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[261]27  <div class="navpath"><a class="el" href="namespacebdm.html">bdm</a>::<a class="el" href="classbdm_1_1PF.html">PF</a>
[259]28  </div>
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30<div class="contents">
31<h1>bdm::PF Class Reference</h1><!-- doxytag: class="bdm::PF" --><!-- doxytag: inherits="bdm::BM" -->Trivial particle filter with proposal density equal to parameter evolution model. 
32<a href="#_details">More...</a>
33<p>
34<code>#include &lt;<a class="el" href="libPF_8h-source.html">libPF.h</a>&gt;</code>
35<p>
36<div class="dynheader">
37Inheritance diagram for bdm::PF:</div>
38<div class="dynsection">
39<p><center><img src="classbdm_1_1PF__inherit__graph.png" border="0" usemap="#bdm_1_1PF__inherit__map" alt="Inheritance graph"></center>
40<map name="bdm_1_1PF__inherit__map">
[261]41<area shape="rect" href="classbdm_1_1MPF.html" title="Marginalized Particle filter." alt="" coords="5,239,152,265"><area shape="rect" href="classbdm_1_1BM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="40,84,117,111"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="23,7,135,33"></map>
[259]42<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
43<div class="dynheader">
44Collaboration diagram for bdm::PF:</div>
45<div class="dynsection">
46<p><center><img src="classbdm_1_1PF__coll__graph.png" border="0" usemap="#bdm_1_1PF__coll__map" alt="Collaboration graph"></center>
47<map name="bdm_1_1PF__coll__map">
[261]48<area shape="rect" href="classbdm_1_1BM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="5,185,83,212"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="128,7,240,33"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="96,87,171,113"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="201,284,292,311"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="173,185,259,212"><area shape="rect" href="classbdm_1_1eEmp.html" title="Weighted empirical density." alt="" coords="81,284,177,311"></map>
[259]49<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
50
51<p>
52<a href="classbdm_1_1PF-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
53<tr><td></td></tr>
54<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="df9e7dc54dbe1c78a4aa503c42f7f8c4"></a><!-- doxytag: member="bdm::PF::PF" ref="df9e7dc54dbe1c78a4aa503c42f7f8c4" args="(const RV &amp;rv0, mpdf &amp;par0, mpdf &amp;obs0, int n0)" -->
56&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#df9e7dc54dbe1c78a4aa503c42f7f8c4">PF</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0, <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> &amp;par0, <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> &amp;obs0, int n0)</td></tr>
57
58<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
59<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6f1988db4c3f602d187a6c15ec89cb1e"></a><!-- doxytag: member="bdm::PF::set_est" ref="6f1988db4c3f602d187a6c15ec89cb1e" args="(const epdf &amp;epdf0)" -->
60void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#6f1988db4c3f602d187a6c15ec89cb1e">set_est</a> (const <a class="el" href="classbdm_1_1epdf.html">epdf</a> &amp;epdf0)</td></tr>
61
62<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set posterior density by sampling from epdf0. <br></td></tr>
63<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#638946eea22d4964bf9350286bb4efd8">bayes</a> (const vec &amp;dt)</td></tr>
64
65<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Incremental Bayes rule.  <a href="#638946eea22d4964bf9350286bb4efd8"></a><br></td></tr>
66<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="78a9f6809827be1d9bfe215d03b1c6ed"></a><!-- doxytag: member="bdm::PF::__w" ref="78a9f6809827be1d9bfe215d03b1c6ed" args="()" -->
67vec *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#78a9f6809827be1d9bfe215d03b1c6ed">__w</a> ()</td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1dee3fddaf021e62d925289660a707dc"></a><!-- doxytag: member="bdm::PF::bayesB" ref="1dee3fddaf021e62d925289660a707dc" args="(const mat &amp;Dt)" -->
71virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#1dee3fddaf021e62d925289660a707dc">bayesB</a> (const mat &amp;Dt)</td></tr>
72
73<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr>
74<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="963258c4c2dd05be001003b19aceefef"></a><!-- doxytag: member="bdm::PF::_epdf" ref="963258c4c2dd05be001003b19aceefef" args="() const =0" -->
75virtual const <a class="el" href="classbdm_1_1epdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#963258c4c2dd05be001003b19aceefef">_epdf</a> () const =0</td></tr>
76
77<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a reference to the <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> representing posterior density on parameters. <br></td></tr>
78<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4ed0f8b880e606316ae800f3a011c3a6"></a><!-- doxytag: member="bdm::PF::_e" ref="4ed0f8b880e606316ae800f3a011c3a6" args="() const =0" -->
79virtual const <a class="el" href="classbdm_1_1epdf.html">epdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#4ed0f8b880e606316ae800f3a011c3a6">_e</a> () const =0</td></tr>
80
81<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classbdm_1_1epdf.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>
82<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#50257e0c1e5b5c73153ea6e716ad8ae0">logpred</a> (const vec &amp;dt) const </td></tr>
83
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0e8ebe61fb14990abe1254bd3dda5fae"></a><!-- doxytag: member="bdm::PF::logpred_m" ref="0e8ebe61fb14990abe1254bd3dda5fae" args="(const mat &amp;dt) const " -->
85vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#0e8ebe61fb14990abe1254bd3dda5fae">logpred_m</a> (const mat &amp;dt) const </td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of logpred. <br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="710e7d69c0d8791fb41a7cd4683cca2c"></a><!-- doxytag: member="bdm::PF::predictor" ref="710e7d69c0d8791fb41a7cd4683cca2c" args="(const RV &amp;rv) const " -->
89virtual <a class="el" href="classbdm_1_1epdf.html">epdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#710e7d69c0d8791fb41a7cd4683cca2c">predictor</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1BM.html#18d6db4af8ee42077741d9e3618153ca">rv</a>) const </td></tr>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructs a predictive density (marginal density on data). <br></td></tr>
92<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="40a3c891996391e3135518053a917793"></a><!-- doxytag: member="bdm::PF::_rv" ref="40a3c891996391e3135518053a917793" args="() const " -->
93const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#40a3c891996391e3135518053a917793">_rv</a> () const </td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5be65d37dedfe33a3671e7065f523a70"></a><!-- doxytag: member="bdm::PF::_ll" ref="5be65d37dedfe33a3671e7065f523a70" args="() const " -->
97double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#5be65d37dedfe33a3671e7065f523a70">_ll</a> () const </td></tr>
98
99<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
100<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="236b3abbcc93594fc97cd86d82c1a83f"></a><!-- doxytag: member="bdm::PF::set_evalll" ref="236b3abbcc93594fc97cd86d82c1a83f" args="(bool evl0)" -->
101void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#236b3abbcc93594fc97cd86d82c1a83f">set_evalll</a> (bool evl0)</td></tr>
102
103<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
104<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual <a class="el" href="classbdm_1_1BM.html">BM</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#3efb3098172f1f67564a312fe732473e">_copy_</a> (bool changerv=false)</td></tr>
105
106<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="eeafaf9b8ad75fe62ee9fd6369e3f7fe"></a><!-- doxytag: member="bdm::PF::n" ref="eeafaf9b8ad75fe62ee9fd6369e3f7fe" args="" -->
108int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#eeafaf9b8ad75fe62ee9fd6369e3f7fe">n</a></td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">number of particles; <br></td></tr>
111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dc049265b9086cad7071f98d00a2b9af"></a><!-- doxytag: member="bdm::PF::est" ref="dc049265b9086cad7071f98d00a2b9af" args="" -->
112<a class="el" href="classbdm_1_1eEmp.html">eEmp</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#dc049265b9086cad7071f98d00a2b9af">est</a></td></tr>
113
114<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">posterior density <br></td></tr>
115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f5149d5522d1095d39240c4c607f61a3"></a><!-- doxytag: member="bdm::PF::_w" ref="f5149d5522d1095d39240c4c607f61a3" args="" -->
116vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#f5149d5522d1095d39240c4c607f61a3">_w</a></td></tr>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">pointer into <code><a class="el" href="classbdm_1_1eEmp.html" title="Weighted empirical density.">eEmp</a></code> <br></td></tr>
119<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="914bd66025692c4018dbd482cb3c47c1"></a><!-- doxytag: member="bdm::PF::_samples" ref="914bd66025692c4018dbd482cb3c47c1" args="" -->
120Array&lt; vec &gt; &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#914bd66025692c4018dbd482cb3c47c1">_samples</a></td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">pointer into <code><a class="el" href="classbdm_1_1eEmp.html" title="Weighted empirical density.">eEmp</a></code> <br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cf3a1b2a407012e47ac878e3aa2fbf34"></a><!-- doxytag: member="bdm::PF::par" ref="cf3a1b2a407012e47ac878e3aa2fbf34" args="" -->
124<a class="el" href="classbdm_1_1mpdf.html">mpdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#cf3a1b2a407012e47ac878e3aa2fbf34">par</a></td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Parameter evolution model. <br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c58b8fa634272c3f48845a9020ba55aa"></a><!-- doxytag: member="bdm::PF::obs" ref="c58b8fa634272c3f48845a9020ba55aa" args="" -->
128<a class="el" href="classbdm_1_1mpdf.html">mpdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1PF.html#c58b8fa634272c3f48845a9020ba55aa">obs</a></td></tr>
129
130<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Observation model. <br></td></tr>
131<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18d6db4af8ee42077741d9e3618153ca"></a><!-- doxytag: member="bdm::PF::rv" ref="18d6db4af8ee42077741d9e3618153ca" args="" -->
132<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#18d6db4af8ee42077741d9e3618153ca">rv</a></td></tr>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Random variable of the posterior. <br></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4064b6559d962633e4372b12f4cd204a"></a><!-- doxytag: member="bdm::PF::ll" ref="4064b6559d962633e4372b12f4cd204a" args="" -->
136double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#4064b6559d962633e4372b12f4cd204a">ll</a></td></tr>
137
138<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of marginalized data likelihood. <br></td></tr>
139<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="faff0ad12556fe7dc0e2807d4fd938ee"></a><!-- doxytag: member="bdm::PF::evalll" ref="faff0ad12556fe7dc0e2807d4fd938ee" args="" -->
140bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#faff0ad12556fe7dc0e2807d4fd938ee">evalll</a></td></tr>
141
142<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">If true, the filter will compute likelihood of the data record and store it in <code>ll</code> . Set to false if you want to save computational time. <br></td></tr>
143</table>
144<hr><a name="_details"></a><h2>Detailed Description</h2>
145Trivial particle filter with proposal density equal to parameter evolution model.
146<p>
147Posterior density is represented by a weighted empirical density (<code><a class="el" href="classbdm_1_1eEmp.html" title="Weighted empirical density.">eEmp</a></code> ). <hr><h2>Member Function Documentation</h2>
148<a class="anchor" name="638946eea22d4964bf9350286bb4efd8"></a><!-- doxytag: member="bdm::PF::bayes" ref="638946eea22d4964bf9350286bb4efd8" args="(const vec &amp;dt)" -->
149<div class="memitem">
150<div class="memproto">
151      <table class="memname">
152        <tr>
153          <td class="memname">void bdm::PF::bayes           </td>
154          <td>(</td>
155          <td class="paramtype">const vec &amp;&nbsp;</td>
156          <td class="paramname"> <em>dt</em>          </td>
157          <td>&nbsp;)&nbsp;</td>
158          <td><code> [virtual]</code></td>
159        </tr>
160      </table>
161</div>
162<div class="memdoc">
163
164<p>
165Incremental Bayes rule.
166<p>
167<dl compact><dt><b>Parameters:</b></dt><dd>
168  <table border="0" cellspacing="2" cellpadding="0">
169    <tr><td valign="top"></td><td valign="top"><em>dt</em>&nbsp;</td><td>vector of input data </td></tr>
170  </table>
171</dl>
172
173<p>Implements <a class="el" href="classbdm_1_1BM.html#60b1779a577367c369a932cabd3a6188">bdm::BM</a>.</p>
174
175<p>Reimplemented in <a class="el" href="classbdm_1_1MPF.html#286d040770d08bd7ff416cea617b1b14">bdm::MPF&lt; BM_T &gt;</a>.</p>
176
[261]177<p>References <a class="el" href="libPF_8h-source.html#l00036">_samples</a>, <a class="el" href="libPF_8h-source.html#l00034">_w</a>, <a class="el" href="libPF_8h-source.html#l00032">est</a>, <a class="el" href="libBM_8h-source.html#l00250">bdm::mpdf::evallogcond()</a>, <a class="el" href="libPF_8h-source.html#l00030">n</a>, <a class="el" href="libPF_8h-source.html#l00040">obs</a>, <a class="el" href="libPF_8h-source.html#l00038">par</a>, <a class="el" href="libEF_8cpp-source.html#l00184">bdm::eEmp::resample()</a>, and <a class="el" href="libBM_8h-source.html#l00234">bdm::mpdf::samplecond()</a>.</p>
[259]178
179</div>
180</div><p>
181<a class="anchor" name="50257e0c1e5b5c73153ea6e716ad8ae0"></a><!-- doxytag: member="bdm::PF::logpred" ref="50257e0c1e5b5c73153ea6e716ad8ae0" args="(const vec &amp;dt) const " -->
182<div class="memitem">
183<div class="memproto">
184      <table class="memname">
185        <tr>
186          <td class="memname">virtual double bdm::BM::logpred           </td>
187          <td>(</td>
188          <td class="paramtype">const vec &amp;&nbsp;</td>
189          <td class="paramname"> <em>dt</em>          </td>
190          <td>&nbsp;)&nbsp;</td>
191          <td> const<code> [inline, virtual, inherited]</code></td>
192        </tr>
193      </table>
194</div>
195<div class="memdoc">
196
197<p>
198Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.
199<p>Reimplemented in <a class="el" href="classbdm_1_1ARX.html#080a7e531e3aa06694112863b15bc6a4">bdm::ARX</a>, <a class="el" href="classbdm_1_1MixEF.html#da724da464a75e07521941e430929efa">bdm::MixEF</a>, and <a class="el" href="classbdm_1_1multiBM.html#e157b607c1e3fa91d42aeea44458e2bf">bdm::multiBM</a>.</p>
200
[261]201<p>Referenced by <a class="el" href="libBM_8h-source.html#l00470">bdm::BM::logpred_m()</a>.</p>
[259]202
203</div>
204</div><p>
205<a class="anchor" name="3efb3098172f1f67564a312fe732473e"></a><!-- doxytag: member="bdm::PF::_copy_" ref="3efb3098172f1f67564a312fe732473e" args="(bool changerv=false)" -->
206<div class="memitem">
207<div class="memproto">
208      <table class="memname">
209        <tr>
210          <td class="memname">virtual <a class="el" href="classbdm_1_1BM.html">BM</a>* bdm::BM::_copy_           </td>
211          <td>(</td>
212          <td class="paramtype">bool&nbsp;</td>
213          <td class="paramname"> <em>changerv</em> = <code>false</code>          </td>
214          <td>&nbsp;)&nbsp;</td>
215          <td><code> [inline, virtual, inherited]</code></td>
216        </tr>
217      </table>
218</div>
219<div class="memdoc">
220
221<p>
222Copy function required in vectors, Arrays of <a class="el" href="classbdm_1_1BM.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="classbdm_1_1BM.html#3efb3098172f1f67564a312fe732473e">_copy_()</a>{<a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities.">BM</a> Tmp*=new Tmp(this*); return Tmp; }
223<p>Reimplemented in <a class="el" href="classbdm_1_1ARX.html#20ff2de8d862f28de7da83444d65bcdb">bdm::ARX</a>, and <a class="el" href="classbdm_1_1BMEF.html#5912dbcf28ae711e30b08c2fa766a3e6">bdm::BMEF</a>.</p>
224
225</div>
226</div><p>
227<hr>The documentation for this class was generated from the following files:<ul>
[261]228<li><a class="el" href="libPF_8h-source.html">libPF.h</a><li>libPF.cpp</ul>
[259]229</div>
[261]230<hr size="1"><address style="text-align: right;"><small>Generated on Fri Feb 6 15:29:51 2009 for mixpp by&nbsp;
[259]231<a href="http://www.doxygen.org/index.html">
232<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
233</body>
234</html>
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