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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="rat" xml:lang="ja">

    <refnamediv>

        <refname>rat</refname>

        <refpurpose>浮動小数点数の有理数近似</refpurpose>

    </refnamediv>

    <refsynopsisdiv>

        <title>呼び出し手順</title>

        <synopsis>[N,D]=rat(X [,tol])

            Y=rat(X [,tol])

        </synopsis>

    </refsynopsisdiv>

    <refsection>

        <title>引数</title>

        <variablelist>

            <varlistentry>

                <term>X</term>

                <listitem>

                    <para>実数のベクトルまたは行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>tol</term>

                <listitem>

                    <para>正の実数スカラー, 許容誤差 (下記参照). デフォルト値は1d-6.</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>N</term>

                <listitem>

                    <para>整数のベクトルまたは行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>D</term>

                <listitem>

                    <para>整数のベクトルまたは行列</para>

                </listitem>

            </varlistentry>

            <varlistentry>

                <term>Y</term>

                <listitem>

                    <para>実数のベクトルまたは行列</para>

                </listitem>

            </varlistentry>

        </variablelist>

    </refsection>

    <refsection>

        <title>説明</title>

        <para>

            <literal>[N,D] = rat(X,tol)</literal> は,

            <literal>abs(N./D - X) &lt;= tol*norm(X,1)</literal>の基準で

            <literal>N./D</literal>が<literal>X</literal>に近くなるような

            2つの整数行列を返します.

        </para>

        <para>

            <literal>y=rat(x,tol)</literal> は商

            <literal>N./D</literal>を返します.

        </para>

        <para>

            有理数近似は分数展開を丸めることにより生成されます.

        </para>

    </refsection>

    <refsection>

        <title>例</title>

        <programlisting role="example"><![CDATA[
[n,d]=rat([3.5, 1.333333,-0.8])
[n,d]=rat(%pi)
[n,d]=rat(%pi,1.d-12)
n/d-%pi
 ]]></programlisting>

    </refsection>

    <refsection role="see also">

        <title>参照</title>

        <simplelist type="inline">

            <member>

                <link linkend="int">int</link>

            </member>

            <member>

                <link linkend="round">round</link>

            </member>

        </simplelist>

    </refsection>

</refentry>
