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69  <div class="navpath"><b>bdm</b>::<a class="el" href="classbdm_1_1ARX.html">ARX</a>
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73<h1>bdm::ARX Class Reference</h1><!-- doxytag: class="bdm::ARX" --><!-- doxytag: inherits="bdm::BMEF" -->
74<p>Linear Autoregressive model with Gaussian noise. 
75<a href="#_details">More...</a></p>
76<hr/><a name="_details"></a><h2>Detailed Description</h2>
77<p>Linear Autoregressive model with Gaussian noise. </p>
78<p>Regression of the following kind: </p>
79<p class="formulaDsp">
80<img class="formulaDsp" alt="\[ y_t = \theta_1 \psi_1 + \theta_2 + \psi_2 +\ldots + \theta_n \psi_n + r e_t \]" src="form_28.png"/>
81</p>
82<p> where unknown parameters <code>rv</code> are <img class="formulaInl" alt="$[\theta r]$" src="form_29.png"/>, regression vector <img class="formulaInl" alt="$\psi=\psi(y_{1:t},u_{1:t})$" src="form_30.png"/> is a known function of past outputs and exogeneous variables <img class="formulaInl" alt="$u_t$" src="form_31.png"/>. Distrubances <img class="formulaInl" alt="$e_t$" src="form_32.png"/> are supposed to be normally distributed: </p>
83<p class="formulaDsp">
84<img class="formulaDsp" alt="\[ e_t \sim \mathcal{N}(0,1). \]" src="form_33.png"/>
85</p>
86<p>See <a class="el" href="tut_arx.html">Theory of ARX model estimation</a> for mathematical treatment.</p>
87<p>The easiest way how to use the class is: </p>
88<div class="fragment"><pre class="fragment"><span class="preprocessor">#include &quot;<a class="code" href="arx_8h.html" title="Bayesian Filtering for generalized autoregressive (ARX) model.">estim/arx.h</a>&quot;</span>
89<span class="keyword">using namespace </span>bdm;
90
91<span class="comment">// estimation of AR(0) model</span>
92<span class="keywordtype">int</span> main() {
93        <span class="comment">//prior</span>
94        mat V0 = 0.00001 * eye ( 2 );
95        V0 ( 0, 0 ) = 0.1; <span class="comment">//</span>
96        ARX Ar;
97        Ar.set_statistics ( 1, V0 ); <span class="comment">//nu is default (set to have finite moments)</span>
98        <span class="comment">// forgetting is default: 1.0</span>
99        mat Data = concat_vertical ( randn ( 1, 100 ), ones ( 1, 100 ) );
100        Ar.bayesB ( Data );
101
102        cout &lt;&lt; <span class="stringliteral">&quot;Expected value of Theta is: &quot;</span> &lt;&lt; Ar.posterior().mean() &lt;&lt; endl;
103}
104</pre></div><dl class="todo"><dt><b><a class="el" href="todo.html#_todo000001">Todo:</a></b></dt><dd>sort out constant terms - bayes should accept vec without additional 1s </dd></dl>
105
106<p><code>#include &lt;<a class="el" href="arx_8h_source.html">arx.h</a>&gt;</code></p>
107
108<p><a href="classbdm_1_1ARX-members.html">List of all members.</a></p>
109<table border="0" cellpadding="0" cellspacing="0">
110<tr><td colspan="2"><h2>Public Member Functions</h2></td></tr>
111<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a539f9d0127423c94b912708d390e67b8"></a><!-- doxytag: member="bdm::ARX::set_statistics" ref="a539f9d0127423c94b912708d390e67b8" args="(const BMEF *BM0)" -->
112void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a539f9d0127423c94b912708d390e67b8">set_statistics</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *BM0)</td></tr>
113<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set sufficient statistics. <br/></td></tr>
114<tr><td class="memItemLeft" align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a9637412df898048bafaefee9dc7e9f6c">from_setting</a> (const Setting &amp;set)</td></tr>
115<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ad2b528b7a41ca67163152142f5404051"></a><!-- doxytag: member="bdm::ARX::set_statistics" ref="ad2b528b7a41ca67163152142f5404051" args="(const BMEF *BM0)" -->
116virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#ad2b528b7a41ca67163152142f5404051">set_statistics</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *BM0)</td></tr>
117<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get statistics from another model <br/></td></tr>
118<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab2916a2e71a958665054473124d5e749"></a><!-- doxytag: member="bdm::ARX::flatten" ref="ab2916a2e71a958665054473124d5e749" args="(const BMEF *B)" -->
119virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#ab2916a2e71a958665054473124d5e749">flatten</a> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *B)</td></tr>
120<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flatten the posterior according to the given <a class="el" href="classbdm_1_1BMEF.html" title="Estimator for Exponential family.">BMEF</a> (of the same type!). <br/></td></tr>
121<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aaf0e6941ba5919cae1bc530e2181b109"></a><!-- doxytag: member="bdm::ARX::to_string" ref="aaf0e6941ba5919cae1bc530e2181b109" args="()" -->
122virtual string&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#aaf0e6941ba5919cae1bc530e2181b109">to_string</a> ()</td></tr>
123<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method returns a basic info about the current instance. <br/></td></tr>
124<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a67d954d255ede776eade7334d4895790"></a><!-- doxytag: member="bdm::ARX::to_setting" ref="a67d954d255ede776eade7334d4895790" args="(Setting &amp;set) const " -->
125virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#a67d954d255ede776eade7334d4895790">to_setting</a> (Setting &amp;set) const </td></tr>
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method save all the instance properties into the Setting structure. <br/></td></tr>
127<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a1c314bd6d6dacb8ba78ea5eb88fd9516"></a><!-- doxytag: member="bdm::ARX::validate" ref="a1c314bd6d6dacb8ba78ea5eb88fd9516" args="()" -->
128virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1root.html#a1c314bd6d6dacb8ba78ea5eb88fd9516">validate</a> ()</td></tr>
129<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">This method TODO. <br/></td></tr>
130<tr><td colspan="2"><div class="groupHeader">Constructors</div></td></tr>
131<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrp559a25fdb98a7d1fd1c3771ac568d5e9"></a> </p>
132<br/><br/></div></td></tr>
133<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a43ed6114f04a3a8756fe2b42eaa35f98"></a><!-- doxytag: member="bdm::ARX::ARX" ref="a43ed6114f04a3a8756fe2b42eaa35f98" args="(const double frg0=1.0)" -->
134&nbsp;</td><td class="memItemRight" valign="bottom"><b>ARX</b> (const double frg0=1.0)</td></tr>
135<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a73a55a3d66bfbeeee4df6c2ae40920ed"></a><!-- doxytag: member="bdm::ARX::ARX" ref="a73a55a3d66bfbeeee4df6c2ae40920ed" args="(const ARX &amp;A0)" -->
136&nbsp;</td><td class="memItemRight" valign="bottom"><b>ARX</b> (const <a class="el" href="classbdm_1_1ARX.html">ARX</a> &amp;A0)</td></tr>
137<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="classbdm_1_1ARX.html">ARX</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#aca0b54c0997cfd567f49377af5def106">_copy_</a> () const </td></tr>
138<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7aef6fe827f15427d534e6fb2c220e04"></a><!-- doxytag: member="bdm::ARX::set_parameters" ref="a7aef6fe827f15427d534e6fb2c220e04" args="(double frg0)" -->
139void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_parameters</b> (double frg0)</td></tr>
140<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="af859f53eab269845a9064bbd92f841af"></a><!-- doxytag: member="bdm::ARX::set_statistics" ref="af859f53eab269845a9064bbd92f841af" args="(int dimx0, const ldmat V0, double nu0=&#45;1.0)" -->
141void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_statistics</b> (int dimx0, const <a class="el" href="classbdm_1_1ldmat.html">ldmat</a> V0, double nu0=-1.0)</td></tr>
142<tr><td colspan="2"><div class="groupHeader">Mathematical operations</div></td></tr>
143<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpfb3595af27ed8bd142c95323c0dab340"></a> </p>
144<br/><br/></div></td></tr>
145<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a17e7fe14654ab3c449846c3f43e66169"></a><!-- doxytag: member="bdm::ARX::bayes" ref="a17e7fe14654ab3c449846c3f43e66169" args="(const vec &amp;dt, const double w)" -->
146void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a17e7fe14654ab3c449846c3f43e66169">bayes</a> (const vec &amp;dt, const double w)</td></tr>
147<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Weighted Bayes <img class="formulaInl" alt="$ dt = [y_t psi_t] $" src="form_35.png"/>. <br/></td></tr>
148<tr><td class="memItemLeft" align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a8bdf2974052e8ce74eb0d4f3791c58a3">bayes</a> (const vec &amp;dt)</td></tr>
149<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Incremental Bayes rule.  <a href="#a8bdf2974052e8ce74eb0d4f3791c58a3"></a><br/></td></tr>
150<tr><td class="memItemLeft" align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a080a7e531e3aa06694112863b15bc6a4">logpred</a> (const vec &amp;dt) const </td></tr>
151<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ae86ab499b116b837d3163ec852961eca"></a><!-- doxytag: member="bdm::ARX::flatten" ref="ae86ab499b116b837d3163ec852961eca" args="(const BMEF *B)" -->
152void&nbsp;</td><td class="memItemRight" valign="bottom"><b>flatten</b> (const <a class="el" href="classbdm_1_1BMEF.html">BMEF</a> *B)</td></tr>
153<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a749827323c034f11bec61b6e2fc3d42a"></a><!-- doxytag: member="bdm::ARX::epredictor" ref="a749827323c034f11bec61b6e2fc3d42a" args="(const vec &amp;rgr) const " -->
154<a class="el" href="classbdm_1_1enorm.html">enorm</a>&lt; <a class="el" href="classbdm_1_1ldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a749827323c034f11bec61b6e2fc3d42a">epredictor</a> (const vec &amp;rgr) const </td></tr>
155<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Conditioned version of the predictor. <br/></td></tr>
156<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a4cdf5e2a7d3480ec31f6247ed4289b15"></a><!-- doxytag: member="bdm::ARX::epredictor" ref="a4cdf5e2a7d3480ec31f6247ed4289b15" args="() const " -->
157<a class="el" href="classbdm_1_1enorm.html">enorm</a>&lt; <a class="el" href="classbdm_1_1ldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a4cdf5e2a7d3480ec31f6247ed4289b15">epredictor</a> () const </td></tr>
158<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Predictor for empty regressor. <br/></td></tr>
159<tr><td class="memItemLeft" align="right" valign="top"><a class="el" href="classbdm_1_1mlnorm.html">mlnorm</a>&lt; <a class="el" href="classbdm_1_1ldmat.html">ldmat</a> &gt; *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a74fe8ae2d88bee8639510fd0eaf73513">predictor</a> () const </td></tr>
160<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">conditional version of the predictor  <a href="#a74fe8ae2d88bee8639510fd0eaf73513"></a><br/></td></tr>
161<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac6a2428a46407fe45b4c7a99069c0801"></a><!-- doxytag: member="bdm::ARX::predictor_student" ref="ac6a2428a46407fe45b4c7a99069c0801" args="() const " -->
162<a class="el" href="classbdm_1_1mlstudent.html">mlstudent</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><b>predictor_student</b> () const </td></tr>
163<tr><td class="memItemLeft" align="right" valign="top">ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a16b02ae03316751664c22d59d90c1e34">structure_est</a> (<a class="el" href="classbdm_1_1egiw.html">egiw</a> Eg0)</td></tr>
164<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Brute force structure estimation.  <a href="#a16b02ae03316751664c22d59d90c1e34"></a><br/></td></tr>
165<tr><td class="memItemLeft" align="right" valign="top">ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a5d0f217ce270e6a8cb43a67b6c4b67fa">structure_est_LT</a> (<a class="el" href="classbdm_1_1egiw.html">egiw</a> Eg0)</td></tr>
166<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Smarter structure estimation by Ludvik Tesar.  <a href="#a5d0f217ce270e6a8cb43a67b6c4b67fa"></a><br/></td></tr>
167<tr><td colspan="2"><div class="groupHeader">Access attributes</div></td></tr>
168<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrp8937227e303215af8852936dc1bf96ca"></a> </p>
169<br/><br/></div></td></tr>
170<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a5a96a50d212648f049122a31d9553618"></a><!-- doxytag: member="bdm::ARX::posterior" ref="a5a96a50d212648f049122a31d9553618" args="() const " -->
171const <a class="el" href="classbdm_1_1egiw.html">egiw</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>posterior</b> () const </td></tr>
172<tr><td colspan="2"><div class="groupHeader">Connection</div></td></tr>
173<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpc2cc7082a89c1ad6631a2f66af5f00c0"></a> </p>
174<br/><br/></div></td></tr>
175<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="adf3dc1b90efc0cc54a3a6e5e858542d1"></a><!-- doxytag: member="bdm::ARX::set_drv" ref="adf3dc1b90efc0cc54a3a6e5e858542d1" args="(const RV &amp;drv0)" -->
176void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_drv</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;drv0)</td></tr>
177<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a7b96872783ab72e135b7b9ee26ef0577"></a><!-- doxytag: member="bdm::ARX::get_yrv" ref="a7b96872783ab72e135b7b9ee26ef0577" args="()" -->
178<a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>get_yrv</b> ()</td></tr>
179<tr><td colspan="2"><div class="groupHeader">Mathematical operations</div></td></tr>
180<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpfb3595af27ed8bd142c95323c0dab340"></a> </p>
181<br/><br/></div></td></tr>
182<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a1dee3fddaf021e62d925289660a707dc"></a><!-- doxytag: member="bdm::ARX::bayesB" ref="a1dee3fddaf021e62d925289660a707dc" args="(const mat &amp;Dt)" -->
183virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a1dee3fddaf021e62d925289660a707dc">bayesB</a> (const mat &amp;Dt)</td></tr>
184<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br/></td></tr>
185<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a0e8ebe61fb14990abe1254bd3dda5fae"></a><!-- doxytag: member="bdm::ARX::logpred_m" ref="a0e8ebe61fb14990abe1254bd3dda5fae" args="(const mat &amp;dt) const " -->
186vec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a0e8ebe61fb14990abe1254bd3dda5fae">logpred_m</a> (const mat &amp;dt) const </td></tr>
187<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of logpred. <br/></td></tr>
188<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr>
189<tr><td colspan="2"><div class="groupText"><p><a class="anchor" id="amgrpb6eb094f9e6af11f8a7d9efa9d8e3623"></a> </p>
190<br/><br/></div></td></tr>
191<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aff2d8755ba0b3def927d31305c03b09c"></a><!-- doxytag: member="bdm::ARX::_drv" ref="aff2d8755ba0b3def927d31305c03b09c" args="() const " -->
192const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_drv</b> () const </td></tr>
193<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab38d92f17620813ad872d86e01a26e5e"></a><!-- doxytag: member="bdm::ARX::set_rv" ref="ab38d92f17620813ad872d86e01a26e5e" args="(const RV &amp;rv)" -->
194void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_rv</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv)</td></tr>
195<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a5be65d37dedfe33a3671e7065f523a70"></a><!-- doxytag: member="bdm::ARX::_ll" ref="a5be65d37dedfe33a3671e7065f523a70" args="() const " -->
196double&nbsp;</td><td class="memItemRight" valign="bottom"><b>_ll</b> () const </td></tr>
197<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a236b3abbcc93594fc97cd86d82c1a83f"></a><!-- doxytag: member="bdm::ARX::set_evalll" ref="a236b3abbcc93594fc97cd86d82c1a83f" args="(bool evl0)" -->
198void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_evalll</b> (bool evl0)</td></tr>
199<tr><td colspan="2"><h2>Protected Attributes</h2></td></tr>
200<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a8e68db2a218d54b09304cad6c0a897d9"></a><!-- doxytag: member="bdm::ARX::dimx" ref="a8e68db2a218d54b09304cad6c0a897d9" args="" -->
201int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a8e68db2a218d54b09304cad6c0a897d9">dimx</a></td></tr>
202<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">size of output variable (needed in regressors) <br/></td></tr>
203<tr><td class="memItemLeft" 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_1ARX.html#a363aaa55b2ab3eec602510cdf53e84ef">_yrv</a></td></tr>
204<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a11474a627367f81b76830cb8477cf026"></a><!-- doxytag: member="bdm::ARX::est" ref="a11474a627367f81b76830cb8477cf026" args="" -->
205<a class="el" href="classbdm_1_1egiw.html">egiw</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a11474a627367f81b76830cb8477cf026">est</a></td></tr>
206<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Posterior estimate of <img class="formulaInl" alt="$\theta,r$" src="form_34.png"/> in the form of Normal-inverse Wishart density. <br/></td></tr>
207<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ade5b7d83ff5d3f5af2f80068db0abdfd"></a><!-- doxytag: member="bdm::ARX::V" ref="ade5b7d83ff5d3f5af2f80068db0abdfd" args="" -->
208<a class="el" href="classbdm_1_1ldmat.html">ldmat</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#ade5b7d83ff5d3f5af2f80068db0abdfd">V</a></td></tr>
209<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.V <br/></td></tr>
210<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a740b0582f180ba13cae91d66e9bdb67f"></a><!-- doxytag: member="bdm::ARX::nu" ref="a740b0582f180ba13cae91d66e9bdb67f" args="" -->
211double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1ARX.html#a740b0582f180ba13cae91d66e9bdb67f">nu</a></td></tr>
212<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.nu <br/></td></tr>
213<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a1331865e10fb1ccef65bb4c47fa3be64"></a><!-- doxytag: member="bdm::ARX::frg" ref="a1331865e10fb1ccef65bb4c47fa3be64" args="" -->
214double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#a1331865e10fb1ccef65bb4c47fa3be64">frg</a></td></tr>
215<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br/></td></tr>
216<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a06e7b3ac03e10017d4288c76888e2865"></a><!-- doxytag: member="bdm::ARX::last_lognc" ref="a06e7b3ac03e10017d4288c76888e2865" args="" -->
217double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BMEF.html#a06e7b3ac03e10017d4288c76888e2865">last_lognc</a></td></tr>
218<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of lognc() in the previous step (used in evaluation of <code>ll</code> ) <br/></td></tr>
219<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ac400357e37d27a4834b2b1d9211009ed"></a><!-- doxytag: member="bdm::ARX::drv" ref="ac400357e37d27a4834b2b1d9211009ed" args="" -->
220<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#ac400357e37d27a4834b2b1d9211009ed">drv</a></td></tr>
221<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Random variable of the data (optional). <br/></td></tr>
222<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a4064b6559d962633e4372b12f4cd204a"></a><!-- doxytag: member="bdm::ARX::ll" ref="a4064b6559d962633e4372b12f4cd204a" args="" -->
223double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a4064b6559d962633e4372b12f4cd204a">ll</a></td></tr>
224<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of marginalized data likelihood. <br/></td></tr>
225<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="afaff0ad12556fe7dc0e2807d4fd938ee"></a><!-- doxytag: member="bdm::ARX::evalll" ref="afaff0ad12556fe7dc0e2807d4fd938ee" args="" -->
226bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#afaff0ad12556fe7dc0e2807d4fd938ee">evalll</a></td></tr>
227<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">If true, the filter will compute likelihood of the data record and store it in <code>ll</code> . Set to false if you want to save computational time. <br/></td></tr>
228<tr><td colspan="2"><h2>Extension to conditional BM</h2></td></tr>
229<tr><td colspan="2"><p><a class="anchor" id="amgrp74e1db869c28ea37aac65bd658ff5da4"></a> This extension is useful e.g. in Marginalized Particle Filter (<a class="el" href="classbdm_1_1MPF.html">bdm::MPF</a>). Alternatively, it can be used for automated connection to <a class="el" href="classbdm_1_1DS.html" title="Abstract class for discrete-time sources of data.">DS</a> when the condition is observed </p>
230<br/><br/></td></tr>
231<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab5e8e016be16e4029c789063cb3f3b33"></a><!-- doxytag: member="bdm::ARX::_rvc" ref="ab5e8e016be16e4029c789063cb3f3b33" args="() const " -->
232const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#ab5e8e016be16e4029c789063cb3f3b33">_rvc</a> () const </td></tr>
233<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br/></td></tr>
234<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a6799f4b16a6a59ed58b1d0d6e17116f4"></a><!-- doxytag: member="bdm::ARX::condition" ref="a6799f4b16a6a59ed58b1d0d6e17116f4" args="(const vec &amp;val)" -->
235virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a6799f4b16a6a59ed58b1d0d6e17116f4">condition</a> (const vec &amp;val)</td></tr>
236<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Substitute <code>val</code> for <code>rvc</code>. <br/></td></tr>
237<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ade95c590d650b2db423d53992f0906cb"></a><!-- doxytag: member="bdm::ARX::rvc" ref="ade95c590d650b2db423d53992f0906cb" args="" -->
238<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#ade95c590d650b2db423d53992f0906cb">rvc</a></td></tr>
239<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Name of extension variable. <br/></td></tr>
240<tr><td colspan="2"><h2>Logging of results</h2></td></tr>
241<tr><td colspan="2"><p><a class="anchor" id="amgrp5b751fa78120752d90ae4487df3bfa73"></a> </p>
242<br/><br/></td></tr>
243<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="aadb539fa2585c8a2a91c54e5aebf330e"></a><!-- doxytag: member="bdm::ARX::set_options" ref="aadb539fa2585c8a2a91c54e5aebf330e" args="(const string &amp;opt)" -->
244virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#aadb539fa2585c8a2a91c54e5aebf330e">set_options</a> (const string &amp;opt)</td></tr>
245<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set boolean options from a string, recognized are: "logbounds,logll". <br/></td></tr>
246<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a2298ca6af9b13a78a4c9e18ab43f1827"></a><!-- doxytag: member="bdm::ARX::log_add" ref="a2298ca6af9b13a78a4c9e18ab43f1827" args="(logger &amp;L, const string &amp;name=&quot;&quot;)" -->
247virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a2298ca6af9b13a78a4c9e18ab43f1827">log_add</a> (<a class="el" href="classbdm_1_1logger.html">logger</a> &amp;L, const string &amp;name=&quot;&quot;)</td></tr>
248<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Add all logged variables to a <a class="el" href="classbdm_1_1logger.html" title="Class for storing results (and semi-results) of an experiment.">logger</a>. <br/></td></tr>
249<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="ab517e1679eaa94e803ea4cd0b8efbcd7"></a><!-- doxytag: member="bdm::ARX::logit" ref="ab517e1679eaa94e803ea4cd0b8efbcd7" args="(logger &amp;L)" -->
250virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><b>logit</b> (<a class="el" href="classbdm_1_1logger.html">logger</a> &amp;L)</td></tr>
251<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a109c1a626a69031658e3a44e9e500cca"></a><!-- doxytag: member="bdm::ARX::LIDs" ref="a109c1a626a69031658e3a44e9e500cca" args="" -->
252ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a109c1a626a69031658e3a44e9e500cca">LIDs</a></td></tr>
253<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">IDs of storages in loggers 4:[1=mean,2=lb,3=ub,4=ll]. <br/></td></tr>
254<tr><td class="memItemLeft" align="right" valign="top"><a class="anchor" id="a398b7e7a162cf37d0022d6126495f207"></a><!-- doxytag: member="bdm::ARX::LFlags" ref="a398b7e7a162cf37d0022d6126495f207" args="" -->
255ivec&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1BM.html#a398b7e7a162cf37d0022d6126495f207">LFlags</a></td></tr>
256<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flags for logging - same size as LIDs, each entry correspond to the same in LIDs. <br/></td></tr>
257</table>
258<hr/><h2>Member Function Documentation</h2>
259<a class="anchor" id="aca0b54c0997cfd567f49377af5def106"></a><!-- doxytag: member="bdm::ARX::_copy_" ref="aca0b54c0997cfd567f49377af5def106" args="() const " -->
260<div class="memitem">
261<div class="memproto">
262      <table class="memname">
263        <tr>
264          <td class="memname"><a class="el" href="classbdm_1_1ARX.html">ARX</a> * bdm::ARX::_copy_ </td>
265          <td>(</td>
266          <td class="paramname"></td>
267          <td>&nbsp;)&nbsp;</td>
268          <td> const<code> [virtual]</code></td>
269        </tr>
270      </table>
271</div>
272<div class="memdoc">
273<p>Copy function required in vectors, Arrays of <a class="el" href="classbdm_1_1BM.html" title="Bayesian Model of a system, i.e. all uncertainty is modeled by probabilities.">BM</a> etc. Have to be DELETED manually! Prototype: </p>
274<div class="fragment"><pre class="fragment"> BM* <a class="code" href="classbdm_1_1ARX.html#aca0b54c0997cfd567f49377af5def106">_copy_</a>()<span class="keyword"> const </span>{<span class="keywordflow">return</span> <span class="keyword">new</span> BM(*<span class="keyword">this</span>);}
275</pre></div> 
276<p>Reimplemented from <a class="el" href="classbdm_1_1BMEF.html#a62d2e4691bed41a1efa6b9c2e35e5c67">bdm::BMEF</a>.</p>
277
278</div>
279</div>
280<a class="anchor" id="a8bdf2974052e8ce74eb0d4f3791c58a3"></a><!-- doxytag: member="bdm::ARX::bayes" ref="a8bdf2974052e8ce74eb0d4f3791c58a3" args="(const vec &amp;dt)" -->
281<div class="memitem">
282<div class="memproto">
283      <table class="memname">
284        <tr>
285          <td class="memname">void bdm::ARX::bayes </td>
286          <td>(</td>
287          <td class="paramtype">const vec &amp;&nbsp;</td>
288          <td class="paramname"> <em>dt</em></td>
289          <td>&nbsp;)&nbsp;</td>
290          <td><code> [inline, virtual]</code></td>
291        </tr>
292      </table>
293</div>
294<div class="memdoc">
295
296<p>Incremental Bayes rule. </p>
297<dl><dt><b>Parameters:</b></dt><dd>
298  <table border="0" cellspacing="2" cellpadding="0">
299    <tr><td valign="top"></td><td valign="top"><em>dt</em>&nbsp;</td><td>vector of input data </td></tr>
300  </table>
301  </dd>
302</dl>
303
304<p>Reimplemented from <a class="el" href="classbdm_1_1BMEF.html#ac287f4c0c1ea31b91572ec45351838f1">bdm::BMEF</a>.</p>
305
306<p>References <a class="el" href="arx_8cpp_source.html#l00004">bayes()</a>.</p>
307
308</div>
309</div>
310<a class="anchor" id="a9637412df898048bafaefee9dc7e9f6c"></a><!-- doxytag: member="bdm::ARX::from_setting" ref="a9637412df898048bafaefee9dc7e9f6c" args="(const Setting &amp;set)" -->
311<div class="memitem">
312<div class="memproto">
313      <table class="memname">
314        <tr>
315          <td class="memname">void bdm::ARX::from_setting </td>
316          <td>(</td>
317          <td class="paramtype">const Setting &amp;&nbsp;</td>
318          <td class="paramname"> <em>set</em></td>
319          <td>&nbsp;)&nbsp;</td>
320          <td><code> [virtual]</code></td>
321        </tr>
322      </table>
323</div>
324<div class="memdoc">
325<p><a class="el" href="classbdm_1_1UI.html" title="UI is an abstract class which collects all the auxiliary functions useful to prepare...">UI</a> for <a class="el" href="classbdm_1_1ARX.html" title="Linear Autoregressive model with Gaussian noise.">ARX</a> estimator</p>
326<p>The <a class="el" href="classbdm_1_1ARX.html" title="Linear Autoregressive model with Gaussian noise.">ARX</a> is constructed from a structure with fields: </p>
327<div class="fragment"><pre class="fragment">        estimator = {
328                <span class="keyword">class </span>= &quot;ARX&quot;;
329                y = {type=<span class="stringliteral">&quot;rv&quot;</span>, ...}   <span class="comment">// description of output variables</span>
330                rgr = {type=<span class="stringliteral">&quot;rv&quot;</span>, ...} <span class="comment">// description of regressor variables</span>
331                constant = <span class="keyword">true</span>;       <span class="comment">// boolean switch if the constant term is modelled or not</span>
332
333                <span class="comment">//optional fields</span>
334                dV0 = [1e-3, 1e-5, 1e-5, 1e-5];
335                                                           <span class="comment">// default: 1e-3 for y, 1e-5 for rgr</span>
336                nu0 = 6;               <span class="comment">// default: rgrlen + 2</span>
337                <a class="code" href="classbdm_1_1BMEF.html#a1331865e10fb1ccef65bb4c47fa3be64" title="forgetting factor">frg</a> = 1.0;             <span class="comment">// forgetting, default frg=1.0</span>
338        };
339</pre></div><p>The estimator will assign names of the posterior in the form ["theta_i" and "r_i"] </p>
340
341<p>Reimplemented from <a class="el" href="classbdm_1_1BM.html#a23c6a8f71f922023ab08dcb0487a86de">bdm::BM</a>.</p>
342
343<p>References <a class="el" href="exp__family_8h_source.html#l00084">bdm::BMEF::frg</a>, <a class="el" href="user__info_8h_source.html#l00443">bdm::UI::get()</a>, and <a class="el" href="bdmbase_8h_source.html#l01158">bdm::BM::set_options()</a>.</p>
344
345</div>
346</div>
347<a class="anchor" id="a080a7e531e3aa06694112863b15bc6a4"></a><!-- doxytag: member="bdm::ARX::logpred" ref="a080a7e531e3aa06694112863b15bc6a4" args="(const vec &amp;dt) const " -->
348<div class="memitem">
349<div class="memproto">
350      <table class="memname">
351        <tr>
352          <td class="memname">double bdm::ARX::logpred </td>
353          <td>(</td>
354          <td class="paramtype">const vec &amp;&nbsp;</td>
355          <td class="paramname"> <em>dt</em></td>
356          <td>&nbsp;)&nbsp;</td>
357          <td> const<code> [virtual]</code></td>
358        </tr>
359      </table>
360</div>
361<div class="memdoc">
362<p>Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out. </p>
363
364<p>Reimplemented from <a class="el" href="classbdm_1_1BM.html#a50257e0c1e5b5c73153ea6e716ad8ae0">bdm::BM</a>.</p>
365
366<p>References <a class="el" href="arx_8h_source.html#l00051">est</a>, <a class="el" href="bdmbase_8h_source.html#l01058">bdm::BM::evalll</a>, <a class="el" href="exp__family_8h_source.html#l00084">bdm::BMEF::frg</a>, <a class="el" href="exp__family_8h_source.html#l00086">bdm::BMEF::last_lognc</a>, <a class="el" href="exp__family_8cpp_source.html#l00050">bdm::egiw::lognc()</a>, <a class="el" href="arx_8h_source.html#l00055">nu</a>, <a class="el" href="square__mat_8cpp_source.html#l00074">bdm::ldmat::opupdt()</a>, <a class="el" href="exp__family_8h_source.html#l00240">bdm::egiw::pow()</a>, and <a class="el" href="arx_8h_source.html#l00053">V</a>.</p>
367
368</div>
369</div>
370<a class="anchor" id="a74fe8ae2d88bee8639510fd0eaf73513"></a><!-- doxytag: member="bdm::ARX::predictor" ref="a74fe8ae2d88bee8639510fd0eaf73513" args="() const " -->
371<div class="memitem">
372<div class="memproto">
373      <table class="memname">
374        <tr>
375          <td class="memname"><a class="el" href="classbdm_1_1mlnorm.html">mlnorm</a>&lt; <a class="el" href="classbdm_1_1ldmat.html">ldmat</a> &gt; * bdm::ARX::predictor </td>
376          <td>(</td>
377          <td class="paramname"></td>
378          <td>&nbsp;)&nbsp;</td>
379          <td> const<code> [virtual]</code></td>
380        </tr>
381      </table>
382</div>
383<div class="memdoc">
384
385<p>conditional version of the predictor </p>
386
387<p><p>&lt;----------- TODO </p>
388</p>
389
390<p>Reimplemented from <a class="el" href="classbdm_1_1BM.html#a598b25e3f3d96a5bc00a5faeb5b3c912">bdm::BM</a>.</p>
391
392<p>References <a class="el" href="bdmerror_8h_source.html#l00047">bdm_assert_debug</a>, <a class="el" href="bdmbase_8h_source.html#l00437">bdm::epdf::dimension()</a>, <a class="el" href="arx_8h_source.html#l00051">est</a>, <a class="el" href="exp__family_8cpp_source.html#l00145">bdm::egiw::mean_mat()</a>, <a class="el" href="square__mat_8h_source.html#l00100">bdm::sqmat::rows()</a>, <a class="el" href="exp__family_8h_source.html#l00560">bdm::mlnorm&lt; sq_T, TEpdf &gt;::set_parameters()</a>, and <a class="el" href="arx_8h_source.html#l00053">V</a>.</p>
393
394</div>
395</div>
396<a class="anchor" id="a16b02ae03316751664c22d59d90c1e34"></a><!-- doxytag: member="bdm::ARX::structure_est" ref="a16b02ae03316751664c22d59d90c1e34" args="(egiw Eg0)" -->
397<div class="memitem">
398<div class="memproto">
399      <table class="memname">
400        <tr>
401          <td class="memname">ivec bdm::ARX::structure_est </td>
402          <td>(</td>
403          <td class="paramtype"><a class="el" href="classbdm_1_1egiw.html">egiw</a>&nbsp;</td>
404          <td class="paramname"> <em>Eg0</em></td>
405          <td>&nbsp;)&nbsp;</td>
406          <td></td>
407        </tr>
408      </table>
409</div>
410<div class="memdoc">
411
412<p>Brute force structure estimation. </p>
413<dl class="return"><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
414
415<p>References <a class="el" href="bdmbase_8h_source.html#l00437">bdm::epdf::dimension()</a>, <a class="el" href="arx_8h_source.html#l00051">est</a>, and <a class="el" href="exp__family_8cpp_source.html#l00050">bdm::egiw::lognc()</a>.</p>
416
417</div>
418</div>
419<a class="anchor" id="a5d0f217ce270e6a8cb43a67b6c4b67fa"></a><!-- doxytag: member="bdm::ARX::structure_est_LT" ref="a5d0f217ce270e6a8cb43a67b6c4b67fa" args="(egiw Eg0)" -->
420<div class="memitem">
421<div class="memproto">
422      <table class="memname">
423        <tr>
424          <td class="memname">ivec bdm::ARX::structure_est_LT </td>
425          <td>(</td>
426          <td class="paramtype"><a class="el" href="classbdm_1_1egiw.html">egiw</a>&nbsp;</td>
427          <td class="paramname"> <em>Eg0</em></td>
428          <td>&nbsp;)&nbsp;</td>
429          <td></td>
430        </tr>
431      </table>
432</div>
433<div class="memdoc">
434
435<p>Smarter structure estimation by Ludvik Tesar. </p>
436<dl class="return"><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
437
438</div>
439</div>
440<hr/><h2>Member Data Documentation</h2>
441<a class="anchor" id="a363aaa55b2ab3eec602510cdf53e84ef"></a><!-- doxytag: member="bdm::ARX::_yrv" ref="a363aaa55b2ab3eec602510cdf53e84ef" args="" -->
442<div class="memitem">
443<div class="memproto">
444      <table class="memname">
445        <tr>
446          <td class="memname"><a class="el" href="classbdm_1_1RV.html">RV</a> <a class="el" href="classbdm_1_1ARX.html#a363aaa55b2ab3eec602510cdf53e84ef">bdm::ARX::_yrv</a><code> [protected]</code></td>
447        </tr>
448      </table>
449</div>
450<div class="memdoc">
451<p>description of modelled data <img class="formulaInl" alt="$ y_t $" src="form_6.png"/> in the likelihood function Do NOT access directly, only via <code>get_yrv()</code>. </p>
452
453</div>
454</div>
455<hr/>The documentation for this class was generated from the following files:<ul>
456<li><a class="el" href="arx_8h_source.html">arx.h</a></li>
457<li>arx.cpp</li>
458</ul>
459</div>
460<hr size="1"/><address style="text-align: right;"><small>Generated on Sun Sep 13 23:08:56 2009 for mixpp by&nbsp;
461<a href="http://www.doxygen.org/index.html">
462<img class="footer" src="doxygen.png" alt="doxygen"/></a> 1.6.1 </small></address>
463</body>
464</html>
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