<?xml version="1.0" encoding="ISO-8859-1"?><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" version="5.0-subset Scilab" xml:lang="en" xml:id="_pl_fusionsci"><info><pubdate>04-Apr-2006</pubdate></info><refnamediv><refname>_pl_fusionsci</refname><refpurpose>[Internal function] Merge 2 increasing sequences using scilab syntax; used to compute the Legendre-Fenchel conjugate.</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>fH = _pl_fusionsci(C,S)</synopsis></refsynopsisdiv>

  
   <refsection><title>Parameters</title>
  
      <variablelist>

    
         <varlistentry>
    
            <term>C</term>
    
            <listitem>
       
               <para>
					Column vector, C(i) = (f(X(i+1) - f(X(i)) / (X(i+1) - X(i))
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					<para></para>-->
					<para>for some function f on a grid X.</para>
			   </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>S</term>
    
            <listitem>
       
               <para>Column vector. The grid on which we want to compute the conjugate: f* is evaluated on S.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>fH</term>
    
            <listitem>
       
               <para>Column vector. Index at which the slope S(i) support the epigraph.
       </para>
    
            </listitem>
    
         </varlistentry>
  
      </variablelist>
  
   </refsection>
 
  
   <refsection><title>Description</title>
     
      <itemizedlist>
     
         <listitem>
     
            <para>
	Calling _pl_fusionsci(C,S) is equivalent to calling <link linkend="_pl_fusion">_pl_fusion</link>(C,S). While the former uses scilab built-in functions to speed-up computation, contrary to the later it does not guarantee a linear worst-case running time. See <link linkend="_pl_fusion">_pl_fusion</link> for more information.
     </para>
     
         </listitem>
     
         <listitem>
	     
            <para>
		     This function is not intended to be used directly but to be called during the computation of the conjugate using the LLT algorithm by the function <link linkend="pl_lft_llt">pl_lft_llt</link>.
	     </para>
     
         </listitem>

     
      </itemizedlist>
  
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
    X=[-5:0.5:5]';
    Y=X.^2;
    C=(Y(2:size(Y,1))-Y(1:size(Y,1)-1))./(X(2:size(X,1))-X(1:size(X,1)-1));
    S=C-0.25*ones(size(C, 1));
    [fH]=_pl_fusionsci(C,S)
  ]]></programlisting></refsection>

  
   <refsection><title>See Also</title><simplelist type="inline">
    
      <member> 
         <link linkend="_pl_fusion">_pl_fusion</link> 
      </member>
    
      <member> 
         <link linkend="pl_lft_llt">pl_lft_llt</link> 
      </member>
  
   </simplelist></refsection>

  
   <refsection><title>Authors</title><para>
	  
      <literal>Yves Lucet</literal>, University of British Columbia, BC, Canada
  </para></refsection>

</refentry>
