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66  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1eDirich.html">eDirich</a>
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69<div class="contents">
70<h1>bdm::eDirich Class Reference</h1><!-- doxytag: class="bdm::eDirich" --><!-- doxytag: inherits="bdm::eEF" -->Dirichlet posterior density. 
71<a href="#_details">More...</a>
72<p>
73<code>#include &lt;<a class="el" href="exp__family_8h_source.html">exp_family.h</a>&gt;</code>
74<p>
75
76<p>
77<a href="classbdm_1_1eDirich-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
78<tr><td></td></tr>
79<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
80<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3290613d31d58daa8a45a54b003871fc"></a><!-- doxytag: member="bdm::eDirich::sample" ref="3290613d31d58daa8a45a54b003871fc" args="() const " -->
81vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#3290613d31d58daa8a45a54b003871fc">sample</a> () const </td></tr>
82
83<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">using sampling procedure from wikipedia <br></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cb343355ec791298bb5a3404cd482fb6"></a><!-- doxytag: member="bdm::eDirich::mean" ref="cb343355ec791298bb5a3404cd482fb6" args="() const " -->
85vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#cb343355ec791298bb5a3404cd482fb6">mean</a> () const </td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">return expected value <br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="43c547a2507e233706f92712d8c2aacc"></a><!-- doxytag: member="bdm::eDirich::variance" ref="43c547a2507e233706f92712d8c2aacc" args="() const " -->
89vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#43c547a2507e233706f92712d8c2aacc">variance</a> () const </td></tr>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">return expected variance (not covariance!) <br></td></tr>
92<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e09a24938e80c3d94b0ee842d1552318"></a><!-- doxytag: member="bdm::eDirich::evallog_nn" ref="e09a24938e80c3d94b0ee842d1552318" args="(const vec &amp;val) const " -->
93double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#e09a24938e80c3d94b0ee842d1552318">evallog_nn</a> (const vec &amp;val) const </td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">In this instance, val is ... <br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="279a99f6266c82fe2273e83841f19eb2"></a><!-- doxytag: member="bdm::eDirich::lognc" ref="279a99f6266c82fe2273e83841f19eb2" args="() const " -->
97double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#279a99f6266c82fe2273e83841f19eb2">lognc</a> () const </td></tr>
98
99<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">logarithm of the normalizing constant, <img class="formulaInl" alt="$\mathcal{I}$" src="form_97.png"> <br></td></tr>
100<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="175e0add26d2105c28d8121eefb9e324"></a><!-- doxytag: member="bdm::eDirich::_beta" ref="175e0add26d2105c28d8121eefb9e324" args="()" -->
101vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#175e0add26d2105c28d8121eefb9e324">_beta</a> ()</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">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#aef2c328917dd80dce689d3d11d09567">from_setting</a> (const Setting &amp;set)</td></tr>
105
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3ee16ce701b850e1c5bdb7005c326a57"></a><!-- doxytag: member="bdm::eDirich::validate" ref="3ee16ce701b850e1c5bdb7005c326a57" args="()" -->
107void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#3ee16ce701b850e1c5bdb7005c326a57">validate</a> ()</td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method TODO. <br></td></tr>
110<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a36d06ecdd6f4c79dc122510eaccc692"></a><!-- doxytag: member="bdm::eDirich::evallog" ref="a36d06ecdd6f4c79dc122510eaccc692" args="(const vec &amp;val) const " -->
111virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eEF.html#a36d06ecdd6f4c79dc122510eaccc692">evallog</a> (const vec &amp;val) const </td></tr>
112
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate normalized log-probability. <br></td></tr>
114<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6886c60b6b690e503913240db5de0c6f"></a><!-- doxytag: member="bdm::eDirich::evallog_m" ref="6886c60b6b690e503913240db5de0c6f" args="(const mat &amp;Val) const " -->
115virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eEF.html#6886c60b6b690e503913240db5de0c6f">evallog_m</a> (const mat &amp;Val) const </td></tr>
116
117<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate normalized log-probability for many samples. <br></td></tr>
118<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d793f4fd6d0dcec5f16bff0ae45fc7d5"></a><!-- doxytag: member="bdm::eDirich::evallog_m" ref="d793f4fd6d0dcec5f16bff0ae45fc7d5" args="(const Array&lt; vec &gt; &amp;Val) const " -->
119virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eEF.html#d793f4fd6d0dcec5f16bff0ae45fc7d5">evallog_m</a> (const Array&lt; vec &gt; &amp;Val) const </td></tr>
120
121<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Evaluate normalized log-probability for many samples. <br></td></tr>
122<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="cf38af29e8e3d650c640509a52396053"></a><!-- doxytag: member="bdm::eDirich::pow" ref="cf38af29e8e3d650c640509a52396053" args="(double p)" -->
123virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eEF.html#cf38af29e8e3d650c640509a52396053">pow</a> (double p)</td></tr>
124
125<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Power of the density, used e.g. to flatten the density. <br></td></tr>
126<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af0e6941ba5919cae1bc530e2181b109"></a><!-- doxytag: member="bdm::eDirich::to_string" ref="af0e6941ba5919cae1bc530e2181b109" args="()" -->
127virtual string&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#af0e6941ba5919cae1bc530e2181b109">to_string</a> ()</td></tr>
128
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method returns a basic info about the current instance. <br></td></tr>
130<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="67d954d255ede776eade7334d4895790"></a><!-- doxytag: member="bdm::eDirich::to_setting" ref="67d954d255ede776eade7334d4895790" args="(Setting &amp;set) const " -->
131virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#67d954d255ede776eade7334d4895790">to_setting</a> (Setting &amp;set) const </td></tr>
132
133<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method save all the instance properties into the Setting structure. <br></td></tr>
134<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d5137485050ca8d67549b514896f602d"></a><!-- doxytag: member="bdm::eDirich::eDirich" ref="d5137485050ca8d67549b514896f602d" args="()" -->
136&nbsp;</td><td class="memItemRight" valign="bottom"><b>eDirich</b> ()</td></tr>
137
138<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="31cc8bf709552c9e7286ac16b27c8e2c"></a><!-- doxytag: member="bdm::eDirich::eDirich" ref="31cc8bf709552c9e7286ac16b27c8e2c" args="(const eDirich &amp;D0)" -->
139&nbsp;</td><td class="memItemRight" valign="bottom"><b>eDirich</b> (const <a class="el" href="classbdm_1_1eDirich.html">eDirich</a> &amp;D0)</td></tr>
140
141<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a961f5846c8db5b2d20e7db483453e0c"></a><!-- doxytag: member="bdm::eDirich::eDirich" ref="a961f5846c8db5b2d20e7db483453e0c" args="(const vec &amp;beta0)" -->
142&nbsp;</td><td class="memItemRight" valign="bottom"><b>eDirich</b> (const vec &amp;beta0)</td></tr>
143
144<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a06af2376976a33e1eceaed7e8da75a5"></a><!-- doxytag: member="bdm::eDirich::set_parameters" ref="a06af2376976a33e1eceaed7e8da75a5" args="(const vec &amp;beta0)" -->
145void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (const vec &amp;beta0)</td></tr>
146
147<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr>
148<tr><td colspan="2"><div class="groupText">Construction of each <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> should support two types of constructors: <ul>
149<li>empty constructor, </li>
150<li>copy constructor,</li>
151</ul>
152The following constructors should be supported for convenience: <ul>
153<li>constructor followed by calling <code>set_parameters()</code> </li>
154<li>constructor accepting random variables calling <code><a class="el" href="classbdm_1_1epdf.html#f423e28448dbb69ef4905295ec8de8ff" title="Name its rv.">set_rv()</a></code> </li>
155</ul>
156All internal data structures are constructed as empty. Their values (including sizes) will be set by method <code>set_parameters()</code>. This way references can be initialized in constructors. <br><br></div></td></tr>
157<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="840de94aa33cf4f2ebd2427f45a165d8"></a><!-- doxytag: member="bdm::eDirich::set_parameters" ref="840de94aa33cf4f2ebd2427f45a165d8" args="(int dim0)" -->
158void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (int dim0)</td></tr>
159
160<tr><td colspan="2"><div class="groupHeader">Matematical Operations</div></td></tr>
161<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b4cf45fd83cc7573ede9fe1215256058"></a><!-- doxytag: member="bdm::eDirich::sample_m" ref="b4cf45fd83cc7573ede9fe1215256058" args="(int N) const " -->
162virtual 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>
163
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns N samples, <img class="formulaInl" alt="$ [x_1 , x_2 , \ldots \ $" src="form_14.png"> from density <img class="formulaInl" alt="$ f_x(rv)$" src="form_15.png">. <br></td></tr>
165<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1499d35b79bce0cfa64fc5cafb9c03b2"></a><!-- doxytag: member="bdm::eDirich::condition" ref="1499d35b79bce0cfa64fc5cafb9c03b2" args="(const RV &amp;rv) const " -->
166virtual <a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>&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_1epdf.html#1499d35b79bce0cfa64fc5cafb9c03b2">condition</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1epdf.html#62c5b8ff71d9ebe6cd58d3c342eb1dc8">rv</a>) const </td></tr>
167
168<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return conditional density on the given <a class="el" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables.">RV</a>, the remaining rvs will be in conditioning. <br></td></tr>
169<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a84b05f5293cab2aeb4e07faffa60906"></a><!-- doxytag: member="bdm::eDirich::marginal" ref="a84b05f5293cab2aeb4e07faffa60906" args="(const RV &amp;rv) const " -->
170virtual <a class="el" href="classbdm_1_1shared__ptr.html">shared_ptr</a>&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_1epdf.html#a84b05f5293cab2aeb4e07faffa60906">marginal</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1epdf.html#62c5b8ff71d9ebe6cd58d3c342eb1dc8">rv</a>) const </td></tr>
171
172<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>
173<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0a7705e80601957f7226d333a0a6d539"></a><!-- doxytag: member="bdm::eDirich::qbounds" ref="0a7705e80601957f7226d333a0a6d539" args="(vec &amp;lb, vec &amp;ub, double percentage=0.95) const " -->
174virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#0a7705e80601957f7226d333a0a6d539">qbounds</a> (vec &amp;lb, vec &amp;ub, double percentage=0.95) const </td></tr>
175
176<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Lower and upper bounds of <code>percentage</code> % quantile, returns mean-2*sigma as default. <br></td></tr>
177<tr><td colspan="2"><div class="groupHeader">Connection to other classes</div></td></tr>
178<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>
179<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f423e28448dbb69ef4905295ec8de8ff"></a><!-- doxytag: member="bdm::eDirich::set_rv" ref="f423e28448dbb69ef4905295ec8de8ff" args="(const RV &amp;rv0)" -->
180void&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>
181
182<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Name its rv. <br></td></tr>
183<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c4b863ff84c7a4882fb3ad18556027f9"></a><!-- doxytag: member="bdm::eDirich::isnamed" ref="c4b863ff84c7a4882fb3ad18556027f9" args="() const " -->
184bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#c4b863ff84c7a4882fb3ad18556027f9">isnamed</a> () const </td></tr>
185
186<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">True if rv is assigned. <br></td></tr>
187<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4ab378d5e004c3ff3e2d4e64f7bba21"></a><!-- doxytag: member="bdm::eDirich::_rv" ref="a4ab378d5e004c3ff3e2d4e64f7bba21" args="() const " -->
188const <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>
189
190<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return name (fails when isnamed is false). <br></td></tr>
191<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr>
192<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7083a65f7b7a0d0d13b2c516bd2ec29c"></a><!-- doxytag: member="bdm::eDirich::dimension" ref="7083a65f7b7a0d0d13b2c516bd2ec29c" args="() const " -->
193int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#7083a65f7b7a0d0d13b2c516bd2ec29c">dimension</a> () const </td></tr>
194
195<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Size of the random variable. <br></td></tr>
196<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
197<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f25886a49b4667af61245de81c83b5d2"></a><!-- doxytag: member="bdm::eDirich::beta" ref="f25886a49b4667af61245de81c83b5d2" args="" -->
198vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eDirich.html#f25886a49b4667af61245de81c83b5d2">beta</a></td></tr>
199
200<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">sufficient statistics <br></td></tr>
201<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="16adac20ec7fe07e1ea0b27d917788ce"></a><!-- doxytag: member="bdm::eDirich::dim" ref="16adac20ec7fe07e1ea0b27d917788ce" args="" -->
202int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#16adac20ec7fe07e1ea0b27d917788ce">dim</a></td></tr>
203
204<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the random variable <br></td></tr>
205<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62c5b8ff71d9ebe6cd58d3c342eb1dc8"></a><!-- doxytag: member="bdm::eDirich::rv" ref="62c5b8ff71d9ebe6cd58d3c342eb1dc8" args="" -->
206<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>
207
208<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Description of the random variable. <br></td></tr>
209</table>
210<hr><a name="_details"></a><h2>Detailed Description</h2>
211Dirichlet posterior density.
212<p>
213Continuous Dirichlet density of <img class="formulaInl" alt="$n$" src="form_76.png">-dimensional variable <img class="formulaInl" alt="$x$" src="form_1.png"> <p class="formulaDsp">
214<img class="formulaDsp" alt="\[ f(x|\beta) = \frac{\Gamma[\gamma]}{\prod_{i=1}^{n}\Gamma(\beta_i)} \prod_{i=1}^{n}x_i^{\beta_i-1} \]" src="form_77.png">
215<p>
216 where <img class="formulaInl" alt="$\gamma=\sum_i \beta_i$" src="form_78.png">. <hr><h2>Member Function Documentation</h2>
217<a class="anchor" name="aef2c328917dd80dce689d3d11d09567"></a><!-- doxytag: member="bdm::eDirich::from_setting" ref="aef2c328917dd80dce689d3d11d09567" args="(const Setting &amp;set)" -->
218<div class="memitem">
219<div class="memproto">
220      <table class="memname">
221        <tr>
222          <td class="memname">void bdm::eDirich::from_setting           </td>
223          <td>(</td>
224          <td class="paramtype">const Setting &amp;&nbsp;</td>
225          <td class="paramname"> <em>set</em>          </td>
226          <td>&nbsp;)&nbsp;</td>
227          <td><code> [inline, virtual]</code></td>
228        </tr>
229      </table>
230</div>
231<div class="memdoc">
232
233<p>
234configuration structure <div class="fragment"><pre class="fragment">                <span class="keyword">class </span>= 'eDirich';   
235                <a class="code" href="classbdm_1_1eDirich.html#f25886a49b4667af61245de81c83b5d2" title="sufficient statistics">beta</a>  = [];           <span class="comment">//parametr beta</span>
236</pre></div> 
237<p>Reimplemented from <a class="el" href="classbdm_1_1epdf.html#fa9efc98a065b31c630fe18cc418f725">bdm::epdf</a>.</p>
238
239<p>References <a class="el" href="exp__family_8h_source.html#l00285">beta</a>, <a class="el" href="user__info_8h_source.html#l00451">bdm::UI::get()</a>, and <a class="el" href="exp__family_8h_source.html#l00340">validate()</a>.</p>
240
241</div>
242</div><p>
243<hr>The documentation for this class was generated from the following file:<ul>
244<li><a class="el" href="exp__family_8h_source.html">exp_family.h</a></ul>
245</div>
246<hr size="1"><address style="text-align: right;"><small>Generated on Wed Oct 7 17:34:48 2009 for mixpp by&nbsp;
247<a href="http://www.doxygen.org/index.html">
248<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.9 </small></address>
249</body>
250</html>
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