 LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
 subroutine chbev ( character JOBZ, character UPLO, integer N, integer KD, complex, dimension( ldab, * ) AB, integer LDAB, real, dimension( * ) W, complex, dimension( ldz, * ) Z, integer LDZ, complex, dimension( * ) WORK, real, dimension( * ) RWORK, integer INFO )

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

Purpose:
``` CHBEV computes all the eigenvalues and, optionally, eigenvectors of
a complex Hermitian 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 COMPLEX array, dimension (LDAB, N) On entry, the upper or lower triangle of the Hermitian 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 COMPLEX 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 COMPLEX array, dimension (N)` [out] RWORK ` RWORK 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.```
Date
November 2011

Definition at line 154 of file chbev.f.

154 *
155 * -- LAPACK driver routine (version 3.4.0) --
156 * -- LAPACK is a software package provided by Univ. of Tennessee, --
157 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158 * November 2011
159 *
160 * .. Scalar Arguments ..
161  CHARACTER jobz, uplo
162  INTEGER info, kd, ldab, ldz, n
163 * ..
164 * .. Array Arguments ..
165  REAL rwork( * ), w( * )
166  COMPLEX ab( ldab, * ), work( * ), z( ldz, * )
167 * ..
168 *
169 * =====================================================================
170 *
171 * .. Parameters ..
172  REAL zero, one
173  parameter ( zero = 0.0e0, one = 1.0e0 )
174 * ..
175 * .. Local Scalars ..
176  LOGICAL lower, wantz
177  INTEGER iinfo, imax, inde, indrwk, iscale
178  REAL anrm, bignum, eps, rmax, rmin, safmin, sigma,
179  \$ smlnum
180 * ..
181 * .. External Functions ..
182  LOGICAL lsame
183  REAL clanhb, slamch
184  EXTERNAL lsame, clanhb, slamch
185 * ..
186 * .. External Subroutines ..
187  EXTERNAL chbtrd, clascl, csteqr, sscal, ssterf, xerbla
188 * ..
189 * .. Intrinsic Functions ..
190  INTRINSIC sqrt
191 * ..
192 * .. Executable Statements ..
193 *
194 * Test the input parameters.
195 *
196  wantz = lsame( jobz, 'V' )
197  lower = lsame( uplo, 'L' )
198 *
199  info = 0
200  IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
201  info = -1
202  ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
203  info = -2
204  ELSE IF( n.LT.0 ) THEN
205  info = -3
206  ELSE IF( kd.LT.0 ) THEN
207  info = -4
208  ELSE IF( ldab.LT.kd+1 ) THEN
209  info = -6
210  ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
211  info = -9
212  END IF
213 *
214  IF( info.NE.0 ) THEN
215  CALL xerbla( 'CHBEV ', -info )
216  RETURN
217  END IF
218 *
219 * Quick return if possible
220 *
221  IF( n.EQ.0 )
222  \$ RETURN
223 *
224  IF( n.EQ.1 ) THEN
225  IF( lower ) THEN
226  w( 1 ) = ab( 1, 1 )
227  ELSE
228  w( 1 ) = ab( kd+1, 1 )
229  END IF
230  IF( wantz )
231  \$ z( 1, 1 ) = one
232  RETURN
233  END IF
234 *
235 * Get machine constants.
236 *
237  safmin = slamch( 'Safe minimum' )
238  eps = slamch( 'Precision' )
239  smlnum = safmin / eps
240  bignum = one / smlnum
241  rmin = sqrt( smlnum )
242  rmax = sqrt( bignum )
243 *
244 * Scale matrix to allowable range, if necessary.
245 *
246  anrm = clanhb( 'M', uplo, n, kd, ab, ldab, rwork )
247  iscale = 0
248  IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
249  iscale = 1
250  sigma = rmin / anrm
251  ELSE IF( anrm.GT.rmax ) THEN
252  iscale = 1
253  sigma = rmax / anrm
254  END IF
255  IF( iscale.EQ.1 ) THEN
256  IF( lower ) THEN
257  CALL clascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
258  ELSE
259  CALL clascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
260  END IF
261  END IF
262 *
263 * Call CHBTRD to reduce Hermitian band matrix to tridiagonal form.
264 *
265  inde = 1
266  CALL chbtrd( jobz, uplo, n, kd, ab, ldab, w, rwork( inde ), z,
267  \$ ldz, work, iinfo )
268 *
269 * For eigenvalues only, call SSTERF. For eigenvectors, call CSTEQR.
270 *
271  IF( .NOT.wantz ) THEN
272  CALL ssterf( n, w, rwork( inde ), info )
273  ELSE
274  indrwk = inde + n
275  CALL csteqr( jobz, n, w, rwork( inde ), z, ldz,
276  \$ rwork( indrwk ), info )
277  END IF
278 *
279 * If matrix was scaled, then rescale eigenvalues appropriately.
280 *
281  IF( iscale.EQ.1 ) THEN
282  IF( info.EQ.0 ) THEN
283  imax = n
284  ELSE
285  imax = info - 1
286  END IF
287  CALL sscal( imax, one / sigma, w, 1 )
288  END IF
289 *
290  RETURN
291 *
292 * End of CHBEV
293 *
subroutine clascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
CLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: clascl.f:145
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine chbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
CHBTRD
Definition: chbtrd.f:165
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:134
real function clanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
CLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm, or the element of largest absolute value of a Hermitian band matrix.
Definition: clanhb.f:134
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:55
real function slamch(CMACH)
SLAMCH
Definition: slamch.f:69
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:88
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55

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