LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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◆ zheev()

subroutine zheev ( character  jobz,
character  uplo,
integer  n,
complex*16, dimension( lda, * )  a,
integer  lda,
double precision, dimension( * )  w,
complex*16, dimension( * )  work,
integer  lwork,
double precision, dimension( * )  rwork,
integer  info 
)

ZHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices

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

Purpose:
 ZHEEV computes all eigenvalues and, optionally, eigenvectors of a
 complex Hermitian 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,out]A
          A is COMPLEX*16 array, dimension (LDA, N)
          On entry, the Hermitian matrix A.  If UPLO = 'U', the
          leading N-by-N upper triangular part of A contains the
          upper triangular part of the matrix A.  If UPLO = 'L',
          the leading N-by-N lower triangular part of A contains
          the lower triangular part of the matrix A.
          On exit, if JOBZ = 'V', then if INFO = 0, A contains the
          orthonormal eigenvectors of the matrix A.
          If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
          or the upper triangle (if UPLO='U') of A, including the
          diagonal, is destroyed.
[in]LDA
          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).
[out]W
          W is DOUBLE PRECISION array, dimension (N)
          If INFO = 0, the eigenvalues in ascending order.
[out]WORK
          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
[in]LWORK
          LWORK is INTEGER
          The length of the array WORK.  LWORK >= max(1,2*N-1).
          For optimal efficiency, LWORK >= (NB+1)*N,
          where NB is the blocksize for ZHETRD returned by ILAENV.

          If LWORK = -1, then a workspace query is assumed; the routine
          only calculates the optimal size of the WORK array, returns
          this value as the first entry of the WORK array, and no error
          message related to LWORK is issued by XERBLA.
[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 138 of file zheev.f.

140*
141* -- LAPACK driver routine --
142* -- LAPACK is a software package provided by Univ. of Tennessee, --
143* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
144*
145* .. Scalar Arguments ..
146 CHARACTER JOBZ, UPLO
147 INTEGER INFO, LDA, LWORK, N
148* ..
149* .. Array Arguments ..
150 DOUBLE PRECISION RWORK( * ), W( * )
151 COMPLEX*16 A( LDA, * ), WORK( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 DOUBLE PRECISION ZERO, ONE
158 parameter( zero = 0.0d0, one = 1.0d0 )
159 COMPLEX*16 CONE
160 parameter( cone = ( 1.0d0, 0.0d0 ) )
161* ..
162* .. Local Scalars ..
163 LOGICAL LOWER, LQUERY, WANTZ
164 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
165 $ LLWORK, LWKOPT, NB
166 DOUBLE PRECISION ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
167 $ SMLNUM
168* ..
169* .. External Functions ..
170 LOGICAL LSAME
171 INTEGER ILAENV
172 DOUBLE PRECISION DLAMCH, ZLANHE
173 EXTERNAL lsame, ilaenv, dlamch, zlanhe
174* ..
175* .. External Subroutines ..
176 EXTERNAL dscal, dsterf, xerbla, zhetrd, zlascl, zsteqr,
177 $ zungtr
178* ..
179* .. Intrinsic Functions ..
180 INTRINSIC max, sqrt
181* ..
182* .. Executable Statements ..
183*
184* Test the input parameters.
185*
186 wantz = lsame( jobz, 'V' )
187 lower = lsame( uplo, 'L' )
188 lquery = ( lwork.EQ.-1 )
189*
190 info = 0
191 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
192 info = -1
193 ELSE IF( .NOT.( lower .OR. lsame( uplo, 'U' ) ) ) THEN
194 info = -2
195 ELSE IF( n.LT.0 ) THEN
196 info = -3
197 ELSE IF( lda.LT.max( 1, n ) ) THEN
198 info = -5
199 END IF
200*
201 IF( info.EQ.0 ) THEN
202 nb = ilaenv( 1, 'ZHETRD', uplo, n, -1, -1, -1 )
203 lwkopt = max( 1, ( nb+1 )*n )
204 work( 1 ) = lwkopt
205*
206 IF( lwork.LT.max( 1, 2*n-1 ) .AND. .NOT.lquery )
207 $ info = -8
208 END IF
209*
210 IF( info.NE.0 ) THEN
211 CALL xerbla( 'ZHEEV ', -info )
212 RETURN
213 ELSE IF( lquery ) THEN
214 RETURN
215 END IF
216*
217* Quick return if possible
218*
219 IF( n.EQ.0 ) THEN
220 RETURN
221 END IF
222*
223 IF( n.EQ.1 ) THEN
224 w( 1 ) = dble( a( 1, 1 ) )
225 work( 1 ) = 1
226 IF( wantz )
227 $ a( 1, 1 ) = cone
228 RETURN
229 END IF
230*
231* Get machine constants.
232*
233 safmin = dlamch( 'Safe minimum' )
234 eps = dlamch( 'Precision' )
235 smlnum = safmin / eps
236 bignum = one / smlnum
237 rmin = sqrt( smlnum )
238 rmax = sqrt( bignum )
239*
240* Scale matrix to allowable range, if necessary.
241*
242 anrm = zlanhe( 'M', uplo, n, a, lda, rwork )
243 iscale = 0
244 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
245 iscale = 1
246 sigma = rmin / anrm
247 ELSE IF( anrm.GT.rmax ) THEN
248 iscale = 1
249 sigma = rmax / anrm
250 END IF
251 IF( iscale.EQ.1 )
252 $ CALL zlascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
253*
254* Call ZHETRD to reduce Hermitian matrix to tridiagonal form.
255*
256 inde = 1
257 indtau = 1
258 indwrk = indtau + n
259 llwork = lwork - indwrk + 1
260 CALL zhetrd( uplo, n, a, lda, w, rwork( inde ), work( indtau ),
261 $ work( indwrk ), llwork, iinfo )
262*
263* For eigenvalues only, call DSTERF. For eigenvectors, first call
264* ZUNGTR to generate the unitary matrix, then call ZSTEQR.
265*
266 IF( .NOT.wantz ) THEN
267 CALL dsterf( n, w, rwork( inde ), info )
268 ELSE
269 CALL zungtr( uplo, n, a, lda, work( indtau ), work( indwrk ),
270 $ llwork, iinfo )
271 indwrk = inde + n
272 CALL zsteqr( jobz, n, w, rwork( inde ), a, lda,
273 $ rwork( indwrk ), 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* Set WORK(1) to optimal complex workspace size.
288*
289 work( 1 ) = lwkopt
290*
291 RETURN
292*
293* End of ZHEEV
294*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
zhetrd
subroutine zhetrd(uplo, n, a, lda, d, e, tau, work, lwork, info)
ZHETRD
Definition zhetrd.f:192
ilaenv
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
dlamch
double precision function dlamch(cmach)
DLAMCH
Definition dlamch.f:69
zlanhe
double precision function zlanhe(norm, uplo, n, a, lda, work)
ZLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition zlanhe.f:124
zlascl
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
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
dscal
subroutine dscal(n, da, dx, incx)
DSCAL
Definition dscal.f:79
zsteqr
subroutine zsteqr(compz, n, d, e, z, ldz, work, info)
ZSTEQR
Definition zsteqr.f:132
dsterf
subroutine dsterf(n, d, e, info)
DSTERF
Definition dsterf.f:86
zungtr
subroutine zungtr(uplo, n, a, lda, tau, work, lwork, info)
ZUNGTR
Definition zungtr.f:123
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