LAPACK  3.10.0 LAPACK: Linear Algebra PACKage

◆ 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 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
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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
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 ssbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
SSBTRD
Definition: ssbtrd.f:163
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:68
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