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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="fit_dat" 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:ns4="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>fit_dat</refname>
<refpurpose>Parameter identification based on measured data</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[p,err]=fit_dat(G,p0,Z [,W] [,pmin,pmax] [,DG])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>G</term>
<listitem>
<para>Scilab function (e=G(p,z), e: nex1, p: npx1, z: nzx1)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>p0</term>
<listitem>
<para>initial guess (size npx1)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>Z</term>
<listitem>
<para>matrix [z_1,z_2,...z_n] where z_i (nzx1) is the ith
measurement</para>
</listitem>
</varlistentry>
<varlistentry>
<term>W</term>
<listitem>
<para>weighting matrix of size nexne (optional; default 1)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>pmin</term>
<listitem>
<para>lower bound on p (optional; size npx1)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>pmax</term>
<listitem>
<para>upper bound on p (optional; size npx1)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>DG</term>
<listitem>
<para>partial of G wrt p (optional; S=DG(p,z), S: nexnp)</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para><literal>fit_dat</literal> is used for fitting data to a model. For
a given function G(p,z), this function finds the best vector of parameters
p for approximating G(p,z_i)=0 for a set of measurement vectors z_i.
Vector p is found by minimizing
<literal>G(p,z_1)'WG(p,z_1)+G(p,z_2)'WG(p,z_2)+...+G(p,z_n)'WG(p,z_n)</literal></para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
deff('y=FF(x)','y=a*(x-b)+c*x.*x')
X=[];Y=[];
a=34;b=12;c=14;for x=0:.1:3, Y=[Y,FF(x)+100*(rand()-.5)];X=[X,x];end
Z=[Y;X];
deff('e=G(p,z)','a=p(1),b=p(2),c=p(3),y=z(1),x=z(2),e=y-FF(x)')
[p,err]=fit_dat(G,[3;5;10],Z)
xset('window',0)
clf();
plot2d(X',Y',-1)
plot2d(X',FF(X)',5,'002')
a=p(1),b=p(2),c=p(3);plot2d(X',FF(X)',12,'002')
a=34;b=12;c=14;
deff('s=DG(p,z)','y=z(1),x=z(2),s=-[x-p(2),-p(1),x*x]')
[p,err]=fit_dat(G,[3;5;10],Z,DG)
xset('window',1)
clf();
plot2d(X',Y',-1)
plot2d(X',FF(X)',5,'002')
a=p(1),b=p(2),c=p(3);plot2d(X',FF(X)',12,'002')
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member><link linkend="optim">optim</link></member>
<member><link linkend="datafit">datafit</link></member>
</simplelist>
</refsection>
</refentry>
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