Changeset 99 for doc/html/classARX.html

Timestamp:

05/09/08 17:30:39 (16 years ago)

Author:

smidl

Message:

doc

Files:

• doc/html/classARX.html (modified) (6 diffs)

doc/html/classARX.html

@@ -24 +24 @@
 </div>
 <div class="contents">
-<h1>ARX Class Reference</h1><!-- doxytag: class="ARX" --><!-- doxytag: inherits="BM" -->Ligear-Gaussian autoregressive model.  
+<h1>ARX Class Reference</h1><!-- doxytag: class="ARX" --><!-- doxytag: inherits="BM" -->Linear Autoregressive model with Gaussian noise.  
 <a href="#_details">More...</a>
 <p>
@@ -41 +41 @@
 <p><center><img src="classARX__coll__graph.png" border="0" usemap="#ARX__coll__map" alt="Collaboration graph"></center>
 <map name="ARX__coll__map">
-<area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="9,95,49,119"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="11,7,48,31"></map>
+<area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="5,146,45,170"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="32,7,69,31"><area shape="rect" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="63,95,108,119"><area shape="rect" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD)." alt="" coords="132,196,185,220"><area shape="rect" href="classegiw.html" title="Gauss&#45;inverse&#45;Wishart density stored in LD form." alt="" coords="63,284,111,308"><area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="132,95,188,119"><area shape="rect" href="classeEF.html" title="General conjugate exponential family posterior density." alt="" coords="63,196,108,220"></map>
 <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
 
@@ -48 +48 @@
 <tr><td></td></tr>
 <tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e9c85cefb7342bced83f38e12913bb68"></a><!-- doxytag: member="ARX::ARX" ref="e9c85cefb7342bced83f38e12913bb68" args="(const RV &amp;rv0)" -->
-&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#e9c85cefb7342bced83f38e12913bb68">ARX</a> (const <a class="el" href="classRV.html">RV</a> &amp;rv0)</td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5fc6c18e73dcc0f1135eef33f42db8be"></a><!-- doxytag: member="ARX::ARX" ref="5fc6c18e73dcc0f1135eef33f42db8be" args="(RV &amp;rv, mat &amp;V0, double &amp;nu0, double frg0=1.0)" -->
+&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#5fc6c18e73dcc0f1135eef33f42db8be">ARX</a> (<a class="el" href="classRV.html">RV</a> &amp;<a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a>, mat &amp;V0, double &amp;nu0, double frg0=1.0)</td></tr>
 
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Default constructor. <br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top">virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#ec6ab76ea10fc8c61006e15c7013b1ff">bayes</a> (const vec &amp;dt)=0</td></tr>
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor. <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="ba82c956ca893826811aefe1e4af465d"></a><!-- doxytag: member="ARX::bayes" ref="ba82c956ca893826811aefe1e4af465d" args="(const vec &amp;dt)" -->
+void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#ba82c956ca893826811aefe1e4af465d">bayes</a> (const vec &amp;dt)</td></tr>
 
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Incremental Bayes rule.  <a href="#ec6ab76ea10fc8c61006e15c7013b1ff"></a><br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="abeb6918ae4c445c31ad340de1279bfa"></a><!-- doxytag: member="ARX::bayes" ref="abeb6918ae4c445c31ad340de1279bfa" args="(mat Dt)" -->
-void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#abeb6918ae4c445c31ad340de1279bfa">bayes</a> (mat Dt)</td></tr>
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Here <img class="formulaInl" alt="$dt = [y_t psi_t] $" src="form_58.png">. <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9d8eff7a9df81786191a4c55b27e5b8a"></a><!-- doxytag: member="ARX::_epdf" ref="9d8eff7a9df81786191a4c55b27e5b8a" args="()" -->
+<a class="el" href="classepdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#9d8eff7a9df81786191a4c55b27e5b8a">_epdf</a> ()</td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classepdf.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>
+<tr><td class="memItemLeft" nowrap align="right" valign="top">ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#130bb7336aac681ce14b027b8f1409fa">structure_est</a> (<a class="el" href="classegiw.html">egiw</a> Eg0)</td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Brute force structure estimation.  <a href="#130bb7336aac681ce14b027b8f1409fa"></a><br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87b07867fd4c133aa89a18543f68d9f9"></a><!-- doxytag: member="ARX::bayes" ref="87b07867fd4c133aa89a18543f68d9f9" args="(mat Dt)" -->
+void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#87b07867fd4c133aa89a18543f68d9f9">bayes</a> (mat Dt)</td></tr>
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="dbd59b76615ff2d2cd623b3107b58c5e"></a><!-- doxytag: member="ARX::_epdf" ref="dbd59b76615ff2d2cd623b3107b58c5e" args="()=0" -->
-virtual <a class="el" href="classepdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#dbd59b76615ff2d2cd623b3107b58c5e">_epdf</a> ()=0</td></tr>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns a pointer to the <a class="el" href="classepdf.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>
 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="126bd2595c48e311fc2a7ab72876092a"></a><!-- doxytag: member="ARX::_rv" ref="126bd2595c48e311fc2a7ab72876092a" args="() const " -->
 const <a class="el" href="classRV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#126bd2595c48e311fc2a7ab72876092a">_rv</a> () const </td></tr>
@@ -72 +76 @@
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
 <tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="89e4fe48c9953307855b372351d290ab"></a><!-- doxytag: member="ARX::V" ref="89e4fe48c9953307855b372351d290ab" args="" -->
-mat&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#89e4fe48c9953307855b372351d290ab">V</a></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="691d023662beffa1dda611b416c0e27e"></a><!-- doxytag: member="ARX::est" ref="691d023662beffa1dda611b416c0e27e" args="" -->
+<a class="el" href="classegiw.html">egiw</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#691d023662beffa1dda611b416c0e27e">est</a></td></tr>
 
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Sufficient statistics. <br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="62641ea852a7eb275acfc291898b8fce"></a><!-- doxytag: member="ARX::epdf" ref="62641ea852a7eb275acfc291898b8fce" args="" -->
-egiw&nbsp;</td><td class="memItemRight" valign="bottom"><b>epdf</b></td></tr>
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Posterior estimate of <img class="formulaInl" alt="$\theta,r$" src="form_57.png"> in the form of Normal-inverse Wishart density. <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2291297861dd74ca0175a01f910a0ef7"></a><!-- doxytag: member="ARX::V" ref="2291297861dd74ca0175a01f910a0ef7" args="" -->
+<a class="el" href="classldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#2291297861dd74ca0175a01f910a0ef7">V</a></td></tr>
 
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.V <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4182c281098b2d86b62518a7493d9be"></a><!-- doxytag: member="ARX::nu" ref="a4182c281098b2d86b62518a7493d9be" args="" -->
+double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#a4182c281098b2d86b62518a7493d9be">nu</a></td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.nu <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="e467144efb0a5acbc10dba4eff8638fe"></a><!-- doxytag: member="ARX::frg" ref="e467144efb0a5acbc10dba4eff8638fe" args="" -->
+double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#e467144efb0a5acbc10dba4eff8638fe">frg</a></td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="6d0cd0f0734aa77cdc5e48f1cf6737ec"></a><!-- doxytag: member="ARX::last_lognc" ref="6d0cd0f0734aa77cdc5e48f1cf6737ec" args="" -->
+double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#6d0cd0f0734aa77cdc5e48f1cf6737ec">last_lognc</a></td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of lognc() in the previous step <br></td></tr>
 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af00f0612fabe66241dd507188cdbf88"></a><!-- doxytag: member="ARX::rv" ref="af00f0612fabe66241dd507188cdbf88" args="" -->
 <a class="el" href="classRV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a></td></tr>
@@ -93 +110 @@
 </table>
 <hr><a name="_details"></a><h2>Detailed Description</h2>
-Ligear-Gaussian autoregressive model. 
+Linear Autoregressive model with Gaussian noise. 
 <p>
-<hr><h2>Member Function Documentation</h2>
-<a class="anchor" name="ec6ab76ea10fc8c61006e15c7013b1ff"></a><!-- doxytag: member="ARX::bayes" ref="ec6ab76ea10fc8c61006e15c7013b1ff" args="(const vec &amp;dt)=0" -->
+Regression of the following kind: <p class="formulaDsp">
+<img class="formulaDsp" alt="\[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \]" src="form_61.png">
+<p>
+ where unknown parameters <code>rv</code> are <img class="formulaInl" alt="$[\theta r]$" src="form_51.png">, regression vector <img class="formulaInl" alt="$\psi=\psi(y_{1:t},u_{1:t})$" src="form_52.png"> is a known function of past outputs and exogeneous variables <img class="formulaInl" alt="$u_t$" src="form_53.png">. Distrubances <img class="formulaInl" alt="$e_t$" src="form_54.png"> are supposed to be normally distributed: <p class="formulaDsp">
+<img class="formulaDsp" alt="\[ e_t \sim \mathcal{N}(0,1). \]" src="form_62.png">
+<p>
+<p>
+Extension for time-variant parameters <img class="formulaInl" alt="$\theta_t,r_t$" src="form_55.png"> may be achived using exponential forgetting (Kulhavy and Zarrop, 1993). In such a case, the forgetting factor <code>frg</code> <img class="formulaInl" alt="$\in <0,1>$" src="form_56.png"> should be given in the constructor. Time-invariant parameters are estimated for <code>frg</code> = 1. <hr><h2>Member Function Documentation</h2>
+<a class="anchor" name="130bb7336aac681ce14b027b8f1409fa"></a><!-- doxytag: member="ARX::structure_est" ref="130bb7336aac681ce14b027b8f1409fa" args="(egiw Eg0)" -->
 <div class="memitem">
 <div class="memproto">
       <table class="memname">
         <tr>
-          <td class="memname">virtual void ARX::bayes           </td>
+          <td class="memname">ivec ARX::structure_est           </td>
           <td>(</td>
-          <td class="paramtype">const vec &amp;&nbsp;</td>
-          <td class="paramname"> <em>dt</em>          </td>
+          <td class="paramtype"><a class="el" href="classegiw.html">egiw</a>&nbsp;</td>
+          <td class="paramname"> <em>Eg0</em>          </td>
           <td>&nbsp;)&nbsp;</td>
-          <td width="100%"><code> [pure virtual]</code></td>
+          <td width="100%"></td>
         </tr>
       </table>
@@ -113 +137 @@
 
 <p>
-Incremental Bayes rule. 
+Brute force structure estimation. 
 <p>
-<dl compact><dt><b>Parameters:</b></dt><dd>
-  <table border="0" cellspacing="2" cellpadding="0">
-    <tr><td valign="top"></td><td valign="top"><em>dt</em>&nbsp;</td><td>vector of input data </td></tr>
-  </table>
-</dl>
+<dl class="return" compact><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
 
-<p>Implements <a class="el" href="classBM.html#a892eff438aab2dd1a9e2efcb7fb5bdf">BM</a>.</p>
+<p>References <a class="el" href="libBM_8h-source.html#l00057">RV::count()</a>, <a class="el" href="arx_8h-source.html#l00039">est</a>, <a class="el" href="libEF_8cpp-source.html#l00031">egiw::lognc()</a>, and <a class="el" href="libBM_8h-source.html#l00224">BM::rv</a>.</p>
 
 </div>
 </div><p>
-<hr>The documentation for this class was generated from the following file:<ul>
-<li>work/mixpp/bdm/stat/<a class="el" href="arx_8h-source.html">arx.h</a></ul>
+<hr>The documentation for this class was generated from the following files:<ul>
+<li>work/mixpp/bdm/estim/<a class="el" href="arx_8h-source.html">arx.h</a><li>work/mixpp/bdm/estim/arx.cpp</ul>
 </div>
-<hr size="1"><address style="text-align: right;"><small>Generated on Tue Apr 29 20:46:35 2008 for mixpp by&nbsp;
+<hr size="1"><address style="text-align: right;"><small>Generated on Fri May 9 16:15:24 2008 for mixpp by&nbsp;
 <a href="http://www.doxygen.org/index.html">
 <img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.5 </small></address>