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Viewing changes to modules/linear_algebra/help/en_US/linsolve.xml

  • Committer: Package Import Robot
  • Author(s): Sylvestre Ledru
  • Date: 2012-08-30 14:42:38 UTC
  • mfrom: (1.4.7)
  • Revision ID: package-import@ubuntu.com-20120830144238-c1y2og7dbm7m9nig
Tags: 5.4.0-beta-3-1~exp1
* New upstream release
* Update the scirenderer dep
* Get ride of libjhdf5-java dependency

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modules/linear_algebra/help/en_US/linsolve.xml
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<?xml version="1.0" encoding="UTF-8"?>
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<!--
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 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
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 * Copyright (C) 2008 - INRIA
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 * 
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 * This file must be used under the terms of the CeCILL.
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 * This source file is licensed as described in the file COPYING, which
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 * you should have received as part of this distribution.  The terms
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 * are also available at    
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 * http://www.cecill.info/licences/Licence_CeCILL_V2-en.txt
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 *
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 -->
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<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">
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  <refnamediv>
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    <refname>linsolve</refname>
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    <refpurpose> linear equation solver</refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[x0,kerA]=linsolve(A,b [,x0])</synopsis>
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  </refsynopsisdiv>
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  <refsection>
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    <title>Arguments</title>
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    <variablelist>
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      <varlistentry>
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        <term>A</term>
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        <listitem>
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          <para>
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            a <literal>na x ma</literal> real matrix (possibly sparse)
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>b</term>
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        <listitem>
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          <para>
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            a <literal>na x 1</literal> vector (same row dimension as <literal>A</literal>)
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          </para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>x0</term>
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        <listitem>
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          <para>a real vector</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>kerA</term>
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        <listitem>
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          <para>
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            a <literal>ma x k</literal> real matrix
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          </para>
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        </listitem>
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      </varlistentry>
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    </variablelist>
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  </refsection>
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  <refsection>
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    <title>Description</title>
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    <para>
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      <literal>linsolve</literal>  computes all the solutions to <literal> A*x+b=0</literal>.
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    </para>
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    <para>
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      <literal>x0</literal> is a particular solution (if any) and <literal> kerA= </literal>nullspace
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      of <literal>A</literal>. Any <literal>x=x0+kerA*w</literal> with arbitrary <literal>w</literal> satisfies
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      <literal> A*x+b=0</literal>.
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    </para>
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    <para>
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      If compatible <literal>x0</literal> is given on entry, <literal>x0</literal> is returned. If not
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      a compatible <literal>x0</literal>, if any, is returned.
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    </para>
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  </refsection>
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  <refsection>
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    <title>Examples</title>
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    <programlisting role="example"><![CDATA[ 
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A=rand(5,3)*rand(3,8);
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b=A*ones(8,1);[x,kerA]=linsolve(A,b);A*x+b   //compatible b
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b=ones(5,1);[x,kerA]=linsolve(A,b);A*x+b   //uncompatible b
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A=rand(5,5);[x,kerA]=linsolve(A,b), -inv(A)*b  //x is unique
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// Benchmark with other linear sparse solver:
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[A,descr,ref,mtype] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa"); 
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b = zeros(size(A,1),1);
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tic();
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res = umfpack(A,'\',b);
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mprintf('\ntime needed to solve the system with umfpack: %.3f\n',toc());
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tic();
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res = linsolve(A,b);
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mprintf('\ntime needed to solve the system with linsolve: %.3f\n',toc());
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tic();
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res = A\b;
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mprintf('\ntime needed to solve the system with the backslash operator: %.3f\n',toc());
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 ]]></programlisting>
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  </refsection>
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  <refsection role="see also">
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    <title>See Also</title>
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    <simplelist type="inline">
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      <member>
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        <link linkend="inv">inv</link>
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      </member>
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      <member>
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        <link linkend="pinv">pinv</link>
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      </member>
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      <member>
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        <link linkend="colcomp">colcomp</link>
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      </member>
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      <member>
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        <link linkend="im_inv">im_inv</link>
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      </member>
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      <member>
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        <link linkend="umfpack">umfpack</link>
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      </member>
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      <member>
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        <link linkend="backslash">backslash</link>
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      </member>
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    </simplelist>
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  </refsection>
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</refentry>