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25  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1mprod.html">mprod</a>
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29<h1>bdm::mprod Class Reference</h1><!-- doxytag: class="bdm::mprod" --><!-- doxytag: inherits="bdm::compositepdf,bdm::mpdf" -->Chain rule decomposition of <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a>. 
30<a href="#_details">More...</a>
31<p>
32<code>#include &lt;<a class="el" href="emix_8h-source.html">emix.h</a>&gt;</code>
33<p>
34<div class="dynheader">
35Inheritance diagram for bdm::mprod:</div>
36<div class="dynsection">
37<p><center><img src="classbdm_1_1mprod__inherit__graph.png" border="0" usemap="#bdm_1_1mprod__inherit__map" alt="Inheritance graph"></center>
38<map name="bdm_1_1mprod__inherit__map">
39<area shape="rect" href="classbdm_1_1compositepdf.html" title="Abstract composition of pdfs, a base for specific classes this abstract class is..." alt="" coords="5,7,149,33"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="173,7,264,33"></map>
40<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
41<div class="dynheader">
42Collaboration diagram for bdm::mprod:</div>
43<div class="dynsection">
44<p><center><img src="classbdm_1_1mprod__coll__graph.png" border="0" usemap="#bdm_1_1mprod__coll__map" alt="Collaboration graph"></center>
45<map name="bdm_1_1mprod__coll__map">
46<area shape="rect" href="classbdm_1_1compositepdf.html" title="Abstract composition of pdfs, a base for specific classes this abstract class is..." alt="" coords="5,284,149,311"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="173,284,264,311"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="160,87,235,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="229,185,315,212"><area shape="rect" href="classbdm_1_1base.html" title="Root class of BDM objects." alt="" coords="201,7,289,33"></map>
47<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
48
49<p>
50<a href="classbdm_1_1mprod-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
51<tr><td></td></tr>
52<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
53<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="680c3e2d95b116c7cfb227c7f2984525"></a><!-- doxytag: member="bdm::mprod::mprod" ref="680c3e2d95b116c7cfb227c7f2984525" args="(Array&lt; mpdf * &gt; mFacs)" -->
54&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mprod.html#680c3e2d95b116c7cfb227c7f2984525">mprod</a> (Array&lt; <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> * &gt; mFacs)</td></tr>
55
56<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor from list of mFacs,. <br></td></tr>
57<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="800f21d94c919137608a2fd5c88719e2"></a><!-- doxytag: member="bdm::mprod::evallogcond" ref="800f21d94c919137608a2fd5c88719e2" args="(const vec &amp;val, const vec &amp;cond)" -->
58double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mprod.html#800f21d94c919137608a2fd5c88719e2">evallogcond</a> (const vec &amp;val, const vec &amp;cond)</td></tr>
59
60<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Shortcut for conditioning and evaluation of the internal <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a>. In some cases, this operation can be implemented efficiently. <br></td></tr>
61<tr><td class="memItemLeft" nowrap align="right" valign="top">vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mprod.html#1a37c2aaba8bde7fce5351c39b6e1168">samplecond</a> (const vec &amp;cond, double &amp;ll)</td></tr>
62
63<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a sample from the density conditioned on <code>cond</code>, <img class="formulaInl" alt="$x \sim epdf(rv|cond)$" src="form_10.png">.  <a href="#1a37c2aaba8bde7fce5351c39b6e1168"></a><br></td></tr>
64<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b493b5565dc6a5617927421d32697cc6"></a><!-- doxytag: member="bdm::mprod::samplecond" ref="b493b5565dc6a5617927421d32697cc6" args="(const vec &amp;cond, vec &amp;ll, int N)" -->
65mat&nbsp;</td><td class="memItemRight" valign="bottom"><b>samplecond</b> (const vec &amp;cond, vec &amp;ll, int N)</td></tr>
66
67<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1compositepdf.html#c73d39acc4378eee6a63155c3517d3c9">getrv</a> (bool checkoverlap=false)</td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">find common rv, flag  <a href="#c73d39acc4378eee6a63155c3517d3c9"></a><br></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c71fc2c51f49d797e61f479f543c75ce"></a><!-- doxytag: member="bdm::mprod::setrvc" ref="c71fc2c51f49d797e61f479f543c75ce" args="(const RV &amp;rv, RV &amp;rvc)" -->
71void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1compositepdf.html#c71fc2c51f49d797e61f479f543c75ce">setrvc</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1mpdf.html#9bcfb45435d30983f436d41c298cbb51">rv</a>, <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1mpdf.html#5a5f08950daa08b85b01ddf4e1c36288">rvc</a>)</td></tr>
72
73<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">common rvc of all mpdfs is written to rvc <br></td></tr>
74<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#ee26963a637b2ea1fb1933652981e652">samplecond_m</a> (const vec &amp;cond, vec &amp;ll, int N)</td></tr>
75
76<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns.  <a href="#ee26963a637b2ea1fb1933652981e652"></a><br></td></tr>
77<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="db94784a9aacf74c65c5a014f6743530"></a><!-- doxytag: member="bdm::mprod::condition" ref="db94784a9aacf74c65c5a014f6743530" args="(const vec &amp;cond)" -->
78virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#db94784a9aacf74c65c5a014f6743530">condition</a> (const vec &amp;cond)</td></tr>
79
80<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Update <code>ep</code> so that it represents this <a class="el" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies.">mpdf</a> conditioned on <code>rvc</code> = cond. <br></td></tr>
81<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0b0ed1ed663071bb7cf4a1349eb94fcb"></a><!-- doxytag: member="bdm::mprod::evallogcond_m" ref="0b0ed1ed663071bb7cf4a1349eb94fcb" args="(const mat &amp;Dt, const vec &amp;cond)" -->
82virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#0b0ed1ed663071bb7cf4a1349eb94fcb">evallogcond_m</a> (const mat &amp;Dt, const vec &amp;cond)</td></tr>
83
84<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of evallogcond. <br></td></tr>
85<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b3aba7311038bf990d706a64cab60cf8"></a><!-- doxytag: member="bdm::mprod::_rvc" ref="b3aba7311038bf990d706a64cab60cf8" args="() const " -->
86<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#b3aba7311038bf990d706a64cab60cf8">_rvc</a> () const </td></tr>
87
88<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
89<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="222d5280e309c5a053ba73841e98c151"></a><!-- doxytag: member="bdm::mprod::_rv" ref="222d5280e309c5a053ba73841e98c151" args="() const " -->
90<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#222d5280e309c5a053ba73841e98c151">_rv</a> () const </td></tr>
91
92<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
93<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1892fe3933488942253679f068e9e7f6"></a><!-- doxytag: member="bdm::mprod::_epdf" ref="1892fe3933488942253679f068e9e7f6" args="()" -->
94<a class="el" href="classbdm_1_1epdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#1892fe3933488942253679f068e9e7f6">_epdf</a> ()</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="05e843fd11c410a99dad2b88c55aca80"></a><!-- doxytag: member="bdm::mprod::_e" ref="05e843fd11c410a99dad2b88c55aca80" args="()" -->
98<a class="el" href="classbdm_1_1epdf.html">epdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#05e843fd11c410a99dad2b88c55aca80">_e</a> ()</td></tr>
99
100<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
101<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="eca722ed1b219727c6c0f8cbc6bf1e51"></a><!-- doxytag: member="bdm::mprod::epdfs" ref="eca722ed1b219727c6c0f8cbc6bf1e51" args="" -->
103Array&lt; <a class="el" href="classbdm_1_1epdf.html">epdf</a> * &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mprod.html#eca722ed1b219727c6c0f8cbc6bf1e51">epdfs</a></td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">pointers to epdfs - shortcut to <a class="el" href="classbdm_1_1compositepdf.html#23faf2debc4dde10836393b8c665914a" title="Elements of composition.">mpdfs()</a>.<a class="el" href="classbdm_1_1mpdf.html#1892fe3933488942253679f068e9e7f6" title="access function">_epdf()</a> <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="acf679b3b1d48629c5a042d9ac0d973f"></a><!-- doxytag: member="bdm::mprod::dls" ref="acf679b3b1d48629c5a042d9ac0d973f" args="" -->
107Array&lt; <a class="el" href="classbdm_1_1datalink__m2m.html">datalink_m2m</a> * &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mprod.html#acf679b3b1d48629c5a042d9ac0d973f">dls</a></td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Data link for each mpdfs. <br></td></tr>
110<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7ca3cd8ed92a7154f5b9ff13b1e9d52a"></a><!-- doxytag: member="bdm::mprod::n" ref="7ca3cd8ed92a7154f5b9ff13b1e9d52a" args="" -->
111int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1compositepdf.html#7ca3cd8ed92a7154f5b9ff13b1e9d52a">n</a></td></tr>
112
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Number of mpdfs in the composite. <br></td></tr>
114<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="23faf2debc4dde10836393b8c665914a"></a><!-- doxytag: member="bdm::mprod::mpdfs" ref="23faf2debc4dde10836393b8c665914a" args="" -->
115Array&lt; <a class="el" href="classbdm_1_1mpdf.html">mpdf</a> * &gt;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1compositepdf.html#23faf2debc4dde10836393b8c665914a">mpdfs</a></td></tr>
116
117<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Elements of composition. <br></td></tr>
118<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bcfb45435d30983f436d41c298cbb51"></a><!-- doxytag: member="bdm::mprod::rv" ref="9bcfb45435d30983f436d41c298cbb51" args="" -->
119<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#9bcfb45435d30983f436d41c298cbb51">rv</a></td></tr>
120
121<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">modeled random variable <br></td></tr>
122<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5a5f08950daa08b85b01ddf4e1c36288"></a><!-- doxytag: member="bdm::mprod::rvc" ref="5a5f08950daa08b85b01ddf4e1c36288" args="" -->
123<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#5a5f08950daa08b85b01ddf4e1c36288">rvc</a></td></tr>
124
125<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">random variable in condition <br></td></tr>
126<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5eea43c56d38e4441bfb30270db949c0"></a><!-- doxytag: member="bdm::mprod::ep" ref="5eea43c56d38e4441bfb30270db949c0" args="" -->
127<a class="el" href="classbdm_1_1epdf.html">epdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#5eea43c56d38e4441bfb30270db949c0">ep</a></td></tr>
128
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">pointer to internal <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> <br></td></tr>
130</table>
131<hr><a name="_details"></a><h2>Detailed Description</h2>
132Chain rule decomposition of <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a>.
133<p>
134Probability density in the form of Chain-rule decomposition: \[ f(x_1,x_2,x_3) = f(x_1|x_2,x_3)f(x_2,x_3)f(x_3) \] Note that <hr><h2>Member Function Documentation</h2>
135<a class="anchor" name="1a37c2aaba8bde7fce5351c39b6e1168"></a><!-- doxytag: member="bdm::mprod::samplecond" ref="1a37c2aaba8bde7fce5351c39b6e1168" args="(const vec &amp;cond, double &amp;ll)" -->
136<div class="memitem">
137<div class="memproto">
138      <table class="memname">
139        <tr>
140          <td class="memname">vec bdm::mprod::samplecond           </td>
141          <td>(</td>
142          <td class="paramtype">const vec &amp;&nbsp;</td>
143          <td class="paramname"> <em>cond</em>, </td>
144        </tr>
145        <tr>
146          <td class="paramkey"></td>
147          <td></td>
148          <td class="paramtype">double &amp;&nbsp;</td>
149          <td class="paramname"> <em>ll</em></td><td>&nbsp;</td>
150        </tr>
151        <tr>
152          <td></td>
153          <td>)</td>
154          <td></td><td></td><td><code> [inline, virtual]</code></td>
155        </tr>
156      </table>
157</div>
158<div class="memdoc">
159
160<p>
161Returns a sample from the density conditioned on <code>cond</code>, <img class="formulaInl" alt="$x \sim epdf(rv|cond)$" src="form_10.png">.
162<p>
163<dl compact><dt><b>Parameters:</b></dt><dd>
164  <table border="0" cellspacing="2" cellpadding="0">
165    <tr><td valign="top"></td><td valign="top"><em>cond</em>&nbsp;</td><td>is numeric value of <code>rv</code> </td></tr>
166    <tr><td valign="top"></td><td valign="top"><em>ll</em>&nbsp;</td><td>is a return value of log-likelihood of the sample. </td></tr>
167  </table>
168</dl>
169
170<p>Reimplemented from <a class="el" href="classbdm_1_1mpdf.html#e4848a428d8ef0549c6e4a9ed386d9f2">bdm::mpdf</a>.</p>
171
172<p>References <a class="el" href="libBM_8h-source.html#l00081">bdm::RV::count()</a>, <a class="el" href="emix_8h-source.html#l00166">dls</a>, <a class="el" href="emix_8h-source.html#l00164">epdfs</a>, <a class="el" href="libBM_8h-source.html#l00367">bdm::compositepdf::mpdfs</a>, <a class="el" href="libBM_8h-source.html#l00365">bdm::compositepdf::n</a>, and <a class="el" href="libBM_8h-source.html#l00222">bdm::mpdf::rv</a>.</p>
173
174</div>
175</div><p>
176<a class="anchor" name="c73d39acc4378eee6a63155c3517d3c9"></a><!-- doxytag: member="bdm::mprod::getrv" ref="c73d39acc4378eee6a63155c3517d3c9" args="(bool checkoverlap=false)" -->
177<div class="memitem">
178<div class="memproto">
179      <table class="memname">
180        <tr>
181          <td class="memname"><a class="el" href="classbdm_1_1RV.html">RV</a> bdm::compositepdf::getrv           </td>
182          <td>(</td>
183          <td class="paramtype">bool&nbsp;</td>
184          <td class="paramname"> <em>checkoverlap</em> = <code>false</code>          </td>
185          <td>&nbsp;)&nbsp;</td>
186          <td><code> [inherited]</code></td>
187        </tr>
188      </table>
189</div>
190<div class="memdoc">
191
192<p>
193find common rv, flag
194<p>
195<dl compact><dt><b>Parameters:</b></dt><dd>
196  <table border="0" cellspacing="2" cellpadding="0">
197    <tr><td valign="top"></td><td valign="top"><em>checkoverlap</em>&nbsp;</td><td>modifies whether overlaps are acceptable </td></tr>
198  </table>
199</dl>
200
201<p>References <a class="el" href="libBM_8cpp-source.html#l00053">bdm::RV::add()</a>, <a class="el" href="libBM_8h-source.html#l00367">bdm::compositepdf::mpdfs</a>, and <a class="el" href="libBM_8h-source.html#l00365">bdm::compositepdf::n</a>.</p>
202
203</div>
204</div><p>
205<a class="anchor" name="ee26963a637b2ea1fb1933652981e652"></a><!-- doxytag: member="bdm::mprod::samplecond_m" ref="ee26963a637b2ea1fb1933652981e652" args="(const vec &amp;cond, vec &amp;ll, int N)" -->
206<div class="memitem">
207<div class="memproto">
208      <table class="memname">
209        <tr>
210          <td class="memname">virtual mat bdm::mpdf::samplecond_m           </td>
211          <td>(</td>
212          <td class="paramtype">const vec &amp;&nbsp;</td>
213          <td class="paramname"> <em>cond</em>, </td>
214        </tr>
215        <tr>
216          <td class="paramkey"></td>
217          <td></td>
218          <td class="paramtype">vec &amp;&nbsp;</td>
219          <td class="paramname"> <em>ll</em>, </td>
220        </tr>
221        <tr>
222          <td class="paramkey"></td>
223          <td></td>
224          <td class="paramtype">int&nbsp;</td>
225          <td class="paramname"> <em>N</em></td><td>&nbsp;</td>
226        </tr>
227        <tr>
228          <td></td>
229          <td>)</td>
230          <td></td><td></td><td><code> [inline, virtual, inherited]</code></td>
231        </tr>
232      </table>
233</div>
234<div class="memdoc">
235
236<p>
237Returns.
238<p>
239<dl compact><dt><b>Parameters:</b></dt><dd>
240  <table border="0" cellspacing="2" cellpadding="0">
241    <tr><td valign="top"></td><td valign="top"><em>N</em>&nbsp;</td><td>samples from the density conditioned on <code>cond</code>, <img class="formulaInl" alt="$x \sim epdf(rv|cond)$" src="form_10.png">. </td></tr>
242    <tr><td valign="top"></td><td valign="top"><em>cond</em>&nbsp;</td><td>is numeric value of <code>rv</code> </td></tr>
243    <tr><td valign="top"></td><td valign="top"><em>ll</em>&nbsp;</td><td>is a return value of log-likelihood of the sample. </td></tr>
244  </table>
245</dl>
246
247<p>References <a class="el" href="libBM_8h-source.html#l00243">bdm::mpdf::condition()</a>, <a class="el" href="libBM_8h-source.html#l00081">bdm::RV::count()</a>, <a class="el" href="libBM_8h-source.html#l00226">bdm::mpdf::ep</a>, <a class="el" href="classbdm_1_1epdf.html#a8e39e2ff5e5cf5471bc159530d3b2d3">bdm::epdf::evallog()</a>, <a class="el" href="libBM_8h-source.html#l00222">bdm::mpdf::rv</a>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
248
249</div>
250</div><p>
251<hr>The documentation for this class was generated from the following file:<ul>
252<li>work/git/mixpp/bdm/stat/<a class="el" href="emix_8h-source.html">emix.h</a></ul>
253</div>
254<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jan 27 16:31:07 2009 for mixpp by&nbsp;
255<a href="http://www.doxygen.org/index.html">
256<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
257</body>
258</html>
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