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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"
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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>
x = lsqnonneg(C,d)
x = 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 doubles, represents the multiplier of the solution x in the expression C*x - d. C is M-by-N, where M is the number of equations, and N is the number of elements of x.</para></listitem></varlistentry>
<varlistentry><term>d :</term>
<listitem><para> a vector of doubles, represents the additive constant term in the expression C*x - d. d is M-by-1, where M is the number of equations.</para></listitem></varlistentry>
<varlistentry><term>xopt :</term>
<listitem><para> a vector of doubles, 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 doubles, solution residuals returned as the vector C*x-d.</para></listitem></varlistentry>
<varlistentry><term>exitflag :</term>
<listitem><para> Integer identifying the reason the algorithm terminated.</para></listitem></varlistentry>
<varlistentry><term>output :</term>
<listitem><para> Structure containing information about the optimization.</para></listitem></varlistentry>
<varlistentry><term>lambda :</term>
<listitem><para> Structure containing the Lagrange multipliers at the solution x (separated by constraint type).</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>
We are calling IPOpt for solving the nonnegative least-squares curve fitting problems, IPOpt is a library written in C++. The code has been written by Andreas Wächter and Carl Laird.
</para>
<para>
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
A basic lsqnonneg problem
C = [
0.0372 0.2869
0.6861 0.7071
0.6233 0.6245
0.6344 0.6170];
d = [
0.8587
0.1781
0.0747
0.8405];
[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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