<?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="expm">

    <refnamediv>

        <refname>expm</refname>

        <refpurpose>正方行列の指数関数</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>expm(X)</synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>X</term>

                <listitem>

                    <para>実数または複素数のエントリを有する正方行列.</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <varname>X</varname> が正方行列の時,

            <literal>expm(X)</literal> は以下の行列となります

        </para>

        <para>

            <literal>expm(X) = I + X + X^2 /2 + ...</literal>

        </para>

        <para>

            計算はまず<varname>X</varname>をブロック対角化した後,

            各ブロックにパデ近似を適用します.

        </para>

        <para>

            パデ近似は関数の有理関数による次数を指定した"最良の"近似です.

            この手法は,フランス人数学者Henri Padeにより開発されました.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
X=[1 2;3 4]
expm(X)
logm(expm(X))
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="logm">logm</link>

            </member>

            <member>

                <link linkend="bdiag">bdiag</link>

            </member>

            <member>

                <link linkend="coff">coff</link>

            </member>

            <member>

                <link linkend="log">log</link>

            </member>

            <member>

                <link linkend="exp">exp</link>

            </member>

        </simplelist>

    </refsection>

</refentry>

