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    2424</div> 
    2525<div class="contents"> 
    26 <h1>MixEF Class Reference</h1><!-- doxytag: class="MixEF" --><!-- doxytag: inherits="BM" -->Mixture of Exponential Family Densities.   
     26<h1>MixEF Class Reference</h1><!-- doxytag: class="MixEF" --><!-- doxytag: inherits="BMEF" -->Mixture of Exponential Family Densities.   
    2727<a href="#_details">More...</a> 
    2828<p> 
     
    3434<p><center><img src="classMixEF__inherit__graph.png" border="0" usemap="#MixEF__inherit__map" alt="Inheritance graph"></center> 
    3535<map name="MixEF__inherit__map"> 
    36 <area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,7,53,33"></map> 
     36<area shape="rect" href="classBMEF.html" title="Estimator for Exponential family." alt="" coords="5,84,61,111"><area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,7,53,33"></map> 
    3737<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> 
    3838<div class="dynheader"> 
     
    4141<p><center><img src="classMixEF__coll__graph.png" border="0" usemap="#MixEF__coll__map" alt="Collaboration graph"></center> 
    4242<map name="MixEF__coll__map"> 
    43 <area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="27,183,67,209"><area shape="rect" href="classBMEF.html" title="Estimator for Exponential family." alt="" coords="19,289,75,316"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="68,7,105,33"><area shape="rect" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="107,103,155,129"><area shape="rect" href="classeprod.html" title="Product of independent epdfs. For dependent pdfs, use mprod." alt="" coords="168,236,227,263"><area shape="rect" href="classeEF.html" title="General conjugate exponential family posterior density." alt="" coords="109,183,152,209"><area shape="rect" href="classmultiBM.html" title="Estimator for Multinomial density." alt="" coords="47,385,119,412"><area shape="rect" href="classeDirich.html" title="Dirichlet posterior density." alt="" coords="99,289,163,316"></map> 
     43<area shape="rect" href="classBMEF.html" title="Estimator for Exponential family." alt="" coords="5,316,61,343"><area shape="rect" href="classmultiBM.html" title="Estimator for Multinomial density." alt="" coords="75,412,147,439"><area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="28,156,68,183"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="61,7,99,33"><area shape="rect" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="93,103,141,129"><area shape="rect" href="classeprod.html" title="Product of independent epdfs. For dependent pdfs, use mprod." alt="" coords="155,263,213,289"><area shape="rect" href="classeEF.html" title="General conjugate exponential family posterior density." alt="" coords="96,209,139,236"><area shape="rect" href="classeDirich.html" title="Dirichlet posterior density." alt="" coords="85,316,149,343"></map> 
    4444<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> 
    4545 
     
    5252 
    5353<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor. <br></td></tr> 
     54<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="51fa3e3953c0af69f4e0162829d7929d"></a><!-- doxytag: member="MixEF::MixEF" ref="51fa3e3953c0af69f4e0162829d7929d" args="()" --> 
     55&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#51fa3e3953c0af69f4e0162829d7929d">MixEF</a> ()</td></tr> 
     56 
     57<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor of empty mixture. <br></td></tr> 
     58<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5f4880febf28803471694d87eab81ec4"></a><!-- doxytag: member="MixEF::MixEF" ref="5f4880febf28803471694d87eab81ec4" args="(const MixEF &amp;M2)" --> 
     59&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#5f4880febf28803471694d87eab81ec4">MixEF</a> (const <a class="el" href="classMixEF.html">MixEF</a> &amp;M2)</td></tr> 
     60 
     61<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Copy constructor. <br></td></tr> 
    5462<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#73a782d2f464c830bbdbb03d34c6d63e">init</a> (<a class="el" href="classBMEF.html">BMEF</a> *Com0, const mat &amp;Data, int c=5)</td></tr> 
    5563 
     
    6270 
    6371<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">EM algorithm. <br></td></tr> 
    64 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e6810daa121ccaff1ac18f26fbad4563"></a><!-- doxytag: member="MixEF::bayesB" ref="e6810daa121ccaff1ac18f26fbad4563" args="(const mat &amp;dt)" --> 
    65 void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#e6810daa121ccaff1ac18f26fbad4563">bayesB</a> (const mat &amp;dt)</td></tr> 
    66  
    67 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr> 
     72<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8f4672ce35c35eec6a7f9c18ce3871a3"></a><!-- doxytag: member="MixEF::bayesB" ref="8f4672ce35c35eec6a7f9c18ce3871a3" args="(const mat &amp;dt, const vec &amp;wData)" --> 
     73void&nbsp;</td><td class="memItemRight" valign="bottom"><b>bayesB</b> (const mat &amp;dt, const vec &amp;wData)</td></tr> 
     74 
    6875<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#424ca64f36d4e41de7a7e7ae921d35ea">logpred</a> (const vec &amp;dt) const </td></tr> 
    6976 
     
    7178const <a class="el" href="classepdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#efb3e20c2151d91c4fc080b7722a2069">_epdf</a> () const </td></tr> 
    7279 
     80<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a reference to the <a class="el" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. <br></td></tr> 
     81<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="324c2f0f7f9a9ee123073c15aeb8d0c1"></a><!-- doxytag: member="MixEF::_e" ref="324c2f0f7f9a9ee123073c15aeb8d0c1" args="() const " --> 
     82const <a class="el" href="classeprod.html">eprod</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#324c2f0f7f9a9ee123073c15aeb8d0c1">_e</a> () const </td></tr> 
     83 
    7384<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. Use with care! <br></td></tr> 
    74 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a93379cf31bb25961ea7f8d3f095513d"></a><!-- doxytag: member="MixEF::predictor" ref="a93379cf31bb25961ea7f8d3f095513d" args="(const RV &amp;rv)" --> 
    75 <a class="el" href="classemix.html">emix</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#a93379cf31bb25961ea7f8d3f095513d">predictor</a> (const <a class="el" href="classRV.html">RV</a> &amp;<a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a>)</td></tr> 
     85<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4d5b5c25280a50df1edfa2c03540d0ac"></a><!-- doxytag: member="MixEF::predictor" ref="4d5b5c25280a50df1edfa2c03540d0ac" args="(const RV &amp;rv) const " --> 
     86<a class="el" href="classemix.html">emix</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#4d5b5c25280a50df1edfa2c03540d0ac">predictor</a> (const <a class="el" href="classRV.html">RV</a> &amp;<a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a>) const </td></tr> 
    7687 
    7788<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs a predictive density (marginal density on data). <br></td></tr> 
    78 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="fdbd5f58778c1ecb68b71945cdff0483"></a><!-- doxytag: member="MixEF::flatten" ref="fdbd5f58778c1ecb68b71945cdff0483" args="(double sumw=1.0)" --> 
    79 void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#fdbd5f58778c1ecb68b71945cdff0483">flatten</a> (double sumw=1.0)</td></tr> 
     89<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7d4d571688a15cc5be10f6f48bfc433d"></a><!-- doxytag: member="MixEF::flatten" ref="7d4d571688a15cc5be10f6f48bfc433d" args="(const BMEF *M2)" --> 
     90void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#7d4d571688a15cc5be10f6f48bfc433d">flatten</a> (const <a class="el" href="classBMEF.html">BMEF</a> *M2)</td></tr> 
    8091 
    8192<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flatten the density as if it was not estimated from the data. <br></td></tr> 
     93<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="959d9b078766e251a3089b501ed78513"></a><!-- doxytag: member="MixEF::_Coms" ref="959d9b078766e251a3089b501ed78513" args="(int i)" --> 
     94<a class="el" href="classBMEF.html">BMEF</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#959d9b078766e251a3089b501ed78513">_Coms</a> (int i)</td></tr> 
     95 
     96<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Access function. <br></td></tr> 
     97<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6576024e16523da5cbaaf233512c53dc"></a><!-- doxytag: member="MixEF::set_method" ref="6576024e16523da5cbaaf233512c53dc" args="(MixEF_METHOD M)" --> 
     98void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#6576024e16523da5cbaaf233512c53dc">set_method</a> (MixEF_METHOD M)</td></tr> 
     99 
     100<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set which method is to be used. <br></td></tr> 
     101<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="30bb40eb1fd31869b2e62e79e1ecdcb4"></a><!-- doxytag: member="MixEF::set_statistics" ref="30bb40eb1fd31869b2e62e79e1ecdcb4" args="(const BMEF *BM0)" --> 
     102virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#30bb40eb1fd31869b2e62e79e1ecdcb4">set_statistics</a> (const <a class="el" href="classBMEF.html">BMEF</a> *BM0)</td></tr> 
     103 
     104<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get statistics from another model <br></td></tr> 
     105<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8f4ecb6e2eaf630155a1fa98f35aa6ad"></a><!-- doxytag: member="MixEF::bayes" ref="8f4ecb6e2eaf630155a1fa98f35aa6ad" args="(const vec &amp;data, const double w)" --> 
     106virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#8f4ecb6e2eaf630155a1fa98f35aa6ad">bayes</a> (const vec &amp;data, const double w)</td></tr> 
     107 
     108<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Weighted update of sufficient statistics (Bayes rule). <br></td></tr> 
     109<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="97f5312efe4a5bedb86d2daec59d8651"></a><!-- doxytag: member="MixEF::_copy_" ref="97f5312efe4a5bedb86d2daec59d8651" args="(bool changerv=false)" --> 
     110<a class="el" href="classBMEF.html">BMEF</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#97f5312efe4a5bedb86d2daec59d8651">_copy_</a> (bool changerv=false)</td></tr> 
     111 
     112<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flatten the posterior as if to keep nu0 data. <br></td></tr> 
     113<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0186270f75189677f390fe088a9947e9"></a><!-- doxytag: member="MixEF::bayesB" ref="0186270f75189677f390fe088a9947e9" args="(const mat &amp;Dt)" --> 
     114virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#0186270f75189677f390fe088a9947e9">bayesB</a> (const mat &amp;Dt)</td></tr> 
     115 
     116<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr> 
    82117<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cd0660f2a1a344b56ac39802708ff165"></a><!-- doxytag: member="MixEF::logpred_m" ref="cd0660f2a1a344b56ac39802708ff165" args="(const mat &amp;dt) const " --> 
    83118vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#cd0660f2a1a344b56ac39802708ff165">logpred_m</a> (const mat &amp;dt) const </td></tr> 
     
    96131 
    97132<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr> 
    98 <tr><td class="memItemLeft" nowrap align="right" valign="top">virtual <a class="el" href="classBM.html">BM</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#eb58c81d6a7b75b05fc6f276eed78887">_copy_</a> (bool changerv=false)</td></tr> 
    99  
    100133<tr><td colspan="2"><br><h2>Protected Member Functions</h2></td></tr> 
    101134<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5ae381b3a7dfbe2c1e5bb579a5d9b9d1"></a><!-- doxytag: member="MixEF::build_est" ref="5ae381b3a7dfbe2c1e5bb579a5d9b9d1" args="()" --> 
     
    120153 
    121154<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Posterior on component parameters. <br></td></tr> 
     155<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6e630b2fd4cae8aa728ea1322708c8f0"></a><!-- doxytag: member="MixEF::method" ref="6e630b2fd4cae8aa728ea1322708c8f0" args="" --> 
     156MixEF_METHOD&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classMixEF.html#6e630b2fd4cae8aa728ea1322708c8f0">method</a></td></tr> 
     157 
     158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flag for a method that is used in the inference. <br></td></tr> 
     159<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="538d632e59f9afa8daa1de74da12ce71"></a><!-- doxytag: member="MixEF::frg" ref="538d632e59f9afa8daa1de74da12ce71" args="" --> 
     160double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#538d632e59f9afa8daa1de74da12ce71">frg</a></td></tr> 
     161 
     162<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br></td></tr> 
     163<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="308cf5d4133cd471fdf1ecd5dfa09d02"></a><!-- doxytag: member="MixEF::last_lognc" ref="308cf5d4133cd471fdf1ecd5dfa09d02" args="" --> 
     164double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#308cf5d4133cd471fdf1ecd5dfa09d02">last_lognc</a></td></tr> 
     165 
     166<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of lognc() in the previous step (used in evaluation of <code>ll</code> ) <br></td></tr> 
    122167<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af00f0612fabe66241dd507188cdbf88"></a><!-- doxytag: member="MixEF::rv" ref="af00f0612fabe66241dd507188cdbf88" args="" --> 
    123168<a class="el" href="classRV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a></td></tr> 
     
    183228</dl> 
    184229 
    185 <p>References <a class="el" href="libBM_8h-source.html#l00360">BM::_copy_()</a>, <a class="el" href="mixef_8h-source.html#l00052">build_est()</a>, <a class="el" href="mixef_8h-source.html#l00044">Coms</a>, <a class="el" href="mixef_8h-source.html#l00048">est</a>, <a class="el" href="mixef_8h-source.html#l00042">n</a>, <a class="el" href="libEF_8h-source.html#l00273">multiBM::set_parameters()</a>, and <a class="el" href="mixef_8h-source.html#l00046">weights</a>.</p> 
    186  
    187 <p>Referenced by <a class="el" href="merger_8cpp-source.html#l00023">merger::merge()</a>.</p> 
     230<p>References <a class="el" href="libEF_8h-source.html#l00097">BMEF::_copy_()</a>, <a class="el" href="mixef_8h-source.html#l00057">build_est()</a>, <a class="el" href="mixef_8h-source.html#l00046">Coms</a>, <a class="el" href="mixef_8h-source.html#l00050">est</a>, <a class="el" href="mixef_8h-source.html#l00044">n</a>, <a class="el" href="libEF_8h-source.html#l00290">multiBM::set_parameters()</a>, and <a class="el" href="mixef_8h-source.html#l00048">weights</a>.</p> 
     231 
     232<p>Referenced by <a class="el" href="merger_8cpp-source.html#l00028">merger::merge()</a>.</p> 
    188233 
    189234</div> 
     
    209254<p>Reimplemented from <a class="el" href="classBM.html#8a8ce6df431689964c41cc6c849cfd06">BM</a>.</p> 
    210255 
    211 <p>References <a class="el" href="libEF_8h-source.html#l00272">multiBM::_epdf()</a>, <a class="el" href="mixef_8h-source.html#l00044">Coms</a>, <a class="el" href="classepdf.html#bf0a070a8f3e67a93604ca724638b870">epdf::mean()</a>, <a class="el" href="mixef_8h-source.html#l00042">n</a>, and <a class="el" href="mixef_8h-source.html#l00046">weights</a>.</p> 
    212  
    213 <p>Referenced by <a class="el" href="merger_8h-source.html#l00062">merger::evalpdflog()</a>, and <a class="el" href="merger_8cpp-source.html#l00023">merger::merge()</a>.</p> 
    214  
    215 </div> 
    216 </div><p> 
    217 <a class="anchor" name="eb58c81d6a7b75b05fc6f276eed78887"></a><!-- doxytag: member="MixEF::_copy_" ref="eb58c81d6a7b75b05fc6f276eed78887" args="(bool changerv=false)" --> 
    218 <div class="memitem"> 
    219 <div class="memproto"> 
    220       <table class="memname"> 
    221         <tr> 
    222           <td class="memname">virtual <a class="el" href="classBM.html">BM</a>* BM::_copy_           </td> 
    223           <td>(</td> 
    224           <td class="paramtype">bool&nbsp;</td> 
    225           <td class="paramname"> <em>changerv</em> = <code>false</code>          </td> 
    226           <td>&nbsp;)&nbsp;</td> 
    227           <td><code> [inline, virtual, inherited]</code></td> 
    228         </tr> 
    229       </table> 
    230 </div> 
    231 <div class="memdoc"> 
    232  
    233 <p> 
    234 Copy function required in vectors, Arrays of <a class="el" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities.">BM</a> etc. Have to be DELETED manually! Prototype: BM* <a class="el" href="classBM.html#eb58c81d6a7b75b05fc6f276eed78887">_copy_()</a>{<a class="el" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities.">BM</a> Tmp*=new Tmp(this*); return Tmp; }  
    235 <p>Reimplemented in <a class="el" href="classARX.html#5de61fbd4f97fa3216760b1f733f5af0">ARX</a>.</p> 
    236  
    237 <p>Referenced by <a class="el" href="mixef_8cpp-source.html#l00007">init()</a>.</p> 
     256<p>References <a class="el" href="libEF_8h-source.html#l00288">multiBM::_epdf()</a>, <a class="el" href="mixef_8h-source.html#l00046">Coms</a>, <a class="el" href="classepdf.html#bf0a070a8f3e67a93604ca724638b870">epdf::mean()</a>, and <a class="el" href="mixef_8h-source.html#l00048">weights</a>.</p> 
     257 
     258<p>Referenced by <a class="el" href="merger_8h-source.html#l00090">merger::evalpdflog()</a>, and <a class="el" href="merger_8cpp-source.html#l00028">merger::merge()</a>.</p> 
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    242263<li>work/git/mixpp/bdm/estim/<a class="el" href="mixef_8h-source.html">mixef.h</a><li>work/git/mixpp/bdm/estim/mixef.cpp</ul> 
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    244 <hr size="1"><address style="text-align: right;"><small>Generated on Wed Oct 15 15:57:16 2008 for mixpp by&nbsp; 
     265<hr size="1"><address style="text-align: right;"><small>Generated on Wed Nov 12 19:18:55 2008 for mixpp by&nbsp; 
    245266<a href="http://www.doxygen.org/index.html"> 
    246267<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>