LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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cheev.f
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1*> \brief <b> CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cheev.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cheev.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cheev.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHEEV( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
22* INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, LDA, LWORK, N
27* ..
28* .. Array Arguments ..
29* REAL RWORK( * ), W( * )
30* COMPLEX A( LDA, * ), WORK( * )
31* ..
32*
33*
34*> \par Purpose:
35* =============
36*>
37*> \verbatim
38*>
39*> CHEEV computes all eigenvalues and, optionally, eigenvectors of a
40*> complex Hermitian matrix A.
41*> \endverbatim
42*
43* Arguments:
44* ==========
45*
46*> \param[in] JOBZ
47*> \verbatim
48*> JOBZ is CHARACTER*1
49*> = 'N': Compute eigenvalues only;
50*> = 'V': Compute eigenvalues and eigenvectors.
51*> \endverbatim
52*>
53*> \param[in] UPLO
54*> \verbatim
55*> UPLO is CHARACTER*1
56*> = 'U': Upper triangle of A is stored;
57*> = 'L': Lower triangle of A is stored.
58*> \endverbatim
59*>
60*> \param[in] N
61*> \verbatim
62*> N is INTEGER
63*> The order of the matrix A. N >= 0.
64*> \endverbatim
65*>
66*> \param[in,out] A
67*> \verbatim
68*> A is COMPLEX array, dimension (LDA, N)
69*> On entry, the Hermitian matrix A. If UPLO = 'U', the
70*> leading N-by-N upper triangular part of A contains the
71*> upper triangular part of the matrix A. If UPLO = 'L',
72*> the leading N-by-N lower triangular part of A contains
73*> the lower triangular part of the matrix A.
74*> On exit, if JOBZ = 'V', then if INFO = 0, A contains the
75*> orthonormal eigenvectors of the matrix A.
76*> If JOBZ = 'N', then on exit the lower triangle (if UPLO='L')
77*> or the upper triangle (if UPLO='U') of A, including the
78*> diagonal, is destroyed.
79*> \endverbatim
80*>
81*> \param[in] LDA
82*> \verbatim
83*> LDA is INTEGER
84*> The leading dimension of the array A. LDA >= max(1,N).
85*> \endverbatim
86*>
87*> \param[out] W
88*> \verbatim
89*> W is REAL array, dimension (N)
90*> If INFO = 0, the eigenvalues in ascending order.
91*> \endverbatim
92*>
93*> \param[out] WORK
94*> \verbatim
95*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
96*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
97*> \endverbatim
98*>
99*> \param[in] LWORK
100*> \verbatim
101*> LWORK is INTEGER
102*> The length of the array WORK. LWORK >= max(1,2*N-1).
103*> For optimal efficiency, LWORK >= (NB+1)*N,
104*> where NB is the blocksize for CHETRD returned by ILAENV.
105*>
106*> If LWORK = -1, then a workspace query is assumed; the routine
107*> only calculates the optimal size of the WORK array, returns
108*> this value as the first entry of the WORK array, and no error
109*> message related to LWORK is issued by XERBLA.
110*> \endverbatim
111*>
112*> \param[out] RWORK
113*> \verbatim
114*> RWORK is REAL array, dimension (max(1, 3*N-2))
115*> \endverbatim
116*>
117*> \param[out] INFO
118*> \verbatim
119*> INFO is INTEGER
120*> = 0: successful exit
121*> < 0: if INFO = -i, the i-th argument had an illegal value
122*> > 0: if INFO = i, the algorithm failed to converge; i
123*> off-diagonal elements of an intermediate tridiagonal
124*> form did not converge to zero.
125*> \endverbatim
126*
127* Authors:
128* ========
129*
130*> \author Univ. of Tennessee
131*> \author Univ. of California Berkeley
132*> \author Univ. of Colorado Denver
133*> \author NAG Ltd.
134*
135*> \ingroup complexHEeigen
136*
137* =====================================================================
138 SUBROUTINE cheev( JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK,
139 \$ INFO )
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
173 EXTERNAL ilaenv, lsame, clanhe, slamch
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 ) = 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 ) = lwkopt
290*
291 RETURN
292*
293* End of CHEEV
294*
295 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine chetrd(UPLO, N, A, LDA, D, E, TAU, WORK, LWORK, INFO)
CHETRD
Definition: chetrd.f:192
subroutine cheev(JOBZ, UPLO, N, A, LDA, W, WORK, LWORK, RWORK, INFO)
CHEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for HE matrices
Definition: cheev.f:140
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
subroutine csteqr(COMPZ, N, D, E, Z, LDZ, WORK, INFO)
CSTEQR
Definition: csteqr.f:132
subroutine cungtr(UPLO, N, A, LDA, TAU, WORK, LWORK, INFO)
CUNGTR
Definition: cungtr.f:123
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79