-
Notifications
You must be signed in to change notification settings - Fork 56
/
uniform.html
704 lines (662 loc) · 20.7 KB
/
uniform.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
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
<html>
<head>
<title>
UNIFORM - A Uniform Random Number Generator
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
UNIFORM <br> A Uniform Random Number Generator
</h1>
<hr>
<p>
<b>UNIFORM</b>
is a MATLAB library which
returns a sequence of uniformly distributed pseudorandom numbers.
</p>
<p>
The fundamental underlying random number generator
is based on a simple, old, and limited linear congruential random
number generator originally used in the IBM System 360. If you want
state of the art random number generation, look elsewhere!
</p>
<p>
MATLAB already has the <b>rand()</b> function, and
it is not the purpose of this library to replace it.
</p>
<p>
However, this library makes it possible to compare certain computations
that use uniform random numbers, written in C, C++, FORTRAN77,
FORTRAN90, Mathematica, MATLAB or Python.
</p>
<p>
Various types of random data can be computed. The routine names
are chosen to indicate the corresponding type:
<ul>
<li>
<b>B</b>, an integer binary value of 0 or 1.
</li>
<li>
<b>C4</b>, complex ( single precision )
</li>
<li>
<b>C8</b>, complex ( double precision )
</li>
<li>
<b>CH</b>, character
</li>
<li>
<b>I4</b>, integer ( single precision )
</li>
<li>
<b>L4</b>, a logical value.
</li>
<li>
<b>R4</b>, real ( single precision )
</li>
<li>
<b>R8</b>, real ( double precision )
</li>
</ul>
</p>
<p>
In some cases, a one dimension vector or two dimensional
array of values is to be generated, and part of the name
will therefore include:
<ul>
<li>
<b>VEC</b>, vector;
</li>
<li>
<b>MAT</b>, a matrix of data;
</li>
</ul>
</p>
<p>
The underlying random numbers are generally defined over some
unit interval or region. Routines are available which return
these "unit" values, while other routines allow the user to
specify limits between which the unit values are rescaled.
The name of a routine will usually include a tag
suggestig which is the case:
<ul>
<li>
<b>01</b>, the data lies in a nit interval or region;
</li>
<li>
<b>AB</b>, the data lies in a scaled interval or region;
</li>
</ul>
</p>
<p>
The random number generator embodied here is not very sophisticated.
It will not have the best properties of distribution, noncorrelation
and long period. It is not the purpose of this library to achieve
such worthy goals. This is simply a reasonably portable library
that can be implemented in various languages, on various machines,
and for which it is possible, for instance, to regard the output
as a function of the seed, and moreover, to work directly with
the sequence of seeds, if necessary.
</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>UNIFORM</b> is available in
<a href = "../../c_src/uniform/uniform.html">a C version</a> and
<a href = "../../cpp_src/uniform/uniform.html">a C++ version</a> and
<a href = "../../f77_src/uniform/uniform.html">a FORTRAN77 version</a> and
<a href = "../../f_src/uniform/uniform.html">a FORTRAN90 version</a> and
<a href = "../../math_src/uniform/uniform.html">a Mathematica version</a> and
<a href = "../../m_src/uniform/uniform.html">a MATLAB version</a> and
<a href = "../../py_src/uniform/uniform.html">a Python version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/asa183/asa183.html">
ASA183</a>,
a MATLAB library which
implements the Wichman-Hill random number generator (RNG).
</p>
<p>
<a href = "../../m_src/faure/faure.html">
FAURE</a>,
a MATLAB library which
computes elements of a Faure quasirandom sequence.
</p>
<p>
<a href = "../../m_src/grid/grid.html">
GRID</a>,
a MATLAB library which
computes elements of a grid dataset.
</p>
<p>
<a href = "../../m_src/halton/halton.html">
HALTON</a>,
a MATLAB library which
computes elements of a Halton quasirandom sequence.
</p>
<p>
<a href = "../../m_src/hammersley/hammersley.html">
HAMMERSLEY</a>,
a MATLAB library which
computes elements of a Hammersley quasirandom sequence.
</p>
<p>
<a href = "../../m_src/matlab_random/matlab_random.html">
MATLAB_RANDOM</a>,
MATLAB programs which
illustrate the use of Matlab's random number generators.
</p>
<p>
<a href = "../../m_src/niederreiter2/niederreiter2.html">
NIEDERREITER2</a>,
a MATLAB library which
computes elements of a
Niederreiter quasirandom sequence with base 2.
</p>
<p>
<a href = "../../m_src/normal/normal.html">
NORMAL</a>,
a MATLAB library which
computes a sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../m_src/randlc/randlc.html">
RANDLC</a>,
a MATLAB library which
generates a sequence of pseudorandom numbers,
used by the NAS Benchmark programs.
</p>
<p>
<a href = "../../m_src/ranlib/ranlib.html">
RANLIB</a>,
a MATLAB library which
produces random samples from Probability Density Functions (PDF's),
including Beta, Chi-square Exponential, F, Gamma, Multivariate normal,
Noncentral chi-square, Noncentral F, Univariate normal, random permutations,
Real uniform, Binomial, Negative Binomial, Multinomial, Poisson
and Integer uniform,
by Barry Brown and James Lovato.
</p>
<p>
<a href = "../../m_src/rnglib/rnglib.html">
RNGLIB</a>,
a MATLAB library which
implements a random number generator (RNG) with splitting facilities,
allowing multiple independent streams to be computed,
by L'Ecuyer and Cote.
</p>
<p>
<a href = "../../m_src/sobol/sobol.html">
SOBOL</a>,
a MATLAB library which
computes elements of a Sobol quasirandom sequence.
</p>
<p>
<a href = "../../m_src/van_der_corput/van_der_corput.html">
VAN_DER_CORPUT</a>,
a MATLAB library which
computes elements of a van der Corput quasirandom sequence.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673,<br>
LC: QA76.9.C65.B73.
</li>
<li>
Bennett Fox,<br>
Algorithm 647:
Implementation and Relative Efficiency of Quasirandom
Sequence Generators,<br>
ACM Transactions on Mathematical Software,<br>
Volume 12, Number 4, December 1986, pages 362-376.
</li>
<li>
Donald Knuth,<br>
The Art of Computer Programming,<br>
Volume 2, Seminumerical Algorithms,<br>
Third Edition,<br>
Addison Wesley, 1997,<br>
ISBN: 0201896842,<br>
LC: QA76.6.K64.
</li>
<li>
Pierre LEcuyer,<br>
Random Number Generation,<br>
in Handbook of Simulation,<br>
edited by Jerry Banks,<br>
Wiley, 1998,<br>
ISBN: 0471134031,<br>
LC: T57.62.H37.
</li>
<li>
Peter Lewis, Allen Goodman, James Miller,<br>
A Pseudo-Random Number Generator for the System/360,<br>
IBM Systems Journal,<br>
Volume 8, Number 2, 1969, pages 136-143.
</li>
<li>
Stephen Park, Keith Miller,<br>
Random Number Generators: Good Ones are Hard to Find,<br>
Communications of the ACM,<br>
Volume 31, Number 10, October 1988, pages 1192-1201.
</li>
<li>
Eric Weisstein,<br>
CRC Concise Encyclopedia of Mathematics,<br>
CRC Press, 2002,<br>
Second edition,<br>
ISBN: 1584883472,<br>
LC: QA5.W45.
</li>
<li>
Barry Wilkinson, Michael Allen,<br>
Parallel Programming:
Techniques and Applications Using Networked Workstations and Parallel Computers,<br>
Prentice Hall,<br>
ISBN: 0-13-140563-2,<br>
LC: QA76.642.W54.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "bvec_print.m">bvec_print.m</a>,
prints a BVEC.
</li>
<li>
<a href = "bvec_uniform.m">bvec_uniform.m</a>,
returns a random BVEC (a binary vector).
</li>
<li>
<a href = "c4_uniform_01.m">c4_uniform_01.m</a>,
returns a unit pseudorandom C4.
</li>
<li>
<a href = "c4mat_print.m">c4mat_print.m</a>,
prints a C4MAT.
</li>
<li>
<a href = "c4mat_print_some.m">c4mat_print_some.m</a>,
prints some of a C4MAT.
</li>
<li>
<a href = "c4mat_uniform_01.m">c4mat_uniform_01.m</a>,
returns a unit pseudorandom C4MAT.
</li>
<li>
<a href = "c4vec_print.m">c4vec_print.m</a>,
prints a C4VEC.
</li>
<li>
<a href = "c4vec_uniform_01.m">c4vec_uniform_01.m</a>,
returns a unit pseudorandom C4VEC.
</li>
<li>
<a href = "c8_uniform_01.m">c8_uniform_01.m</a>,
returns a unit pseudorandom C8.
</li>
<li>
<a href = "c8mat_print.m">c8mat_print.m</a>,
prints a C8MAT.
</li>
<li>
<a href = "c8mat_print_some.m">c8mat_print_some.m</a>,
prints some of a C8MAT.
</li>
<li>
<a href = "c8mat_uniform_01.m">c8mat_uniform_01.m</a>,
returns an array of unit pseudorandom double precision
complex numbers.
</li>
<li>
<a href = "c8vec_print.m">c8vec_print.m</a>,
prints a C8VEC.
</li>
<li>
<a href = "c8vec_uniform_01.m">c8vec_uniform_01.m</a>,
returns a unit pseudorandom C8VEC.
</li>
<li>
<a href = "ch_uniform_ab.m">ch_uniform_ab.m</a>,
returns a scaled pseudorandom CH.
</li>
<li>
<a href = "congruence.m">congruence.m</a>,
solves a congruence of the form A * X = C ( mod B ).
</li>
<li>
<a href = "get_seed.m">get_seed.m</a>,
returns a random seed for the random number generator.
</li>
<li>
<a href = "i4_gcd.m">i4_gcd.m</a>,
returns the greatest common divisor of two I4's.
</li>
<li>
<a href = "i4_huge.m">i4_huge.m</a>,
returns a huge I4.
</li>
<li>
<a href = "i4_seed_advance.m">i4_seed_advance.m</a>,
"advances" the seed.
</li>
<li>
<a href = "i4_sign.m">i4_sign.m</a>,
returns the sign of an I4.
</li>
<li>
<a href = "i4_uniform_0i.m">i4_uniform_0i.m</a>,
returns a pseudorandom I4 between 1 and 2^(31)-1.
</li>
<li>
<a href = "i4_uniform_ab.m">i4_uniform_ab.m</a>,
returns a scaled random I4 between A and B.
</li>
<li>
<a href = "i4mat_print.m">i4mat_print.m</a>,
prints an I4MAT;
</li>
<li>
<a href = "i4mat_print_some.m">i4mat_print_some.m</a>,
prints some of an I4MAT;
</li>
<li>
<a href = "i4mat_uniform_ab.m">i4mat_uniform_ab.m</a>,
returns a scaled pseudorangom I4MAT.
</li>
<li>
<a href = "i4vec_print.m">i4vec_print.m</a>,
prints an I4VEC.
</li>
<li>
<a href = "i4vec_uniform_ab.m">i4vec_uniform_ab.m</a>,
returns a scaled pseudorandom I4VEC.
</li>
<li>
<a href = "l4_uniform.m">l4_uniform.m</a>,
returns a scaled random L4 (a logical value).
</li>
<li>
<a href = "l4mat_print.m">l4mat_print.m</a>,
prints an L4MAT;
</li>
<li>
<a href = "l4mat_print_some.m">l4mat_print_some.m</a>,
prints some of an L4MAT;
</li>
<li>
<a href = "l4mat_uniform.m">l4mat_uniform.m</a>,
returns a random L4MAT (a logical matrix).
</li>
<li>
<a href = "l4vec_print.m">l4vec_print.m</a>,
prints an L4VEC.
</li>
<li>
<a href = "l4vec_uniform.m">l4vec_uniform.m</a>,
returns a random L4VEC (a logical vector).
</li>
<li>
<a href = "lcrg_anbn.m">lcrg_anbn.m</a>,
computes the "N-th power" of a linear congruential generator.
</li>
<li>
<a href = "lcrg_evaluate.m">lcrg_evaluate.m</a>,
evaluates an LCRG, y = ( A * x + B ) mod C.
</li>
<li>
<a href = "lcrg_seed.m">lcrg_seed.m</a>,
computes the N-th seed of a linear congruential random
number generator.
</li>
<li>
<a href = "power_mod.m">power_mod.m</a>,
computes mod ( A^N, M ).
</li>
<li>
<a href = "r4_uniform_01.m">r4_uniform_01.m</a>,
returns a unit pseudorandom R4.
</li>
<li>
<a href = "r4_uniform_ab.m">r4_uniform_ab.m</a>,
returns a scaled pseudorandom R4.
</li>
<li>
<a href = "r4mat_print.m">r4mat_print.m</a>,
prints an R4MAT;
</li>
<li>
<a href = "r4mat_print_some.m">r4mat_print_some.m</a>,
prints some of an R4MAT;
</li>
<li>
<a href = "r4mat_uniform_01.m">r4mat_uniform_01.m</a>,
returns a unit pseudorandom R4MAT.
</li>
<li>
<a href = "r4mat_uniform_ab.m">r4mat_uniform_ab.m</a>,
returns a scaled pseudorandom R4MAT.
</li>
<li>
<a href = "r4vec_print.m">r4vec_print.m</a>,
prints an R4VEC.
</li>
<li>
<a href = "r4vec_uniform_01.m">r4vec_uniform_01.m</a>,
returns a unit pseudorandom R4VEC.
</li>
<li>
<a href = "r4vec_uniform_ab.m">r4vec_uniform_ab.m</a>,
returns a scaled pseudorandom R4VEC.
</li>
<li>
<a href = "r8_uniform_01.m">r8_uniform_01.m</a>,
returns a unit pseudorandom R8.
</li>
<li>
<a href = "r8_uniform_ab.m">r8_uniform_ab.m</a>,
returns a scaled pseudorandom R8.
</li>
<li>
<a href = "r8col_uniform_abvec.m">
r8col_uniform_abvec.m</a>,
fills an R8COL with scaled pseudorandom numbers.
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>,
prints an R8MAT;
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>,
prints some of an R8MAT;
</li>
<li>
<a href = "r8mat_uniform_01.m">r8mat_uniform_01.m</a>,
returns a unit pseudorandom R8MAT.
</li>
<li>
<a href = "r8mat_uniform_ab.m">r8mat_uniform_ab.m</a>,
returns a scaled pseudorandom R8MAT.
</li>
<li>
<a href = "r8row_uniform_abvec.m">
r8row_uniform_abvec.m</a>,
fills an R8ROW with scaled pseudorandom numbers.
</li>
<li>
<a href = "r8vec_normal_01.m">r8vec_normal_01.m</a>,
returns a unit normal random R8VEC.
</li>
<li>
<a href = "r8vec_print.m">r8vec_print.m</a>,
prints an R8VEC.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>,
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "r8vec_uniform_ab.m">r8vec_uniform_ab.m</a>,
returns a scaled pseudorandom R8VEC.
</li>
<li>
<a href = "r8vec_uniform_abvec.m">r8vec_uniform_abvec.m</a>,
returns a scaled pseudorandom R8VEC.
</li>
<li>
<a href = "r8vec_uniform_unit.m">r8vec_uniform_unit.m</a>,
returns a random unit vector.
</li>
<li>
<a href = "s_len_trim.m">s_len_trim.m</a>,
returns the length of a string to the last nonblank.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>,
prints the current YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "uniform_test.m">uniform_test.m</a>,
a script that runs all the tests.
</li>
<li>
<a href = "uniform_test_output.txt">uniform_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "bvec_uniform_test.m">bvec_uniform_test.m</a>
</li>
<li>
<a href = "c4_uniform_01_test.m">c4_uniform_01_test.m</a>
</li>
<li>
<a href = "c4mat_uniform_01_test.m">c4mat_uniform_01_test.m</a>
</li>
<li>
<a href = "c4vec_uniform_01_test.m">c4vec_uniform_01_test.m</a>
</li>
<li>
<a href = "c8_uniform_01_test.m">c8_uniform_01_test.m</a>
</li>
<li>
<a href = "c8mat_uniform_01_test.m">c8mat_uniform_01_test.m</a>
</li>
<li>
<a href = "c8vec_uniform_01_test.m">c8vec_uniform_01_test.m</a>
</li>
<li>
<a href = "ch_uniform_ab_test.m">ch_uniform_ab_test.m</a>
</li>
<li>
<a href = "get_seed_test.m">get_seed_test.m</a>
</li>
<li>
<a href = "i4_seed_advance_test.m">i4_seed_advance_test.m</a>
</li>
<li>
<a href = "i4_uniform_0i_test.m">i4_uniform_0i_test.m</a>
</li>
<li>
<a href = "i4_uniform_ab_test.m">i4_uniform_ab_test.m</a>
</li>
<li>
<a href = "i4mat_uniform_ab_test.m">i4mat_uniform_ab_test.m</a>
</li>
<li>
<a href = "i4vec_uniform_ab_test.m">i4vec_uniform_ab_test.m</a>
</li>
<li>
<a href = "l4_uniform_test.m">l4_uniform_test.m</a>
</li>
<li>
<a href = "l4mat_uniform_test.m">l4mat_uniform_test.m</a>
</li>
<li>
<a href = "l4vec_uniform_test.m">l4vec_uniform_test.m</a>
</li>
<li>
<a href = "lcrg_anbn_test.m">lcrg_anbn_test.m</a>
</li>
<li>
<a href = "lcrg_seed_test.m">lcrg_seed_test.m</a>
</li>
<li>
<a href = "r4_uniform_01_test.m">r4_uniform_01_test.m</a>
</li>
<li>
<a href = "r4_uniform_ab_test.m">r4_uniform_ab_test.m</a>
</li>
<li>
<a href = "r4mat_uniform_ab_test.m">r4mat_uniform_ab_test.m</a>
</li>
<li>
<a href = "r4vec_uniform_ab_test.m">r4vec_uniform_ab_test.m</a>
</li>
<li>
<a href = "r8_uniform_01_test.m">r8_uniform_01_test.m</a>
</li>
<li>
<a href = "r8_uniform_ab_test.m">r8_uniform_ab_test.m</a>
</li>
<li>
<a href = "r8col_uniform_abvec_test.m">r8col_uniform_abvec_test.m</a>
</li>
<li>
<a href = "r8mat_uniform_ab_test.m">r8mat_uniform_ab_test.m</a>
</li>
<li>
<a href = "r8row_uniform_abvec_test.m">r8row_uniform_abvec_test.m</a>
</li>
<li>
<a href = "r8vec_uniform_01_test.m">r8vec_uniform_01_test.m</a>
</li>
<li>
<a href = "r8vec_uniform_ab_test.m">r8vec_uniform_ab_test.m</a>
</li>
<li>
<a href = "r8vec_uniform_abvec_test.m">r8vec_uniform_abvec_test.m</a>
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 29 December 2014.
</i>
<!-- John Burkardt -->
</body>
</html>