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 * 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,
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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="en">
    <refnamediv>
        <refname>rat</refname>
        <refpurpose>Floating point rational approximation</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>[N, D] = rat(X [,tol])
            Y = rat(X [,tol])
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>X</term>
                <listitem>
                    <para>real vector or matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>real positive scalar, the tolerance (see below). Default value is 1d-6.</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>N</term>
                <listitem>
                    <para>integer vector or matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>D</term>
                <listitem>
                    <para>integer vector or matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>Y</term>
                <listitem>
                    <para>real vector or matrix</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>[N, D] = rat(X, tol)</literal> returns two integer matrices
            so that <literal>N./D</literal> is close to <literal>X</literal> in the
            sense that <literal>abs(N./D - X) &lt;= tol * norm(X, 1)</literal>.
        </para>
        <para>
            <literal>y = rat(x, tol)</literal> returns the quotient
            <literal>N./D</literal>
        </para>
        <para>
            The rational approximations are generated by truncating
            continued fraction expansions.
        </para>
    </refsection>
    <refsection>
        <title>Examples</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>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="int">int</link>
            </member>
            <member>
                <link linkend="round">round</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
