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<?xml version="1.0" encoding="UTF-8"?>
<!--
* Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
* Copyright (C) 2008 - INRIA
*
* This file must be used under the terms of the CeCILL.
* This source file is licensed as described in the file COPYING, which
* you should have received as part of this distribution. The terms
* are also available at
* http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
*
-->
<refentry version="5.0-subset Scilab" xml:id="numdiff" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
xmlns:xlink="http://www.w3.org/1999/xlink"
xmlns:svg="http://www.w3.org/2000/svg"
xmlns:ns5="http://www.w3.org/1999/xhtml"
xmlns:mml="http://www.w3.org/1998/Math/MathML"
xmlns:db="http://docbook.org/ns/docbook">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>numdiff</refname>
<refpurpose>numerical gradient estimation</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>g=numdiff(fun,x [,dx])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>fun</term>
<listitem>
<para>an external, Scilab function or list. See below for calling
sequence, see also <link linkend="external">external</link> for
details about external functions.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x</term>
<listitem>
<para>vector, the argument of the function
<literal>fun</literal></para>
</listitem>
</varlistentry>
<varlistentry>
<term>dx</term>
<listitem>
<para>vector, the finite difference step. Default value is
<literal>dx=sqrt(%eps)*(1+1d-3*abs(x))</literal></para>
</listitem>
</varlistentry>
<varlistentry>
<term>g</term>
<listitem>
<para>vector, the estimated gradient</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>given a function <literal>fun(x)</literal> from
<literal>R^n</literal> to <literal>R^p</literal> computes the matrix
<literal>g</literal> such as</para>
<programlisting role = ""><![CDATA[
g(i,j) = (df_i)/(dx_j)
]]></programlisting>
<para>using finite difference methods.</para>
<para>
Without parameters, the function fun calling sequence is
<literal>y=fun(x)</literal>, and numdiff can be called as
<literal>g=numdiff(fun,x)</literal>. Else the function fun calling
sequence must be <literal>y=fun(x,param_1,pararm_2,..,param_q)</literal>.
If parameters <literal>param_1,param_2,..param_q</literal> exist then
<literal>numdiff</literal> can be called as follow
<literal>g=numdiff(list(fun,param_1,param_2,..param_q),x)</literal>.
</para>
<para>
See the
<link linkend="derivative">derivative</link> with respect to numerical accuracy
issues and comparison between the two algorithms.
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
// example 1 (without parameters)
// myfun is a function from R^2 to R : (x(1),x(2)) |--> myfun(x)
function f=myfun(x)
f=x(1)*x(1)+x(1)*x(2)
endfunction
x=[5 8]
g=numdiff(myfun,x)
// The exact gradient (i.e derivate belong x(1) :first component and derivate belong x(2): second component) is
exact=[2*x(1)+x(2) x(1)]
//example 2 (with parameters)
// myfun is a function from R to R: x(1) |--> myfun(x)
// myfun contains 3 parameters, a, b, c
function f=myfun(x,a,b,c)
f=(x+a)^c+b
endfunction
a=3; b=4; c=2;
x=1
g2=numdiff(list(myfun,a,b,c),x)
// The exact gradient, i.e derivate belong x(1), is :
exact2=c*(x+a)^(c-1)
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member><link linkend="optim">optim</link></member>
<member><link linkend="derivative">derivative</link></member>
<member><link linkend="external">external</link></member>
</simplelist>
</refsection>
</refentry>
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