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<a name="jacobs"></a>
<p>
Previous: <a rel="previous" accesskey="p" href="cdiff.html#cdiff">cdiff</a>,
Up: <a rel="up" accesskey="u" href="Gradient-functions.html#Gradient-functions">Gradient functions</a>
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<h3 class="section">4.6 Complex step derivatives</h3>
<p><a name="index-jacobs-84"></a>
<!-- jacobs ../inst/jacobs.m -->
<a name="XREFjacobs"></a>
<div class="defun">
— Function File: Df = <b>jacobs</b> (<var>x, f</var>)<var><a name="index-jacobs-85"></a></var><br>
— Function File: Df = <b>jacobs</b> (<var>x, f, hook</var>)<var><a name="index-jacobs-86"></a></var><br>
<blockquote><p>Calculate the jacobian of a function using the complex step method.
<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 <samp><span class="command">jacobs</span></samp> 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>The optional argument <var>hook</var> is a structure with additional options. <var>hook</var>
can have the following fields:
<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><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.
</ul>
<p>For example:
<pre class="example"> f = @(x) [x(1)^2 + x(2); x(2)*exp(x(1))];
Df = jacobs ([1, 2], f)
</pre>
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