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
|
*> \brief \b DCHKEQ
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DCHKEQ( THRESH, NOUT )
*
* .. Scalar Arguments ..
* INTEGER NOUT
* DOUBLE PRECISION THRESH
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DCHKEQ tests DGEEQU, DGBEQU, DPOEQU, DPPEQU and DPBEQU
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] THRESH
*> \verbatim
*> THRESH is DOUBLE PRECISION
*> Threshold for testing routines. Should be between 2 and 10.
*> \endverbatim
*>
*> \param[in] NOUT
*> \verbatim
*> NOUT is INTEGER
*> The unit number for output.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup double_lin
*
* =====================================================================
SUBROUTINE DCHKEQ( THRESH, NOUT )
*
* -- 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 NOUT
DOUBLE PRECISION THRESH
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO, ONE, TEN
PARAMETER ( ZERO = 0.0D0, ONE = 1.0D+0, TEN = 1.0D1 )
INTEGER NSZ, NSZB
PARAMETER ( NSZ = 5, NSZB = 3*NSZ-2 )
INTEGER NSZP, NPOW
PARAMETER ( NSZP = ( NSZ*( NSZ+1 ) ) / 2,
$ NPOW = 2*NSZ+1 )
* ..
* .. Local Scalars ..
LOGICAL OK
CHARACTER*3 PATH
INTEGER I, INFO, J, KL, KU, M, N
DOUBLE PRECISION CCOND, EPS, NORM, RATIO, RCMAX, RCMIN, RCOND
* ..
* .. Local Arrays ..
DOUBLE PRECISION A( NSZ, NSZ ), AB( NSZB, NSZ ), AP( NSZP ),
$ C( NSZ ), POW( NPOW ), R( NSZ ), RESLTS( 5 ),
$ RPOW( NPOW )
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH
EXTERNAL DLAMCH
* ..
* .. External Subroutines ..
EXTERNAL DGBEQU, DGEEQU, DPBEQU, DPOEQU, DPPEQU
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN
* ..
* .. Executable Statements ..
*
PATH( 1: 1 ) = 'Double precision'
PATH( 2: 3 ) = 'EQ'
*
EPS = DLAMCH( 'P' )
DO 10 I = 1, 5
RESLTS( I ) = ZERO
10 CONTINUE
DO 20 I = 1, NPOW
POW( I ) = TEN**( I-1 )
RPOW( I ) = ONE / POW( I )
20 CONTINUE
*
* Test DGEEQU
*
DO 80 N = 0, NSZ
DO 70 M = 0, NSZ
*
DO 40 J = 1, NSZ
DO 30 I = 1, NSZ
IF( I.LE.M .AND. J.LE.N ) THEN
A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
ELSE
A( I, J ) = ZERO
END IF
30 CONTINUE
40 CONTINUE
*
CALL DGEEQU( M, N, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 1 ) = ONE
ELSE
IF( N.NE.0 .AND. M.NE.0 ) THEN
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( RCOND-RPOW( M ) ) / RPOW( M ) ) )
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( CCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( NORM-POW( N+M+1 ) ) / POW( N+M+
$ 1 ) ) )
DO 50 I = 1, M
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( R( I )-RPOW( I+N+1 ) ) /
$ RPOW( I+N+1 ) ) )
50 CONTINUE
DO 60 J = 1, N
RESLTS( 1 ) = MAX( RESLTS( 1 ),
$ ABS( ( C( J )-POW( N-J+1 ) ) /
$ POW( N-J+1 ) ) )
60 CONTINUE
END IF
END IF
*
70 CONTINUE
80 CONTINUE
*
* Test with zero rows and columns
*
DO 90 J = 1, NSZ
A( MAX( NSZ-1, 1 ), J ) = ZERO
90 CONTINUE
CALL DGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 1 ) = ONE
*
DO 100 J = 1, NSZ
A( MAX( NSZ-1, 1 ), J ) = ONE
100 CONTINUE
DO 110 I = 1, NSZ
A( I, MAX( NSZ-1, 1 ) ) = ZERO
110 CONTINUE
CALL DGEEQU( NSZ, NSZ, A, NSZ, R, C, RCOND, CCOND, NORM, INFO )
IF( INFO.NE.NSZ+MAX( NSZ-1, 1 ) )
$ RESLTS( 1 ) = ONE
RESLTS( 1 ) = RESLTS( 1 ) / EPS
*
* Test DGBEQU
*
DO 250 N = 0, NSZ
DO 240 M = 0, NSZ
DO 230 KL = 0, MAX( M-1, 0 )
DO 220 KU = 0, MAX( N-1, 0 )
*
DO 130 J = 1, NSZ
DO 120 I = 1, NSZB
AB( I, J ) = ZERO
120 CONTINUE
130 CONTINUE
DO 150 J = 1, N
DO 140 I = 1, M
IF( I.LE.MIN( M, J+KL ) .AND. I.GE.
$ MAX( 1, J-KU ) .AND. J.LE.N ) THEN
AB( KU+1+I-J, J ) = POW( I+J+1 )*
$ ( -1 )**( I+J )
END IF
140 CONTINUE
150 CONTINUE
*
CALL DGBEQU( M, N, KL, KU, AB, NSZB, R, C, RCOND,
$ CCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
IF( .NOT.( ( N+KL.LT.M .AND. INFO.EQ.N+KL+1 ) .OR.
$ ( M+KU.LT.N .AND. INFO.EQ.2*M+KU+1 ) ) ) THEN
RESLTS( 2 ) = ONE
END IF
ELSE
IF( N.NE.0 .AND. M.NE.0 ) THEN
*
RCMIN = R( 1 )
RCMAX = R( 1 )
DO 160 I = 1, M
RCMIN = MIN( RCMIN, R( I ) )
RCMAX = MAX( RCMAX, R( I ) )
160 CONTINUE
RATIO = RCMIN / RCMAX
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( RCOND-RATIO ) / RATIO ) )
*
RCMIN = C( 1 )
RCMAX = C( 1 )
DO 170 J = 1, N
RCMIN = MIN( RCMIN, C( J ) )
RCMAX = MAX( RCMAX, C( J ) )
170 CONTINUE
RATIO = RCMIN / RCMAX
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( CCOND-RATIO ) / RATIO ) )
*
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ( NORM-POW( N+M+1 ) ) /
$ POW( N+M+1 ) ) )
DO 190 I = 1, M
RCMAX = ZERO
DO 180 J = 1, N
IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
RATIO = ABS( R( I )*POW( I+J+1 )*
$ C( J ) )
RCMAX = MAX( RCMAX, RATIO )
END IF
180 CONTINUE
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ONE-RCMAX ) )
190 CONTINUE
*
DO 210 J = 1, N
RCMAX = ZERO
DO 200 I = 1, M
IF( I.LE.J+KL .AND. I.GE.J-KU ) THEN
RATIO = ABS( R( I )*POW( I+J+1 )*
$ C( J ) )
RCMAX = MAX( RCMAX, RATIO )
END IF
200 CONTINUE
RESLTS( 2 ) = MAX( RESLTS( 2 ),
$ ABS( ONE-RCMAX ) )
210 CONTINUE
END IF
END IF
*
220 CONTINUE
230 CONTINUE
240 CONTINUE
250 CONTINUE
RESLTS( 2 ) = RESLTS( 2 ) / EPS
*
* Test DPOEQU
*
DO 290 N = 0, NSZ
*
DO 270 I = 1, NSZ
DO 260 J = 1, NSZ
IF( I.LE.N .AND. J.EQ.I ) THEN
A( I, J ) = POW( I+J+1 )*( -1 )**( I+J )
ELSE
A( I, J ) = ZERO
END IF
260 CONTINUE
270 CONTINUE
*
CALL DPOEQU( N, A, NSZ, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 3 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 280 I = 1, N
RESLTS( 3 ) = MAX( RESLTS( 3 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
280 CONTINUE
END IF
END IF
290 CONTINUE
A( MAX( NSZ-1, 1 ), MAX( NSZ-1, 1 ) ) = -ONE
CALL DPOEQU( NSZ, A, NSZ, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 3 ) = ONE
RESLTS( 3 ) = RESLTS( 3 ) / EPS
*
* Test DPPEQU
*
DO 360 N = 0, NSZ
*
* Upper triangular packed storage
*
DO 300 I = 1, ( N*( N+1 ) ) / 2
AP( I ) = ZERO
300 CONTINUE
DO 310 I = 1, N
AP( ( I*( I+1 ) ) / 2 ) = POW( 2*I+1 )
310 CONTINUE
*
CALL DPPEQU( 'U', N, AP, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 4 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 320 I = 1, N
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
320 CONTINUE
END IF
END IF
*
* Lower triangular packed storage
*
DO 330 I = 1, ( N*( N+1 ) ) / 2
AP( I ) = ZERO
330 CONTINUE
J = 1
DO 340 I = 1, N
AP( J ) = POW( 2*I+1 )
J = J + ( N-I+1 )
340 CONTINUE
*
CALL DPPEQU( 'L', N, AP, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 4 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 350 I = 1, N
RESLTS( 4 ) = MAX( RESLTS( 4 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) / RPOW( I+
$ 1 ) ) )
350 CONTINUE
END IF
END IF
*
360 CONTINUE
I = ( NSZ*( NSZ+1 ) ) / 2 - 2
AP( I ) = -ONE
CALL DPPEQU( 'L', NSZ, AP, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( NSZ-1, 1 ) )
$ RESLTS( 4 ) = ONE
RESLTS( 4 ) = RESLTS( 4 ) / EPS
*
* Test DPBEQU
*
DO 460 N = 0, NSZ
DO 450 KL = 0, MAX( N-1, 0 )
*
* Test upper triangular storage
*
DO 380 J = 1, NSZ
DO 370 I = 1, NSZB
AB( I, J ) = ZERO
370 CONTINUE
380 CONTINUE
DO 390 J = 1, N
AB( KL+1, J ) = POW( 2*J+1 )
390 CONTINUE
*
CALL DPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 5 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 400 I = 1, N
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) /
$ RPOW( I+1 ) ) )
400 CONTINUE
END IF
END IF
IF( N.NE.0 ) THEN
AB( KL+1, MAX( N-1, 1 ) ) = -ONE
CALL DPBEQU( 'U', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( N-1, 1 ) )
$ RESLTS( 5 ) = ONE
END IF
*
* Test lower triangular storage
*
DO 420 J = 1, NSZ
DO 410 I = 1, NSZB
AB( I, J ) = ZERO
410 CONTINUE
420 CONTINUE
DO 430 J = 1, N
AB( 1, J ) = POW( 2*J+1 )
430 CONTINUE
*
CALL DPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
*
IF( INFO.NE.0 ) THEN
RESLTS( 5 ) = ONE
ELSE
IF( N.NE.0 ) THEN
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( RCOND-RPOW( N ) ) / RPOW( N ) ) )
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( NORM-POW( 2*N+1 ) ) / POW( 2*N+
$ 1 ) ) )
DO 440 I = 1, N
RESLTS( 5 ) = MAX( RESLTS( 5 ),
$ ABS( ( R( I )-RPOW( I+1 ) ) /
$ RPOW( I+1 ) ) )
440 CONTINUE
END IF
END IF
IF( N.NE.0 ) THEN
AB( 1, MAX( N-1, 1 ) ) = -ONE
CALL DPBEQU( 'L', N, KL, AB, NSZB, R, RCOND, NORM, INFO )
IF( INFO.NE.MAX( N-1, 1 ) )
$ RESLTS( 5 ) = ONE
END IF
450 CONTINUE
460 CONTINUE
RESLTS( 5 ) = RESLTS( 5 ) / EPS
OK = ( RESLTS( 1 ).LE.THRESH ) .AND.
$ ( RESLTS( 2 ).LE.THRESH ) .AND.
$ ( RESLTS( 3 ).LE.THRESH ) .AND.
$ ( RESLTS( 4 ).LE.THRESH ) .AND. ( RESLTS( 5 ).LE.THRESH )
WRITE( NOUT, FMT = * )
IF( OK ) THEN
WRITE( NOUT, FMT = 9999 )PATH
ELSE
IF( RESLTS( 1 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9998 )RESLTS( 1 ), THRESH
IF( RESLTS( 2 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9997 )RESLTS( 2 ), THRESH
IF( RESLTS( 3 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9996 )RESLTS( 3 ), THRESH
IF( RESLTS( 4 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9995 )RESLTS( 4 ), THRESH
IF( RESLTS( 5 ).GT.THRESH )
$ WRITE( NOUT, FMT = 9994 )RESLTS( 5 ), THRESH
END IF
9999 FORMAT( 1X, 'All tests for ', A3,
$ ' routines passed the threshold' )
9998 FORMAT( ' DGEEQU failed test with value ', D10.3, ' exceeding',
$ ' threshold ', D10.3 )
9997 FORMAT( ' DGBEQU failed test with value ', D10.3, ' exceeding',
$ ' threshold ', D10.3 )
9996 FORMAT( ' DPOEQU failed test with value ', D10.3, ' exceeding',
$ ' threshold ', D10.3 )
9995 FORMAT( ' DPPEQU failed test with value ', D10.3, ' exceeding',
$ ' threshold ', D10.3 )
9994 FORMAT( ' DPBEQU failed test with value ', D10.3, ' exceeding',
$ ' threshold ', D10.3 )
RETURN
*
* End of DCHKEQ
*
END
|
