File: Monte-Carlo-Interface.html

package info (click to toggle)
gsl-ref-html 2.3-1
  • links: PTS
  • area: non-free
  • in suites: bullseye, buster, sid
  • size: 6,876 kB
  • ctags: 4,574
  • sloc: makefile: 35
file content (169 lines) | stat: -rw-r--r-- 6,802 bytes parent folder | download
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
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<html>
<!-- Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016 The GSL Team.

Permission is granted to copy, distribute and/or modify this document
under the terms of the GNU Free Documentation License, Version 1.3 or
any later version published by the Free Software Foundation; with the
Invariant Sections being "GNU General Public License" and "Free Software
Needs Free Documentation", the Front-Cover text being "A GNU Manual",
and with the Back-Cover Text being (a) (see below). A copy of the
license is included in the section entitled "GNU Free Documentation
License".

(a) The Back-Cover Text is: "You have the freedom to copy and modify this
GNU Manual." -->
<!-- Created by GNU Texinfo 5.1, http://www.gnu.org/software/texinfo/ -->
<head>
<title>GNU Scientific Library &ndash; Reference Manual: Monte Carlo Interface</title>

<meta name="description" content="GNU Scientific Library &ndash; Reference Manual: Monte Carlo Interface">
<meta name="keywords" content="GNU Scientific Library &ndash; Reference Manual: Monte Carlo Interface">
<meta name="resource-type" content="document">
<meta name="distribution" content="global">
<meta name="Generator" content="makeinfo">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<link href="index.html#Top" rel="start" title="Top">
<link href="Function-Index.html#Function-Index" rel="index" title="Function Index">
<link href="Monte-Carlo-Integration.html#Monte-Carlo-Integration" rel="up" title="Monte Carlo Integration">
<link href="PLAIN-Monte-Carlo.html#PLAIN-Monte-Carlo" rel="next" title="PLAIN Monte Carlo">
<link href="Monte-Carlo-Integration.html#Monte-Carlo-Integration" rel="previous" title="Monte Carlo Integration">
<style type="text/css">
<!--
a.summary-letter {text-decoration: none}
blockquote.smallquotation {font-size: smaller}
div.display {margin-left: 3.2em}
div.example {margin-left: 3.2em}
div.indentedblock {margin-left: 3.2em}
div.lisp {margin-left: 3.2em}
div.smalldisplay {margin-left: 3.2em}
div.smallexample {margin-left: 3.2em}
div.smallindentedblock {margin-left: 3.2em; font-size: smaller}
div.smalllisp {margin-left: 3.2em}
kbd {font-style:oblique}
pre.display {font-family: inherit}
pre.format {font-family: inherit}
pre.menu-comment {font-family: serif}
pre.menu-preformatted {font-family: serif}
pre.smalldisplay {font-family: inherit; font-size: smaller}
pre.smallexample {font-size: smaller}
pre.smallformat {font-family: inherit; font-size: smaller}
pre.smalllisp {font-size: smaller}
span.nocodebreak {white-space:nowrap}
span.nolinebreak {white-space:nowrap}
span.roman {font-family:serif; font-weight:normal}
span.sansserif {font-family:sans-serif; font-weight:normal}
ul.no-bullet {list-style: none}
-->
</style>


</head>

<body lang="en" bgcolor="#FFFFFF" text="#000000" link="#0000FF" vlink="#800080" alink="#FF0000">
<a name="Monte-Carlo-Interface"></a>
<div class="header">
<p>
Next: <a href="PLAIN-Monte-Carlo.html#PLAIN-Monte-Carlo" accesskey="n" rel="next">PLAIN Monte Carlo</a>, Up: <a href="Monte-Carlo-Integration.html#Monte-Carlo-Integration" accesskey="u" rel="up">Monte Carlo Integration</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Interface"></a>
<h3 class="section">25.1 Interface</h3>
<p>All of the Monte Carlo integration routines use the same general form of
interface.  There is an allocator to allocate memory for control
variables and workspace, a routine to initialize those control
variables, the integrator itself, and a function to free the space when
done.
</p>
<p>Each integration function requires a random number generator to be
supplied, and returns an estimate of the integral and its standard
deviation.  The accuracy of the result is determined by the number of
function calls specified by the user.  If a known level of accuracy is
required this can be achieved by calling the integrator several times
and averaging the individual results until the desired accuracy is
obtained.  
</p>
<p>Random sample points used within the Monte Carlo routines are always
chosen strictly within the integration region, so that endpoint
singularities are automatically avoided.
</p>
<p>The function to be integrated has its own datatype, defined in the
header file <samp>gsl_monte.h</samp>.
</p>
<dl>
<dt><a name="index-gsl_005fmonte_005ffunction"></a>Data Type: <strong>gsl_monte_function</strong></dt>
<dd>
<p>This data type defines a general function with parameters for Monte
Carlo integration.
</p>
<dl compact="compact">
<dt><code>double (* f) (double * <var>x</var>, size_t <var>dim</var>, void * <var>params</var>)</code></dt>
<dd><p>this function should return the value
<em>f(x,params)</em> for the argument <var>x</var> and parameters <var>params</var>,
where <var>x</var> is an array of size <var>dim</var> giving the coordinates of
the point where the function is to be evaluated.
</p>
</dd>
<dt><code>size_t dim</code></dt>
<dd><p>the number of dimensions for <var>x</var>.
</p>
</dd>
<dt><code>void * params</code></dt>
<dd><p>a pointer to the parameters of the function.
</p></dd>
</dl>
</dd></dl>

<p>Here is an example for a quadratic function in two dimensions,
</p>
<div class="example">
<pre class="example">f(x,y) = a x^2 + b x y + c y^2
</pre></div>

<p>with <em>a = 3</em>, <em>b = 2</em>, <em>c = 1</em>.  The following code
defines a <code>gsl_monte_function</code> <code>F</code> which you could pass to an
integrator:
</p>
<div class="example">
<pre class="example">struct my_f_params { double a; double b; double c; };

double
my_f (double x[], size_t dim, void * p) {
   struct my_f_params * fp = (struct my_f_params *)p;

   if (dim != 2)
      {
        fprintf (stderr, &quot;error: dim != 2&quot;);
        abort ();
      }

   return  fp-&gt;a * x[0] * x[0] 
             + fp-&gt;b * x[0] * x[1] 
               + fp-&gt;c * x[1] * x[1];
}

gsl_monte_function F;
struct my_f_params params = { 3.0, 2.0, 1.0 };

F.f = &amp;my_f;
F.dim = 2;
F.params = &amp;params;
</pre></div>

<p>The function <em>f(x)</em> can be evaluated using the following macro,
</p>
<div class="example">
<pre class="example">#define GSL_MONTE_FN_EVAL(F,x) 
    (*((F)-&gt;f))(x,(F)-&gt;dim,(F)-&gt;params)
</pre></div>

<hr>
<div class="header">
<p>
Next: <a href="PLAIN-Monte-Carlo.html#PLAIN-Monte-Carlo" accesskey="n" rel="next">PLAIN Monte Carlo</a>, Up: <a href="Monte-Carlo-Integration.html#Monte-Carlo-Integration" accesskey="u" rel="up">Monte Carlo Integration</a> &nbsp; [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>



</body>
</html>