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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 xmlns="http://docbook.org/ns/docbook" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:svg="http://www.w3.org/2000/svg" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:lang="en" xml:id="linsolve">
<info>
<pubdate>$LastChangedDate$</pubdate>
</info>
<refnamediv>
<refname>linsolve</refname>
<refpurpose> linear equation solver</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Parameters</title>
<variablelist>
<varlistentry>
<term>A</term>
<listitem>
<para>a <literal>na x ma</literal> real matrix (possibly sparse)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>b</term>
<listitem>
<para>a <literal>na x 1</literal> vector (same row dimension as <literal>A</literal>)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x0</term>
<listitem>
<para>a real vector</para>
</listitem>
</varlistentry>
<varlistentry>
<term>kerA</term>
<listitem>
<para>a <literal>ma x k</literal> real matrix</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para><literal>linsolve</literal> computes all the solutions to <literal> A*x+b=0</literal>.</para>
<para><literal>x0</literal> is a particular solution (if any) and <literal> kerA= </literal>nullspace
of <literal>A</literal>. Any <literal>x=x0+kerA*w</literal> with arbitrary <literal>w</literal> satisfies
<literal> A*x+b=0</literal>.</para>
<para>
If compatible <literal>x0</literal> is given on entry, <literal>x0</literal> is returned. If not
a compatible <literal>x0</literal>, if any, is returned.</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
A=rand(5,3)*rand(3,8);
b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b //compatible b
b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b //uncompatible b
A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b //x is unique
// Benchmark with other linear sparse solver:
[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa");
b = 0*ones(size(A,1),1);
tic();
res = umfpack(A,'\',b);
printf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
tic();
res = linsolve(A,b);
printf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
tic();
res = A\b;
printf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
]]></programlisting>
</refsection>
<refsection>
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="inv">inv</link>
</member>
<member>
<link linkend="pinv">pinv</link>
</member>
<member>
<link linkend="colcomp">colcomp</link>
</member>
<member>
<link linkend="im_inv">im_inv</link>
</member>
<member>
<link linkend="umfpack">umfpack</link>
</member>
<member>
<link linkend="backslash">backslash</link>
</member>
</simplelist>
</refsection>
</refentry>
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