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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/elementary_functions/help/en_US/norm.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:ns5="http://www.w3.org/1999/xhtml" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:db="http://docbook.org/ns/docbook" version="5.0-subset Scilab" xml:id="norm" xml:lang="en">
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  <refnamediv>
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    <refname>norm</refname>
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    <refpurpose>matrix norm</refpurpose>
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  </refnamediv>
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  <refsynopsisdiv>
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    <title>Calling Sequence</title>
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    <synopsis>[y]=norm(x [,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>x</term>
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        <listitem>
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          <para>real or complex vector or matrix (full or sparse
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            storage)
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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>flag</term>
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        <listitem>
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          <para>string (type of norm) (default value =2)</para>
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        </listitem>
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      </varlistentry>
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      <varlistentry>
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        <term>y</term>
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        <listitem>
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          <para>
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            norm
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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>For matrices</para>
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    <variablelist>
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      <varlistentry>
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        <term>norm(x)</term>
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        <listitem>
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          <para>
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            or <literal>norm(x,2)</literal> is the largest singular value
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            of <literal>x</literal> (<literal>max(svd(x))</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>norm(x,1)</term>
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        <listitem>
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          <para>
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            The l_1 norm <literal>x</literal> (the largest column sum :
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            <literal>max(sum(abs(x),'r'))</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>norm(x,'inf'),norm(x,%inf)</term>
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        <listitem>
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          <para>
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            The infinity norm of <literal>x</literal> (the largest row sum
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            : <literal>max(sum(abs(x),'c'))</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>norm(x,'fro')</term>
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        <listitem>
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          <para>Frobenius norm i.e.
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            <literal>sqrt(sum(diag(x'*x)))</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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    <para>For vectors</para>
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    <variablelist>
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      <varlistentry>
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        <term>norm(v,p)</term>
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        <listitem>
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          <para>
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            The l_p norm (<literal>sum(v(i)^p))^(1/p)</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>norm(v), norm(v,2)</term>
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        <listitem>
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          <para>
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            The l_2 norm
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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>norm(v,'inf')</term>
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        <listitem>
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          <para>
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            <literal>max(abs(v(i)))</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>Examples</title>
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    <programlisting role="example"><![CDATA[ 
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A=[1,2,3];
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norm(A,1)
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norm(A,'inf')
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A=[1,2;3,4]
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max(svd(A))-norm(A)
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A=sparse([1 0 0 33 -1])
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norm(A)
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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="h_norm">h_norm</link>
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      </member>
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      <member>
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        <link linkend="dhnorm">dhnorm</link>
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      </member>
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      <member>
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        <link linkend="h2norm">h2norm</link>
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      </member>
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      <member>
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        <link linkend="abs">abs</link>
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      </member>
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      <member>
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        <link linkend="svd">svd</link>
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      </member>
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    </simplelist>
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  </refsection>
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</refentry>