<?xml version="1.0" encoding="UTF-8"?>
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 * Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
 * Copyright (C) 2008 - INRIA
 *
 * Copyright (C) 2012 - 2016 - Scilab Enterprises
 *
 * This file is hereby licensed under the terms of the GNU GPL v2.0,
 * pursuant to article 5.3.4 of the CeCILL v.2.1.
 * This file was originally licensed under the terms of the CeCILL v2.1,
 * and continues to be available under such terms.
 * For more information, see the COPYING file which you should have received
 * along with this program.
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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" xmlns:scilab="http://www.scilab.org" xml:lang="en" xml:id="sva">
    <refnamediv>
        <refname>sva</refname>
        <refpurpose>singular value approximation</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[U,s,V]=sva(A,k)
            [U,s,V]=sva(A,tol)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>real or complex matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>k</term>
                <listitem>
                    <para>integer</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>nonnegative real number</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            Singular value approximation.
        </para>
        <para>
            <literal>[U,S,V]=sva(A,k)</literal> with <literal>k</literal> an integer
            &gt;=1, returns <literal>U,S</literal> and <literal>V</literal> such that
            <literal>B=U*S*V'</literal> is the best L2 approximation of
            <literal>A</literal> with rank(<literal>B</literal>)=<literal>k</literal>.
        </para>
        <para>
            <literal>[U,S,V]=sva(A,tol)</literal> with <literal>tol</literal> a real
            number, returns <literal>U,S</literal> and <literal>V</literal> such that
            <literal>B=U*S*V'</literal> such that L2-norm of <literal>A-B</literal>
            is at most <literal>tol</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=rand(5,4)*rand(4,5);
[U,s,V]=sva(A,2);
B=U*s*V';
svd(A)
svd(B)
clean(svd(A-B))
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="svd">svd</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
