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26<h1>ARX Class Reference</h1><!-- doxytag: class="ARX" --><!-- doxytag: inherits="BMEF" -->Linear Autoregressive model with Gaussian noise. 
27<a href="#_details">More...</a>
28<p>
29<code>#include &lt;<a class="el" href="arx_8h-source.html">arx.h</a>&gt;</code>
30<p>
31<div class="dynheader">
32Inheritance diagram for ARX:</div>
33<div class="dynsection">
34<p><center><img src="classARX__inherit__graph.png" border="0" usemap="#ARX__inherit__map" alt="Inheritance graph"></center>
35<map name="ARX__inherit__map">
36<area shape="rect" href="classBMEF.html" title="Estimator for Exponential family." alt="" coords="5,84,61,111"><area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="13,7,53,33"></map>
37<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
38<div class="dynheader">
39Collaboration diagram for ARX:</div>
40<div class="dynsection">
41<p><center><img src="classARX__coll__graph.png" border="0" usemap="#ARX__coll__map" alt="Collaboration graph"></center>
42<map name="ARX__coll__map">
43<area shape="rect" href="classBMEF.html" title="Estimator for Exponential family." alt="" coords="5,263,61,289"><area shape="rect" href="classBM.html" title="Bayesian Model of the world, i.e. all uncertainty is modeled by probabilities." alt="" coords="12,156,52,183"><area shape="rect" href="classRV.html" title="Class representing variables, most often random variables." alt="" coords="39,7,76,33"><area shape="rect" href="classepdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="69,103,117,129"><area shape="rect" href="classldmat.html" title="Matrix stored in LD form, (typically known as UD)." alt="" coords="139,209,197,236"><area shape="rect" href="classegiw.html" title="Gauss&#45;inverse&#45;Wishart density stored in LD form." alt="" coords="71,316,119,343"><area shape="rect" href="classsqmat.html" title="Virtual class for representation of double symmetric matrices in square&#45;root form..." alt="" coords="141,103,203,129"><area shape="rect" href="classeEF.html" title="General conjugate exponential family posterior density." alt="" coords="72,209,115,236"></map>
44<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
45
46<p>
47<a href="classARX-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
48<tr><td></td></tr>
49<tr><td colspan="2"><br><h2>Public Member Functions</h2></td></tr>
50<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="545e269bf7852c81484cf361b54d9917"></a><!-- doxytag: member="ARX::ARX" ref="545e269bf7852c81484cf361b54d9917" args="(const RV &amp;rv, const mat &amp;V0, const double &amp;nu0, const double frg0=1.0)" -->
51&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#545e269bf7852c81484cf361b54d9917">ARX</a> (const <a class="el" href="classRV.html">RV</a> &amp;<a class="el" href="classBM.html#af00f0612fabe66241dd507188cdbf88">rv</a>, const mat &amp;V0, const double &amp;nu0, const double frg0=1.0)</td></tr>
52
53<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Full constructor. <br></td></tr>
54<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a5358883a49b52f50755ad8770c2bbdb"></a><!-- doxytag: member="ARX::ARX" ref="a5358883a49b52f50755ad8770c2bbdb" args="(const ARX &amp;A0)" -->
55&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#a5358883a49b52f50755ad8770c2bbdb">ARX</a> (const <a class="el" href="classARX.html">ARX</a> &amp;A0)</td></tr>
56
57<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Copy constructor. <br></td></tr>
58<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="d2751057811c6fb8f4ff86e1648bcddc"></a><!-- doxytag: member="ARX::_copy_" ref="d2751057811c6fb8f4ff86e1648bcddc" args="(bool changerv=false)" -->
59<a class="el" href="classBM.html">BM</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#d2751057811c6fb8f4ff86e1648bcddc">_copy_</a> (bool changerv=false)</td></tr>
60
61<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Auxiliary function. <br></td></tr>
62<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bc8c36399e82b2fc504baed845ed2007"></a><!-- doxytag: member="ARX::set_parameters" ref="bc8c36399e82b2fc504baed845ed2007" args="(const ldmat &amp;V0, const double &amp;nu0)" -->
63void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#bc8c36399e82b2fc504baed845ed2007">set_parameters</a> (const <a class="el" href="classldmat.html">ldmat</a> &amp;V0, const double &amp;nu0)</td></tr>
64
65<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set sufficient statistics. <br></td></tr>
66<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="26925d66dfc366815c497d67b62ee49c"></a><!-- doxytag: member="ARX::set_statistics" ref="26925d66dfc366815c497d67b62ee49c" args="(const BMEF *BM0)" -->
67void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#26925d66dfc366815c497d67b62ee49c">set_statistics</a> (const <a class="el" href="classBMEF.html">BMEF</a> *BM0)</td></tr>
68
69<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">get statistics from another model <br></td></tr>
70<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="29f55b43b8b6f5c4a55f6176aa85c494"></a><!-- doxytag: member="ARX::get_parameters" ref="29f55b43b8b6f5c4a55f6176aa85c494" args="(mat &amp;V0, double &amp;nu0)" -->
71void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#29f55b43b8b6f5c4a55f6176aa85c494">get_parameters</a> (mat &amp;V0, double &amp;nu0)</td></tr>
72
73<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns sufficient statistics. <br></td></tr>
74<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="14d62abfe355275ea3b8d0c5d40f01a0"></a><!-- doxytag: member="ARX::bayes" ref="14d62abfe355275ea3b8d0c5d40f01a0" args="(const vec &amp;dt, const double w)" -->
75void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#14d62abfe355275ea3b8d0c5d40f01a0">bayes</a> (const vec &amp;dt, const double w)</td></tr>
76
77<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>
78<tr><td class="memItemLeft" nowrap align="right" valign="top">void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#ba82c956ca893826811aefe1e4af465d">bayes</a> (const vec &amp;dt)</td></tr>
79
80<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Incremental Bayes rule.  <a href="#ba82c956ca893826811aefe1e4af465d"></a><br></td></tr>
81<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="c13df43e0af87697fda6b457d56a6d45"></a><!-- doxytag: member="ARX::_epdf" ref="c13df43e0af87697fda6b457d56a6d45" args="() const " -->
82const <a class="el" href="classepdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#c13df43e0af87697fda6b457d56a6d45">_epdf</a> () const </td></tr>
83
84<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>
85<tr><td class="memItemLeft" nowrap align="right" valign="top">double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#e7f9e7823aec9bf7ddc3b42d9b3304c4">logpred</a> (const vec &amp;dt) const </td></tr>
86
87<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="365092d4fd1ab769fcf62bf28f364fab"></a><!-- doxytag: member="ARX::flatten" ref="365092d4fd1ab769fcf62bf28f364fab" args="(BMEF *B)" -->
88void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#365092d4fd1ab769fcf62bf28f364fab">flatten</a> (<a class="el" href="classBMEF.html">BMEF</a> *B)</td></tr>
89
90<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Flatten the posterior. <br></td></tr>
91<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>
92
93<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Brute force structure estimation.  <a href="#130bb7336aac681ce14b027b8f1409fa"></a><br></td></tr>
94<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="0186270f75189677f390fe088a9947e9"></a><!-- doxytag: member="ARX::bayesB" ref="0186270f75189677f390fe088a9947e9" args="(const mat &amp;Dt)" -->
95virtual void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#0186270f75189677f390fe088a9947e9">bayesB</a> (const mat &amp;Dt)</td></tr>
96
97<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Batch Bayes rule (columns of Dt are observations). <br></td></tr>
98<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="126bd2595c48e311fc2a7ab72876092a"></a><!-- doxytag: member="ARX::_rv" ref="126bd2595c48e311fc2a7ab72876092a" args="() const " -->
99const <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>
100
101<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
102<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="87f4a547d2c29180be88175e5eab9c88"></a><!-- doxytag: member="ARX::_ll" ref="87f4a547d2c29180be88175e5eab9c88" args="() const " -->
103double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#87f4a547d2c29180be88175e5eab9c88">_ll</a> () const </td></tr>
104
105<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
106<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1ffa9f23669aabecc3760c06c6987522"></a><!-- doxytag: member="ARX::set_evalll" ref="1ffa9f23669aabecc3760c06c6987522" args="(bool evl0)" -->
107void&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#1ffa9f23669aabecc3760c06c6987522">set_evalll</a> (bool evl0)</td></tr>
108
109<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
110<tr><td colspan="2"><br><h2>Protected Attributes</h2></td></tr>
111<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="691d023662beffa1dda611b416c0e27e"></a><!-- doxytag: member="ARX::est" ref="691d023662beffa1dda611b416c0e27e" args="" -->
112<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>
113
114<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>
115<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="2291297861dd74ca0175a01f910a0ef7"></a><!-- doxytag: member="ARX::V" ref="2291297861dd74ca0175a01f910a0ef7" args="" -->
116<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>
117
118<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.V <br></td></tr>
119<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="a4182c281098b2d86b62518a7493d9be"></a><!-- doxytag: member="ARX::nu" ref="a4182c281098b2d86b62518a7493d9be" args="" -->
120double &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classARX.html#a4182c281098b2d86b62518a7493d9be">nu</a></td></tr>
121
122<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cached value of est.nu <br></td></tr>
123<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="538d632e59f9afa8daa1de74da12ce71"></a><!-- doxytag: member="ARX::frg" ref="538d632e59f9afa8daa1de74da12ce71" args="" -->
124double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#538d632e59f9afa8daa1de74da12ce71">frg</a></td></tr>
125
126<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">forgetting factor <br></td></tr>
127<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="308cf5d4133cd471fdf1ecd5dfa09d02"></a><!-- doxytag: member="ARX::last_lognc" ref="308cf5d4133cd471fdf1ecd5dfa09d02" args="" -->
128double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBMEF.html#308cf5d4133cd471fdf1ecd5dfa09d02">last_lognc</a></td></tr>
129
130<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>
131<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="af00f0612fabe66241dd507188cdbf88"></a><!-- doxytag: member="ARX::rv" ref="af00f0612fabe66241dd507188cdbf88" args="" -->
132<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>
133
134<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Random variable of the posterior. <br></td></tr>
135<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5623fef6572a08c2b53b8c87b82dc979"></a><!-- doxytag: member="ARX::ll" ref="5623fef6572a08c2b53b8c87b82dc979" args="" -->
136double&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#5623fef6572a08c2b53b8c87b82dc979">ll</a></td></tr>
137
138<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Logarithm of marginalized data likelihood. <br></td></tr>
139<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="bf6fb59b30141074f8ee1e2f43d03129"></a><!-- doxytag: member="ARX::evalll" ref="bf6fb59b30141074f8ee1e2f43d03129" args="" -->
140bool&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classBM.html#bf6fb59b30141074f8ee1e2f43d03129">evalll</a></td></tr>
141
142<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>
143</table>
144<hr><a name="_details"></a><h2>Detailed Description</h2>
145Linear Autoregressive model with Gaussian noise.
146<p>
147Regression of the following kind: <p class="formulaDsp">
148<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">
149<p>
150 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">
151<img class="formulaDsp" alt="\[ e_t \sim \mathcal{N}(0,1). \]" src="form_62.png">
152<p>
153<p>
154Extension 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>
155<a class="anchor" name="ba82c956ca893826811aefe1e4af465d"></a><!-- doxytag: member="ARX::bayes" ref="ba82c956ca893826811aefe1e4af465d" args="(const vec &amp;dt)" -->
156<div class="memitem">
157<div class="memproto">
158      <table class="memname">
159        <tr>
160          <td class="memname">void ARX::bayes           </td>
161          <td>(</td>
162          <td class="paramtype">const vec &amp;&nbsp;</td>
163          <td class="paramname"> <em>dt</em>          </td>
164          <td>&nbsp;)&nbsp;</td>
165          <td><code> [inline, virtual]</code></td>
166        </tr>
167      </table>
168</div>
169<div class="memdoc">
170
171<p>
172Incremental Bayes rule.
173<p>
174<dl compact><dt><b>Parameters:</b></dt><dd>
175  <table border="0" cellspacing="2" cellpadding="0">
176    <tr><td valign="top"></td><td valign="top"><em>dt</em>&nbsp;</td><td>vector of input data </td></tr>
177  </table>
178</dl>
179
180<p>Reimplemented from <a class="el" href="classBMEF.html#52b7719312d545215cca1ff87722a35a">BMEF</a>.</p>
181
182<p>References <a class="el" href="bdm_2estim_2arx_8cpp-source.html#l00005">bayes()</a>.</p>
183
184</div>
185</div><p>
186<a class="anchor" name="e7f9e7823aec9bf7ddc3b42d9b3304c4"></a><!-- doxytag: member="ARX::logpred" ref="e7f9e7823aec9bf7ddc3b42d9b3304c4" args="(const vec &amp;dt) const " -->
187<div class="memitem">
188<div class="memproto">
189      <table class="memname">
190        <tr>
191          <td class="memname">double ARX::logpred           </td>
192          <td>(</td>
193          <td class="paramtype">const vec &amp;&nbsp;</td>
194          <td class="paramname"> <em>dt</em>          </td>
195          <td>&nbsp;)&nbsp;</td>
196          <td> const<code> [virtual]</code></td>
197        </tr>
198      </table>
199</div>
200<div class="memdoc">
201
202<p>
203Evaluates predictive log-likelihood of the given data record I.e. marginal likelihood of the data with the posterior integrated out.
204<p>Reimplemented from <a class="el" href="classBM.html#8a8ce6df431689964c41cc6c849cfd06">BM</a>.</p>
205
206<p>References <a class="el" href="libEF_8h-source.html#l00185">egiw::_nu()</a>, <a class="el" href="libEF_8h-source.html#l00183">egiw::_V()</a>, <a class="el" href="arx_8h-source.html#l00039">est</a>, <a class="el" href="libBM_8h-source.html#l00280">BM::evalll</a>, <a class="el" href="libEF_8h-source.html#l00078">BMEF::frg</a>, <a class="el" href="libEF_8h-source.html#l00080">BMEF::last_lognc</a>, <a class="el" href="libEF_8cpp-source.html#l00044">egiw::lognc()</a>, <a class="el" href="arx_8h-source.html#l00043">nu</a>, <a class="el" href="libDC_8cpp-source.html#l00058">ldmat::opupdt()</a>, <a class="el" href="libEF_8cpp-source.html#l00099">egiw::pow()</a>, and <a class="el" href="arx_8h-source.html#l00041">V</a>.</p>
207
208</div>
209</div><p>
210<a class="anchor" name="130bb7336aac681ce14b027b8f1409fa"></a><!-- doxytag: member="ARX::structure_est" ref="130bb7336aac681ce14b027b8f1409fa" args="(egiw Eg0)" -->
211<div class="memitem">
212<div class="memproto">
213      <table class="memname">
214        <tr>
215          <td class="memname">ivec ARX::structure_est           </td>
216          <td>(</td>
217          <td class="paramtype"><a class="el" href="classegiw.html">egiw</a>&nbsp;</td>
218          <td class="paramname"> <em>Eg0</em>          </td>
219          <td>&nbsp;)&nbsp;</td>
220          <td></td>
221        </tr>
222      </table>
223</div>
224<div class="memdoc">
225
226<p>
227Brute force structure estimation.
228<p>
229<dl class="return" compact><dt><b>Returns:</b></dt><dd>indeces of accepted regressors. </dd></dl>
230
231<p>References <a class="el" href="libBM_8h-source.html#l00069">RV::count()</a>, <a class="el" href="arx_8h-source.html#l00039">est</a>, <a class="el" href="libEF_8cpp-source.html#l00044">egiw::lognc()</a>, and <a class="el" href="libBM_8h-source.html#l00276">BM::rv</a>.</p>
232
233</div>
234</div><p>
235<hr>The documentation for this class was generated from the following files:<ul>
236<li>work/git/mixpp/bdm/estim/<a class="el" href="arx_8h-source.html">arx.h</a><li>work/git/mixpp/bdm/estim/arx.cpp</ul>
237</div>
238<hr size="1"><address style="text-align: right;"><small>Generated on Tue Sep 23 16:00:48 2008 for mixpp by&nbsp;
239<a href="http://www.doxygen.org/index.html">
240<img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>
241</body>
242</html>
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