-
Notifications
You must be signed in to change notification settings - Fork 59
/
cvt_dataset.html
677 lines (621 loc) · 19.2 KB
/
cvt_dataset.html
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
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
<html>
<head>
<title>
CVT_DATASET - An Interactive Centroidal Voronoi Tessellation Program
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_DATASET <br> Generate CVT Datasets
</h1>
<hr>
<p>
<b>CVT_DATASET</b>
is a FORTRAN90 program which
creates a CVT dataset and writes it to a file.
</p>
<p>
The program is interactive, and allows the user to choose the parameters
that define the dataset.
</p>
<p>
Normally, data is computed in the unit hypercube, with uniform
density. However, if you wish to work in a more interesting
geometry, or to control the density function, it is necessary
to modify the <b>USER</b> routine in the <b>CVT</b> library,
and then direct <b>CVT_DATASET</b> to use that routine for
initialization and sampling.
</p>
<p>
The data that the user may set includes:
<ul>
<li>
<b>DIM_NUM</b>, the spatial dimension,
</li>
<li>
<b>N</b>, the number of points to generate,
</li>
<li>
<b>SEED</b>, a seed to use for random number generation;
</li>
<li>
<b>INIT</b>, initialize the points:
<ul>
<li>
<i>file</i>, by reading data from file;
</li>
<li>
<i>GRID</i>, picking points from a grid;
</li>
<li>
<i>HALTON</i>, from a Halton sequence;
</li>
<li>
<i>RANDOM</i>, using FORTRAN RANDOM function;
</li>
<li>
<i>UNIFORM</i>, using a simple uniform RNG;
</li>
<li>
<i>USER</i>, by calling the "user" routine;
</li>
</ul>
</li>
<li>
<b>IT_MAX</b>, the maximum number of iterations;
</li>
<li>
<b>IT_FIXED</b>, the number of iterations for which each
set of sample points should be used (between 1 and <b>IT_MAX</b>);
</li>
<li>
<b>SAMPLE</b>, how to conduct the sampling:
<ul>
<li>
<i>GRID</i>, picking points from a grid;
</li>
<li>
<i>HALTON</i>, from a Halton sequence;
</li>
<li>
<i>RANDOM</i>, using FORTRAN RANDOM function;
</li>
<li>
<i>UNIFORM</i>, using a simple uniform RNG;
</li>
<li>
<i>USER</i>, by calling the "user" routine;
</li>
</ul>
</li>
<li>
<b>SAMPLE_NUM</b>, the number of sampling points;
</li>
<li>
<b>BATCH</b>, the number of sampling points to create
at one time (between 1 and <b>SAMPLE_NUM</b>);
</li>
<li>
<b>OUTPUT</b>, a file in which to store the data.
</li>
</ul>
</p>
<p>
A "CVT" is a Centroidal Voronoi Tessellation. Essentially, a
CVT is a set of sample points in a (finite) region with the
property that each point is the centroid of its Voronoi subregion.
A "random" set of sample points will not have this property.
However, it is possible to begin with a random set of sample
points, and drive it towards a CVT set, by applying an iterative
refinement process.
</p>
<p>
The generation of a CVT dataset is of necessity more complicated than
for a quasirandom sequence. An iteration is involved, so there
must be an initial assignment for the generators, and then a
number of iterations. Moreover, in each iteration, estimates must
be made of the volume and location of the Voronoi subregions. This is
typically done by Monte Carlo sampling. The accuracy of the resulting
CVT depends in part on the number of sampling points and the number
of iterations taken.
</p>
<p>
A reasonable set of input data might be:
<pre>
2 <i>spatial dimension is 2</i>
10 <i>compute 10 points</i>
123456789 <i>seed for random numbers</i>
uniform <i>initialize by UNIFORM</i>
40 <i>40 iterations</i>
0.0 <i>zero tolerance; won't stop early</i>
uniform <i>sample using UNIFORM</i>
10000 <i>use 10,000 sample points on each iteration</i>
1000 <i>create 1,000 sample points at a time</i>
-1 <i>stop; don't want to define another set.</i>
</pre>
</p>
<p>
Once these parameters are set, the program generates the data
and writes it to a file. The user may then specify another set of
input data, or terminate the program.
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages
</h3>
<p>
<b>CVT_DATASET</b> is available in
<a href = "../../cpp_src/cvt_dataset/cvt_dataset.html">a C++ version</a> and
<a href = "../../f_src/cvt_dataset/cvt_dataset.html">a FORTRAN90 version</a> and
<a href = "../../m_src/cvt_dataset/cvt_dataset.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../f_src/cvt/cvt.html">
CVT</a>,
a FORTRAN90 library which
computes Centroidal Voronoi
Tessellations. A compiled copy of this library is required in order
to build <b>CVT_DATASET</b>.
</p>
<p>
<a href = "../../datasets/cvt/cvt.html">
CVT</a>,
a dataset collection which
contains many CVT's.
</p>
<p>
<a href = "../../f_src/faure_dataset/faure_dataset.html">
FAURE_DATASET</a>,
a FORTRAN90 program which
creates a Faure quasirandom dataset;
</p>
<p>
<a href = "../../f_src/grid_dataset/grid_dataset.html">
GRID_DATASET</a>,
a FORTRAN90 program which
creates a grid sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/latin_center_dataset/latin_center_dataset.html">
LATIN_CENTER_DATASET</a>,
a FORTRAN90 program which
creates a Latin Center Hypercube dataset;
</p>
<p>
<a href = "../../f_src/latin_edge_dataset/latin_edge_dataset.html">
LATIN_EDGE_DATASET</a>,
a FORTRAN90 program which
creates a Latin Edge Hypercube dataset;
</p>
<p>
<a href = "../../f_src/latin_random_dataset/latin_random_dataset.html">
LATIN_RANDOM_DATASET</a>,
a FORTRAN90 program which
creates a Latin Random Hypercube dataset;
</p>
<p>
<a href = "../../f_src/niederreiter2_dataset/niederreiter2_dataset.html">
NIEDERREITER2_DATASET</a>,
a FORTRAN90 program which
creates a Niederreiter quasirandom dataset with base 2;
</p>
<p>
<a href = "../../f_src/normal_dataset/normal_dataset.html">
NORMAL_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate normal pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/sobol_dataset/sobol_dataset.html">
SOBOL_DATASET</a>,
a FORTRAN90 program which
computes a Sobol quasirandom sequence and writes it to a file.
</p>
<p>
<a href = "../../f_src/uniform_dataset/uniform_dataset.html">
UNIFORM_DATASET</a>,
a FORTRAN90 program which
generates a dataset of multivariate uniform pseudorandom values and writes them to a file.
</p>
<p>
<a href = "../../f_src/van_der_corput_dataset/van_der_corput_dataset.html">
VAN_DER_CORPUT_DATASET</a>,
a FORTRAN90 program which
creates a van der Corput quasirandom sequence and writes it to a file.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
John Burkardt, Max Gunzburger, Janet Peterson, Rebecca Brannon,<br>
User Manual and Supporting Information for Library of Codes
for Centroidal Voronoi Placement and Associated Zeroth,
First, and Second Moment Determination,<br>
Sandia National Laboratories Technical Report SAND2002-0099,<br>
February 2002,<br>
<a href = "../../publications/bgpb_2002.pdf">
../../publications/bgpb_2002.pdf </a>
</li>
<li>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review,<br>
Volume 41, 1999, pages 637-676.
</li>
<li>
Lili Ju, Qiang Du, Max Gunzburger,<br>
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,<br>
Parallel Computing,<br>
Volume 28, 2002, pages 1477-1500.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "cvt_dataset.f90">cvt_dataset.f90</a>, the source code;
</li>
<li>
<a href = "cvt_dataset.sh">cvt_dataset.sh</a>,
commands to compile and load the source code;
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>Test 1</b> computes 85 CVT points in 2 dimensions, using uniform
initialization, a seed of 123456789, 40 iterations, a zero tolerance,
uniform sampling, 10,000 sample points in batches of 1000:
<ul>
<li>
<a href = "input01.txt">input01.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output01.txt">output01.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt01.txt">cvt01.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt01.png">cvt01.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 2</b> repeats test 1, but with 80 iterations:
<ul>
<li>
<a href = "input02.txt">input02.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output02.txt">output02.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt02.txt">cvt02.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt02.png">cvt02.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 3</b> repeats test 1, but with 1,000,000 sample points:
<ul>
<li>
<a href = "input03.txt">input03.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output03.txt">output03.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt03.txt">cvt03.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt03.png">cvt03.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 4</b> repeats test 1, but with Halton sampling:
<ul>
<li>
<a href = "input04.txt">input04.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output04.txt">output04.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt04.txt">cvt04.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt04.png">cvt04.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 5</b> repeats test 1, but with Grid sampling:
<ul>
<li>
<a href = "input05.txt">input05.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output05.txt">output05.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt05.txt">cvt05.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt05.png">cvt05.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 6</b> repeats test 1, but with Random sampling:
<ul>
<li>
<a href = "input06.txt">input06.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output06.txt">output06.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt06.txt">cvt06.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt06.png">cvt06.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 7</b> repeats test 1, but with a seed of 987654321:
<ul>
<li>
<a href = "input07.txt">input07.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output07.txt">output07.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt07.txt">cvt07.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt07.png">cvt07.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 8</b> repeats test 1, but with a batch size of 5:
<ul>
<li>
<a href = "input08.txt">input08.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output08.txt">output08.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt08.txt">cvt08.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt08.png">cvt08.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 9</b> computes 100 CVT points in 3 dimensions, using uniform
initialization, a seed of 123456789, 40 iterations, a tolerance
of 0.000001, uniform sampling, 10,000 sample points in batches of 1000:
<ul>
<li>
<a href = "input09.txt">input09.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output09.txt">output09.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt09.txt">cvt09.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 10</b> investigates the unstable CVT formed by a Cartesian
grid of 100 points in 2D. Starting from this unstable solution,
the iteration proceeds towards a more "hexagonal" pattern :
<ul>
<li>
<a href = "input10.txt">input10.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output10.txt">output10.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt10.txt">cvt10.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt10.png">cvt10.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 11</b> shows how the user may specify the initial point locations
in a file. 15 points are specified in 2D:
<ul>
<li>
<a href = "input11.txt">input11.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output11.txt">output11.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "initial11.txt">initial11.txt</a>,
the initial dataset, created by the user;
</li>
<li>
<a href = "initial11.png">initial11.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the initial dataset;
</li>
<li>
<a href = "cvt11.txt">cvt11.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt11.png">cvt11.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<p>
<b>Test 12</b>:
<ul>
<li>
<a href = "input12.txt">input12.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output12.txt">output12.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt12.txt">cvt12.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 13</b>:
<ul>
<li>
<a href = "input13.txt">input13.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output13.txt">output13.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt13.txt">cvt13.txt</a>,
the dataset created by the commands;
</li>
</ul>
</p>
<p>
<b>Test 14</b> shows how the user may refer to the USER routine
for a different geometry. The default USER routine is set up
to sample the unit circle in 2D. 100 points are requested:
<ul>
<li>
<a href = "input14.txt">input14.txt</a>,
the input defining the dataset;
</li>
<li>
<a href = "output14.txt">output14.txt</a>,
the printed response to the commands;
</li>
<li>
<a href = "cvt14.txt">cvt14.txt</a>,
the dataset created by the commands;
</li>
<li>
<a href = "cvt14.png">cvt14.png</a>,
a <a href = "../../data/png/png.html">PNG</a> image of
the dataset;
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for CVT_DATASET.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 18 September 2005.
</i>
<!-- John Burkardt -->
</body>
</html>