<?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_lft_plt"><info><pubdate>02-May-2006</pubdate></info><refnamediv><refname>pl_lft_plt</refname><refpurpose>Parametric Legendre Transform, PLT algorithm</refpurpose></refnamediv>
  
   
  
   
  
   
  
   
  
   

  
   <refsynopsisdiv><title>Calling Sequence</title><synopsis>[Conj, S] = pl_lft_plt(X, f, df)</synopsis></refsynopsisdiv>

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

    
         <varlistentry>
    
            <term>X</term>
    
            <listitem>
       
               <para>column vector. A grid of points on which the function is sampled.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>f</term>
    
            <listitem>
       
               <para>column vector. The value of the function on the grid X: usually Y(i)=f(X(i)) for some function f.
       </para>
    
            </listitem>
    
         </varlistentry>

    
         <varlistentry>
    
            <term>df</term>
    
            <listitem>
       
               <para>column vector. The value of the derivative of the function f evaluated on X, which is also the slope.
       </para>
    
            </listitem>
    
         </varlistentry>

  
      </variablelist>
  
   </refsection>
 
  
   <refsection><title>Description</title>
     
         <para>
        Compute numerically the Legendre Fenchel transform
	by generating a uniform grid between an interval a,b and
	computing s[i] = f'(x), and f*(s[i]) = x[i]s[i] - f(x[i]). Which returns a set S of slopes in the dom of f* and the values of f* on S.
     </para>
  
   </refsection>

  
   <refsection><title>Examples</title><programlisting role="example"><![CDATA[
    function y = f(x), y=0.5 * x.^2, endfunction;
    function s = df(x), s= x, endfunction;
    b=%T;n=8;
    X=(-n/2:1:n/2)';S=df(X);Y=f(X);
    [Conj, S] = pl_lft_plt(X, f, df);
  ]]></programlisting></refsection>

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

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

</refentry>
