LAPACK  3.4.2
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zstegr.f
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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
9 *> Download ZSTEGR + dependencies
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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 compatability 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 *> \endverbatim
109 *>
110 *> \param[in] VU
111 *> \verbatim
112 *> VU is DOUBLE PRECISION
113 *>
114 *> If RANGE='V', the lower and upper bounds of the interval to
115 *> be searched for eigenvalues. VL < VU.
116 *> Not referenced if RANGE = 'A' or 'I'.
117 *> \endverbatim
118 *>
119 *> \param[in] IL
120 *> \verbatim
121 *> IL is INTEGER
122 *> \endverbatim
123 *>
124 *> \param[in] IU
125 *> \verbatim
126 *> IU is INTEGER
127 *>
128 *> If RANGE='I', the indices (in ascending order) of the
129 *> smallest and largest eigenvalues to be returned.
130 *> 1 <= IL <= IU <= N, if N > 0.
131 *> Not referenced if RANGE = 'A' or 'V'.
132 *> \endverbatim
133 *>
134 *> \param[in] ABSTOL
135 *> \verbatim
136 *> ABSTOL is DOUBLE PRECISION
137 *> Unused. Was the absolute error tolerance for the
138 *> eigenvalues/eigenvectors in previous versions.
139 *> \endverbatim
140 *>
141 *> \param[out] M
142 *> \verbatim
143 *> M is INTEGER
144 *> The total number of eigenvalues found. 0 <= M <= N.
145 *> If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
146 *> \endverbatim
147 *>
148 *> \param[out] W
149 *> \verbatim
150 *> W is DOUBLE PRECISION array, dimension (N)
151 *> The first M elements contain the selected eigenvalues in
152 *> ascending order.
153 *> \endverbatim
154 *>
155 *> \param[out] Z
156 *> \verbatim
157 *> Z is COMPLEX*16 array, dimension (LDZ, max(1,M) )
158 *> If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
159 *> contain the orthonormal eigenvectors of the matrix T
160 *> corresponding to the selected eigenvalues, with the i-th
161 *> column of Z holding the eigenvector associated with W(i).
162 *> If JOBZ = 'N', then Z is not referenced.
163 *> Note: the user must ensure that at least max(1,M) columns are
164 *> supplied in the array Z; if RANGE = 'V', the exact value of M
165 *> is not known in advance and an upper bound must be used.
166 *> Supplying N columns is always safe.
167 *> \endverbatim
168 *>
169 *> \param[in] LDZ
170 *> \verbatim
171 *> LDZ is INTEGER
172 *> The leading dimension of the array Z. LDZ >= 1, and if
173 *> JOBZ = 'V', then LDZ >= max(1,N).
174 *> \endverbatim
175 *>
176 *> \param[out] ISUPPZ
177 *> \verbatim
178 *> ISUPPZ is INTEGER ARRAY, dimension ( 2*max(1,M) )
179 *> The support of the eigenvectors in Z, i.e., the indices
180 *> indicating the nonzero elements in Z. The i-th computed eigenvector
181 *> is nonzero only in elements ISUPPZ( 2*i-1 ) through
182 *> ISUPPZ( 2*i ). This is relevant in the case when the matrix
183 *> is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
184 *> \endverbatim
185 *>
186 *> \param[out] WORK
187 *> \verbatim
188 *> WORK is DOUBLE PRECISION array, dimension (LWORK)
189 *> On exit, if INFO = 0, WORK(1) returns the optimal
190 *> (and minimal) LWORK.
191 *> \endverbatim
192 *>
193 *> \param[in] LWORK
194 *> \verbatim
195 *> LWORK is INTEGER
196 *> The dimension of the array WORK. LWORK >= max(1,18*N)
197 *> if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
198 *> If LWORK = -1, then a workspace query is assumed; the routine
199 *> only calculates the optimal size of the WORK array, returns
200 *> this value as the first entry of the WORK array, and no error
201 *> message related to LWORK is issued by XERBLA.
202 *> \endverbatim
203 *>
204 *> \param[out] IWORK
205 *> \verbatim
206 *> IWORK is INTEGER array, dimension (LIWORK)
207 *> On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
208 *> \endverbatim
209 *>
210 *> \param[in] LIWORK
211 *> \verbatim
212 *> LIWORK is INTEGER
213 *> The dimension of the array IWORK. LIWORK >= max(1,10*N)
214 *> if the eigenvectors are desired, and LIWORK >= max(1,8*N)
215 *> if only the eigenvalues are to be computed.
216 *> If LIWORK = -1, then a workspace query is assumed; the
217 *> routine only calculates the optimal size of the IWORK array,
218 *> returns this value as the first entry of the IWORK array, and
219 *> no error message related to LIWORK is issued by XERBLA.
220 *> \endverbatim
221 *>
222 *> \param[out] INFO
223 *> \verbatim
224 *> INFO is INTEGER
225 *> On exit, INFO
226 *> = 0: successful exit
227 *> < 0: if INFO = -i, the i-th argument had an illegal value
228 *> > 0: if INFO = 1X, internal error in DLARRE,
229 *> if INFO = 2X, internal error in ZLARRV.
230 *> Here, the digit X = ABS( IINFO ) < 10, where IINFO is
231 *> the nonzero error code returned by DLARRE or
232 *> ZLARRV, respectively.
233 *> \endverbatim
234 *
235 * Authors:
236 * ========
237 *
238 *> \author Univ. of Tennessee
239 *> \author Univ. of California Berkeley
240 *> \author Univ. of Colorado Denver
241 *> \author NAG Ltd.
242 *
243 *> \date November 2011
244 *
245 *> \ingroup complex16OTHERcomputational
246 *
247 *> \par Contributors:
248 * ==================
249 *>
250 *> Inderjit Dhillon, IBM Almaden, USA \n
251 *> Osni Marques, LBNL/NERSC, USA \n
252 *> Christof Voemel, LBNL/NERSC, USA \n
253 *
254 * =====================================================================
255  SUBROUTINE zstegr( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
256  $ abstol, m, w, z, ldz, isuppz, work, lwork, iwork,
257  $ liwork, info )
258 *
259 * -- LAPACK computational routine (version 3.4.0) --
260 * -- LAPACK is a software package provided by Univ. of Tennessee, --
261 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
262 * November 2011
263 *
264 * .. Scalar Arguments ..
265  CHARACTER jobz, range
266  INTEGER il, info, iu, ldz, liwork, lwork, m, n
267  DOUBLE PRECISION abstol, vl, vu
268 * ..
269 * .. Array Arguments ..
270  INTEGER isuppz( * ), iwork( * )
271  DOUBLE PRECISION d( * ), e( * ), w( * ), work( * )
272  COMPLEX*16 z( ldz, * )
273 * ..
274 *
275 * =====================================================================
276 *
277 * .. Local Scalars ..
278  LOGICAL tryrac
279 * ..
280 * .. External Subroutines ..
281  EXTERNAL zstemr
282 * ..
283 * .. Executable Statements ..
284  info = 0
285  tryrac = .false.
286 
287  CALL zstemr( jobz, range, n, d, e, vl, vu, il, iu,
288  $ m, w, z, ldz, n, isuppz, tryrac, work, lwork,
289  $ iwork, liwork, info )
290 *
291 * End of ZSTEGR
292 *
293  END