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  • 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/projspec.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="projspec">
 
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    <refnamediv>
 
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        <refname>projspec</refname>
 
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        <refpurpose> spectral operators</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[S,P,D,i]=projspec(A)</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>square matrix</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>S, P, D</term>
 
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                <listitem>
 
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                    <para>square matrices</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>i</term>
 
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                <listitem>
 
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                    <para>
 
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                        integer (index of the zero eigenvalue of <literal>A</literal>).
 
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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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            Spectral characteristics of <literal>A</literal> at 0.
 
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        </para>
 
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        <para>
 
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            <literal>S</literal> = reduced resolvent at 0 (<literal>S</literal> = -Drazin_inverse(<literal>A</literal>)).
 
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        </para>
 
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        <para>
 
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            <literal>P</literal> = spectral projection at 0.
 
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        </para>
 
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        <para>
 
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            <literal>D</literal> = nilpotent operator at 0.
 
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        </para>
 
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        <para>
 
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            <literal>index</literal> = index of the 0 eigenvalue.
 
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        </para>
 
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        <para>
 
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            One has <literal>(s*eye()-A)^(-1) = D^(i-1)/s^i +... + D/s^2 + P/s - S - s*S^2 -...</literal>
 
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            around the singularity s=0.
 
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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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deff('j=jdrn(n)','j=zeros(n,n);for k=1:n-1;j(k,k+1)=1;end')
 
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A=sysdiag(jdrn(3),jdrn(2),rand(2,2));X=rand(7,7);
 
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A=X*A*inv(X);
 
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[S,P,D,index]=projspec(A);
 
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index   //size of J-block
 
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trace(P)  //sum of dimensions of J-blocks
 
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A*S-(eye()-P)
 
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norm(D^index,1)
 
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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="coff">coff</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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</refentry>