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

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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="ja" xml:id="pinv">

    <refnamediv>

        <refname>pinv</refname>

        <refpurpose>擬似逆行列</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>pinv(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>tol</term>

                <listitem>

                    <para>実数</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>X= pinv(A)</literal> は,

            <literal>A'</literal>と同じ次元の以下のような

            行列<literal>X</literal>を出力します:

        </para>

        <para>

            <literal>A*X*A = A, X*A*X = X</literal>  そして

            <literal>A*X</literal> および <literal>X*A</literal>

            は共にエルミート行列です.

        </para>

        <para>

            計算は特異値分解に基づいており,

            許容値よりも小さい特異値は 0 として扱われます:

            この許容誤差は <literal>X=pinv(A,tol)</literal>

            でアクセスされます.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
A=rand(5,2)*rand(2,4);
norm(A*pinv(A)*A-A,1)
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="rank">rank</link>

            </member>

            <member>

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

            </member>

            <member>

                <link linkend="qr">qr</link>

            </member>

        </simplelist>

    </refsection>

    <refsection>

        <title>使用される関数</title>

        <para>

            <literal>pinv</literal> 関数は特異値分解に基づいています

            (Scilab関数 <literal>svd</literal>).

        </para>

    </refsection>

</refentry>

