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<?xml version="1.0" encoding="UTF-8"?>
<!--
*
* This help file was generated from lsqnonneg.sci using help_from_sci().
*
-->
<refentry version="5.0-subset Scilab" xml:id="lsqnonneg" xml:lang="en"
xmlns="http://docbook.org/ns/docbook"
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xmlns:scilab="http://www.scilab.org"
xmlns:db="http://docbook.org/ns/docbook">
<refnamediv>
<refname>lsqnonneg</refname>
<refpurpose>Solves nonnegative least-squares curve fitting problems.</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>
xopt = lsqnonneg(C,d)
xopt = lsqnonneg(C,d,param)
[xopt,resnorm,residual,exitflag,output,lambda] = lsqnonneg( ... )
</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry><term>C :</term>
<listitem><para> a matrix of double, represents the multiplier of the solution x in the expression C*x - d. Number of columns in C is equal to the number of elements in x.</para></listitem></varlistentry>
<varlistentry><term>d :</term>
<listitem><para> a vector of double, represents the additive constant term in the expression C*x - d. Number of elements in d is equal to the number of rows in C matrix.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of double, the computed solution of the optimization problem.</para></listitem></varlistentry>
<varlistentry><term>resnorm :</term>
<listitem><para> a double, objective value returned as the scalar value norm(C*x-d)^2.</para></listitem></varlistentry>
<varlistentry><term>residual :</term>
<listitem><para> a vector of double, solution residuals returned as the vector d-C*x.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> A flag showing returned exit flag from Ipopt. It could be 0, 1 or 2 etc. i.e. Optimal, Maximum Number of Iterations Exceeded, CPU time exceeded. Other flags one can see in the lsqlin macro.</para></listitem></varlistentry>
<varlistentry><term>output :</term>
<listitem><para> Structure containing information about the optimization. This version only contains number of iterations.</para></listitem></varlistentry>
<varlistentry><term>lambda :</term>
<listitem><para> Structure containing the Lagrange multipliers at the solution xopt. It contains lower, upper bound multiplier and linear equality, inequality constraint multiplier.</para></listitem></varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
Solves nonnegative least-squares curve fitting problems specified by :
</para>
<para>
<latex>
\begin{eqnarray}
&\mbox{min}_{x}
& 1/2||C⋅x - d||_2^2 \\
& & x \geq 0 \\
\end{eqnarray}
</latex>
</para>
<para>
The routine calls Ipopt for solving the nonnegative least-squares curve fitting problems, Ipopt is a library written in C++.
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
// A basic lsqnonneg problem
C = [1 1 1;
1 1 0;
0 1 1;
1 0 0;
0 0 1]
d = [89;
67;
53;
35;
20;]
[xopt,resnorm,residual,exitflag,output,lambda] = lsqnonneg(C,d)
]]></programlisting>
</refsection>
<refsection>
<title>Authors</title>
<simplelist type="vert">
<member>Harpreet Singh</member>
</simplelist>
</refsection>
</refentry>
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