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Viewing changes to modules/linear_algebra/help/en_US/eigen/bdiag.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/eigen/bdiag.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="bdiag">
 
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    <refnamediv>
 
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        <refname>bdiag</refname>
 
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        <refpurpose> block diagonalization, generalized eigenvectors</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[Ab [,X [,bs]]]=bdiag(A [,rmax])</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>real or complex square matrix</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>rmax</term>
 
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                <listitem>
 
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                    <para>real number</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>Ab</term>
 
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                <listitem>
 
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                    <para>real or complex square matrix</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>X</term>
 
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                <listitem>
 
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                    <para>real or complex non-singular matrix</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>bs</term>
 
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                <listitem>
 
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                    <para>vector of integers</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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        <programlisting role=""><![CDATA[ 
 
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[Ab [,X [,bs]]]=bdiag(A [,rmax]) 
 
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 ]]></programlisting>
 
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        <para>
 
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            performs the block-diagonalization of matrix <literal>A</literal>.  bs
 
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            gives the structure of the blocks (respective sizes of the
 
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            blocks).  <literal>X</literal> is the change of basis i.e 
 
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            <literal>Ab = inv(X)*A*X</literal>is block diagonal.
 
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        </para>
 
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        <para>
 
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            <literal>rmax</literal> controls the conditioning of <literal>X</literal>; the
 
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            default value is the l1 norm of <literal>A</literal>.
 
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        </para>
 
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        <para>
 
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            To get a diagonal form (if it exists) choose a large value for
 
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            <literal>rmax</literal> (<literal>rmax=1/%eps</literal> for example).
 
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            Generically (for real random A) the blocks are (1x1) and (2x2) and
 
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            <literal>X</literal> is the matrix of eigenvectors.
 
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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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//Real case: 1x1 and 2x2 blocks
 
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a=rand(5,5);[ab,x,bs]=bdiag(a);ab
 
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//Complex case: complex 1x1 blocks
 
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[ab,x,bs]=bdiag(a+%i*0);ab
 
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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="schur">schur</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="sylv">sylv</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="spec">spec</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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</refentry>