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<?xml version="1.0" encoding="UTF-8"?>
<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="rafiter">
<refnamediv>
<refname>rafiter</refname>
<refpurpose>
Iterative refinement for a s.p.d. linear system. <emphasis role="bold">This function is obsolete.</emphasis>
</refpurpose>
</refnamediv>
<refsynopsisdiv>
<title>Calling Sequence</title>
<synopsis>[xn, rn] = rafiter(A, C_ptr, b, x0, [, nb_iter, verb])</synopsis>
</refsynopsisdiv>
<refsection>
<title>Arguments</title>
<variablelist>
<varlistentry>
<term>A </term>
<listitem>
<para>a real symmetric positive definite sparse matrix</para>
</listitem>
</varlistentry>
<varlistentry>
<term>C_ptr </term>
<listitem>
<para>a pointer to a Cholesky factorization (got with taucs_chfact)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>b </term>
<listitem>
<para>column vector (r.h.s of the linear system) but "matrix" (multiple r.h.s.) are allowed.</para>
</listitem>
</varlistentry>
<varlistentry>
<term>x0 </term>
<listitem>
<para>first solution obtained with taucs_chsolve(C_ptr, b)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>nb_iter </term>
<listitem>
<para>(optional) number of raffinement iterations (default 2)</para>
</listitem>
</varlistentry>
<varlistentry>
<term>verb </term>
<listitem>
<para>(optional) boolean, must be %t for displaying the intermediary results,
and %f (default) if you do not want.
</para>
</listitem>
</varlistentry>
<varlistentry>
<term>xn </term>
<listitem>
<para>new refined solution</para>
</listitem>
</varlistentry>
<varlistentry>
<term>rn </term>
<listitem>
<para>
residual (<literal>A*xn - b</literal>)
</para>
</listitem>
</varlistentry>
</variablelist>
</refsection>
<refsection>
<title>Description</title>
<para>
This function is somewhat obsolete, use <literal>x = taucs_chsolve(C_ptr,b,A)</literal>
(see <link linkend="taucs_chsolve">taucs_chsolve</link>) which do one iterative refinement step.
</para>
<para>
To use if you want to improve a little the solution got with taucs_chsolve.
Note that with verb=%t the displayed internal steps are essentially meaningful
in the case where b is a column vector.
</para>
</refsection>
<refsection>
<title>Caution</title>
<para>
Currently there is no verification for the input parameters !
</para>
</refsection>
<refsection>
<title>Examples</title>
<programlisting role="example"><![CDATA[
[A] = ReadHBSparse(SCI+"/modules/umfpack/examples/bcsstk24.rsa");
C_ptr = taucs_chfact(A);
b = rand(size(A,1),1);
x0 = taucs_chsolve(C_ptr, b);
norm(A*x0 - b)
[xn, rn] = rafiter(A, C_ptr, b, x0, verb=%t);
norm(A*xn - b)
taucs_chdel(C_ptr)
]]></programlisting>
</refsection>
<refsection role="see also">
<title>See Also</title>
<simplelist type="inline">
<member>
<link linkend="taucs_chsolve">taucs_chsolve</link>
</member>
<member>
<link linkend="taucs_chfact">taucs_chfact</link>
</member>
</simplelist>
</refsection>
</refentry>
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