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

 subroutine ssbev ( character jobz, character uplo, integer n, integer kd, real, dimension( ldab, * ) ab, integer ldab, real, dimension( * ) w, real, dimension( ldz, * ) z, integer ldz, real, dimension( * ) work, integer info )

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

Purpose:
``` SSBEV 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 REAL 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 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 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 REAL 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.```

Definition at line 144 of file ssbev.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 REAL AB( LDAB, * ), W( * ), WORK( * ), Z( LDZ, * )
157* ..
158*
159* =====================================================================
160*
161* .. Parameters ..
162 REAL ZERO, ONE
163 parameter( zero = 0.0e0, one = 1.0e0 )
164* ..
165* .. Local Scalars ..
166 LOGICAL LOWER, WANTZ
167 INTEGER IINFO, IMAX, INDE, INDWRK, ISCALE
168 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
169 \$ SMLNUM
170* ..
171* .. External Functions ..
172 LOGICAL LSAME
173 REAL SLAMCH, SLANSB
174 EXTERNAL lsame, slamch, slansb
175* ..
176* .. External Subroutines ..
177 EXTERNAL slascl, ssbtrd, sscal, ssteqr, ssterf, 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( 'SSBEV ', -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 = slamch( 'Safe minimum' )
228 eps = slamch( '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 = slansb( '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 slascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
248 ELSE
249 CALL slascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
250 END IF
251 END IF
252*
253* Call SSBTRD to reduce symmetric band matrix to tridiagonal form.
254*
255 inde = 1
256 indwrk = inde + n
257 CALL ssbtrd( jobz, uplo, n, kd, ab, ldab, w, work( inde ), z, ldz,
258 \$ work( indwrk ), iinfo )
259*
260* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR.
261*
262 IF( .NOT.wantz ) THEN
263 CALL ssterf( n, w, work( inde ), info )
264 ELSE
265 CALL ssteqr( 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 sscal( imax, one / sigma, w, 1 )
278 END IF
279*
280 RETURN
281*
282* End of SSBEV
283*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine ssbtrd(vect, uplo, n, kd, ab, ldab, d, e, q, ldq, work, info)
SSBTRD
Definition ssbtrd.f:163
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function slansb(norm, uplo, n, k, ab, ldab, work)
SLANSB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition slansb.f:129
subroutine slascl(type, kl, ku, cfrom, cto, m, n, a, lda, info)
SLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition slascl.f:143
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
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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