<?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="en" xml:id="pinv">
    <refnamediv>
        <refname>pinv</refname>
        <refpurpose>pseudoinverse</refpurpose>
    </refnamediv>
    <refsynopsisdiv>
        <title>Syntax</title>
        <synopsis>pinv(A,[tol])</synopsis>
    </refsynopsisdiv>
    <refsection>
        <title>Arguments</title>
        <variablelist>
            <varlistentry>
                <term>A</term>
                <listitem>
                    <para>real or complex matrix</para>
                </listitem>
            </varlistentry>
            <varlistentry>
                <term>tol</term>
                <listitem>
                    <para>real number</para>
                </listitem>
            </varlistentry>
        </variablelist>
    </refsection>
    <refsection>
        <title>Description</title>
        <para>
            <literal>X= pinv(A)</literal> produces a matrix <literal>X</literal> of the
            same dimensions as <literal>A'</literal> such that:
        </para>
        <para>
            <literal>A*X*A = A, X*A*X = X</literal>  and both
            <literal>A*X</literal> and <literal>X*A</literal> are Hermitian .
        </para>
        <para>
            The computation is  based  on SVD and  any  singular values
            lower than a tolerance are treated   as zero: this  tolerance
            is accessed by <literal>X=pinv(A,tol)</literal>.
        </para>
    </refsection>
    <refsection>
        <title>Examples</title>
        <programlisting role="example"><![CDATA[
A=rand(5,2)*rand(2,4);
norm(A*pinv(A)*A-A,1)
 ]]></programlisting>
    </refsection>
    <refsection role="see also">
        <title>See also</title>
        <simplelist type="inline">
            <member>
                <link linkend="rank">rank</link>
            </member>
            <member>
                <link linkend="svd">svd</link>
            </member>
            <member>
                <link linkend="qr">qr</link>
            </member>
        </simplelist>
    </refsection>
    <refsection>
        <title>Used Functions</title>
        <para>
            <literal>pinv</literal> function is  based on the singular value decomposition
            (Scilab function <literal>svd</literal>).
        </para>
    </refsection>
</refentry>
