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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/psmall.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="psmall">
 
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    <refnamediv>
 
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        <refname>psmall</refname>
 
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        <refpurpose> spectral projection</refpurpose>
 
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    </refnamediv>
 
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    <refsynopsisdiv>
 
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        <title>Calling Sequence</title>
 
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        <synopsis>[Q,M]=psmall(A,thres,flag)</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 square matrix</para>
 
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                </listitem>
 
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            </varlistentry>
 
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            <varlistentry>
 
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                <term>thres</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>flag</term>
 
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                <listitem>
 
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                    <para>
 
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                        character string (<literal>'c'</literal> or <literal>'d'</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>Q,M</term>
 
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                <listitem>
 
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                    <para>real matrices</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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            Projection on eigen-subspace associated with eigenvalues with real
 
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            part &lt; <literal>thres</literal> (<literal>flag='c'</literal>) or
 
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            with modulus &lt; <literal>thres</literal>
 
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            (<literal>flag='d'</literal>).
 
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        </para>
 
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        <para>
 
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            The projection is defined by <literal>Q*M</literal>, <literal>Q</literal> is
 
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            full column rank, <literal>M</literal> is full row rank and
 
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            <literal>M*Q=eye</literal>.
 
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        </para>
 
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        <para>
 
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            If <literal>flag='c'</literal>, the eigenvalues of
 
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            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with real part
 
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            &lt; <literal>thres</literal>.
 
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        </para>
 
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        <para>
 
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            If <literal>flag='d'</literal>, the eigenvalues of
 
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            <literal>M*A*Q</literal> = eigenvalues of <literal>A</literal> with magnitude
 
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            &lt; <literal>thres</literal>.
 
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        </para>
 
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        <para>
 
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            If <literal>flag='c'</literal> and if <literal>[Q1,M1]</literal> =
 
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            full rank factorization (<literal>fullrf</literal>) of
 
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            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
 
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            eigenvalues of <literal>A</literal> with real part &gt;=
 
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            <literal>thres</literal>.
 
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        </para>
 
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        <para>
 
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            If <literal>flag='d'</literal> and if <literal>[Q1,M1]</literal> =
 
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            full rank factorization (<literal>fullrf</literal>) of
 
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            <literal>eye()-Q*M</literal> then eigenvalues of <literal>M1*A*Q1</literal> =
 
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            eigenvalues of <literal>A</literal> with magnitude &gt;=
 
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            <literal>thres</literal>.
 
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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=diag([1,2,3]);X=rand(A);A=inv(X)*A*X;
 
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[Q,M]=psmall(A,2.5,'d');
 
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spec(M*A*Q)
 
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[Q1,M1]=fullrf(eye()-Q*M);
 
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spec(M1*A*Q1)
 
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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="pbig">pbig</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="proj">proj</link>
 
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            </member>
 
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            <member>
 
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                <link linkend="projspec">projspec</link>
 
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            </member>
 
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        </simplelist>
 
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    </refsection>
 
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    <refsection>
 
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        <title>Used Functions</title>
 
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        <para>
 
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            This function is  based on the ordered schur form (scilab
 
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            function <literal>schur</literal>).
 
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        </para>
 
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    </refsection>
 
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</refentry>