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
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
|
*> \brief \b SGET38
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE SGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* .. Scalar Arguments ..
* INTEGER KNT, NIN
* ..
* .. Array Arguments ..
* INTEGER LMAX( 3 ), NINFO( 3 )
* REAL RMAX( 3 )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SGET38 tests STRSEN, a routine for estimating condition numbers of a
*> cluster of eigenvalues and/or its associated right invariant subspace
*>
*> The test matrices are read from a file with logical unit number NIN.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[out] RMAX
*> \verbatim
*> RMAX is REAL array, dimension (3)
*> Values of the largest test ratios.
*> RMAX(1) = largest residuals from SHST01 or comparing
*> different calls to STRSEN
*> RMAX(2) = largest error in reciprocal condition
*> numbers taking their conditioning into account
*> RMAX(3) = largest error in reciprocal condition
*> numbers not taking their conditioning into
*> account (may be larger than RMAX(2))
*> \endverbatim
*>
*> \param[out] LMAX
*> \verbatim
*> LMAX is INTEGER array, dimension (3)
*> LMAX(i) is example number where largest test ratio
*> RMAX(i) is achieved. Also:
*> If SGEHRD returns INFO nonzero on example i, LMAX(1)=i
*> If SHSEQR returns INFO nonzero on example i, LMAX(2)=i
*> If STRSEN returns INFO nonzero on example i, LMAX(3)=i
*> \endverbatim
*>
*> \param[out] NINFO
*> \verbatim
*> NINFO is INTEGER array, dimension (3)
*> NINFO(1) = No. of times SGEHRD returned INFO nonzero
*> NINFO(2) = No. of times SHSEQR returned INFO nonzero
*> NINFO(3) = No. of times STRSEN returned INFO nonzero
*> \endverbatim
*>
*> \param[out] KNT
*> \verbatim
*> KNT is INTEGER
*> Total number of examples tested.
*> \endverbatim
*>
*> \param[in] NIN
*> \verbatim
*> NIN is INTEGER
*> Input logical unit number.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup single_eig
*
* =====================================================================
SUBROUTINE SGET38( RMAX, LMAX, NINFO, KNT, NIN )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER KNT, NIN
* ..
* .. Array Arguments ..
INTEGER LMAX( 3 ), NINFO( 3 )
REAL RMAX( 3 )
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO, ONE, TWO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0, TWO = 2.0E0 )
REAL EPSIN
PARAMETER ( EPSIN = 5.9605E-8 )
INTEGER LDT, LWORK
PARAMETER ( LDT = 20, LWORK = 2*LDT*( 10+LDT ) )
INTEGER LIWORK
PARAMETER ( LIWORK = LDT*LDT )
* ..
* .. Local Scalars ..
INTEGER I, INFO, ISCL, ITMP, J, KMIN, M, N, NDIM
REAL BIGNUM, EPS, S, SEP, SEPIN, SEPTMP, SIN,
$ SMLNUM, STMP, TNRM, TOL, TOLIN, V, VIMIN, VMAX,
$ VMUL, VRMIN
* ..
* .. Local Arrays ..
LOGICAL SELECT( LDT )
INTEGER IPNT( LDT ), ISELEC( LDT ), IWORK( LIWORK )
REAL Q( LDT, LDT ), QSAV( LDT, LDT ),
$ QTMP( LDT, LDT ), RESULT( 2 ), T( LDT, LDT ),
$ TMP( LDT, LDT ), TSAV( LDT, LDT ),
$ TSAV1( LDT, LDT ), TTMP( LDT, LDT ), VAL( 3 ),
$ WI( LDT ), WITMP( LDT ), WORK( LWORK ),
$ WR( LDT ), WRTMP( LDT )
* ..
* .. External Functions ..
REAL SLAMCH, SLANGE
EXTERNAL SLAMCH, SLANGE
* ..
* .. External Subroutines ..
EXTERNAL SCOPY, SGEHRD, SHSEQR, SHST01, SLABAD, SLACPY,
$ SORGHR, SSCAL, STRSEN
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, REAL, SQRT
* ..
* .. Executable Statements ..
*
EPS = SLAMCH( 'P' )
SMLNUM = SLAMCH( 'S' ) / EPS
BIGNUM = ONE / SMLNUM
CALL SLABAD( SMLNUM, BIGNUM )
*
* EPSIN = 2**(-24) = precision to which input data computed
*
EPS = MAX( EPS, EPSIN )
RMAX( 1 ) = ZERO
RMAX( 2 ) = ZERO
RMAX( 3 ) = ZERO
LMAX( 1 ) = 0
LMAX( 2 ) = 0
LMAX( 3 ) = 0
KNT = 0
NINFO( 1 ) = 0
NINFO( 2 ) = 0
NINFO( 3 ) = 0
*
VAL( 1 ) = SQRT( SMLNUM )
VAL( 2 ) = ONE
VAL( 3 ) = SQRT( SQRT( BIGNUM ) )
*
* Read input data until N=0. Assume input eigenvalues are sorted
* lexicographically (increasing by real part, then decreasing by
* imaginary part)
*
10 CONTINUE
READ( NIN, FMT = * )N, NDIM
IF( N.EQ.0 )
$ RETURN
READ( NIN, FMT = * )( ISELEC( I ), I = 1, NDIM )
DO 20 I = 1, N
READ( NIN, FMT = * )( TMP( I, J ), J = 1, N )
20 CONTINUE
READ( NIN, FMT = * )SIN, SEPIN
*
TNRM = SLANGE( 'M', N, N, TMP, LDT, WORK )
DO 160 ISCL = 1, 3
*
* Scale input matrix
*
KNT = KNT + 1
CALL SLACPY( 'F', N, N, TMP, LDT, T, LDT )
VMUL = VAL( ISCL )
DO 30 I = 1, N
CALL SSCAL( N, VMUL, T( 1, I ), 1 )
30 CONTINUE
IF( TNRM.EQ.ZERO )
$ VMUL = ONE
CALL SLACPY( 'F', N, N, T, LDT, TSAV, LDT )
*
* Compute Schur form
*
CALL SGEHRD( N, 1, N, T, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N,
$ INFO )
IF( INFO.NE.0 ) THEN
LMAX( 1 ) = KNT
NINFO( 1 ) = NINFO( 1 ) + 1
GO TO 160
END IF
*
* Generate orthogonal matrix
*
CALL SLACPY( 'L', N, N, T, LDT, Q, LDT )
CALL SORGHR( N, 1, N, Q, LDT, WORK( 1 ), WORK( N+1 ), LWORK-N,
$ INFO )
*
* Compute Schur form
*
CALL SHSEQR( 'S', 'V', N, 1, N, T, LDT, WR, WI, Q, LDT, WORK,
$ LWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 2 ) = KNT
NINFO( 2 ) = NINFO( 2 ) + 1
GO TO 160
END IF
*
* Sort, select eigenvalues
*
DO 40 I = 1, N
IPNT( I ) = I
SELECT( I ) = .FALSE.
40 CONTINUE
CALL SCOPY( N, WR, 1, WRTMP, 1 )
CALL SCOPY( N, WI, 1, WITMP, 1 )
DO 60 I = 1, N - 1
KMIN = I
VRMIN = WRTMP( I )
VIMIN = WITMP( I )
DO 50 J = I + 1, N
IF( WRTMP( J ).LT.VRMIN ) THEN
KMIN = J
VRMIN = WRTMP( J )
VIMIN = WITMP( J )
END IF
50 CONTINUE
WRTMP( KMIN ) = WRTMP( I )
WITMP( KMIN ) = WITMP( I )
WRTMP( I ) = VRMIN
WITMP( I ) = VIMIN
ITMP = IPNT( I )
IPNT( I ) = IPNT( KMIN )
IPNT( KMIN ) = ITMP
60 CONTINUE
DO 70 I = 1, NDIM
SELECT( IPNT( ISELEC( I ) ) ) = .TRUE.
70 CONTINUE
*
* Compute condition numbers
*
CALL SLACPY( 'F', N, N, Q, LDT, QSAV, LDT )
CALL SLACPY( 'F', N, N, T, LDT, TSAV1, LDT )
CALL STRSEN( 'B', 'V', SELECT, N, T, LDT, Q, LDT, WRTMP, WITMP,
$ M, S, SEP, WORK, LWORK, IWORK, LIWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 160
END IF
SEPTMP = SEP / VMUL
STMP = S
*
* Compute residuals
*
CALL SHST01( N, 1, N, TSAV, LDT, T, LDT, Q, LDT, WORK, LWORK,
$ RESULT )
VMAX = MAX( RESULT( 1 ), RESULT( 2 ) )
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
*
* Compare condition number for eigenvalue cluster
* taking its condition number into account
*
V = MAX( TWO*REAL( N )*EPS*TNRM, SMLNUM )
IF( TNRM.EQ.ZERO )
$ V = ONE
IF( V.GT.SEPTMP ) THEN
TOL = ONE
ELSE
TOL = V / SEPTMP
END IF
IF( V.GT.SEPIN ) THEN
TOLIN = ONE
ELSE
TOLIN = V / SEPIN
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( SIN-TOLIN ).GT.STMP+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( SIN-TOLIN.GT.STMP+TOL ) THEN
VMAX = ( SIN-TOLIN ) / ( STMP+TOL )
ELSE IF( SIN+TOLIN.LT.EPS*( STMP-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( SIN+TOLIN.LT.STMP-TOL ) THEN
VMAX = ( STMP-TOL ) / ( SIN+TOLIN )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 2 ) ) THEN
RMAX( 2 ) = VMAX
IF( NINFO( 2 ).EQ.0 )
$ LMAX( 2 ) = KNT
END IF
*
* Compare condition numbers for invariant subspace
* taking its condition number into account
*
IF( V.GT.SEPTMP*STMP ) THEN
TOL = SEPTMP
ELSE
TOL = V / STMP
END IF
IF( V.GT.SEPIN*SIN ) THEN
TOLIN = SEPIN
ELSE
TOLIN = V / SIN
END IF
TOL = MAX( TOL, SMLNUM / EPS )
TOLIN = MAX( TOLIN, SMLNUM / EPS )
IF( EPS*( SEPIN-TOLIN ).GT.SEPTMP+TOL ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN-TOLIN.GT.SEPTMP+TOL ) THEN
VMAX = ( SEPIN-TOLIN ) / ( SEPTMP+TOL )
ELSE IF( SEPIN+TOLIN.LT.EPS*( SEPTMP-TOL ) ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN+TOLIN.LT.SEPTMP-TOL ) THEN
VMAX = ( SEPTMP-TOL ) / ( SEPIN+TOLIN )
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 2 ) ) THEN
RMAX( 2 ) = VMAX
IF( NINFO( 2 ).EQ.0 )
$ LMAX( 2 ) = KNT
END IF
*
* Compare condition number for eigenvalue cluster
* without taking its condition number into account
*
IF( SIN.LE.REAL( 2*N )*EPS .AND. STMP.LE.REAL( 2*N )*EPS ) THEN
VMAX = ONE
ELSE IF( EPS*SIN.GT.STMP ) THEN
VMAX = ONE / EPS
ELSE IF( SIN.GT.STMP ) THEN
VMAX = SIN / STMP
ELSE IF( SIN.LT.EPS*STMP ) THEN
VMAX = ONE / EPS
ELSE IF( SIN.LT.STMP ) THEN
VMAX = STMP / SIN
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 3 ) ) THEN
RMAX( 3 ) = VMAX
IF( NINFO( 3 ).EQ.0 )
$ LMAX( 3 ) = KNT
END IF
*
* Compare condition numbers for invariant subspace
* without taking its condition number into account
*
IF( SEPIN.LE.V .AND. SEPTMP.LE.V ) THEN
VMAX = ONE
ELSE IF( EPS*SEPIN.GT.SEPTMP ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN.GT.SEPTMP ) THEN
VMAX = SEPIN / SEPTMP
ELSE IF( SEPIN.LT.EPS*SEPTMP ) THEN
VMAX = ONE / EPS
ELSE IF( SEPIN.LT.SEPTMP ) THEN
VMAX = SEPTMP / SEPIN
ELSE
VMAX = ONE
END IF
IF( VMAX.GT.RMAX( 3 ) ) THEN
RMAX( 3 ) = VMAX
IF( NINFO( 3 ).EQ.0 )
$ LMAX( 3 ) = KNT
END IF
*
* Compute eigenvalue condition number only and compare
* Update Q
*
VMAX = ZERO
CALL SLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
CALL SLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
SEPTMP = -ONE
STMP = -ONE
CALL STRSEN( 'E', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
$ LIWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 160
END IF
IF( S.NE.STMP )
$ VMAX = ONE / EPS
IF( -ONE.NE.SEPTMP )
$ VMAX = ONE / EPS
DO 90 I = 1, N
DO 80 J = 1, N
IF( TTMP( I, J ).NE.T( I, J ) )
$ VMAX = ONE / EPS
IF( QTMP( I, J ).NE.Q( I, J ) )
$ VMAX = ONE / EPS
80 CONTINUE
90 CONTINUE
*
* Compute invariant subspace condition number only and compare
* Update Q
*
CALL SLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
CALL SLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
SEPTMP = -ONE
STMP = -ONE
CALL STRSEN( 'V', 'V', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
$ LIWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 160
END IF
IF( -ONE.NE.STMP )
$ VMAX = ONE / EPS
IF( SEP.NE.SEPTMP )
$ VMAX = ONE / EPS
DO 110 I = 1, N
DO 100 J = 1, N
IF( TTMP( I, J ).NE.T( I, J ) )
$ VMAX = ONE / EPS
IF( QTMP( I, J ).NE.Q( I, J ) )
$ VMAX = ONE / EPS
100 CONTINUE
110 CONTINUE
*
* Compute eigenvalue condition number only and compare
* Do not update Q
*
CALL SLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
CALL SLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
SEPTMP = -ONE
STMP = -ONE
CALL STRSEN( 'E', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
$ LIWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 160
END IF
IF( S.NE.STMP )
$ VMAX = ONE / EPS
IF( -ONE.NE.SEPTMP )
$ VMAX = ONE / EPS
DO 130 I = 1, N
DO 120 J = 1, N
IF( TTMP( I, J ).NE.T( I, J ) )
$ VMAX = ONE / EPS
IF( QTMP( I, J ).NE.QSAV( I, J ) )
$ VMAX = ONE / EPS
120 CONTINUE
130 CONTINUE
*
* Compute invariant subspace condition number only and compare
* Do not update Q
*
CALL SLACPY( 'F', N, N, TSAV1, LDT, TTMP, LDT )
CALL SLACPY( 'F', N, N, QSAV, LDT, QTMP, LDT )
SEPTMP = -ONE
STMP = -ONE
CALL STRSEN( 'V', 'N', SELECT, N, TTMP, LDT, QTMP, LDT, WRTMP,
$ WITMP, M, STMP, SEPTMP, WORK, LWORK, IWORK,
$ LIWORK, INFO )
IF( INFO.NE.0 ) THEN
LMAX( 3 ) = KNT
NINFO( 3 ) = NINFO( 3 ) + 1
GO TO 160
END IF
IF( -ONE.NE.STMP )
$ VMAX = ONE / EPS
IF( SEP.NE.SEPTMP )
$ VMAX = ONE / EPS
DO 150 I = 1, N
DO 140 J = 1, N
IF( TTMP( I, J ).NE.T( I, J ) )
$ VMAX = ONE / EPS
IF( QTMP( I, J ).NE.QSAV( I, J ) )
$ VMAX = ONE / EPS
140 CONTINUE
150 CONTINUE
IF( VMAX.GT.RMAX( 1 ) ) THEN
RMAX( 1 ) = VMAX
IF( NINFO( 1 ).EQ.0 )
$ LMAX( 1 ) = KNT
END IF
160 CONTINUE
GO TO 10
*
* End of SGET38
*
END
|
