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66  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1eiWishartCh.html">eiWishartCh</a>
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70<h1>bdm::eiWishartCh Class Reference</h1><!-- doxytag: class="bdm::eiWishartCh" --><!-- doxytag: inherits="bdm::epdf" -->Inverse Wishart on Choleski decomposition. 
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_1eiWishartCh-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="f463caed9d22d9949f3ee67614e7dcd3"></a><!-- doxytag: member="bdm::eiWishartCh::set_parameters" ref="f463caed9d22d9949f3ee67614e7dcd3" args="(const mat &amp;Y0, const double delta0)" -->
81void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#f463caed9d22d9949f3ee67614e7dcd3">set_parameters</a> (const mat &amp;Y0, const double delta0)</td></tr>
82
83<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">constructor function <br></td></tr>
84<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2f668192cc9c2e3a5b7e608164685a3e"></a><!-- doxytag: member="bdm::eiWishartCh::sample" ref="2f668192cc9c2e3a5b7e608164685a3e" args="() const " -->
85vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#2f668192cc9c2e3a5b7e608164685a3e">sample</a> () const </td></tr>
86
87<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a sample, <img class="formulaInl" alt="$ x $" src="form_3.png"> from density <img class="formulaInl" alt="$ f_x()$" src="form_13.png">. <br></td></tr>
88<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d9947933dfc94546cbd6a81f95ec5af5"></a><!-- doxytag: member="bdm::eiWishartCh::_setY" ref="d9947933dfc94546cbd6a81f95ec5af5" args="(const vec &amp;y0)" -->
89void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#d9947933dfc94546cbd6a81f95ec5af5">_setY</a> (const vec &amp;y0)</td></tr>
90
91<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
92<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a6ddbd815b8b666dd542e97f009f89bb"></a><!-- doxytag: member="bdm::eiWishartCh::evallog" ref="a6ddbd815b8b666dd542e97f009f89bb" args="(const vec &amp;val) const " -->
93virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#a6ddbd815b8b666dd542e97f009f89bb">evallog</a> (const vec &amp;val) const </td></tr>
94
95<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Compute log-probability of argument <code>val</code> In case the argument is out of suport return -Infinity. <br></td></tr>
96<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#fa9efc98a065b31c630fe18cc418f725">from_setting</a> (const Setting &amp;set)</td></tr>
97
98<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Load from structure with elements:.  <a href="#fa9efc98a065b31c630fe18cc418f725"></a><br></td></tr>
99<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af0e6941ba5919cae1bc530e2181b109"></a><!-- doxytag: member="bdm::eiWishartCh::to_string" ref="af0e6941ba5919cae1bc530e2181b109" args="()" -->
100virtual string&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#af0e6941ba5919cae1bc530e2181b109">to_string</a> ()</td></tr>
101
102<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method returns a basic info about the current instance. <br></td></tr>
103<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="67d954d255ede776eade7334d4895790"></a><!-- doxytag: member="bdm::eiWishartCh::to_setting" ref="67d954d255ede776eade7334d4895790" args="(Setting &amp;set) const " -->
104virtual 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>
105
106<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method save all the instance properties into the Setting structure. <br></td></tr>
107<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1c314bd6d6dacb8ba78ea5eb88fd9516"></a><!-- doxytag: member="bdm::eiWishartCh::validate" ref="1c314bd6d6dacb8ba78ea5eb88fd9516" args="()" -->
108virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#1c314bd6d6dacb8ba78ea5eb88fd9516">validate</a> ()</td></tr>
109
110<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method TODO. <br></td></tr>
111<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr>
112<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>
113<li>empty constructor, </li>
114<li>copy constructor,</li>
115</ul>
116The following constructors should be supported for convenience: <ul>
117<li>constructor followed by calling <code><a class="el" href="classbdm_1_1eiWishartCh.html#f463caed9d22d9949f3ee67614e7dcd3" title="constructor function">set_parameters()</a></code> </li>
118<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>
119</ul>
120All internal data structures are constructed as empty. Their values (including sizes) will be set by method <code><a class="el" href="classbdm_1_1eiWishartCh.html#f463caed9d22d9949f3ee67614e7dcd3" title="constructor function">set_parameters()</a></code>. This way references can be initialized in constructors. <br><br></div></td></tr>
121<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="840de94aa33cf4f2ebd2427f45a165d8"></a><!-- doxytag: member="bdm::eiWishartCh::set_parameters" ref="840de94aa33cf4f2ebd2427f45a165d8" args="(int dim0)" -->
122void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (int dim0)</td></tr>
123
124<tr><td colspan="2"><div class="groupHeader">Matematical Operations</div></td></tr>
125<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b4cf45fd83cc7573ede9fe1215256058"></a><!-- doxytag: member="bdm::eiWishartCh::sample_m" ref="b4cf45fd83cc7573ede9fe1215256058" args="(int N) const " -->
126virtual 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>
127
128<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>
129<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d08b68a5abd461f1b6519597e344caf8"></a><!-- doxytag: member="bdm::eiWishartCh::evallog_m" ref="d08b68a5abd461f1b6519597e344caf8" args="(const mat &amp;Val) const " -->
130virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#d08b68a5abd461f1b6519597e344caf8">evallog_m</a> (const mat &amp;Val) const </td></tr>
131
132<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Compute log-probability of multiple values argument <code>val</code>. <br></td></tr>
133<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bc02dae61584138443baf6b1cbc1ac9"></a><!-- doxytag: member="bdm::eiWishartCh::evallog_m" ref="9bc02dae61584138443baf6b1cbc1ac9" args="(const Array&lt; vec &gt; &amp;Avec) const " -->
134virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#9bc02dae61584138443baf6b1cbc1ac9">evallog_m</a> (const Array&lt; vec &gt; &amp;Avec) const </td></tr>
135
136<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Compute log-probability of multiple values argument <code>val</code>. <br></td></tr>
137<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1499d35b79bce0cfa64fc5cafb9c03b2"></a><!-- doxytag: member="bdm::eiWishartCh::condition" ref="1499d35b79bce0cfa64fc5cafb9c03b2" args="(const RV &amp;rv) const " -->
138virtual <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>
139
140<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>
141<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a84b05f5293cab2aeb4e07faffa60906"></a><!-- doxytag: member="bdm::eiWishartCh::marginal" ref="a84b05f5293cab2aeb4e07faffa60906" args="(const RV &amp;rv) const " -->
142virtual <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>
143
144<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>
145<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0c8d13d788094605b3cdab20a6e22b75"></a><!-- doxytag: member="bdm::eiWishartCh::mean" ref="0c8d13d788094605b3cdab20a6e22b75" args="() const " -->
146virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#0c8d13d788094605b3cdab20a6e22b75">mean</a> () const </td></tr>
147
148<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">return expected value <br></td></tr>
149<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="4543d40ccfc5d549b0c831a57a3ed84c"></a><!-- doxytag: member="bdm::eiWishartCh::variance" ref="4543d40ccfc5d549b0c831a57a3ed84c" args="() const " -->
150virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#4543d40ccfc5d549b0c831a57a3ed84c">variance</a> () const </td></tr>
151
152<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">return expected variance (not covariance!) <br></td></tr>
153<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0a7705e80601957f7226d333a0a6d539"></a><!-- doxytag: member="bdm::eiWishartCh::qbounds" ref="0a7705e80601957f7226d333a0a6d539" args="(vec &amp;lb, vec &amp;ub, double percentage=0.95) const " -->
154virtual 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>
155
156<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>
157<tr><td colspan="2"><div class="groupHeader">Connection to other classes</div></td></tr>
158<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>
159<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f423e28448dbb69ef4905295ec8de8ff"></a><!-- doxytag: member="bdm::eiWishartCh::set_rv" ref="f423e28448dbb69ef4905295ec8de8ff" args="(const RV &amp;rv0)" -->
160void&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>
161
162<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Name its rv. <br></td></tr>
163<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c4b863ff84c7a4882fb3ad18556027f9"></a><!-- doxytag: member="bdm::eiWishartCh::isnamed" ref="c4b863ff84c7a4882fb3ad18556027f9" args="() const " -->
164bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#c4b863ff84c7a4882fb3ad18556027f9">isnamed</a> () const </td></tr>
165
166<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">True if rv is assigned. <br></td></tr>
167<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4ab378d5e004c3ff3e2d4e64f7bba21"></a><!-- doxytag: member="bdm::eiWishartCh::_rv" ref="a4ab378d5e004c3ff3e2d4e64f7bba21" args="() const " -->
168const <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>
169
170<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Return name (fails when isnamed is false). <br></td></tr>
171<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr>
172<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7083a65f7b7a0d0d13b2c516bd2ec29c"></a><!-- doxytag: member="bdm::eiWishartCh::dimension" ref="7083a65f7b7a0d0d13b2c516bd2ec29c" args="() const " -->
173int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#7083a65f7b7a0d0d13b2c516bd2ec29c">dimension</a> () const </td></tr>
174
175<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Size of the random variable. <br></td></tr>
176<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
177<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c6b684b52dc62b8d46e67d5992f98b9a"></a><!-- doxytag: member="bdm::eiWishartCh::W" ref="c6b684b52dc62b8d46e67d5992f98b9a" args="" -->
178<a class="el" href="classbdm_1_1eWishartCh.html">eWishartCh</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#c6b684b52dc62b8d46e67d5992f98b9a">W</a></td></tr>
179
180<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Internal instance of Wishart density. <br></td></tr>
181<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c11f1c41183f743b97fbb73a4e9ba6cd"></a><!-- doxytag: member="bdm::eiWishartCh::p" ref="c11f1c41183f743b97fbb73a4e9ba6cd" args="" -->
182int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#c11f1c41183f743b97fbb73a4e9ba6cd">p</a></td></tr>
183
184<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">size of Ch <br></td></tr>
185<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ca3035f7bd5e4597cc1843cf07af8464"></a><!-- doxytag: member="bdm::eiWishartCh::delta" ref="ca3035f7bd5e4597cc1843cf07af8464" args="" -->
186double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1eiWishartCh.html#ca3035f7bd5e4597cc1843cf07af8464">delta</a></td></tr>
187
188<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">parameter delta <br></td></tr>
189<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="16adac20ec7fe07e1ea0b27d917788ce"></a><!-- doxytag: member="bdm::eiWishartCh::dim" ref="16adac20ec7fe07e1ea0b27d917788ce" args="" -->
190int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1epdf.html#16adac20ec7fe07e1ea0b27d917788ce">dim</a></td></tr>
191
192<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the random variable <br></td></tr>
193<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62c5b8ff71d9ebe6cd58d3c342eb1dc8"></a><!-- doxytag: member="bdm::eiWishartCh::rv" ref="62c5b8ff71d9ebe6cd58d3c342eb1dc8" args="" -->
194<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>
195
196<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Description of the random variable. <br></td></tr>
197</table>
198<hr><a name="_details"></a><h2>Detailed Description</h2>
199Inverse Wishart on Choleski decomposition.
200<p>
201Being computed by conversion from `standard' Wishart <hr><h2>Member Function Documentation</h2>
202<a class="anchor" name="fa9efc98a065b31c630fe18cc418f725"></a><!-- doxytag: member="bdm::eiWishartCh::from_setting" ref="fa9efc98a065b31c630fe18cc418f725" args="(const Setting &amp;set)" -->
203<div class="memitem">
204<div class="memproto">
205      <table class="memname">
206        <tr>
207          <td class="memname">void bdm::epdf::from_setting           </td>
208          <td>(</td>
209          <td class="paramtype">const Setting &amp;&nbsp;</td>
210          <td class="paramname"> <em>set</em>          </td>
211          <td>&nbsp;)&nbsp;</td>
212          <td><code> [inline, virtual, inherited]</code></td>
213        </tr>
214      </table>
215</div>
216<div class="memdoc">
217
218<p>
219Load from structure with elements:.
220<p>
221<div class="fragment"><pre class="fragment">         { rv = {<span class="keyword">class</span>=<span class="stringliteral">"RV"</span>, names=(...),}; <span class="comment">// RV describing meaning of random variable</span>
222           <span class="comment">// elements of offsprings</span>
223         }
224</pre></div> 
225<p>Reimplemented from <a class="el" href="classbdm_1_1root.html#0551e3121091c5199bf4413b50522176">bdm::root</a>.</p>
226
227<p>Reimplemented in <a class="el" href="classbdm_1_1enorm.html#61bd470764020bea6e1ed35000f259e6">bdm::enorm&lt; sq_T &gt;</a>, <a class="el" href="classbdm_1_1egiw.html#55b76ec75bd2df5ef9cab3be20a33bbb">bdm::egiw</a>, <a class="el" href="classbdm_1_1eDirich.html#aef2c328917dd80dce689d3d11d09567">bdm::eDirich</a>, <a class="el" href="classbdm_1_1egamma.html#8a6fd1a1c0190f3e0d95a2a1f99aafc1">bdm::egamma</a>, <a class="el" href="classbdm_1_1euni.html#77f5fef1f006fe056066da23b9e5f042">bdm::euni</a>, <a class="el" href="classbdm_1_1merger__base.html#10dd390fc6f0d1733bb07cb51977160c">bdm::merger_base</a>, <a class="el" href="classbdm_1_1merger__mix.html#9f12b2c66344e25e6b3ef0255d000478">bdm::merger_mix</a>, <a class="el" href="classbdm_1_1enorm.html#61bd470764020bea6e1ed35000f259e6">bdm::enorm&lt; ldmat &gt;</a>, <a class="el" href="classbdm_1_1enorm.html#61bd470764020bea6e1ed35000f259e6">bdm::enorm&lt; chmat &gt;</a>, and <a class="el" href="classbdm_1_1enorm.html#61bd470764020bea6e1ed35000f259e6">bdm::enorm&lt; fsqmat &gt;</a>.</p>
228
229<p>References <a class="el" href="bdmbase_8h_source.html#l00414">bdm::epdf::set_rv()</a>.</p>
230
231</div>
232</div><p>
233<hr>The documentation for this class was generated from the following file:<ul>
234<li><a class="el" href="exp__family_8h_source.html">exp_family.h</a></ul>
235</div>
236<hr size="1"><address style="text-align: right;"><small>Generated on Wed Oct 7 17:34:49 2009 for mixpp by&nbsp;
237<a href="http://www.doxygen.org/index.html">
238<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.9 </small></address>
239</body>
240</html>
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