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
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
|
*> \brief \b DSB2ST_KERNELS
*
* @generated from zhb2st_kernels.f, fortran z -> d, Wed Dec 7 08:22:39 2016
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download DSB2ST_KERNELS + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dsb2st_kernels.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dsb2st_kernels.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dsb2st_kernels.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
* ST, ED, SWEEP, N, NB, IB,
* A, LDA, V, TAU, LDVT, WORK)
*
* IMPLICIT NONE
*
* .. Scalar Arguments ..
* CHARACTER UPLO
* LOGICAL WANTZ
* INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
* ..
* .. Array Arguments ..
* DOUBLE PRECISION A( LDA, * ), V( * ),
* TAU( * ), WORK( * )
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSB2ST_KERNELS is an internal routine used by the DSYTRD_SB2ST
*> subroutine.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*> WANTZ is LOGICAL which indicate if Eigenvalue are requested or both
*> Eigenvalue/Eigenvectors.
*> \endverbatim
*>
*> \param[in] TTYPE
*> \verbatim
*> TTYPE is INTEGER
*> \endverbatim
*>
*> \param[in] ST
*> \verbatim
*> ST is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] ED
*> \verbatim
*> ED is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] SWEEP
*> \verbatim
*> SWEEP is INTEGER
*> internal parameter for indices.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER. The order of the matrix A.
*> \endverbatim
*>
*> \param[in] NB
*> \verbatim
*> NB is INTEGER. The size of the band.
*> \endverbatim
*>
*> \param[in] IB
*> \verbatim
*> IB is INTEGER.
*> \endverbatim
*>
*> \param[in, out] A
*> \verbatim
*> A is DOUBLE PRECISION array. A pointer to the matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER. The leading dimension of the matrix A.
*> \endverbatim
*>
*> \param[out] V
*> \verbatim
*> V is DOUBLE PRECISION array, dimension 2*n if eigenvalues only are
*> requested or to be queried for vectors.
*> \endverbatim
*>
*> \param[out] TAU
*> \verbatim
*> TAU is DOUBLE PRECISION array, dimension (2*n).
*> The scalar factors of the Householder reflectors are stored
*> in this array.
*> \endverbatim
*>
*> \param[in] LDVT
*> \verbatim
*> LDVT is INTEGER.
*> \endverbatim
*>
*> \param[in] WORK
*> \verbatim
*> WORK is DOUBLE PRECISION array. Workspace of size nb.
*> \endverbatim
*>
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Implemented by Azzam Haidar.
*>
*> All details are available on technical report, SC11, SC13 papers.
*>
*> Azzam Haidar, Hatem Ltaief, and Jack Dongarra.
*> Parallel reduction to condensed forms for symmetric eigenvalue problems
*> using aggregated fine-grained and memory-aware kernels. In Proceedings
*> of 2011 International Conference for High Performance Computing,
*> Networking, Storage and Analysis (SC '11), New York, NY, USA,
*> Article 8 , 11 pages.
*> http://doi.acm.org/10.1145/2063384.2063394
*>
*> A. Haidar, J. Kurzak, P. Luszczek, 2013.
*> An improved parallel singular value algorithm and its implementation
*> for multicore hardware, In Proceedings of 2013 International Conference
*> for High Performance Computing, Networking, Storage and Analysis (SC '13).
*> Denver, Colorado, USA, 2013.
*> Article 90, 12 pages.
*> http://doi.acm.org/10.1145/2503210.2503292
*>
*> A. Haidar, R. Solca, S. Tomov, T. Schulthess and J. Dongarra.
*> A novel hybrid CPU-GPU generalized eigensolver for electronic structure
*> calculations based on fine-grained memory aware tasks.
*> International Journal of High Performance Computing Applications.
*> Volume 28 Issue 2, Pages 196-209, May 2014.
*> http://hpc.sagepub.com/content/28/2/196
*>
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DSB2ST_KERNELS( UPLO, WANTZ, TTYPE,
$ ST, ED, SWEEP, N, NB, IB,
$ A, LDA, V, TAU, LDVT, WORK)
*
IMPLICIT NONE
*
* -- 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..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER UPLO
LOGICAL WANTZ
INTEGER TTYPE, ST, ED, SWEEP, N, NB, IB, LDA, LDVT
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), V( * ),
$ TAU( * ), WORK( * )
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE
PARAMETER ( ZERO = 0.0D+0,
$ ONE = 1.0D+0 )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, J1, J2, LM, LN, VPOS, TAUPOS,
$ DPOS, OFDPOS, AJETER
DOUBLE PRECISION CTMP
* ..
* .. External Subroutines ..
EXTERNAL DLARFG, DLARFX, DLARFY
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* ..
* .. Executable Statements ..
*
AJETER = IB + LDVT
UPPER = LSAME( UPLO, 'U' )
IF( UPPER ) THEN
DPOS = 2 * NB + 1
OFDPOS = 2 * NB
ELSE
DPOS = 1
OFDPOS = 2
ENDIF
*
* Upper case
*
IF( UPPER ) THEN
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ENDIF
*
IF( TTYPE.EQ.1 ) THEN
LM = ED - ST + 1
*
V( VPOS ) = ONE
DO 10 I = 1, LM-1
V( VPOS+I ) = ( A( OFDPOS-I, ST+I ) )
A( OFDPOS-I, ST+I ) = ZERO
10 CONTINUE
CTMP = ( A( OFDPOS, ST ) )
CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
A( OFDPOS, ST ) = CTMP
*
LM = ED - ST + 1
CALL DLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.3 ) THEN
*
LM = ED - ST + 1
CALL DLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.2 ) THEN
J1 = ED+1
J2 = MIN( ED+NB, N )
LN = ED-ST+1
LM = J2-J1+1
IF( LM.GT.0) THEN
CALL DLARFX( 'Left', LN, LM, V( VPOS ),
$ ( TAU( TAUPOS ) ),
$ A( DPOS-NB, J1 ), LDA-1, WORK)
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ENDIF
*
V( VPOS ) = ONE
DO 30 I = 1, LM-1
V( VPOS+I ) =
$ ( A( DPOS-NB-I, J1+I ) )
A( DPOS-NB-I, J1+I ) = ZERO
30 CONTINUE
CTMP = ( A( DPOS-NB, J1 ) )
CALL DLARFG( LM, CTMP, V( VPOS+1 ), 1, TAU( TAUPOS ) )
A( DPOS-NB, J1 ) = CTMP
*
CALL DLARFX( 'Right', LN-1, LM, V( VPOS ),
$ TAU( TAUPOS ),
$ A( DPOS-NB+1, J1 ), LDA-1, WORK)
ENDIF
ENDIF
*
* Lower case
*
ELSE
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + ST
TAUPOS = MOD( SWEEP-1, 2 ) * N + ST
ENDIF
*
IF( TTYPE.EQ.1 ) THEN
LM = ED - ST + 1
*
V( VPOS ) = ONE
DO 20 I = 1, LM-1
V( VPOS+I ) = A( OFDPOS+I, ST-1 )
A( OFDPOS+I, ST-1 ) = ZERO
20 CONTINUE
CALL DLARFG( LM, A( OFDPOS, ST-1 ), V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
*
LM = ED - ST + 1
*
CALL DLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.3 ) THEN
LM = ED - ST + 1
*
CALL DLARFY( UPLO, LM, V( VPOS ), 1,
$ ( TAU( TAUPOS ) ),
$ A( DPOS, ST ), LDA-1, WORK)
ENDIF
*
IF( TTYPE.EQ.2 ) THEN
J1 = ED+1
J2 = MIN( ED+NB, N )
LN = ED-ST+1
LM = J2-J1+1
*
IF( LM.GT.0) THEN
CALL DLARFX( 'Right', LM, LN, V( VPOS ),
$ TAU( TAUPOS ), A( DPOS+NB, ST ),
$ LDA-1, WORK)
*
IF( WANTZ ) THEN
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ELSE
VPOS = MOD( SWEEP-1, 2 ) * N + J1
TAUPOS = MOD( SWEEP-1, 2 ) * N + J1
ENDIF
*
V( VPOS ) = ONE
DO 40 I = 1, LM-1
V( VPOS+I ) = A( DPOS+NB+I, ST )
A( DPOS+NB+I, ST ) = ZERO
40 CONTINUE
CALL DLARFG( LM, A( DPOS+NB, ST ), V( VPOS+1 ), 1,
$ TAU( TAUPOS ) )
*
CALL DLARFX( 'Left', LM, LN-1, V( VPOS ),
$ ( TAU( TAUPOS ) ),
$ A( DPOS+NB-1, ST+1 ), LDA-1, WORK)
ENDIF
ENDIF
ENDIF
*
RETURN
*
* END OF DSB2ST_KERNELS
*
END
|
