LAPACK 3.11.0 LAPACK: Linear Algebra PACKage
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chpevd.f
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1*> \brief <b> CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrices</b>
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
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13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/chpevd.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CHPEVD( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
22* RWORK, LRWORK, IWORK, LIWORK, INFO )
23*
24* .. Scalar Arguments ..
25* CHARACTER JOBZ, UPLO
26* INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
27* ..
28* .. Array Arguments ..
29* INTEGER IWORK( * )
30* REAL RWORK( * ), W( * )
31* COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
32* ..
33*
34*
35*> \par Purpose:
36* =============
37*>
38*> \verbatim
39*>
40*> CHPEVD computes all the eigenvalues and, optionally, eigenvectors of
41*> a complex Hermitian matrix A in packed storage. If eigenvectors are
42*> desired, it uses a divide and conquer algorithm.
43*>
44*> The divide and conquer algorithm makes very mild assumptions about
45*> floating point arithmetic. It will work on machines with a guard
46*> digit in add/subtract, or on those binary machines without guard
47*> digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or
48*> Cray-2. It could conceivably fail on hexadecimal or decimal machines
49*> without guard digits, but we know of none.
50*> \endverbatim
51*
52* Arguments:
53* ==========
54*
55*> \param[in] JOBZ
56*> \verbatim
57*> JOBZ is CHARACTER*1
58*> = 'N': Compute eigenvalues only;
59*> = 'V': Compute eigenvalues and eigenvectors.
60*> \endverbatim
61*>
62*> \param[in] UPLO
63*> \verbatim
64*> UPLO is CHARACTER*1
65*> = 'U': Upper triangle of A is stored;
66*> = 'L': Lower triangle of A is stored.
67*> \endverbatim
68*>
69*> \param[in] N
70*> \verbatim
71*> N is INTEGER
72*> The order of the matrix A. N >= 0.
73*> \endverbatim
74*>
75*> \param[in,out] AP
76*> \verbatim
77*> AP is COMPLEX array, dimension (N*(N+1)/2)
78*> On entry, the upper or lower triangle of the Hermitian matrix
79*> A, packed columnwise in a linear array. The j-th column of A
80*> is stored in the array AP as follows:
81*> if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
82*> if UPLO = 'L', AP(i + (j-1)*(2*n-j)/2) = A(i,j) for j<=i<=n.
83*>
84*> On exit, AP is overwritten by values generated during the
85*> reduction to tridiagonal form. If UPLO = 'U', the diagonal
86*> and first superdiagonal of the tridiagonal matrix T overwrite
87*> the corresponding elements of A, and if UPLO = 'L', the
88*> diagonal and first subdiagonal of T overwrite the
89*> corresponding elements of A.
90*> \endverbatim
91*>
92*> \param[out] W
93*> \verbatim
94*> W is REAL array, dimension (N)
95*> If INFO = 0, the eigenvalues in ascending order.
96*> \endverbatim
97*>
98*> \param[out] Z
99*> \verbatim
100*> Z is COMPLEX array, dimension (LDZ, N)
101*> If JOBZ = 'V', then if INFO = 0, Z contains the orthonormal
102*> eigenvectors of the matrix A, with the i-th column of Z
103*> holding the eigenvector associated with W(i).
104*> If JOBZ = 'N', then Z is not referenced.
105*> \endverbatim
106*>
107*> \param[in] LDZ
108*> \verbatim
109*> LDZ is INTEGER
110*> The leading dimension of the array Z. LDZ >= 1, and if
111*> JOBZ = 'V', LDZ >= max(1,N).
112*> \endverbatim
113*>
114*> \param[out] WORK
115*> \verbatim
116*> WORK is COMPLEX array, dimension (MAX(1,LWORK))
117*> On exit, if INFO = 0, WORK(1) returns the required LWORK.
118*> \endverbatim
119*>
120*> \param[in] LWORK
121*> \verbatim
122*> LWORK is INTEGER
123*> The dimension of array WORK.
124*> If N <= 1, LWORK must be at least 1.
125*> If JOBZ = 'N' and N > 1, LWORK must be at least N.
126*> If JOBZ = 'V' and N > 1, LWORK must be at least 2*N.
127*>
128*> If LWORK = -1, then a workspace query is assumed; the routine
129*> only calculates the required sizes of the WORK, RWORK and
130*> IWORK arrays, returns these values as the first entries of
131*> the WORK, RWORK and IWORK arrays, and no error message
132*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
133*> \endverbatim
134*>
135*> \param[out] RWORK
136*> \verbatim
137*> RWORK is REAL array, dimension (MAX(1,LRWORK))
138*> On exit, if INFO = 0, RWORK(1) returns the required LRWORK.
139*> \endverbatim
140*>
141*> \param[in] LRWORK
142*> \verbatim
143*> LRWORK is INTEGER
144*> The dimension of array RWORK.
145*> If N <= 1, LRWORK must be at least 1.
146*> If JOBZ = 'N' and N > 1, LRWORK must be at least N.
147*> If JOBZ = 'V' and N > 1, LRWORK must be at least
148*> 1 + 5*N + 2*N**2.
149*>
150*> If LRWORK = -1, then a workspace query is assumed; the
151*> routine only calculates the required sizes of the WORK, RWORK
152*> and IWORK arrays, returns these values as the first entries
153*> of the WORK, RWORK and IWORK arrays, and no error message
154*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
155*> \endverbatim
156*>
157*> \param[out] IWORK
158*> \verbatim
159*> IWORK is INTEGER array, dimension (MAX(1,LIWORK))
160*> On exit, if INFO = 0, IWORK(1) returns the required LIWORK.
161*> \endverbatim
162*>
163*> \param[in] LIWORK
164*> \verbatim
165*> LIWORK is INTEGER
166*> The dimension of array IWORK.
167*> If JOBZ = 'N' or N <= 1, LIWORK must be at least 1.
168*> If JOBZ = 'V' and N > 1, LIWORK must be at least 3 + 5*N.
169*>
170*> If LIWORK = -1, then a workspace query is assumed; the
171*> routine only calculates the required sizes of the WORK, RWORK
172*> and IWORK arrays, returns these values as the first entries
173*> of the WORK, RWORK and IWORK arrays, and no error message
174*> related to LWORK or LRWORK or LIWORK is issued by XERBLA.
175*> \endverbatim
176*>
177*> \param[out] INFO
178*> \verbatim
179*> INFO is INTEGER
180*> = 0: successful exit
181*> < 0: if INFO = -i, the i-th argument had an illegal value.
182*> > 0: if INFO = i, the algorithm failed to converge; i
183*> off-diagonal elements of an intermediate tridiagonal
184*> form did not converge to zero.
185*> \endverbatim
186*
187* Authors:
188* ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup complexOTHEReigen
196*
197* =====================================================================
198 SUBROUTINE chpevd( JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK,
199 \$ RWORK, LRWORK, IWORK, LIWORK, INFO )
200*
201* -- LAPACK driver routine --
202* -- LAPACK is a software package provided by Univ. of Tennessee, --
203* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
204*
205* .. Scalar Arguments ..
206 CHARACTER JOBZ, UPLO
207 INTEGER INFO, LDZ, LIWORK, LRWORK, LWORK, N
208* ..
209* .. Array Arguments ..
210 INTEGER IWORK( * )
211 REAL RWORK( * ), W( * )
212 COMPLEX AP( * ), WORK( * ), Z( LDZ, * )
213* ..
214*
215* =====================================================================
216*
217* .. Parameters ..
218 REAL ZERO, ONE
219 parameter( zero = 0.0e+0, one = 1.0e+0 )
220 COMPLEX CONE
221 parameter( cone = ( 1.0e+0, 0.0e+0 ) )
222* ..
223* .. Local Scalars ..
224 LOGICAL LQUERY, WANTZ
225 INTEGER IINFO, IMAX, INDE, INDRWK, INDTAU, INDWRK,
226 \$ iscale, liwmin, llrwk, llwrk, lrwmin, lwmin
227 REAL ANRM, BIGNUM, EPS, RMAX, RMIN, SAFMIN, SIGMA,
228 \$ smlnum
229* ..
230* .. External Functions ..
231 LOGICAL LSAME
232 REAL CLANHP, SLAMCH
233 EXTERNAL lsame, clanhp, slamch
234* ..
235* .. External Subroutines ..
236 EXTERNAL chptrd, csscal, cstedc, cupmtr, sscal, ssterf,
237 \$ xerbla
238* ..
239* .. Intrinsic Functions ..
240 INTRINSIC sqrt
241* ..
242* .. Executable Statements ..
243*
244* Test the input parameters.
245*
246 wantz = lsame( jobz, 'V' )
247 lquery = ( lwork.EQ.-1 .OR. lrwork.EQ.-1 .OR. liwork.EQ.-1 )
248*
249 info = 0
250 IF( .NOT.( wantz .OR. lsame( jobz, 'N' ) ) ) THEN
251 info = -1
252 ELSE IF( .NOT.( lsame( uplo, 'L' ) .OR. lsame( uplo, 'U' ) ) )
253 \$ THEN
254 info = -2
255 ELSE IF( n.LT.0 ) THEN
256 info = -3
257 ELSE IF( ldz.LT.1 .OR. ( wantz .AND. ldz.LT.n ) ) THEN
258 info = -7
259 END IF
260*
261 IF( info.EQ.0 ) THEN
262 IF( n.LE.1 ) THEN
263 lwmin = 1
264 liwmin = 1
265 lrwmin = 1
266 ELSE
267 IF( wantz ) THEN
268 lwmin = 2*n
269 lrwmin = 1 + 5*n + 2*n**2
270 liwmin = 3 + 5*n
271 ELSE
272 lwmin = n
273 lrwmin = n
274 liwmin = 1
275 END IF
276 END IF
277 work( 1 ) = lwmin
278 rwork( 1 ) = lrwmin
279 iwork( 1 ) = liwmin
280*
281 IF( lwork.LT.lwmin .AND. .NOT.lquery ) THEN
282 info = -9
283 ELSE IF( lrwork.LT.lrwmin .AND. .NOT.lquery ) THEN
284 info = -11
285 ELSE IF( liwork.LT.liwmin .AND. .NOT.lquery ) THEN
286 info = -13
287 END IF
288 END IF
289*
290 IF( info.NE.0 ) THEN
291 CALL xerbla( 'CHPEVD', -info )
292 RETURN
293 ELSE IF( lquery ) THEN
294 RETURN
295 END IF
296*
297* Quick return if possible
298*
299 IF( n.EQ.0 )
300 \$ RETURN
301*
302 IF( n.EQ.1 ) THEN
303 w( 1 ) = real( ap( 1 ) )
304 IF( wantz )
305 \$ z( 1, 1 ) = cone
306 RETURN
307 END IF
308*
309* Get machine constants.
310*
311 safmin = slamch( 'Safe minimum' )
312 eps = slamch( 'Precision' )
313 smlnum = safmin / eps
314 bignum = one / smlnum
315 rmin = sqrt( smlnum )
316 rmax = sqrt( bignum )
317*
318* Scale matrix to allowable range, if necessary.
319*
320 anrm = clanhp( 'M', uplo, n, ap, rwork )
321 iscale = 0
322 IF( anrm.GT.zero .AND. anrm.LT.rmin ) THEN
323 iscale = 1
324 sigma = rmin / anrm
325 ELSE IF( anrm.GT.rmax ) THEN
326 iscale = 1
327 sigma = rmax / anrm
328 END IF
329 IF( iscale.EQ.1 ) THEN
330 CALL csscal( ( n*( n+1 ) ) / 2, sigma, ap, 1 )
331 END IF
332*
333* Call CHPTRD to reduce Hermitian packed matrix to tridiagonal form.
334*
335 inde = 1
336 indtau = 1
337 indrwk = inde + n
338 indwrk = indtau + n
339 llwrk = lwork - indwrk + 1
340 llrwk = lrwork - indrwk + 1
341 CALL chptrd( uplo, n, ap, w, rwork( inde ), work( indtau ),
342 \$ iinfo )
343*
344* For eigenvalues only, call SSTERF. For eigenvectors, first call
345* CUPGTR to generate the orthogonal matrix, then call CSTEDC.
346*
347 IF( .NOT.wantz ) THEN
348 CALL ssterf( n, w, rwork( inde ), info )
349 ELSE
350 CALL cstedc( 'I', n, w, rwork( inde ), z, ldz, work( indwrk ),
351 \$ llwrk, rwork( indrwk ), llrwk, iwork, liwork,
352 \$ info )
353 CALL cupmtr( 'L', uplo, 'N', n, n, ap, work( indtau ), z, ldz,
354 \$ work( indwrk ), iinfo )
355 END IF
356*
357* If matrix was scaled, then rescale eigenvalues appropriately.
358*
359 IF( iscale.EQ.1 ) THEN
360 IF( info.EQ.0 ) THEN
361 imax = n
362 ELSE
363 imax = info - 1
364 END IF
365 CALL sscal( imax, one / sigma, w, 1 )
366 END IF
367*
368 work( 1 ) = lwmin
369 rwork( 1 ) = lrwmin
370 iwork( 1 ) = liwmin
371 RETURN
372*
373* End of CHPEVD
374*
375 END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine ssterf(N, D, E, INFO)
SSTERF
Definition: ssterf.f:86
subroutine csscal(N, SA, CX, INCX)
CSSCAL
Definition: csscal.f:78
subroutine chptrd(UPLO, N, AP, D, E, TAU, INFO)
CHPTRD
Definition: chptrd.f:151
subroutine cupmtr(SIDE, UPLO, TRANS, M, N, AP, TAU, C, LDC, WORK, INFO)
CUPMTR
Definition: cupmtr.f:150
subroutine cstedc(COMPZ, N, D, E, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CSTEDC
Definition: cstedc.f:212
subroutine chpevd(JOBZ, UPLO, N, AP, W, Z, LDZ, WORK, LWORK, RWORK, LRWORK, IWORK, LIWORK, INFO)
CHPEVD computes the eigenvalues and, optionally, the left and/or right eigenvectors for OTHER matrice...
Definition: chpevd.f:200
subroutine sscal(N, SA, SX, INCX)
SSCAL
Definition: sscal.f:79