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<a name="residmin_005fstat"></a>
<div class="header">
<p>
Next: <a href="curvefit_005fstat.html#curvefit_005fstat" accesskey="n" rel="next">curvefit_stat</a>, Previous: <a href="lm_005fsvd_005ffeasible.html#lm_005fsvd_005ffeasible" accesskey="p" rel="prev">lm_svd_feasible</a>, Up: <a href="Residual-optimization.html#Residual-optimization" accesskey="u" rel="up">Residual optimization</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
</div>
<hr>
<a name="Statistics-for-residual-minimization"></a>
<h3 class="section">2.4 Statistics for residual minimization</h3>
<a name="index-residmin_005fstat-1"></a>
<a name="XREFresidmin_005fstat"></a><dl>
<dt><a name="index-residmin_005fstat"></a>Function File: <em><var>info</var> =</em> <strong>residmin_stat</strong> <em>(<var>f</var>, <var>p</var>, <var>settings</var>)</em></dt>
<dd><p>Frontend for computation of statistics for a residual-based
minimization.
</p>
<p><var>settings</var> is a structure whose fields can be set by
<code>optimset</code>. With <var>settings</var> the computation of certain
statistics is requested by setting the fields
<code>ret_<name_of_statistic></code> to <code>true</code>. The respective
statistics will be returned in a structure as fields with name
<code><name_of_statistic></code>. Depending on the requested statistic and
on the additional information provided in <var>settings</var>, <var>f</var> and
<var>p</var> may be empty. Otherwise, <var>f</var> is the model function of an
optimization (the interface of <var>f</var> is described e.g. in
<code>nonlin_residmin</code>, please see there), and <var>p</var> is a real
column vector with parameters resulting from the same optimization.
</p>
<p>Currently, the following statistics (or general information) can be
requested (the <code>ret_</code> is prepended so that the option name is
complete):
</p>
<p><code>ret_dfdp</code>: Jacobian of model function with respect to
parameters.
</p>
<p><code>ret_covd</code>: Covariance matrix of data (typically guessed by
applying a factor to the covariance matrix of the residuals).
</p>
<p><code>ret_covp</code>: Covariance matrix of final parameters.
</p>
<p><code>ret_corp</code>: Correlation matrix of final parameters.
</p>
<p><strong>See also:</strong> <a href="curvefit_005fstat.html#XREFcurvefit_005fstat">curvefit_stat</a>.
</p></dd></dl>
<a name="Further-settings"></a>
<h4 class="subheading">Further settings</h4>
<p>The fields of the <var>settings</var> structure can be set with
<a href="https://www.gnu.org/software/octave/doc/interpreter/XREFoptimset.html#XREFoptimset">(octave)optimset</a>.
</p>
<p>For settings common to all frontends
see
<a href="Common-frontend-options.html#Common-frontend-options">Common frontend options</a>.
</p>
<a name="Additional-settings_003a-2"></a>
<h4 class="subsubheading">Additional settings:</h4>
<dl compact="compact">
<dt><code>objf_type</code></dt>
<dd><p>Type of objective function of the optimization; must be specified in
many cases. This determines which backends to use. Currently, there are
only backends for the type "wls" (weighted least squares).
</p></dd>
<dt><code>residuals</code></dt>
<dt><code>covd</code></dt>
<dd><p>Optional information on the result of optimization, residuals and
covariance matrix of data, respectively.
</p></dd>
<dt><code>weights</code></dt>
<dd><p>Array of weights applied to the residuals in the previous
optimization. Dimensions must match those of the residuals.
</p></dd>
<dt><code>dfdp</code></dt>
<dd><p>Can be set in the same way and has the same default as in
<code>nonlin_residmin</code> (
see
<a href="nonlin_005fresidmin.html#nonlin_005fresidmin">nonlin_residmin</a>), but alternatively may
already contain the computed Jacobian of the model function at the final
parameters in matrix- or structure-form.
</p></dd>
<dt><code>complex_step_derivative_f</code></dt>
<dd><p>Estimate Jacobian of model function with complex step derivative
approximation. Use only if you know that your model function is suitable
for this. No user function for the Jacobian (<code>dfdp</code>) must be
specified.
</p></dd>
</dl>
<a name="Structure-based-parameter-handling-2"></a>
<h4 class="subheading">Structure based parameter handling</h4>
<p>Please
see
<a href="Parameter-structures.html#Parameter-structures">Parameter structures</a>.
</p>
<a name="Backend-information-2"></a>
<h4 class="subheading">Backend information</h4>
<p>Please
see
<a href="Residual-optimization.html#Residual-optimization">Residual optimization</a> and choose backend from menu under
‘Statistics backends’.
</p>
<hr>
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<p>
Next: <a href="curvefit_005fstat.html#curvefit_005fstat" accesskey="n" rel="next">curvefit_stat</a>, Previous: <a href="lm_005fsvd_005ffeasible.html#lm_005fsvd_005ffeasible" accesskey="p" rel="prev">lm_svd_feasible</a>, Up: <a href="Residual-optimization.html#Residual-optimization" accesskey="u" rel="up">Residual optimization</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
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