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<title>Providing a function to minimize - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">35.4 Providing a function to minimize</h3>
<p>You must provide a parametric function of n variables for the
minimizers to operate on. You may also need to provide a routine which
calculates the gradient of the function and a third routine which
calculates both the function value and the gradient together. In order
to allow for general parameters the functions are defined by the
following data types:
<div class="defun">
— Data Type: <b>gsl_multimin_function_fdf</b><var><a name="index-gsl_005fmultimin_005ffunction_005ffdf-2335"></a></var><br>
<blockquote><p>This data type defines a general function of n variables with
parameters and the corresponding gradient vector of derivatives,
<dl>
<dt><code>double (* f) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>)</code><dd>this function should return the result
<!-- {$f(x,\hbox{\it params})$} -->
f(x,params) for argument <var>x</var> and parameters <var>params</var>.
<br><dt><code>void (* df) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, gsl_vector * </code><var>g</var><code>)</code><dd>this function should store the <var>n</var>-dimensional gradient
<!-- {$g_i = \partial f(x,\hbox{\it params}) / \partial x_i$} -->
g_i = d f(x,params) / d x_i in the vector <var>g</var> for argument <var>x</var>
and parameters <var>params</var>, returning an appropriate error code if the
function cannot be computed.
<br><dt><code>void (* fdf) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, double * f, gsl_vector * </code><var>g</var><code>)</code><dd>This function should set the values of the <var>f</var> and <var>g</var> as above,
for arguments <var>x</var> and parameters <var>params</var>. This function
provides an optimization of the separate functions for f(x) and
g(x)—it is always faster to compute the function and its
derivative at the same time.
<br><dt><code>size_t n</code><dd>the dimension of the system, i.e. the number of components of the
vectors <var>x</var>.
<br><dt><code>void * params</code><dd>a pointer to the parameters of the function.
</dl>
</p></blockquote></div>
<div class="defun">
— Data Type: <b>gsl_multimin_function</b><var><a name="index-gsl_005fmultimin_005ffunction-2336"></a></var><br>
<blockquote><p>This data type defines a general function of n variables with
parameters,
<dl>
<dt><code>double (* f) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>)</code><dd>this function should return the result
<!-- {$f(x,\hbox{\it params})$} -->
f(x,params) for argument <var>x</var> and parameters <var>params</var>.
<br><dt><code>size_t n</code><dd>the dimension of the system, i.e. the number of components of the
vectors <var>x</var>.
<br><dt><code>void * params</code><dd>a pointer to the parameters of the function.
</dl>
</p></blockquote></div>
<p class="noindent">The following example function defines a simple two-dimensional
paraboloid with five parameters,
<pre class="example"><pre class="verbatim"> /* Paraboloid centered on (p[0],p[1]), with
scale factors (p[2],p[3]) and minimum p[4] */
double
my_f (const gsl_vector *v, void *params)
{
double x, y;
double *p = (double *)params;
x = gsl_vector_get(v, 0);
y = gsl_vector_get(v, 1);
return p[2] * (x - p[0]) * (x - p[0]) +
p[3] * (y - p[1]) * (y - p[1]) + p[4];
}
/* The gradient of f, df = (df/dx, df/dy). */
void
my_df (const gsl_vector *v, void *params,
gsl_vector *df)
{
double x, y;
double *p = (double *)params;
x = gsl_vector_get(v, 0);
y = gsl_vector_get(v, 1);
gsl_vector_set(df, 0, 2.0 * p[2] * (x - p[0]));
gsl_vector_set(df, 1, 2.0 * p[3] * (y - p[1]));
}
/* Compute both f and df together. */
void
my_fdf (const gsl_vector *x, void *params,
double *f, gsl_vector *df)
{
*f = my_f(x, params);
my_df(x, params, df);
}
</pre></pre>
<p class="noindent">The function can be initialized using the following code,
<pre class="example"> gsl_multimin_function_fdf my_func;
/* Paraboloid center at (1,2), scale factors (10, 20),
minimum value 30 */
double p[5] = { 1.0, 2.0, 10.0, 20.0, 30.0 };
my_func.n = 2; /* number of function components */
my_func.f = &my_f;
my_func.df = &my_df;
my_func.fdf = &my_fdf;
my_func.params = (void *)p;
</pre>
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