summaryrefslogtreecommitdiff
path: root/SRC/sstegr.f
blob: 99a4be62b71489754c8dc940b66d2292d58522a4 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
*> \brief \b SSTEGR
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SSTEGR + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sstegr.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sstegr.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sstegr.f">
*> [TXT]</a>
*> \endhtmlonly
*
*  Definition:
*  ===========
*
*       SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
*                  ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
*                  LIWORK, INFO )
*
*       .. Scalar Arguments ..
*       CHARACTER          JOBZ, RANGE
*       INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
*       REAL             ABSTOL, VL, VU
*       ..
*       .. Array Arguments ..
*       INTEGER            ISUPPZ( * ), IWORK( * )
*       REAL               D( * ), E( * ), W( * ), WORK( * )
*       REAL               Z( LDZ, * )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SSTEGR computes selected eigenvalues and, optionally, eigenvectors
*> of a real symmetric tridiagonal matrix T. Any such unreduced matrix has
*> a well defined set of pairwise different real eigenvalues, the corresponding
*> real eigenvectors are pairwise orthogonal.
*>
*> The spectrum may be computed either completely or partially by specifying
*> either an interval (VL,VU] or a range of indices IL:IU for the desired
*> eigenvalues.
*>
*> SSTEGR is a compatibility wrapper around the improved SSTEMR routine.
*> See SSTEMR for further details.
*>
*> One important change is that the ABSTOL parameter no longer provides any
*> benefit and hence is no longer used.
*>
*> Note : SSTEGR and SSTEMR work only on machines which follow
*> IEEE-754 floating-point standard in their handling of infinities and
*> NaNs.  Normal execution may create these exceptiona values and hence
*> may abort due to a floating point exception in environments which
*> do not conform to the IEEE-754 standard.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] JOBZ
*> \verbatim
*>          JOBZ is CHARACTER*1
*>          = 'N':  Compute eigenvalues only;
*>          = 'V':  Compute eigenvalues and eigenvectors.
*> \endverbatim
*>
*> \param[in] RANGE
*> \verbatim
*>          RANGE is CHARACTER*1
*>          = 'A': all eigenvalues will be found.
*>          = 'V': all eigenvalues in the half-open interval (VL,VU]
*>                 will be found.
*>          = 'I': the IL-th through IU-th eigenvalues will be found.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The order of the matrix.  N >= 0.
*> \endverbatim
*>
*> \param[in,out] D
*> \verbatim
*>          D is REAL array, dimension (N)
*>          On entry, the N diagonal elements of the tridiagonal matrix
*>          T. On exit, D is overwritten.
*> \endverbatim
*>
*> \param[in,out] E
*> \verbatim
*>          E is REAL array, dimension (N)
*>          On entry, the (N-1) subdiagonal elements of the tridiagonal
*>          matrix T in elements 1 to N-1 of E. E(N) need not be set on
*>          input, but is used internally as workspace.
*>          On exit, E is overwritten.
*> \endverbatim
*>
*> \param[in] VL
*> \verbatim
*>          VL is REAL
*>
*>          If RANGE='V', the lower bound of the interval to
*>          be searched for eigenvalues. VL < VU.
*>          Not referenced if RANGE = 'A' or 'I'.
*> \endverbatim
*>
*> \param[in] VU
*> \verbatim
*>          VU is REAL
*>
*>          If RANGE='V', the upper bound of the interval to
*>          be searched for eigenvalues. VL < VU.
*>          Not referenced if RANGE = 'A' or 'I'.
*> \endverbatim
*>
*> \param[in] IL
*> \verbatim
*>          IL is INTEGER
*>
*>          If RANGE='I', the index of the
*>          smallest eigenvalue to be returned.
*>          1 <= IL <= IU <= N, if N > 0.
*>          Not referenced if RANGE = 'A' or 'V'.
*> \endverbatim
*>
*> \param[in] IU
*> \verbatim
*>          IU is INTEGER
*>
*>          If RANGE='I', the index of the
*>          largest eigenvalue to be returned.
*>          1 <= IL <= IU <= N, if N > 0.
*>          Not referenced if RANGE = 'A' or 'V'.
*> \endverbatim
*>
*> \param[in] ABSTOL
*> \verbatim
*>          ABSTOL is REAL
*>          Unused.  Was the absolute error tolerance for the
*>          eigenvalues/eigenvectors in previous versions.
*> \endverbatim
*>
*> \param[out] M
*> \verbatim
*>          M is INTEGER
*>          The total number of eigenvalues found.  0 <= M <= N.
*>          If RANGE = 'A', M = N, and if RANGE = 'I', M = IU-IL+1.
*> \endverbatim
*>
*> \param[out] W
*> \verbatim
*>          W is REAL array, dimension (N)
*>          The first M elements contain the selected eigenvalues in
*>          ascending order.
*> \endverbatim
*>
*> \param[out] Z
*> \verbatim
*>          Z is REAL array, dimension (LDZ, max(1,M) )
*>          If JOBZ = 'V', and if INFO = 0, then the first M columns of Z
*>          contain the orthonormal eigenvectors of the matrix T
*>          corresponding to the selected eigenvalues, with the i-th
*>          column of Z holding the eigenvector associated with W(i).
*>          If JOBZ = 'N', then Z is not referenced.
*>          Note: the user must ensure that at least max(1,M) columns are
*>          supplied in the array Z; if RANGE = 'V', the exact value of M
*>          is not known in advance and an upper bound must be used.
*>          Supplying N columns is always safe.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*>          LDZ is INTEGER
*>          The leading dimension of the array Z.  LDZ >= 1, and if
*>          JOBZ = 'V', then LDZ >= max(1,N).
*> \endverbatim
*>
*> \param[out] ISUPPZ
*> \verbatim
*>          ISUPPZ is INTEGER array, dimension ( 2*max(1,M) )
*>          The support of the eigenvectors in Z, i.e., the indices
*>          indicating the nonzero elements in Z. The i-th computed eigenvector
*>          is nonzero only in elements ISUPPZ( 2*i-1 ) through
*>          ISUPPZ( 2*i ). This is relevant in the case when the matrix
*>          is split. ISUPPZ is only accessed when JOBZ is 'V' and N > 0.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LWORK)
*>          On exit, if INFO = 0, WORK(1) returns the optimal
*>          (and minimal) LWORK.
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK. LWORK >= max(1,18*N)
*>          if JOBZ = 'V', and LWORK >= max(1,12*N) if JOBZ = 'N'.
*>          If LWORK = -1, then a workspace query is assumed; the routine
*>          only calculates the optimal size of the WORK array, returns
*>          this value as the first entry of the WORK array, and no error
*>          message related to LWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] IWORK
*> \verbatim
*>          IWORK is INTEGER array, dimension (LIWORK)
*>          On exit, if INFO = 0, IWORK(1) returns the optimal LIWORK.
*> \endverbatim
*>
*> \param[in] LIWORK
*> \verbatim
*>          LIWORK is INTEGER
*>          The dimension of the array IWORK.  LIWORK >= max(1,10*N)
*>          if the eigenvectors are desired, and LIWORK >= max(1,8*N)
*>          if only the eigenvalues are to be computed.
*>          If LIWORK = -1, then a workspace query is assumed; the
*>          routine only calculates the optimal size of the IWORK array,
*>          returns this value as the first entry of the IWORK array, and
*>          no error message related to LIWORK is issued by XERBLA.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*>          INFO is INTEGER
*>          On exit, INFO
*>          = 0:  successful exit
*>          < 0:  if INFO = -i, the i-th argument had an illegal value
*>          > 0:  if INFO = 1X, internal error in SLARRE,
*>                if INFO = 2X, internal error in SLARRV.
*>                Here, the digit X = ABS( IINFO ) < 10, where IINFO is
*>                the nonzero error code returned by SLARRE or
*>                SLARRV, respectively.
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date June 2016
*
*> \ingroup realOTHERcomputational
*
*> \par Contributors:
*  ==================
*>
*> Inderjit Dhillon, IBM Almaden, USA \n
*> Osni Marques, LBNL/NERSC, USA \n
*> Christof Voemel, LBNL/NERSC, USA \n
*
*  =====================================================================
      SUBROUTINE SSTEGR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
     $           ABSTOL, M, W, Z, LDZ, ISUPPZ, WORK, LWORK, IWORK,
     $           LIWORK, INFO )
*
*  -- LAPACK computational routine (version 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     June 2016
*
*     .. Scalar Arguments ..
      CHARACTER          JOBZ, RANGE
      INTEGER            IL, INFO, IU, LDZ, LIWORK, LWORK, M, N
      REAL             ABSTOL, VL, VU
*     ..
*     .. Array Arguments ..
      INTEGER            ISUPPZ( * ), IWORK( * )
      REAL               D( * ), E( * ), W( * ), WORK( * )
      REAL               Z( LDZ, * )
*     ..
*
*  =====================================================================
*
*     .. Local Scalars ..
      LOGICAL TRYRAC
*     ..
*     .. External Subroutines ..
      EXTERNAL SSTEMR
*     ..
*     .. Executable Statements ..
      INFO = 0
      TRYRAC = .FALSE.

      CALL SSTEMR( JOBZ, RANGE, N, D, E, VL, VU, IL, IU,
     $                   M, W, Z, LDZ, N, ISUPPZ, TRYRAC, WORK, LWORK,
     $                   IWORK, LIWORK, INFO )
*
*     End of SSTEGR
*
      END