-
Notifications
You must be signed in to change notification settings - Fork 57
/
ziggurat.html
283 lines (244 loc) · 7.52 KB
/
ziggurat.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
<html>
<head>
<title>
ZIGGURAT - Ziggurat Random Number Generator (RNG)
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
ZIGGURAT <br> Ziggurat Random Number Generator (RNG)
</h1>
<hr>
<p>
<b>ZIGGURAT</b>
is a MATLAB library which
rapidly generates random variates from the uniform, normal or
exponential distributions,
by Marsaglia and Tsang.
</p>
<p>
The uniform numbers are generated directly. The ziggurat method is used
to compute the normal and exponential values.
</p>
<p>
In the reference, the underlying generators are implemented "inline",
invoking a function call only in exceptional cases. This results in
very fast execution.
</p>
<p>
In this implementation, the advantages of inline code are not used.
All the routines and inline functions are isolated in a separate file,
so that a user invokes them through the familiar library interface.
</p>
<p>
<i>
This code is a translation of software written in C. The C code used
unsigned integers for the underlying SHR3 algorithm. Getting the MATLAB
code to reproduce the results of the C code has been somewhat tricky.
The results seem to match the C code, but I have not tried to be
efficient in my modifications.
</i>
</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>ZIGGURAT</b> is available in
<a href = "../../c_src/ziggurat/ziggurat.html">a C version</a> and
<a href = "../../cpp_src/ziggurat/ziggurat.html">a C++ version</a> and
<a href = "../../f77_src/ziggurat/ziggurat.html">a FORTRAN77 version</a> and
<a href = "../../f_src/ziggurat/ziggurat.html">a FORTRAN90 version</a> and
<a href = "../../m_src/ziggurat/ziggurat.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<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/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/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 elements of a sequence of pseudorandom normally distributed values.
</p>
<p>
<a href = "../../c_src/rbox/rbox.html">
RBOX</a>,
a C program which
generates a set of points in a region, selected at random according to a given distribution.
</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/uniform/uniform.html">
UNIFORM</a>,
a MATLAB library which
computes elements of uniform pseudorandom 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">
Author:
</h3>
<p>
George Marsaglia, Wai Wan Tsang.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Philip Leong, Guanglie Zhang, Dong-U Lee, Wayne Luk, John Villasenor,<br>
A comment on the implementation of the ziggurat method,<br>
Journal of Statistical Software,<br>
Volume 12, Number 7, February 2005.
</li>
<li>
George Marsaglia, Wai Wan Tsang,<br>
The Ziggurat Method for Generating Random Variables,<br>
Journal of Statistical Software,<br>
Volume 5, Number 8, October 2000, seven pages.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "r4_exp.m">r4_exp.m</a>
returns an exponentially distributed single precision real value.
</li>
<li>
<a href = "r4_exp_setup.m">r4_exp_setup.m</a>
sets data needed by R4_EXP.
</li>
<li>
<a href = "r4_nor.m">r4_nor.m</a>
returns a normally distributed single precision real value.
</li>
<li>
<a href = "r4_nor_setup.m">r4_nor_setup.m</a>
sets data needed by R4_NOR.
</li>
<li>
<a href = "r4_uni.m">r4_uni.m</a>
returns a uniformly distributed real value.
</li>
<li>
<a href = "shr3.m">shr3.m</a>
evaluates the SHR3 generator for integers.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
returns the YMDHMS date as a timestamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "ziggurat_test.m">ziggurat_test.m</a>
calls all the tests.
</li>
<li>
<a href = "ziggurat_test_output.txt">ziggurat_test_output.txt</a>,
the output file.
</li>
<li>
<a href = "ziggurat_test001.m">ziggurat_test001.m</a>
checks the behavior of SHR3 based on the seed value.
</li>
<li>
<a href = "ziggurat_test02.m">ziggurat_test02.m</a>
checks the behavior of R4_UNI based on the seed value.
</li>
<li>
<a href = "ziggurat_test03.m">ziggurat_test03.m</a>
checks the behavior of R4_NOR based on the seed value.
</li>
<li>
<a href = "ziggurat_test04.m">ziggurat_test04.m</a>
checks the behavior of R4_EXP based on the seed value.
</li>
<li>
<a href = "ziggurat_test05.m">ziggurat_test05.m</a>
times SHR3.
</li>
<li>
<a href = "ziggurat_test06.m">ziggurat_test06.m</a>
times R4_UNI.
</li>
<li>
<a href = "ziggurat_test07.m">ziggurat_test07.m</a>
times R4_NOR.
</li>
<li>
<a href = "ziggurat_test08.m">ziggurat_test08.m</a>
times R4_EXP.
</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 20 May 2008.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>