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<title>Providing the Function to be Minimized - GNU Scientific Library -- Reference Manual</title>
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<h3 class="section">37.3 Providing the Function to be Minimized</h3>
<p>You must provide n functions of p variables for the
minimization algorithms to operate on. In order to allow for
arbitrary parameters the functions are defined by the following data
types:
<div class="defun">
— Data Type: <b>gsl_multifit_function</b><var><a name="index-gsl_005fmultifit_005ffunction-2403"></a></var><br>
<blockquote><p>This data type defines a general system of functions with arbitrary parameters.
<dl>
<dt><code>int (* f) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, gsl_vector * </code><var>f</var><code>)</code><dd>this function should store the vector result
<!-- {$f(x,\hbox{\it params})$} -->
f(x,params) in <var>f</var> for argument <var>x</var> and arbitrary parameters <var>params</var>,
returning an appropriate error code if the function cannot be computed.
<br><dt><code>size_t n</code><dd>the number of functions, i.e. the number of components of the
vector <var>f</var>.
<br><dt><code>size_t p</code><dd>the number of independent variables, i.e. the number of components of
the vector <var>x</var>.
<br><dt><code>void * params</code><dd>a pointer to the arbitrary parameters of the function.
</dl>
</p></blockquote></div>
<div class="defun">
— Data Type: <b>gsl_multifit_function_fdf</b><var><a name="index-gsl_005fmultifit_005ffunction_005ffdf-2404"></a></var><br>
<blockquote><p>This data type defines a general system of functions with arbitrary parameters and
the corresponding Jacobian matrix of derivatives,
<dl>
<dt><code>int (* f) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, gsl_vector * </code><var>f</var><code>)</code><dd>this function should store the vector result
<!-- {$f(x,\hbox{\it params})$} -->
f(x,params) in <var>f</var> for argument <var>x</var> and arbitrary parameters <var>params</var>,
returning an appropriate error code if the function cannot be computed.
<br><dt><code>int (* df) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, gsl_matrix * </code><var>J</var><code>)</code><dd>this function should store the <var>n</var>-by-<var>p</var> matrix result
<!-- {$J_{ij} = \partial f_i(x,\hbox{\it params}) / \partial x_j$} -->
J_ij = d f_i(x,params) / d x_j in <var>J</var> for argument <var>x</var>
and arbitrary parameters <var>params</var>, returning an appropriate error code if the
function cannot be computed.
<br><dt><code>int (* fdf) (const gsl_vector * </code><var>x</var><code>, void * </code><var>params</var><code>, gsl_vector * </code><var>f</var><code>, gsl_matrix * </code><var>J</var><code>)</code><dd>This function should set the values of the <var>f</var> and <var>J</var> as above,
for arguments <var>x</var> and arbitrary parameters <var>params</var>. This function
provides an optimization of the separate functions for f(x) and
J(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 number of functions, i.e. the number of components of the
vector <var>f</var>.
<br><dt><code>size_t p</code><dd>the number of independent variables, i.e. the number of components of
the vector <var>x</var>.
<br><dt><code>void * params</code><dd>a pointer to the arbitrary parameters of the function.
</dl>
</p></blockquote></div>
<p>Note that when fitting a non-linear model against experimental data,
the data is passed to the functions above using the
<var>params</var> argument and the trial best-fit parameters through the
<var>x</var> argument.
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