 LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
Searching...
No Matches

## ◆ zhbev()

 subroutine zhbev ( character JOBZ, character UPLO, integer N, integer KD, complex*16, dimension( ldab, * ) AB, integer LDAB, double precision, dimension( * ) W, complex*16, dimension( ldz, * ) Z, integer LDZ, complex*16, dimension( * ) WORK, double precision, dimension( * ) RWORK, integer INFO )

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

Purpose:
``` ZHBEV 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*16 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 DOUBLE PRECISION array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] Z ``` Z is COMPLEX*16 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*16 array, dimension (N)` [out] RWORK ` RWORK 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.```

Definition at line 150 of file zhbev.f.

152*
153* -- LAPACK driver routine --
154* -- LAPACK is a software package provided by Univ. of Tennessee, --
155* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156*
157* .. Scalar Arguments ..
158 CHARACTER JOBZ, UPLO
159 INTEGER INFO, KD, LDAB, LDZ, N
160* ..
161* .. Array Arguments ..
162 DOUBLE PRECISION RWORK( * ), W( * )
163 COMPLEX*16 AB( LDAB, * ), WORK( * ), Z( LDZ, * )
164* ..
165*
166* =====================================================================
167*
168* .. Parameters ..
169 DOUBLE PRECISION ZERO, ONE
170 parameter( zero = 0.0d0, one = 1.0d0 )
171* ..
172* .. Local Scalars ..
173 LOGICAL LOWER, WANTZ
174 INTEGER IINFO, IMAX, INDE, INDRWK, ISCALE
175 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
176 \$ SMLNUM
177* ..
178* .. External Functions ..
179 LOGICAL LSAME
180 DOUBLE PRECISION DLAMCH, ZLANHB
181 EXTERNAL lsame, dlamch, zlanhb
182* ..
183* .. External Subroutines ..
184 EXTERNAL dscal, dsterf, xerbla, zhbtrd, zlascl, zsteqr
185* ..
186* .. Intrinsic Functions ..
187 INTRINSIC sqrt
188* ..
189* .. Executable Statements ..
190*
191* Test the input parameters.
192*
193 wantz = lsame( jobz, 'V' )
194 lower = lsame( uplo, 'L' )
195*
196 info = 0
197 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
198 info = -1
199 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
200 info = -2
201 ELSE IF( n.LT.0 ) THEN
202 info = -3
203 ELSE IF( kd.LT.0 ) THEN
204 info = -4
205 ELSE IF( ldab.LT.kd+1 ) THEN
206 info = -6
207 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
208 info = -9
209 END IF
210*
211 IF( info.NE.0 ) THEN
212 CALL xerbla( 'ZHBEV ', -info )
213 RETURN
214 END IF
215*
216* Quick return if possible
217*
218 IF( n.EQ.0 )
219 \$ RETURN
220*
221 IF( n.EQ.1 ) THEN
222 IF( lower ) THEN
223 w( 1 ) = dble( ab( 1, 1 ) )
224 ELSE
225 w( 1 ) = dble( ab( kd+1, 1 ) )
226 END IF
227 IF( wantz )
228 \$ z( 1, 1 ) = one
229 RETURN
230 END IF
231*
232* Get machine constants.
233*
234 safmin = dlamch( 'Safe minimum' )
235 eps = dlamch( 'Precision' )
236 smlnum = safmin / eps
237 bignum = one / smlnum
238 rmin = sqrt( smlnum )
239 rmax = sqrt( bignum )
240*
241* Scale matrix to allowable range, if necessary.
242*
243 anrm = zlanhb( 'M', uplo, n, kd, ab, ldab, rwork )
244 iscale = 0
245 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
246 iscale = 1
247 sigma = rmin / anrm
248 ELSE IF( anrm.GT.rmax ) THEN
249 iscale = 1
250 sigma = rmax / anrm
251 END IF
252 IF( iscale.EQ.1 ) THEN
253 IF( lower ) THEN
254 CALL zlascl( 'B', kd, kd, one, sigma, n, n, ab, ldab, info )
255 ELSE
256 CALL zlascl( 'Q', kd, kd, one, sigma, n, n, ab, ldab, info )
257 END IF
258 END IF
259*
260* Call ZHBTRD to reduce Hermitian band matrix to tridiagonal form.
261*
262 inde = 1
263 CALL zhbtrd( jobz, uplo, n, kd, ab, ldab, w, rwork( inde ), z,
264 \$ ldz, work, iinfo )
265*
266* For eigenvalues only, call DSTERF. For eigenvectors, call ZSTEQR.
267*
268 IF( .NOT.wantz ) THEN
269 CALL dsterf( n, w, rwork( inde ), info )
270 ELSE
271 indrwk = inde + n
272 CALL zsteqr( jobz, n, w, rwork( inde ), z, ldz,
273 \$ rwork( indrwk ), info )
274 END IF
275*
276* If matrix was scaled, then rescale eigenvalues appropriately.
277*
278 IF( iscale.EQ.1 ) THEN
279 IF( info.EQ.0 ) THEN
280 imax = n
281 ELSE
282 imax = info - 1
283 END IF
284 CALL dscal( imax, one / sigma, w, 1 )
285 END IF
286*
287 RETURN
288*
289* End of ZHBEV
290*
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
subroutine dsterf(N, D, E, INFO)
DSTERF
Definition: dsterf.f:86
subroutine zlascl(TYPE, KL, KU, CFROM, CTO, M, N, A, LDA, INFO)
ZLASCL multiplies a general rectangular matrix by a real scalar defined as cto/cfrom.
Definition: zlascl.f:143
double precision function zlanhb(NORM, UPLO, N, K, AB, LDAB, WORK)
ZLANHB returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition: zlanhb.f:132
subroutine zsteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
ZSTEQR
Definition: zsteqr.f:132
subroutine zhbtrd(VECT, UPLO, N, KD, AB, LDAB, D, E, Q, LDQ, WORK, INFO)
ZHBTRD
Definition: zhbtrd.f:163
subroutine dscal(N, DA, DX, INCX)
DSCAL
Definition: dscal.f:79
Here is the call graph for this function:
Here is the caller graph for this function: