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

 subroutine cheev ( character jobz, character uplo, integer n, complex, dimension( lda, * ) a, integer lda, real, dimension( * ) w, complex, dimension( * ) work, integer lwork, real, dimension( * ) rwork, integer info )

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

Purpose:
``` CHEEV 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 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 REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order.``` [out] WORK ``` WORK is COMPLEX 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 CHETRD 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 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.```

Definition at line 138 of file cheev.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 REAL RWORK( * ), W( * )
151 COMPLEX A( LDA, * ), WORK( * )
152* ..
153*
154* =====================================================================
155*
156* .. Parameters ..
157 REAL ZERO, ONE
158 parameter( zero = 0.0e0, one = 1.0e0 )
159 COMPLEX CONE
160 parameter( cone = ( 1.0e0, 0.0e0 ) )
161* ..
162* .. Local Scalars ..
163 LOGICAL LOWER, LQUERY, WANTZ
164 INTEGER IINFO, IMAX, INDE, INDTAU, INDWRK, ISCALE,
165 \$ LLWORK, LWKOPT, NB
166 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
167 \$ SMLNUM
168* ..
169* .. External Functions ..
170 LOGICAL LSAME
171 INTEGER ILAENV
172 REAL CLANHE, SLAMCH, SROUNDUP_LWORK
174* ..
175* .. External Subroutines ..
176 EXTERNAL chetrd, clascl, csteqr, cungtr, sscal, ssterf,
177 \$ xerbla
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, 'CHETRD', uplo, n, -1, -1, -1 )
203 lwkopt = max( 1, ( nb+1 )*n )
204 work( 1 ) = sroundup_lwork(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( 'CHEEV ', -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 ) = real( 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 = slamch( 'Safe minimum' )
234 eps = slamch( '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 = clanhe( '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 clascl( uplo, 0, 0, one, sigma, n, n, a, lda, info )
253*
254* Call CHETRD 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 chetrd( uplo, n, a, lda, w, rwork( inde ), work( indtau ),
261 \$ work( indwrk ), llwork, iinfo )
262*
263* For eigenvalues only, call SSTERF. For eigenvectors, first call
264* CUNGTR to generate the unitary matrix, then call CSTEQR.
265*
266 IF( .NOT.wantz ) THEN
267 CALL ssterf( n, w, rwork( inde ), info )
268 ELSE
269 CALL cungtr( uplo, n, a, lda, work( indtau ), work( indwrk ),
270 \$ llwork, iinfo )
271 indwrk = inde + n
272 CALL csteqr( 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 sscal( imax, one / sigma, w, 1 )
285 END IF
286*
287* Set WORK(1) to optimal complex workspace size.
288*
289 work( 1 ) = sroundup_lwork(lwkopt)
290*
291 RETURN
292*
293* End of CHEEV
294*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
subroutine chetrd(uplo, n, a, lda, d, e, tau, work, lwork, info)
CHETRD
Definition chetrd.f:192
integer function ilaenv(ispec, name, opts, n1, n2, n3, n4)
ILAENV
Definition ilaenv.f:162
real function slamch(cmach)
SLAMCH
Definition slamch.f:68
real function clanhe(norm, uplo, n, a, lda, work)
CLANHE returns the value of the 1-norm, or the Frobenius norm, or the infinity norm,...
Definition clanhe.f:124
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:143
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
real function sroundup_lwork(lwork)
SROUNDUP_LWORK
subroutine sscal(n, sa, sx, incx)
SSCAL
Definition sscal.f:79
subroutine csteqr(compz, n, d, e, z, ldz, work, info)
CSTEQR
Definition csteqr.f:132
subroutine ssterf(n, d, e, info)
SSTERF
Definition ssterf.f:86
subroutine cungtr(uplo, n, a, lda, tau, work, lwork, info)
CUNGTR
Definition cungtr.f:123
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