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

 subroutine zhpev ( character jobz, character uplo, integer n, complex*16, dimension( * ) ap, double precision, dimension( * ) w, complex*16, dimension( ldz, * ) z, integer ldz, complex*16, dimension( * ) work, double precision, dimension( * ) rwork, integer info )

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

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Purpose:
``` ZHPEV computes all the eigenvalues and, optionally, eigenvectors of a
complex Hermitian matrix in packed storage.```
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,out] AP ``` AP is COMPLEX*16 array, dimension (N*(N+1)/2) On entry, the upper or lower triangle of the Hermitian matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array AP as follows: if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j; if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n. On exit, AP is overwritten by values generated during the reduction to tridiagonal form. If UPLO = 'U', the diagonal and first superdiagonal of the tridiagonal matrix T overwrite the corresponding elements of A, and if UPLO = 'L', the diagonal and first subdiagonal of T overwrite the corresponding elements of A.``` [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 (max(1, 2*N-1))` [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 136 of file zhpev.f.

138*
139* -- LAPACK driver routine --
140* -- LAPACK is a software package provided by Univ. of Tennessee, --
141* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
142*
143* .. Scalar Arguments ..
144 CHARACTER JOBZ, UPLO
145 INTEGER INFO, LDZ, N
146* ..
147* .. Array Arguments ..
148 DOUBLE PRECISION RWORK( * ), W( * )
149 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
150* ..
151*
152* =====================================================================
153*
154* .. Parameters ..
155 DOUBLE PRECISION ZERO, ONE
156 parameter( zero = 0.0d0, one = 1.0d0 )
157* ..
158* .. Local Scalars ..
159 LOGICAL WANTZ
160 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
161 \$ ISCALE
162 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
163 \$ SMLNUM
164* ..
165* .. External Functions ..
166 LOGICAL LSAME
167 DOUBLE PRECISION DLAMCH, ZLANHP
168 EXTERNAL lsame, dlamch, zlanhp
169* ..
170* .. External Subroutines ..
171 EXTERNAL dscal, dsterf, xerbla, zdscal, zhptrd, zsteqr,
172 \$ zupgtr
173* ..
174* .. Intrinsic Functions ..
175 INTRINSIC sqrt
176* ..
177* .. Executable Statements ..
178*
179* Test the input parameters.
180*
181 wantz = lsame( jobz, 'V' )
182*
183 info = 0
184 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
185 info = -1
186 ELSE IF( .NOT.( lsame( uplo, 'L' ) .OR. lsame( uplo, 'U' ) ) )
187 \$ THEN
188 info = -2
189 ELSE IF( n.LT.0 ) THEN
190 info = -3
191 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
192 info = -7
193 END IF
194*
195 IF( info.NE.0 ) THEN
196 CALL xerbla( 'ZHPEV ', -info )
197 RETURN
198 END IF
199*
200* Quick return if possible
201*
202 IF( n.EQ.0 )
203 \$ RETURN
204*
205 IF( n.EQ.1 ) THEN
206 w( 1 ) = dble( ap( 1 ) )
207 rwork( 1 ) = 1
208 IF( wantz )
209 \$ z( 1, 1 ) = one
210 RETURN
211 END IF
212*
213* Get machine constants.
214*
215 safmin = dlamch( 'Safe minimum' )
216 eps = dlamch( 'Precision' )
217 smlnum = safmin / eps
218 bignum = one / smlnum
219 rmin = sqrt( smlnum )
220 rmax = sqrt( bignum )
221*
222* Scale matrix to allowable range, if necessary.
223*
224 anrm = zlanhp( 'M', uplo, n, ap, rwork )
225 iscale = 0
226 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
227 iscale = 1
228 sigma = rmin / anrm
229 ELSE IF( anrm.GT.rmax ) THEN
230 iscale = 1
231 sigma = rmax / anrm
232 END IF
233 IF( iscale.EQ.1 ) THEN
234 CALL zdscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
235 END IF
236*
237* Call ZHPTRD to reduce Hermitian packed matrix to tridiagonal form.
238*
239 inde = 1
240 indtau = 1
241 CALL zhptrd( uplo, n, ap, w, rwork( inde ), work( indtau ),
242 \$ iinfo )
243*
244* For eigenvalues only, call DSTERF. For eigenvectors, first call
245* ZUPGTR to generate the orthogonal matrix, then call ZSTEQR.
246*
247 IF( .NOT.wantz ) THEN
248 CALL dsterf( n, w, rwork( inde ), info )
249 ELSE
250 indwrk = indtau + n
251 CALL zupgtr( uplo, n, ap, work( indtau ), z, ldz,
252 \$ work( indwrk ), iinfo )
253 indrwk = inde + n
254 CALL zsteqr( jobz, n, w, rwork( inde ), z, ldz,
255 \$ rwork( indrwk ), info )
256 END IF
257*
258* If matrix was scaled, then rescale eigenvalues appropriately.
259*
260 IF( iscale.EQ.1 ) THEN
261 IF( info.EQ.0 ) THEN
262 imax = n
263 ELSE
264 imax = info - 1
265 END IF
266 CALL dscal( imax, one / sigma, w, 1 )
267 END IF
268*
269 RETURN
270*
271* End of ZHPEV
272*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine zhptrd(uplo, n, ap, d, e, tau, info)
ZHPTRD
Definition zhptrd.f:151
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
double precision function zlanhp(norm, uplo, n, ap, work)
ZLANHP returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhp.f:117
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
subroutine zsteqr(compz, n, d, e, z, ldz, work, info)
ZSTEQR
Definition zsteqr.f:132
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:86
subroutine zupgtr(uplo, n, ap, tau, q, ldq, work, info)
ZUPGTR
Definition zupgtr.f:114
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