LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
zstegr.f
Go to the documentation of this file.
1 *> \brief \b ZSTEGR
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/zstegr.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zstegr.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zstegr.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE ZSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
22 * ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
23 * LIWORK, INFO )
24 *
25 * .. Scalar Arguments ..
26 * CHARACTER JOBZ, RANGE
27 * INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
28 * DOUBLE PRECISION ABSTOL, VL, VU
29 * ..
30 * .. Array Arguments ..
31 * INTEGER ISUPPZ( * ), IWORK( * )
32 * DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
33 * COMPLEX*16 Z( LDZ, * )
34 * ..
35 *
36 *
37 *> \par Purpose:
38 * =============
39 *>
40 *> \verbatim
41 *>
42 *> ZSTEGR computes selected eigenvalues and, optionally, eigenvectors
43 *> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
44 *> a well defined set of pairwise different real eigenvalues, the corresponding
45 *> real eigenvectors are pairwise orthogonal.
46 *>
47 *> The spectrum may be computed either completely or partially by specifying
48 *> either an interval (VL,VU] or a range of indices IL:IU for the desired
49 *> eigenvalues.
50 *>
51 *> ZSTEGR is a compatibility wrapper around the improved ZSTEMR routine.
52 *> See DSTEMR for further details.
53 *>
54 *> One important change is that the ABSTOL parameter no longer provides any
55 *> benefit and hence is no longer used.
56 *>
57 *> Note : ZSTEGR and ZSTEMR work only on machines which follow
58 *> IEEE-754 floating-point standard in their handling of infinities and
59 *> NaNs. Normal execution may create these exceptiona values and hence
60 *> may abort due to a floating point exception in environments which
61 *> do not conform to the IEEE-754 standard.
62 *> \endverbatim
63 *
64 * Arguments:
65 * ==========
66 *
67 *> \param[in] JOBZ
68 *> \verbatim
69 *> JOBZ is CHARACTER*1
70 *> = 'N': Compute eigenvalues only;
71 *> = 'V': Compute eigenvalues and eigenvectors.
72 *> \endverbatim
73 *>
74 *> \param[in] RANGE
75 *> \verbatim
76 *> RANGE is CHARACTER*1
77 *> = 'A': all eigenvalues will be found.
78 *> = 'V': all eigenvalues in the half-open interval (VL,VU]
79 *> will be found.
80 *> = 'I': the IL-th through IU-th eigenvalues will be found.
81 *> \endverbatim
82 *>
83 *> \param[in] N
84 *> \verbatim
85 *> N is INTEGER
86 *> The order of the matrix. N >= 0.
87 *> \endverbatim
88 *>
89 *> \param[in,out] D
90 *> \verbatim
91 *> D is DOUBLE PRECISION array, dimension (N)
92 *> On entry, the N diagonal elements of the tridiagonal matrix
93 *> T. On exit, D is overwritten.
94 *> \endverbatim
95 *>
96 *> \param[in,out] E
97 *> \verbatim
98 *> E is DOUBLE PRECISION array, dimension (N)
99 *> On entry, the (N-1) subdiagonal elements of the tridiagonal
100 *> matrix T in elements 1 to N-1 of E. E(N) need not be set on
101 *> input, but is used internally as workspace.
102 *> On exit, E is overwritten.
103 *> \endverbatim
104 *>
105 *> \param[in] VL
106 *> \verbatim
107 *> VL is DOUBLE PRECISION
108 *>
109 *> If RANGE='V', the lower bound of the interval to
110 *> be searched for eigenvalues. VL < VU.
111 *> Not referenced if RANGE = 'A' or 'I'.
112 *> \endverbatim
113 *>
114 *> \param[in] VU
115 *> \verbatim
116 *> VU is DOUBLE PRECISION
117 *>
118 *> If RANGE='V', the upper bound of the interval to
119 *> be searched for eigenvalues. VL < VU.
120 *> Not referenced if RANGE = 'A' or 'I'.
121 *> \endverbatim
122 *>
123 *> \param[in] IL
124 *> \verbatim
125 *> IL is INTEGER
126 *>
127 *> If RANGE='I', the index of the
128 *> smallest eigenvalue to be returned.
129 *> 1 <= IL <= IU <= N, if N > 0.
130 *> Not referenced if RANGE = 'A' or 'V'.
131 *> \endverbatim
132 *>
133 *> \param[in] IU
134 *> \verbatim
135 *> IU is INTEGER
136 *>
137 *> If RANGE='I', the index of the
138 *> largest eigenvalue to be returned.
139 *> 1 <= IL <= IU <= N, if N > 0.
140 *> Not referenced if RANGE = 'A' or 'V'.
141 *> \endverbatim
142 *>
143 *> \param[in] ABSTOL
144 *> \verbatim
145 *> ABSTOL is DOUBLE PRECISION
146 *> Unused. Was the absolute error tolerance for the
147 *> eigenvalues/eigenvectors in previous versions.
148 *> \endverbatim
149 *>
150 *> \param[out] M
151 *> \verbatim
152 *> M is INTEGER
153 *> The total number of eigenvalues found. 0 <= M <= N.
154 *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
155 *> \endverbatim
156 *>
157 *> \param[out] W
158 *> \verbatim
159 *> W is DOUBLE PRECISION array, dimension (N)
160 *> The first M elements contain the selected eigenvalues in
161 *> ascending order.
162 *> \endverbatim
163 *>
164 *> \param[out] Z
165 *> \verbatim
166 *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M) )
167 *> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
168 *> contain the orthonormal eigenvectors of the matrix T
169 *> corresponding to the selected eigenvalues, with the i-th
170 *> column of Z holding the eigenvector associated with W(i).
171 *> If JOBZ = 'N', then Z is not referenced.
172 *> Note: the user must ensure that at least max(1,M) columns are
173 *> supplied in the array Z; if RANGE = 'V', the exact value of M
174 *> is not known in advance and an upper bound must be used.
175 *> Supplying N columns is always safe.
176 *> \endverbatim
177 *>
178 *> \param[in] LDZ
179 *> \verbatim
180 *> LDZ is INTEGER
181 *> The leading dimension of the array Z. LDZ >= 1, and if
182 *> JOBZ = 'V', then LDZ >= max(1,N).
183 *> \endverbatim
184 *>
185 *> \param[out] ISUPPZ
186 *> \verbatim
187 *> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
188 *> The support of the eigenvectors in Z, i.e., the indices
189 *> indicating the nonzero elements in Z. The i-th computed eigenvector
190 *> is nonzero only in elements ISUPPZ( 2*i-1 ) through
191 *> ISUPPZ( 2*i ). This is relevant in the case when the matrix
192 *> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
193 *> \endverbatim
194 *>
195 *> \param[out] WORK
196 *> \verbatim
197 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
198 *> On exit, if INFO = 0, WORK(1) returns the optimal
199 *> (and minimal) LWORK.
200 *> \endverbatim
201 *>
202 *> \param[in] LWORK
203 *> \verbatim
204 *> LWORK is INTEGER
205 *> The dimension of the array WORK. LWORK >= max(1,18*N)
206 *> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
207 *> If LWORK = -1, then a workspace query is assumed; the routine
208 *> only calculates the optimal size of the WORK array, returns
209 *> this value as the first entry of the WORK array, and no error
210 *> message related to LWORK is issued by XERBLA.
211 *> \endverbatim
212 *>
213 *> \param[out] IWORK
214 *> \verbatim
215 *> IWORK is INTEGER array, dimension (LIWORK)
216 *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
217 *> \endverbatim
218 *>
219 *> \param[in] LIWORK
220 *> \verbatim
221 *> LIWORK is INTEGER
222 *> The dimension of the array IWORK. LIWORK >= max(1,10*N)
223 *> if the eigenvectors are desired, and LIWORK >= max(1,8*N)
224 *> if only the eigenvalues are to be computed.
225 *> If LIWORK = -1, then a workspace query is assumed; the
226 *> routine only calculates the optimal size of the IWORK array,
227 *> returns this value as the first entry of the IWORK array, and
228 *> no error message related to LIWORK is issued by XERBLA.
229 *> \endverbatim
230 *>
231 *> \param[out] INFO
232 *> \verbatim
233 *> INFO is INTEGER
234 *> On exit, INFO
235 *> = 0: successful exit
236 *> < 0: if INFO = -i, the i-th argument had an illegal value
237 *> > 0: if INFO = 1X, internal error in DLARRE,
238 *> if INFO = 2X, internal error in ZLARRV.
239 *> Here, the digit X = ABS( IINFO ) < 10, where IINFO is
240 *> the nonzero error code returned by DLARRE or
241 *> ZLARRV, respectively.
242 *> \endverbatim
243 *
244 * Authors:
245 * ========
246 *
247 *> \author Univ. of Tennessee
248 *> \author Univ. of California Berkeley
249 *> \author Univ. of Colorado Denver
250 *> \author NAG Ltd.
251 *
252 *> \date June 2016
253 *
254 *> \ingroup complex16OTHERcomputational
255 *
256 *> \par Contributors:
257 * ==================
258 *>
259 *> Inderjit Dhillon, IBM Almaden, USA \n
260 *> Osni Marques, LBNL/NERSC, USA \n
261 *> Christof Voemel, LBNL/NERSC, USA \n
262 *
263 * =====================================================================
264  SUBROUTINE zstegr( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
265  \$ abstol, m, w, z, ldz, isuppz, work, lwork, iwork,
266  \$ liwork, info )
267 *
268 * -- LAPACK computational routine (version 3.6.1) --
269 * -- LAPACK is a software package provided by Univ. of Tennessee, --
270 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
271 * June 2016
272 *
273 * .. Scalar Arguments ..
274  CHARACTER JOBZ, RANGE
275  INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
276  DOUBLE PRECISION ABSTOL, VL, VU
277 * ..
278 * .. Array Arguments ..
279  INTEGER ISUPPZ( * ), IWORK( * )
280  DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
281  COMPLEX*16 Z( ldz, * )
282 * ..
283 *
284 * =====================================================================
285 *
286 * .. Local Scalars ..
287  LOGICAL TRYRAC
288 * ..
289 * .. External Subroutines ..
290  EXTERNAL zstemr
291 * ..
292 * .. Executable Statements ..
293  info = 0
294  tryrac = .false.
295
296  CALL zstemr( jobz, range, n, d, e, vl, vu, il, iu,
297  \$ m, w, z, ldz, n, isuppz, tryrac, work, lwork,
298  \$ iwork, liwork, info )
299 *
300 * End of ZSTEGR
301 *
302  END
subroutine zstegr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK, LIWORK, INFO)
ZSTEGR
Definition: zstegr.f:267
subroutine zstemr(JOBZ, RANGE, N, D, E, VL, VU, IL, IU, M, W, Z, LDZ, NZC, ISUPPZ, TRYRAC, WORK, LWORK, IWORK, LIWORK, INFO)
ZSTEMR
Definition: zstemr.f:340