE PRECISION AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
157* ..
158*
159* =====================================================================
160*
161* .. Parameters ..
162 DOUBLE PRECISION ZERO, ONE
163 parameter( zero = 0.0d0, one = 1.0d0 )
164* ..
165* .. Local Scalars ..
166 LOGICAL LOWER, WANTZ
167 INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE
168 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
169 $ SMLNUM
170* ..
171* .. External Functions ..
172 LOGICAL LSAME
173 DOUBLE PRECISION DLAMCH, DLANSB
174 EXTERNAL lsame, dlamch, dlansb
175* ..
176* .. External Subroutines ..
177 EXTERNAL dlascl, dsbtrd, dscal, dsteqr, dsterf, xerbla
178* ..
179* .. Intrinsic Functions ..
180 INTRINSIC sqrt
181* ..
182* .. Executable Statements ..
183*
184* Test the input parameters.
185*
186 wantz = lsame( jobz, 'V' )
187 lower = lsame( uplo, 'L' )
188*
189 info = 0
190 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
191 info = -1
192 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
193 info = -2
194 ELSE IF( n.LT.0 ) THEN
195 info = -3
196 ELSE IF( kd.LT.0 ) THEN
197 info = -4
198 ELSE IF( ldab.LT.kd+1 ) THEN
199 info = -6
200 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
201 info = -9
202 END IF
203*
204 IF( info.NE.0 ) THEN
205 CALL xerbla( 'DSBEV ', -info )
206 RETURN
207 END IF
208*
209* Quick return if possible
210*
211 IF( n.EQ.0 )
212 $ RETURN
213*
214 IF( n.EQ.1 ) THEN
215 IF( lower ) THEN
216 w( 1 ) = ab( 1, 1 )
217 ELSE
218 w( 1 ) = ab( kd+1, 1 )
219 END IF
220 IF( wantz )
221 $ z( 1, 1 ) = one
222 RETURN
223 END IF
224*
225* Get machine constants.
226*
227 safmin = dlamch( 'Safe minimum' )
228 eps = dlamch( 'Precision' )
229 smlnum = safmin / eps
230 bignum = one / smlnum
231 rmin = sqrt( smlnum )
232 rmax = sqrt( bignum )
233*
234* Scale matrix to allowable range, if necessary.
235*
236 anrm = dlansb( 'M', uplo, n, kd, ab, ldab, work )
237 iscale = 0
238 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
239 iscale = 1
240 sigma = rmin / anrm
241 ELSE IF( anrm.GT.rmax ) THEN
242 iscale = 1
243 sigma = rmax / anrm
244 END IF
245 IF( iscale.EQ.1 ) THEN
246 IF( lower ) THEN
247 CALL dlascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
248 ELSE
249 CALL dlascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
250 END IF
251 END IF
252*
253* Call DSBTRD to reduce symmetric band matrix to tridiagonal form.
254*
255 inde = 1
256 indwrk = inde + n
257 CALL dsbtrd( jobz, uplo, n, kd, ab, ldab, w, work( inde ), z, ldz,
258 $ work( indwrk ), iinfo )
259*
260* For eigenvalues only, call DSTERF. For eigenvectors, call SSTEQR.
261*
262 IF( .NOT.wantz ) THEN
263 CALL dsterf( n, w, work( inde ), info )
264 ELSE
265 CALL dsteqr( jobz, n, w, work( inde ), z, ldz, work( indwrk ),
266 $ info )
267 END IF
268*
269* If matrix was scaled, then rescale eigenvalues appropriately.
270*
271 IF( iscale.EQ.1 ) THEN
272 IF( info.EQ.0 ) THEN
273 imax = n
274 ELSE
275 imax = info - 1
276 END IF
277 CALL dscal( imax, one / sigma, w, 1 )
278 END IF
279*
280 RETURN
281*
282* End of DSBEV
283*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dsbtrd
subroutine dsbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
DSBTRD
Definition dsbtrd.f:163
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:129
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:143
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
dsteqr
subroutine dsteqr(compz, n, d, e, z, ldz, work, info)
DSTEQR
Definition dsteqr.f:131
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:86
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