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<h3 class="section">23.1 Interface</h3>
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<p>All of the Monte Carlo integration routines use the same general form of
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interface. There is an allocator to allocate memory for control
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variables and workspace, a routine to initialize those control
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variables, the integrator itself, and a function to free the space when
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<p>Each integration function requires a random number generator to be
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supplied, and returns an estimate of the integral and its standard
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deviation. The accuracy of the result is determined by the number of
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function calls specified by the user. If a known level of accuracy is
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required this can be achieved by calling the integrator several times
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and averaging the individual results until the desired accuracy is
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<p>Random sample points used within the Monte Carlo routines are always
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chosen strictly within the integration region, so that endpoint
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singularities are automatically avoided.
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<p>The function to be integrated has its own datatype, defined in the
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header file <samp><span class="file">gsl_monte.h</span></samp>.
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— Data Type: <b>gsl_monte_function</b><var><a name="index-gsl_005fmonte_005ffunction-1870"></a></var><br>
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<p>This data type defines a general function with parameters for Monte
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<dt><code>double (* f) (double * </code><var>x</var><code>, size_t </code><var>dim</var><code>, void * </code><var>params</var><code>)</code><dd>this function should return the value
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<!-- {$f(x,\hbox{\it params})$} -->
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f(x,params) for the argument <var>x</var> and parameters <var>params</var>,
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where <var>x</var> is an array of size <var>dim</var> giving the coordinates of
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the point where the function is to be evaluated.
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<br><dt><code>size_t dim</code><dd>the number of dimensions for <var>x</var>.
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<br><dt><code>void * params</code><dd>a pointer to the parameters of the function.
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</p></blockquote></div>
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<p class="noindent">Here is an example for a quadratic function in two dimensions,
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with a = 3, b = 2, c = 1. The following code
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defines a <code>gsl_monte_function</code> <code>F</code> which you could pass to an
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<pre class="example"> struct my_f_params { double a; double b; double c; };
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my_f (double x[], size_t dim, void * p) {
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struct my_f_params * fp = (struct my_f_params *)p;
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fprintf (stderr, "error: dim != 2");
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return fp->a * x[0] * x[0]
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+ fp->b * x[0] * x[1]
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+ fp->c * x[1] * x[1];
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gsl_monte_function F;
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struct my_f_params params = { 3.0, 2.0, 1.0 };
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F.params = &params;
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<p class="noindent">The function f(x) can be evaluated using the following macro,
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<pre class="example"> #define GSL_MONTE_FN_EVAL(F,x)
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(*((F)->f))(x,(F)->dim,(F)->params)
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