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<title>GNU Scientific Library – Reference Manual: Providing the Function to be Minimized</title>
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<a name="Providing-the-Function-to-be-Minimized"></a>
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<p>
Next: <a href="Finite-Difference-Jacobian.html#Finite-Difference-Jacobian" accesskey="n" rel="next">Finite Difference Jacobian</a>, Previous: <a href="Initializing-the-Nonlinear-Least_002dSquares-Solver.html#Initializing-the-Nonlinear-Least_002dSquares-Solver" accesskey="p" rel="previous">Initializing the Nonlinear Least-Squares Solver</a>, Up: <a href="Nonlinear-Least_002dSquares-Fitting.html#Nonlinear-Least_002dSquares-Fitting" accesskey="u" rel="up">Nonlinear Least-Squares Fitting</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Providing-the-Function-to-be-Minimized-1"></a>
<h3 class="section">38.3 Providing the Function to be Minimized</h3>
<p>You must provide <em>n</em> functions of <em>p</em> variables for the
minimization algorithms to operate on. In order to allow for
arbitrary parameters the functions are defined by the following data
types:
</p>
<dl>
<dt><a name="index-gsl_005fmultifit_005ffunction"></a>Data Type: <strong>gsl_multifit_function</strong></dt>
<dd><p>This data type defines a general system of functions with arbitrary parameters.
</p>
<dl compact="compact">
<dt><code>int (* f) (const gsl_vector * <var>x</var>, void * <var>params</var>, gsl_vector * <var>f</var>)</code></dt>
<dd><p>this function should store the vector result
<em>f(x,params)</em> 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.
</p>
</dd>
<dt><code>size_t n</code></dt>
<dd><p>the number of functions, i.e. the number of components of the
vector <var>f</var>.
</p>
</dd>
<dt><code>size_t p</code></dt>
<dd><p>the number of independent variables, i.e. the number of components of
the vector <var>x</var>.
</p>
</dd>
<dt><code>void * params</code></dt>
<dd><p>a pointer to the arbitrary parameters of the function.
</p></dd>
</dl>
</dd></dl>
<dl>
<dt><a name="index-gsl_005fmultifit_005ffunction_005ffdf"></a>Data Type: <strong>gsl_multifit_function_fdf</strong></dt>
<dd><p>This data type defines a general system of functions with arbitrary parameters and
the corresponding Jacobian matrix of derivatives,
</p>
<dl compact="compact">
<dt><code>int (* f) (const gsl_vector * <var>x</var>, void * <var>params</var>, gsl_vector * <var>f</var>)</code></dt>
<dd><p>this function should store the vector result
<em>f(x,params)</em> 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.
</p>
</dd>
<dt><code>int (* df) (const gsl_vector * <var>x</var>, void * <var>params</var>, gsl_matrix * <var>J</var>)</code></dt>
<dd><p>this function should store the <var>n</var>-by-<var>p</var> matrix result
<em>J_ij = d f_i(x,params) / d x_j</em> 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. If an analytic Jacobian is unavailable, or too expensive
to compute, this function pointer may be set to NULL, in which
case the Jacobian will be internally computed using finite difference approximations
of the function <var>f</var>.
</p>
</dd>
<dt><code>int (* fdf) (const gsl_vector * <var>x</var>, void * <var>params</var>, gsl_vector * <var>f</var>, gsl_matrix * <var>J</var>)</code></dt>
<dd><p>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 <em>f(x)</em> and
<em>J(x)</em>—it is always faster to compute the function and its
derivative at the same time. If an analytic Jacobian is unavailable, or too expensive
to compute, this function pointer may be set to NULL, in which
case the Jacobian will be internally computed using finite difference approximations
of the function <var>f</var>.
</p>
</dd>
<dt><code>size_t n</code></dt>
<dd><p>the number of functions, i.e. the number of components of the
vector <var>f</var>.
</p>
</dd>
<dt><code>size_t p</code></dt>
<dd><p>the number of independent variables, i.e. the number of components of
the vector <var>x</var>.
</p>
</dd>
<dt><code>void * params</code></dt>
<dd><p>a pointer to the arbitrary parameters of the function.
</p></dd>
</dl>
</dd></dl>
<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.
</p>
<hr>
<div class="header">
<p>
Next: <a href="Finite-Difference-Jacobian.html#Finite-Difference-Jacobian" accesskey="n" rel="next">Finite Difference Jacobian</a>, Previous: <a href="Initializing-the-Nonlinear-Least_002dSquares-Solver.html#Initializing-the-Nonlinear-Least_002dSquares-Solver" accesskey="p" rel="previous">Initializing the Nonlinear Least-Squares Solver</a>, Up: <a href="Nonlinear-Least_002dSquares-Fitting.html#Nonlinear-Least_002dSquares-Fitting" accesskey="u" rel="up">Nonlinear Least-Squares Fitting</a> [<a href="Function-Index.html#Function-Index" title="Index" rel="index">Index</a>]</p>
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