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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" xmlns:scilab="http://www.scilab.org" xml:id="diff" xml:lang="ja">
    <refnamediv>
        <refname>diff</refname>
        <refpurpose>差分および離散微分</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>呼び出し手順</title>
        <synopsis>
            y = diff(x)
            y = diff(x, n)
            y = diff(x, n, dim)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>引数</title>
        <variablelist>
            <varlistentry>
                <term>x</term>
                <listitem>
                    <para>ベクトルまたは行列 (実数, 複素数, 疎行列 または多項式)</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>n</term>
                <listitem>
                    <para>整数,差分の次数</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>dim</term>
                <listitem>
                    <para>整数または"r","c" および "*"を値とする文字列</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>y</term>
                <listitem>
                    <para>スカラーまたはベクトル</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>説明</title>
        <para>
            <literal>y=diff(x)</literal> は差分関数
            y=x(2:$)-x(1:$-1)を計算します.
        </para>
        <para>
            <literal>diff(x,n,dim)</literal> は,
            次元<literal>dim</literal>方向の<literal>n</literal> 次
            差分関数です.
        </para>
        <para>
            <literal>diff(x,n,"*")</literal> は
            diff(x(:),n)と等価です.
        </para>
        <para>
            <literal>n</literal>のデフォルト値は 1です.
            <literal>dim</literal> のデフォルト値は <literal>"*"</literal>です.
        </para>
        <para>
            <literal>dim='r'</literal> は <literal>dim=1</literal>と
            等価で,
            <literal>dim='c'</literal> は
            <literal>dim=2</literal>と等価です.
        </para>
    </refsection>
    <refsection>
        <title>例</title>
        <programlisting role="example"><![CDATA[
v = (1:8)^3;
diff(v)
diff(v,3)
A = [(1:8)^2
     (1:8)^3
     (1:8)^4];
diff(A,3,2)

//approximate differentiation
step = 0.001
t = 0:step:10;
y = sin(t);
dy = diff(sin(t))/step; //approximate differentiation of sine function
norm(dy-cos(t(1:$-1)),%inf)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>参照</title>
        <simplelist type="inline">
            <member>
                <link linkend="interp">interp</link>
            </member>
            <member>
                <link linkend="interp2d">interp2d</link>
            </member>
            <member>
                <link linkend="splin">splin</link>
            </member>
            <member>
                <link linkend="eval_cshep2d">eval_cshep2d</link>
            </member>
            <member>
                <link linkend="numderivative">numderivative</link>
            </member>
        </simplelist>
    </refsection>
</refentry>