1: *> \brief \b DSTEGR
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DSTEGR + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dstegr.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dstegr.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dstegr.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DSTEGR( 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: * DOUBLE PRECISION Z( LDZ, * )
34: * ..
35: *
36: *
37: *> \par Purpose:
38: * =============
39: *>
40: *> \verbatim
41: *>
42: *> DSTEGR 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: *> DSTEGR is a compatibility wrapper around the improved DSTEMR 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 : DSTEGR and DSTEMR 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 DOUBLE PRECISION 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 DLARRV.
239: *> Here, the digit X = ABS( IINFO ) < 10, where IINFO is
240: *> the nonzero error code returned by DLARRE or
241: *> DLARRV, 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: *> \ingroup doubleOTHERcomputational
253: *
254: *> \par Contributors:
255: * ==================
256: *>
257: *> Inderjit Dhillon, IBM Almaden, USA \n
258: *> Osni Marques, LBNL/NERSC, USA \n
259: *> Christof Voemel, LBNL/NERSC, USA \n
260: *
261: * =====================================================================
262: SUBROUTINE DSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
263: $ ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
264: $ LIWORK, INFO )
265: *
266: * -- LAPACK computational routine --
267: * -- LAPACK is a software package provided by Univ. of Tennessee, --
268: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
269: *
270: * .. Scalar Arguments ..
271: CHARACTER JOBZ, RANGE
272: INTEGER IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
273: DOUBLE PRECISION ABSTOL, VL, VU
274: * ..
275: * .. Array Arguments ..
276: INTEGER ISUPPZ( * ), IWORK( * )
277: DOUBLE PRECISION D( * ), E( * ), W( * ), WORK( * )
278: DOUBLE PRECISION Z( LDZ, * )
279: * ..
280: *
281: * =====================================================================
282: *
283: * .. Local Scalars ..
284: LOGICAL TRYRAC
285: * ..
286: * .. External Subroutines ..
287: EXTERNAL DSTEMR
288: * ..
289: * .. Executable Statements ..
290: INFO = 0
291: TRYRAC = .FALSE.
292:
293: CALL DSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
294: $ M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
295: $ IWORK, LIWORK, INFO )
296: *
297: * End of DSTEGR
298: *
299: END
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