-
Notifications
You must be signed in to change notification settings - Fork 57
/
diaphony.html
163 lines (135 loc) · 4.36 KB
/
diaphony.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
<html>
<head>
<title>
DIAPHONY - Compute the Diaphony of an M-dimensional Pointset
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
DIAPHONY <br> the "Diaphony" (dispersion) <br>
of an M-dimensional Pointset
</h1>
<hr>
<p>
<b>DIAPHONY</b>
is a MATLAB program which
computes the "diaphony" of an M-dimensional pointset.
</p>
<p>
The "diaphony" of an M-dimensional pointset is a numeric measure
of the uniformity of the dispersion of the points throughout
the unit hypercube.
</p>
<p>
Regarded as a random variable itself, the diaphony of a set of N points
has an expected value of 1/sqrt(N).
</p>
<p>
For the Halton datasets in 2D, 7D and 16D, here is the table
of the number of points versus the diaphony:
<table "border=1">
<tr><th>Diaphony(M,N)</th><th>M=2D</th><th>M=7D</th><th>M=16D</th>
<th>1/Sqrt(N)</th></tr>
<tr><th> N=10</th><td>0.246</td><td>0.316</td>
<td>0.316</td><td>0.316</td></tr>
<tr><th> N=100</th><td>0.043</td><td>0.099</td>
<td>0.099</td><td>0.100</td></tr>
<tr><th> N=1000</th><td>0.006</td><td>0.031</td>
<td>0.031</td><td>0.031</td></tr>
<tr><th>N=10000</th><td>0.001</td><td>0.009</td>
<td>0.009</td><td>0.010</td></tr>
</table>
</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>DIAPHONY</b> is available in
<a href = "../../c_src/diaphony/diaphony.html">a C version</a> and
<a href = "../../cpp_src/diaphony/diaphony.html">a C++ version</a> and
<a href = "../../f77_src/diaphony/diaphony.html">a FORTRAN77 version</a> and
<a href = "../../f_src/diaphony/diaphony.html">a FORTRAN90 version</a> and
<a href = "../../m_src/diaphony/diaphony.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/star_discrepancy/star_discrepancy.html">
STAR_DISCREPANCY</a>,
a C++ program which
reads a <b>TABLE file</b> of points (presumed to lie in the
unit hypercube) and computes bounds on the star discrepancy,
a measure of dispersion, by Eric Thiemard.
</p>
<p>
<a href = "../../m_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a MATLAB program which
reads a file of
points and creates a "latinized" version by adjusting the data.
</p>
<p>
<a href = "../../m_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a MATLAB program which
reads a file of points and computes the quality of dispersion.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Peter Heelekalek,<br>
On Correlation Analysis of Pseudorandom Numbers,
in Monte Carlo and Quasi-Monte Carlo Methods 1996,<br>
edited by Harald Niederreiter, Peter Hellekalek,
Gerhard Larcher, and Peter Zinterhof,<br>
Volume 127 of Lecture Notes in Statistics,<br>
Springer Verlag, 1997, pages 251-265.
</li>
<li>
Peter Heelekalek, Harald Niederreiter,<br>
The Weighted Spectral Test: Diaphony,<br>
ACM Transactions on Modeling and Computer Simulation,<br>
Volume 8, Number 1, January 1998, pages 43-60.
</li>
<li>
Peter Heelekalek, Hannes Leeb,<br>
Dyadic Diaphony,<br>
Acta Arithmetica,<br>
Volume 80, Number 2, 1997, pages 187-196.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "diaphony.m">diaphony.m</a>, the source code.
</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 25 January 2012.
</i>
<!-- John Burkardt -->
</body>
<!-- Initial HTML skeleton created by HTMLINDEX. -->
</html>