<?xml version="1.0" encoding="UTF-8"?>

<!--
 * 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.
 *
 -->

<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="ja" xml:id="sva">

    <refnamediv>

        <refname>sva</refname>

        <refpurpose>特異値近似</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[U,s,V]=sva(A,k)

            [U,s,V]=sva(A,tol)

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>A</term>

                <listitem>

                    <para>実数または複素数の行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>k</term>

                <listitem>

                    <para>整数</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>非負の実数</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            特異値近似.

        </para>

        <para>

            <literal>k</literal>を&gt;=1の整数とするとき,

            <literal>[U,S,V]=sva(A,k)</literal> は,

            rank(<literal>B</literal>)=<literal>k</literal>として

            <literal>B=U*S*V'</literal>が<literal>A</literal>の最良のL2近似となる

            ような

            <literal>U,S</literal> および<literal>V</literal>を返します.

        </para>

        <para>

            実数<literal>tol</literal>を指定した<literal>[U,S,V]=sva(A,tol)</literal>は,

            <literal>A-B</literal>のL2ノルムである<literal>B=U*S*V'</literal>の

            最大値が<literal>tol</literal>となるような

            <literal>U,S</literal> および <literal>V</literal> を返します.

        </para>

    </refsection>

    <refsection>

        <title>例</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>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="svd">svd</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

