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
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 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
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