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25  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1mgamma__fix.html">mgamma_fix</a>
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29<h1>bdm::mgamma_fix Class Reference</h1><!-- doxytag: class="bdm::mgamma_fix" --><!-- doxytag: inherits="bdm::mgamma" -->Gamma random walk around a fixed point. 
30<a href="#_details">More...</a>
31<p>
32<code>#include &lt;<a class="el" href="libEF_8h-source.html">libEF.h</a>&gt;</code>
33<p>
34<div class="dynheader">
35Inheritance diagram for bdm::mgamma_fix:</div>
36<div class="dynsection">
37<p><center><img src="classbdm_1_1mgamma__fix__inherit__graph.png" border="0" usemap="#bdm_1_1mgamma__fix__inherit__map" alt="Inheritance graph"></center>
38<map name="bdm_1_1mgamma__fix__inherit__map">
39<area shape="rect" href="classbdm_1_1mgamma.html" title="Gamma random walk." alt="" coords="16,161,136,188"><area shape="rect" href="classbdm_1_1mEF.html" title="Exponential family model." alt="" coords="33,84,119,111"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="31,7,121,33"></map>
40<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
41<div class="dynheader">
42Collaboration diagram for bdm::mgamma_fix:</div>
43<div class="dynsection">
44<p><center><img src="classbdm_1_1mgamma__fix__coll__graph.png" border="0" usemap="#bdm_1_1mgamma__fix__coll__map" alt="Collaboration graph"></center>
45<map name="bdm_1_1mgamma__fix__coll__map">
46<area shape="rect" href="classbdm_1_1mgamma.html" title="Gamma random walk." alt="" coords="60,460,180,487"><area shape="rect" href="classbdm_1_1mEF.html" title="Exponential family model." alt="" coords="5,364,91,391"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="8,284,99,311"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="27,87,101,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="96,185,181,212"><area shape="rect" href="classbdm_1_1base.html" title="Root class of BDM objects." alt="" coords="68,7,156,33"><area shape="rect" href="classbdm_1_1eEF.html" title="General conjugate exponential family posterior density." alt="" coords="129,284,209,311"><area shape="rect" href="classbdm_1_1egamma.html" title="Gamma posterior density." alt="" coords="115,364,229,391"></map>
47<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
48
49<p>
50<a href="classbdm_1_1mgamma__fix-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="c73571f45ab2926e5a7fb9c3791b5614"></a><!-- doxytag: member="bdm::mgamma_fix::mgamma_fix" ref="c73571f45ab2926e5a7fb9c3791b5614" args="(const RV &amp;rv, const RV &amp;rvc)" -->
54&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#c73571f45ab2926e5a7fb9c3791b5614">mgamma_fix</a> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1mpdf.html#9bcfb45435d30983f436d41c298cbb51">rv</a>, const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;<a class="el" href="classbdm_1_1mpdf.html#5a5f08950daa08b85b01ddf4e1c36288">rvc</a>)</td></tr>
55
56<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
57<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1bfd30e90db9dc1fbda4a9fbb0b716b2"></a><!-- doxytag: member="bdm::mgamma_fix::set_parameters" ref="1bfd30e90db9dc1fbda4a9fbb0b716b2" args="(double k0, vec ref0, double l0)" -->
58void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#1bfd30e90db9dc1fbda4a9fbb0b716b2">set_parameters</a> (double k0, vec ref0, double l0)</td></tr>
59
60<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set value of <code>k</code>. <br></td></tr>
61<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1d539591deb7a38bb3403c2b396c8ff7"></a><!-- doxytag: member="bdm::mgamma_fix::condition" ref="1d539591deb7a38bb3403c2b396c8ff7" args="(const vec &amp;val)" -->
62void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#1d539591deb7a38bb3403c2b396c8ff7">condition</a> (const vec &amp;val)</td></tr>
63
64<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>
65<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0b486f7e52a3d8a39adbcbd325461c0d"></a><!-- doxytag: member="bdm::mgamma_fix::set_parameters" ref="0b486f7e52a3d8a39adbcbd325461c0d" args="(double k)" -->
66void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#0b486f7e52a3d8a39adbcbd325461c0d">set_parameters</a> (double <a class="el" href="classbdm_1_1mgamma.html#b20cf88cca1fe9b0b8f2a412608bfd09">k</a>)</td></tr>
67
68<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set value of <code>k</code>. <br></td></tr>
69<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#e4848a428d8ef0549c6e4a9ed386d9f2">samplecond</a> (const vec &amp;cond, double &amp;ll)</td></tr>
70
71<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="#e4848a428d8ef0549c6e4a9ed386d9f2"></a><br></td></tr>
72<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>
73
74<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns.  <a href="#ee26963a637b2ea1fb1933652981e652"></a><br></td></tr>
75<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6336a8a72462e2a56a3989a220f18b1b"></a><!-- doxytag: member="bdm::mgamma_fix::evallogcond" ref="6336a8a72462e2a56a3989a220f18b1b" args="(const vec &amp;dt, const vec &amp;cond)" -->
76virtual double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#6336a8a72462e2a56a3989a220f18b1b">evallogcond</a> (const vec &amp;dt, const vec &amp;cond)</td></tr>
77
78<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>
79<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0b0ed1ed663071bb7cf4a1349eb94fcb"></a><!-- doxytag: member="bdm::mgamma_fix::evallogcond_m" ref="0b0ed1ed663071bb7cf4a1349eb94fcb" args="(const mat &amp;Dt, const vec &amp;cond)" -->
80virtual 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>
81
82<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of evallogcond. <br></td></tr>
83<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b3aba7311038bf990d706a64cab60cf8"></a><!-- doxytag: member="bdm::mgamma_fix::_rvc" ref="b3aba7311038bf990d706a64cab60cf8" args="() const " -->
84<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>
85
86<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
87<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="222d5280e309c5a053ba73841e98c151"></a><!-- doxytag: member="bdm::mgamma_fix::_rv" ref="222d5280e309c5a053ba73841e98c151" args="() const " -->
88<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>
89
90<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
91<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1892fe3933488942253679f068e9e7f6"></a><!-- doxytag: member="bdm::mgamma_fix::_epdf" ref="1892fe3933488942253679f068e9e7f6" args="()" -->
92<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>
93
94<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
95<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="05e843fd11c410a99dad2b88c55aca80"></a><!-- doxytag: member="bdm::mgamma_fix::_e" ref="05e843fd11c410a99dad2b88c55aca80" args="()" -->
96<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>
97
98<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
99<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
100<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1eb701506aabb2e6af007e487212d6fa"></a><!-- doxytag: member="bdm::mgamma_fix::l" ref="1eb701506aabb2e6af007e487212d6fa" args="" -->
101double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#1eb701506aabb2e6af007e487212d6fa">l</a></td></tr>
102
103<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">parameter l <br></td></tr>
104<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="018c6f901a04e419455308a07eb3b0b2"></a><!-- doxytag: member="bdm::mgamma_fix::refl" ref="018c6f901a04e419455308a07eb3b0b2" args="" -->
105vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#018c6f901a04e419455308a07eb3b0b2">refl</a></td></tr>
106
107<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">reference vector <br></td></tr>
108<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bdc9f1e9e03c09e91103fee269864438"></a><!-- doxytag: member="bdm::mgamma_fix::epdf" ref="bdc9f1e9e03c09e91103fee269864438" args="" -->
109<a class="el" href="classbdm_1_1egamma.html">egamma</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#bdc9f1e9e03c09e91103fee269864438">epdf</a></td></tr>
110
111<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Internal <a class="el" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density.">epdf</a> that arise by conditioning on <code>rvc</code>. <br></td></tr>
112<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="b20cf88cca1fe9b0b8f2a412608bfd09"></a><!-- doxytag: member="bdm::mgamma_fix::k" ref="b20cf88cca1fe9b0b8f2a412608bfd09" args="" -->
113double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#b20cf88cca1fe9b0b8f2a412608bfd09">k</a></td></tr>
114
115<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constant <img class="formulaInl" alt="$k$" src="form_41.png">. <br></td></tr>
116<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f6a652ce70fa2eb4d2c7ba6d5a6ae343"></a><!-- doxytag: member="bdm::mgamma_fix::_beta" ref="f6a652ce70fa2eb4d2c7ba6d5a6ae343" args="" -->
117vec *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#f6a652ce70fa2eb4d2c7ba6d5a6ae343">_beta</a></td></tr>
118
119<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cache of epdf.beta <br></td></tr>
120<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bcfb45435d30983f436d41c298cbb51"></a><!-- doxytag: member="bdm::mgamma_fix::rv" ref="9bcfb45435d30983f436d41c298cbb51" args="" -->
121<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>
122
123<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">modeled random variable <br></td></tr>
124<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5a5f08950daa08b85b01ddf4e1c36288"></a><!-- doxytag: member="bdm::mgamma_fix::rvc" ref="5a5f08950daa08b85b01ddf4e1c36288" args="" -->
125<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>
126
127<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">random variable in condition <br></td></tr>
128<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5eea43c56d38e4441bfb30270db949c0"></a><!-- doxytag: member="bdm::mgamma_fix::ep" ref="5eea43c56d38e4441bfb30270db949c0" args="" -->
129<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>
130
131<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>
132</table>
133<hr><a name="_details"></a><h2>Detailed Description</h2>
134Gamma random walk around a fixed point.
135<p>
136Mean value, <img class="formulaInl" alt="$\mu$" src="form_14.png">, of this density is given by a geometric combination of <code>rvc</code> and given fixed point, <img class="formulaInl" alt="$p$" src="form_42.png">. <img class="formulaInl" alt="$l$" src="form_43.png"> is the coefficient of the geometric combimation <p class="formulaDsp">
137<img class="formulaDsp" alt="\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]" src="form_18.png">
138<p>
139<p>
140Standard deviation of the random walk is proportional to one <img class="formulaInl" alt="$k$" src="form_41.png">-th the mean. This is achieved by setting <img class="formulaInl" alt="$\alpha=k$" src="form_11.png"> and <img class="formulaInl" alt="$\beta=k/\mu$" src="form_12.png">.<p>
141The standard deviation of the walk is then: <img class="formulaInl" alt="$\mu/\sqrt(k)$" src="form_13.png">. <hr><h2>Member Function Documentation</h2>
142<a class="anchor" name="e4848a428d8ef0549c6e4a9ed386d9f2"></a><!-- doxytag: member="bdm::mgamma_fix::samplecond" ref="e4848a428d8ef0549c6e4a9ed386d9f2" args="(const vec &amp;cond, double &amp;ll)" -->
143<div class="memitem">
144<div class="memproto">
145      <table class="memname">
146        <tr>
147          <td class="memname">virtual vec bdm::mpdf::samplecond           </td>
148          <td>(</td>
149          <td class="paramtype">const vec &amp;&nbsp;</td>
150          <td class="paramname"> <em>cond</em>, </td>
151        </tr>
152        <tr>
153          <td class="paramkey"></td>
154          <td></td>
155          <td class="paramtype">double &amp;&nbsp;</td>
156          <td class="paramname"> <em>ll</em></td><td>&nbsp;</td>
157        </tr>
158        <tr>
159          <td></td>
160          <td>)</td>
161          <td></td><td></td><td><code> [inline, virtual, inherited]</code></td>
162        </tr>
163      </table>
164</div>
165<div class="memdoc">
166
167<p>
168Returns a sample from the density conditioned on <code>cond</code>, <img class="formulaInl" alt="$x \sim epdf(rv|cond)$" src="form_10.png">.
169<p>
170<dl compact><dt><b>Parameters:</b></dt><dd>
171  <table border="0" cellspacing="2" cellpadding="0">
172    <tr><td valign="top"></td><td valign="top"><em>cond</em>&nbsp;</td><td>is numeric value of <code>rv</code> </td></tr>
173    <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>
174  </table>
175</dl>
176
177<p>Reimplemented in <a class="el" href="classbdm_1_1mprod.html#1a37c2aaba8bde7fce5351c39b6e1168">bdm::mprod</a>.</p>
178
179<p>References <a class="el" href="libBM_8h-source.html#l00243">bdm::mpdf::condition()</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>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
180
181<p>Referenced by <a class="el" href="libPF_8h-source.html#l00144">bdm::MPF&lt; BM_T &gt;::bayes()</a>, and <a class="el" href="libPF_8cpp-source.html#l00007">bdm::PF::bayes()</a>.</p>
182
183</div>
184</div><p>
185<a class="anchor" name="ee26963a637b2ea1fb1933652981e652"></a><!-- doxytag: member="bdm::mgamma_fix::samplecond_m" ref="ee26963a637b2ea1fb1933652981e652" args="(const vec &amp;cond, vec &amp;ll, int N)" -->
186<div class="memitem">
187<div class="memproto">
188      <table class="memname">
189        <tr>
190          <td class="memname">virtual mat bdm::mpdf::samplecond_m           </td>
191          <td>(</td>
192          <td class="paramtype">const vec &amp;&nbsp;</td>
193          <td class="paramname"> <em>cond</em>, </td>
194        </tr>
195        <tr>
196          <td class="paramkey"></td>
197          <td></td>
198          <td class="paramtype">vec &amp;&nbsp;</td>
199          <td class="paramname"> <em>ll</em>, </td>
200        </tr>
201        <tr>
202          <td class="paramkey"></td>
203          <td></td>
204          <td class="paramtype">int&nbsp;</td>
205          <td class="paramname"> <em>N</em></td><td>&nbsp;</td>
206        </tr>
207        <tr>
208          <td></td>
209          <td>)</td>
210          <td></td><td></td><td><code> [inline, virtual, inherited]</code></td>
211        </tr>
212      </table>
213</div>
214<div class="memdoc">
215
216<p>
217Returns.
218<p>
219<dl compact><dt><b>Parameters:</b></dt><dd>
220  <table border="0" cellspacing="2" cellpadding="0">
221    <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>
222    <tr><td valign="top"></td><td valign="top"><em>cond</em>&nbsp;</td><td>is numeric value of <code>rv</code> </td></tr>
223    <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>
224  </table>
225</dl>
226
227<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>
228
229</div>
230</div><p>
231<hr>The documentation for this class was generated from the following file:<ul>
232<li>work/git/mixpp/bdm/stat/<a class="el" href="libEF_8h-source.html">libEF.h</a></ul>
233</div>
234<hr size="1"><address style="text-align: right;"><small>Generated on Tue Jan 27 16:31:47 2009 for mixpp by&nbsp;
235<a href="http://www.doxygen.org/index.html">
236<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
237</body>
238</html>
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