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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="en" xml:id="givens">
    <refnamediv>
        <refname>givens</refname>
        <refpurpose>Givens transformation</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>U=givens(xy)
            U=givens(x,y)
            [U,c]=givens(xy)
            [U,c]=givens(x,y)
        </synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>x,y</term>
                <listitem>
                    <para>two real or complex numbers</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>xy</term>
                <listitem>
                    <para> real or complex size 2 column vector</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>U</term>
                <listitem>
                    <para>2x2 unitary matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>c</term>
                <listitem>
                    <para> real or complex size 2 column vector</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>U= givens(x, y)</literal> or <literal>U = givens(xy)</literal> with <literal>xy = [x;y]</literal>
            returns a <literal>2</literal>x<literal>2</literal> unitary matrix <literal>U</literal> such that:
        </para>
        <para>
            <literal>U*xy=[r;0]=c</literal>.
        </para>
        <para>
            <note>
                Note that <literal>givens(x,y)</literal> and <literal>givens([x;y])</literal> are equivalent.
            </note>
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=[3,4;5,6];
U=givens(A(:,1));
U*A
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="qr">qr</link>
            </member>
        </simplelist>
    </refsection>
</refentry>
