LAPACK 3.12.1
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

Download ZHPEV + dependencies [TGZ] [ZIP] [TXT]

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.
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 134 of file zhpev.f.

136*
137* -- LAPACK driver routine --
138* -- LAPACK is a software package provided by Univ. of Tennessee, --
139* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
140*
141* .. Scalar Arguments ..
142 CHARACTER JOBZ, UPLO
143 INTEGER INFO, LDZ, N
144* ..
145* .. Array Arguments ..
146 DOUBLE PRECISION RWORK( * ), W( * )
147 COMPLEX*16 AP( * ), WORK( * ), Z( LDZ, * )
148* ..
149*
150* =====================================================================
151*
152* .. Parameters ..
153 DOUBLE PRECISION ZERO, ONE
154 parameter( zero = 0.0d0, one = 1.0d0 )
155* ..
156* .. Local Scalars ..
157 LOGICAL WANTZ
158 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
159 $ ISCALE
160 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
161 $ SMLNUM
162* ..
163* .. External Functions ..
164 LOGICAL LSAME
165 DOUBLE PRECISION DLAMCH, ZLANHP
166 EXTERNAL lsame, dlamch, zlanhp
167* ..
168* .. External Subroutines ..
169 EXTERNAL dscal, dsterf, xerbla, zdscal, zhptrd,
170 $ zsteqr,
171 $ zupgtr
172* ..
173* .. Intrinsic Functions ..
174 INTRINSIC sqrt
175* ..
176* .. Executable Statements ..
177*
178* Test the input parameters.
179*
180 wantz = lsame( jobz, 'V' )
181*
182 info = 0
183 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
184 info = -1
185 ELSE IF( .NOT.( lsame( uplo, 'L' ) .OR.
186 $ 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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zhptrd
subroutine zhptrd(uplo, n, ap, d, e, tau, info)
ZHPTRD
Definition zhptrd.f:149
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlanhp
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:115
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
zdscal
subroutine zdscal(n, da, zx, incx)
ZDSCAL
Definition zdscal.f:78
zsteqr
subroutine zsteqr(compz, n, d, e, z, ldz, work, info)
ZSTEQR
Definition zsteqr.f:130
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:84
zupgtr
subroutine zupgtr(uplo, n, ap, tau, q, ldq, work, info)
ZUPGTR
Definition zupgtr.f:112
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