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Timestamp:
02/16/09 10:02:08 (16 years ago)
Author:
smidl
Message:

Changes in the very root classes!
* rv and rvc are no longer compulsory,
* samplecond does not return ll
* BM has drv

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1 modified

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  • doc/html/classbdm_1_1egiw.html

    r269 r270  
    2929</div> 
    3030<div class="contents"> 
    31 <h1>bdm::egiw Class Reference</h1><!-- doxytag: class="bdm::egiw" --><!-- doxytag: inherits="bdm::eEF" -->Gauss-inverse-Wishart density stored in LD form.   
    32 <a href="#_details">More...</a> 
    33 <p> 
    34 <code>#include &lt;<a class="el" href="libEF_8h-source.html">libEF.h</a>&gt;</code> 
     31<h1>bdm::egiw Class Reference</h1><!-- doxytag: class="bdm::egiw" --><!-- doxytag: inherits="bdm::eEF" --><code>#include &lt;<a class="el" href="libEF_8h-source.html">libEF.h</a>&gt;</code> 
    3532<p> 
    3633<div class="dynheader"> 
     
    4138<area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="21,161,101,188"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="19,84,104,111"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="5,7,117,33"></map> 
    4239<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> 
    43 <div class="dynheader"> 
    44 Collaboration diagram for bdm::egiw:</div> 
    45 <div class="dynsection"> 
    46 <p><center><img src="classbdm_1_1egiw__coll__graph.png" border="0" usemap="#bdm_1_1egiw__coll__map" alt="Collaboration graph"></center> 
    47 <map name="bdm_1_1egiw__coll__map"> 
    48 <area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="19,263,99,289"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="13,183,99,209"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="5,7,117,33"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="72,87,147,113"><area shape="rect" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD)." alt="" coords="124,263,183,289"><area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="123,183,184,209"></map> 
    49 <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div> 
    5040 
    5141<p> 
    52 <a href="classbdm_1_1egiw-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0"> 
     42<a href="classbdm_1_1egiw-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2> 
     43Gauss-inverse-Wishart density stored in LD form.  
     44<p> 
     45For <img class="formulaInl" alt="$p$" src="form_42.png">-variate densities, given rv.count() should be <img class="formulaInl" alt="$p\times$" src="form_72.png"> V.rows(). <table border="0" cellpadding="0" cellspacing="0"> 
    5346<tr><td></td></tr> 
    5447<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr> 
    55 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a60e072c191acf65ab480deeb11c5b88"></a><!-- doxytag: member="bdm::egiw::egiw" ref="a60e072c191acf65ab480deeb11c5b88" args="(RV rv, mat V0, double nu0=-1.0)" --> 
    56 &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#a60e072c191acf65ab480deeb11c5b88">egiw</a> (<a class="el" href="classbdm_1_1RV.html">RV</a> <a class="el" href="classbdm_1_1epdf.html#62c5b8ff71d9ebe6cd58d3c342eb1dc8">rv</a>, mat V0, double nu0=-1.0)</td></tr> 
    57  
    58 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor, if nu0&lt;0 a minimal nu0 will be computed. <br></td></tr> 
    59 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bc3db93cb60dd29187eb3c6cfd557f97"></a><!-- doxytag: member="bdm::egiw::egiw" ref="bc3db93cb60dd29187eb3c6cfd557f97" args="(RV rv, ldmat V0, double nu0=-1.0)" --> 
    60 &nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#bc3db93cb60dd29187eb3c6cfd557f97">egiw</a> (<a class="el" href="classbdm_1_1RV.html">RV</a> <a class="el" href="classbdm_1_1epdf.html#62c5b8ff71d9ebe6cd58d3c342eb1dc8">rv</a>, <a class="el" href="classldmat.html">ldmat</a> V0, double nu0=-1.0)</td></tr> 
    61  
    62 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor for V in <a class="el" href="classldmat.html" title="Matrix stored in LD form, (commonly known as UD).">ldmat</a> form. <br></td></tr> 
    6348<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="920f21548b7a3723923dd108fe514c61"></a><!-- doxytag: member="bdm::egiw::sample" ref="920f21548b7a3723923dd108fe514c61" args="() const " --> 
    6449vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#920f21548b7a3723923dd108fe514c61">sample</a> () const </td></tr> 
    6550 
    66 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a sample, <img class="formulaInl" alt="$x$" src="form_28.png"> from density <img class="formulaInl" alt="$epdf(rv)$" src="form_59.png">. <br></td></tr> 
     51<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a sample, <img class="formulaInl" alt="$ x $" src="form_106.png"> from density <img class="formulaInl" alt="$ f_x()$" src="form_107.png">. <br></td></tr> 
    6752<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="df70c05f918c3a6f86d60f10c1fd6ba2"></a><!-- doxytag: member="bdm::egiw::mean" ref="df70c05f918c3a6f86d60f10c1fd6ba2" args="() const " --> 
    6853vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#df70c05f918c3a6f86d60f10c1fd6ba2">mean</a> () const </td></tr> 
     
    8469 
    8570<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">logarithm of the normalizing constant, <img class="formulaInl" alt="$\mathcal{I}$" src="form_60.png"> <br></td></tr> 
    86 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="15792f3112e5cf67d572f491b09324c8"></a><!-- doxytag: member="bdm::egiw::_V" ref="15792f3112e5cf67d572f491b09324c8" args="()" --> 
    87 <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#15792f3112e5cf67d572f491b09324c8">_V</a> ()</td></tr> 
    88  
    89 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">returns a pointer to the internal statistics. Use with Care! <br></td></tr> 
    90 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ad9c539a80a552e837245ddcebcbbba4"></a><!-- doxytag: member="bdm::egiw::_V" ref="ad9c539a80a552e837245ddcebcbbba4" args="() const " --> 
    91 const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#ad9c539a80a552e837245ddcebcbbba4">_V</a> () const </td></tr> 
    92  
    93 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">returns a pointer to the internal statistics. Use with Care! <br></td></tr> 
    94 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a025ee710274ca142dd0ae978735ad4a"></a><!-- doxytag: member="bdm::egiw::_nu" ref="a025ee710274ca142dd0ae978735ad4a" args="()" --> 
    95 double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#a025ee710274ca142dd0ae978735ad4a">_nu</a> ()</td></tr> 
    96  
    97 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">returns a pointer to the internal statistics. Use with Care! <br></td></tr> 
    98 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cf3b2bcb158c15c24788bba90e4154e4"></a><!-- doxytag: member="bdm::egiw::_nu" ref="cf3b2bcb158c15c24788bba90e4154e4" args="() const " --> 
    99 const double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_nu</b> () const </td></tr> 
    100  
    10171<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="8e610e95401a11baf34f65e16ecd87be"></a><!-- doxytag: member="bdm::egiw::pow" ref="8e610e95401a11baf34f65e16ecd87be" args="(double p)" --> 
    10272void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#8e610e95401a11baf34f65e16ecd87be">pow</a> (double p)</td></tr> 
     
    11585 
    11686<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate normalized log-probability for many samples. <br></td></tr> 
     87<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr> 
     88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="50149cf136c9120b4fff71c117f0bb2e"></a><!-- doxytag: member="bdm::egiw::egiw" ref="50149cf136c9120b4fff71c117f0bb2e" args="()" --> 
     89&nbsp;</td><td class="memItemRight" valign="bottom"><b>egiw</b> ()</td></tr> 
     90 
     91<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="79037e048e717a076f342eb1d276870e"></a><!-- doxytag: member="bdm::egiw::egiw" ref="79037e048e717a076f342eb1d276870e" args="(int dimx0, ldmat V0, double nu0=-1.0)" --> 
     92&nbsp;</td><td class="memItemRight" valign="bottom"><b>egiw</b> (int dimx0, <a class="el" href="classldmat.html">ldmat</a> V0, double nu0=-1.0)</td></tr> 
     93 
     94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40b04f8ef133d089c4be2c7983e18b5c"></a><!-- doxytag: member="bdm::egiw::set_parameters" ref="40b04f8ef133d089c4be2c7983e18b5c" args="(int dimx0, ldmat V0, double nu0=-1.0)" --> 
     95void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (int dimx0, <a class="el" href="classldmat.html">ldmat</a> V0, double nu0=-1.0)</td></tr> 
     96 
     97<tr><td colspan="2"><div class="groupHeader">Access attributes</div></td></tr> 
     98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="15792f3112e5cf67d572f491b09324c8"></a><!-- doxytag: member="bdm::egiw::_V" ref="15792f3112e5cf67d572f491b09324c8" args="()" --> 
     99<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_V</b> ()</td></tr> 
     100 
     101<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ad9c539a80a552e837245ddcebcbbba4"></a><!-- doxytag: member="bdm::egiw::_V" ref="ad9c539a80a552e837245ddcebcbbba4" args="() const " --> 
     102const <a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_V</b> () const </td></tr> 
     103 
     104<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a025ee710274ca142dd0ae978735ad4a"></a><!-- doxytag: member="bdm::egiw::_nu" ref="a025ee710274ca142dd0ae978735ad4a" args="()" --> 
     105double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_nu</b> ()</td></tr> 
     106 
     107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cf3b2bcb158c15c24788bba90e4154e4"></a><!-- doxytag: member="bdm::egiw::_nu" ref="cf3b2bcb158c15c24788bba90e4154e4" args="() const " --> 
     108const double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_nu</b> () const </td></tr> 
     109 
     110<tr><td colspan="2"><div class="groupHeader">Matematical Operations</div></td></tr> 
    117111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b4cf45fd83cc7573ede9fe1215256058"></a><!-- doxytag: member="bdm::egiw::sample_m" ref="b4cf45fd83cc7573ede9fe1215256058" args="(int N) const " --> 
    118112virtual mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#b4cf45fd83cc7573ede9fe1215256058">sample_m</a> (int N) const </td></tr> 
    119113 
    120 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns N samples from density <img class="formulaInl" alt="$epdf(rv)$" src="form_59.png">. <br></td></tr> 
     114<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns N samples, <img class="formulaInl" alt="$ [x_1 , x_2 , \ldots \ $" src="form_108.png"> from density <img class="formulaInl" alt="$ f_x(rv)$" src="form_109.png">. <br></td></tr> 
    121115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="34956d4dd3176eeb5937cf48a1546b62"></a><!-- doxytag: member="bdm::egiw::evallog_m" ref="34956d4dd3176eeb5937cf48a1546b62" args="(const mat &amp;Val) const " --> 
    122116virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#34956d4dd3176eeb5937cf48a1546b62">evallog_m</a> (const mat &amp;Val) const </td></tr> 
     
    131125 
    132126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return marginal density on the given <a class="el" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables.">RV</a>, the remainig rvs are intergrated out. <br></td></tr> 
     127<tr><td colspan="2"><div class="groupHeader">Connection to other classes</div></td></tr> 
     128<tr><td colspan="2"><div class="groupText">Description of the random quantity via attribute <code>rv</code> is optional. For operations such as sampling <code>rv</code> does not need to be set. However, for <code>marginalization</code> and <code>conditioning</code> <code>rv</code> has to be set. NB: <br><br></div></td></tr> 
     129<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f423e28448dbb69ef4905295ec8de8ff"></a><!-- doxytag: member="bdm::egiw::set_rv" ref="f423e28448dbb69ef4905295ec8de8ff" args="(const RV &amp;rv0)" --> 
     130void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#f423e28448dbb69ef4905295ec8de8ff">set_rv</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0)</td></tr> 
     131 
     132<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Name its rv. <br></td></tr> 
     133<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c4b863ff84c7a4882fb3ad18556027f9"></a><!-- doxytag: member="bdm::egiw::isnamed" ref="c4b863ff84c7a4882fb3ad18556027f9" args="() const " --> 
     134bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#c4b863ff84c7a4882fb3ad18556027f9">isnamed</a> () const </td></tr> 
     135 
     136<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">True if rv is assigned. <br></td></tr> 
    133137<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4ab378d5e004c3ff3e2d4e64f7bba21"></a><!-- doxytag: member="bdm::egiw::_rv" ref="a4ab378d5e004c3ff3e2d4e64f7bba21" args="() const " --> 
    134138const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#a4ab378d5e004c3ff3e2d4e64f7bba21">_rv</a> () const </td></tr> 
    135139 
    136 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function, possibly dangerous! <br></td></tr> 
    137 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62e88cbce0ce77a8692f5e15d76e805f"></a><!-- doxytag: member="bdm::egiw::_renewrv" ref="62e88cbce0ce77a8692f5e15d76e805f" args="(const RV &amp;in_rv)" --> 
    138 void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#62e88cbce0ce77a8692f5e15d76e805f">_renewrv</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;in_rv)</td></tr> 
     140<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return name (fails when isnamed is false). <br></td></tr> 
     141<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr> 
     142<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="46dfe100cd621716ee5c7ee25a20f24b"></a><!-- doxytag: member="bdm::egiw::dimension" ref="46dfe100cd621716ee5c7ee25a20f24b" args="() const " --> 
     143bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#46dfe100cd621716ee5c7ee25a20f24b">dimension</a> () const </td></tr> 
    139144 
    140 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">modifier function - useful when copying epdfs <br></td></tr> 
     145<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Size of the random variable. <br></td></tr> 
    141146<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr> 
    142147<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ae56852845c6af176fd9017dbebbbd52"></a><!-- doxytag: member="bdm::egiw::V" ref="ae56852845c6af176fd9017dbebbbd52" args="" --> 
     
    148153 
    149154<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Number of data records (degrees of freedom) of sufficient statistics. <br></td></tr> 
    150 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40b68a9c3b2120fba94cc4d2fcd291e1"></a><!-- doxytag: member="bdm::egiw::xdim" ref="40b68a9c3b2120fba94cc4d2fcd291e1" args="" --> 
    151 int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#40b68a9c3b2120fba94cc4d2fcd291e1">xdim</a></td></tr> 
     155<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="23e4d78bea7e98840f3da30e76a2b57a"></a><!-- doxytag: member="bdm::egiw::dimx" ref="23e4d78bea7e98840f3da30e76a2b57a" args="" --> 
     156int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1egiw.html#23e4d78bea7e98840f3da30e76a2b57a">dimx</a></td></tr> 
    152157 
    153158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Dimension of the output. <br></td></tr> 
     
    156161 
    157162<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Dimension of the regressor. <br></td></tr> 
     163<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="16adac20ec7fe07e1ea0b27d917788ce"></a><!-- doxytag: member="bdm::egiw::dim" ref="16adac20ec7fe07e1ea0b27d917788ce" args="" --> 
     164int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#16adac20ec7fe07e1ea0b27d917788ce">dim</a></td></tr> 
     165 
     166<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the random variable <br></td></tr> 
    158167<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62c5b8ff71d9ebe6cd58d3c342eb1dc8"></a><!-- doxytag: member="bdm::egiw::rv" ref="62c5b8ff71d9ebe6cd58d3c342eb1dc8" args="" --> 
    159168<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#62c5b8ff71d9ebe6cd58d3c342eb1dc8">rv</a></td></tr> 
    160169 
    161 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Identified of the random variable. <br></td></tr> 
     170<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Description of the random variable. <br></td></tr> 
    162171</table> 
    163 <hr><a name="_details"></a><h2>Detailed Description</h2> 
    164 Gauss-inverse-Wishart density stored in LD form.  
    165 <p> 
    166 For <img class="formulaInl" alt="$p$" src="form_42.png">-variate densities, given rv.count() should be <img class="formulaInl" alt="$p\times$" src="form_72.png"> V.rows(). <hr>The documentation for this class was generated from the following files:<ul> 
     172<hr>The documentation for this class was generated from the following files:<ul> 
    167173<li><a class="el" href="libEF_8h-source.html">libEF.h</a><li>libEF.cpp</ul> 
    168174</div> 
    169 <hr size="1"><address style="text-align: right;"><small>Generated on Wed Feb 11 10:21:05 2009 for mixpp by&nbsp; 
     175<hr size="1"><address style="text-align: right;"><small>Generated on Wed Feb 11 23:34:06 2009 for mixpp by&nbsp; 
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    171177<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>