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<a name="Monte-Carlo-Interface"></a>
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<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> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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<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, "error: dim != 2");
abort ();
}
return fp->a * x[0] * x[0]
+ fp->b * x[0] * x[1]
+ fp->c * x[1] * x[1];
}
gsl_monte_function F;
struct my_f_params params = { 3.0, 2.0, 1.0 };
F.f = &my_f;
F.dim = 2;
F.params = &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)->f))(x,(F)->dim,(F)->params)
</pre></div>
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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> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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