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<a name="jacobs"></a>
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<p>
Previous: <a href="cdiff.html#cdiff" accesskey="p" rel="prev">cdiff</a>, Up: <a href="Gradient-functions.html#Gradient-functions" accesskey="u" rel="up">Gradient functions</a> [<a href="Function-index.html#Function-index" title="Index" rel="index">Index</a>]</p>
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<a name="Complex-step-derivatives"></a>
<h3 class="section">4.6 Complex step derivatives</h3>
<a name="index-jacobs-2"></a>
<a name="XREFjacobs"></a><dl>
<dt><a name="index-jacobs"></a>Function File: <em>Df =</em> <strong>jacobs</strong> <em>(<var>x</var>, <var>f</var>)</em></dt>
<dt><a name="index-jacobs-1"></a>Function File: <em>Df =</em> <strong>jacobs</strong> <em>(<var>x</var>, <var>f</var>, <var>hook</var>)</em></dt>
<dd><p>Calculate the jacobian of a function using the complex step method.
</p>
<p>Let <var>f</var> be a user-supplied function. Given a point <var>x</var> at
which we seek for the Jacobian, the function <code>jacobs</code> returns
the Jacobian matrix <code>d(f(1), …, df(end))/d(x(1), …,
x(n))</code>. The function uses the complex step method and thus can be
applied to real analytic functions.
</p>
<p>The optional argument <var>hook</var> is a structure with additional options. <var>hook</var>
can have the following fields:
</p><ul>
<li> <code>h</code> - can be used to define the magnitude of the complex step and defaults
to 1e-20; steps larger than 1e-3 are not allowed.
</li><li> <code>fixed</code> - is a logical vector internally usable by some optimization
functions; it indicates for which elements of <var>x</var> no gradient should be
computed, but zero should be returned.
</li></ul>
<p>For example:
</p>
<div class="example">
<pre class="example">f = @(x) [x(1)^2 + x(2); x(2)*exp(x(1))];
Df = jacobs ([1, 2], f)
</pre></div>
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