Changeset 270 for doc/html/classbdm_1_1mgamma__fix.html

Timestamp:

02/16/09 10:02:08 (16 years ago)

Author:

smidl

Message:

Changes in the very root classes!
* rv and rvc are no longer compulsory,
* samplecond does not return ll
* BM has drv

Files:

• doc/html/classbdm_1_1mgamma__fix.html (modified) (11 diffs)

doc/html/classbdm_1_1mgamma__fix.html

@@ -29 +29 @@
 </div>
 <div class="contents">
-<h1>bdm::mgamma_fix Class Reference</h1><!-- doxytag: class="bdm::mgamma_fix" --><!-- doxytag: inherits="bdm::mgamma" -->Gamma random walk around a fixed point.  
-<a href="#_details">More...</a>
-<p>
-<code>#include &lt;<a class="el" href="libEF_8h-source.html">libEF.h</a>&gt;</code>
+<h1>bdm::mgamma_fix Class Reference</h1><!-- doxytag: class="bdm::mgamma_fix" --><!-- doxytag: inherits="bdm::mgamma" --><code>#include &lt;<a class="el" href="libEF_8h-source.html">libEF.h</a>&gt;</code>
 <p>
 <div class="dynheader">
@@ -41 +38 @@
 <area shape="rect" href="classbdm_1_1mgamma.html" title="Gamma random walk." alt="" coords="16,239,136,265"><area shape="rect" href="classbdm_1_1mEF.html" title="Exponential family model." alt="" coords="33,161,119,188"><area shape="rect" href="classbdm_1_1mpdf.html" title="Conditional probability density, e.g. modeling some dependencies." alt="" coords="31,84,121,111"><area shape="rect" href="classbdm_1_1bdmroot.html" title="Root class of BDM objects." alt="" coords="20,7,132,33"></map>
 <center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
-<div class="dynheader">
-Collaboration diagram for bdm::mgamma_fix:</div>
-<div class="dynsection">
-<p><center><img src="classbdm_1_1mgamma__fix__coll__graph.png" border="0" usemap="#bdm_1_1mgamma__fix__coll__map" alt="Collaboration graph"></center>
-<map name="bdm_1_1mgamma__fix__coll__map">
-<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_1bdmroot.html" title="Root class of BDM objects." alt="" coords="19,7,131,33"><area shape="rect" href="classbdm_1_1RV.html" title="Class representing variables, most often random variables." alt="" coords="37,87,112,113"><area shape="rect" href="classbdm_1_1epdf.html" title="Probability density function with numerical statistics, e.g. posterior density." alt="" coords="105,185,191,212"><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>
-<center><font size="2">[<a href="graph_legend.html">legend</a>]</font></center></div>
-
-<p>
-<a href="classbdm_1_1mgamma__fix-members.html">List of all members.</a><table border="0" cellpadding="0" cellspacing="0">
+
+<p>
+<a href="classbdm_1_1mgamma__fix-members.html">List of all members.</a><hr><a name="_details"></a><h2>Detailed Description</h2>
+Gamma random walk around a fixed point. 
+<p>
+Mean 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">
+<img class="formulaDsp" alt="\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]" src="form_18.png">
+<p>
+<p>
+Standard 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>
+The standard deviation of the walk is then: <img class="formulaInl" alt="$\mu/\sqrt(k)$" src="form_13.png">. <table border="0" cellpadding="0" cellspacing="0">
 <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="c73571f45ab2926e5a7fb9c3791b5614"></a><!-- doxytag: member="bdm::mgamma_fix::mgamma_fix" ref="c73571f45ab2926e5a7fb9c3791b5614" args="(const RV &amp;rv, const RV &amp;rvc)" -->
-&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>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9a31bc9b4b60188a18a2a6b588dc4b2d"></a><!-- doxytag: member="bdm::mgamma_fix::mgamma_fix" ref="9a31bc9b4b60188a18a2a6b588dc4b2d" args="()" -->
+&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma__fix.html#9a31bc9b4b60188a18a2a6b588dc4b2d">mgamma_fix</a> ()</td></tr>
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constructor. <br></td></tr>
@@ -69 +67 @@
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Set value of <code>k</code>. <br></td></tr>
+<tr><td colspan="2"><div class="groupHeader">Matematical operations</div></td></tr>
 <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#f0c1db6fcbb3aae2dd6123884457a367">samplecond</a> (const vec &amp;cond)</td></tr>
 
 <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="#f0c1db6fcbb3aae2dd6123884457a367"></a><br></td></tr>
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns.  <a href="#ee26963a637b2ea1fb1933652981e652"></a><br></td></tr>
+<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#afe4185b26baeb03688202e254d3b005">samplecond_m</a> (const vec &amp;cond, int N)</td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Returns.  <a href="#afe4185b26baeb03688202e254d3b005"></a><br></td></tr>
 <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)" -->
 virtual 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>
@@ -83 +82 @@
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Matrix version of evallogcond. <br></td></tr>
-<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 " -->
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
-<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 " -->
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
+<tr><td colspan="2"><div class="groupHeader">Access to attributes</div></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5571482d150fbcb72cc36f6694ce1a10"></a><!-- doxytag: member="bdm::mgamma_fix::_rv" ref="5571482d150fbcb72cc36f6694ce1a10" args="()" -->
+<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>_rv</b> ()</td></tr>
+
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="26001264236846897bd11e4baad47245"></a><!-- doxytag: member="bdm::mgamma_fix::_rvc" ref="26001264236846897bd11e4baad47245" args="()" -->
+<a class="el" href="classbdm_1_1RV.html">RV</a>&nbsp;</td><td class="memItemRight" valign="bottom"><b>_rvc</b> ()</td></tr>
+
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1c2bae3e1e90874e72941863974ec0ed"></a><!-- doxytag: member="bdm::mgamma_fix::dimension" ref="1c2bae3e1e90874e72941863974ec0ed" args="()" -->
+int&nbsp;</td><td class="memItemRight" valign="bottom"><b>dimension</b> ()</td></tr>
+
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="35e135910aed187b7290742f50e61bc8"></a><!-- doxytag: member="bdm::mgamma_fix::dimensionc" ref="35e135910aed187b7290742f50e61bc8" args="()" -->
+int&nbsp;</td><td class="memItemRight" valign="bottom"><b>dimensionc</b> ()</td></tr>
+
 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="1892fe3933488942253679f068e9e7f6"></a><!-- doxytag: member="bdm::mgamma_fix::_epdf" ref="1892fe3933488942253679f068e9e7f6" args="()" -->
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
+<a class="el" href="classbdm_1_1epdf.html">epdf</a> &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><b>_epdf</b> ()</td></tr>
+
 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="05e843fd11c410a99dad2b88c55aca80"></a><!-- doxytag: member="bdm::mgamma_fix::_e" ref="05e843fd11c410a99dad2b88c55aca80" args="()" -->
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">access function <br></td></tr>
+<a class="el" href="classbdm_1_1epdf.html">epdf</a> *&nbsp;</td><td class="memItemRight" valign="bottom"><b>_e</b> ()</td></tr>
+
+<tr><td colspan="2"><div class="groupHeader">Connection to other objects</div></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7631a5570e4ade1420065e8df78f4401"></a><!-- doxytag: member="bdm::mgamma_fix::set_rvc" ref="7631a5570e4ade1420065e8df78f4401" args="(const RV &amp;rvc0)" -->
+void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_rvc</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rvc0)</td></tr>
+
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="18ac26bc2f96ae01ef4eb06178abbd75"></a><!-- doxytag: member="bdm::mgamma_fix::set_rv" ref="18ac26bc2f96ae01ef4eb06178abbd75" args="(const RV &amp;rv0)" -->
+void&nbsp;</td><td class="memItemRight" valign="bottom"><b>set_rv</b> (const <a class="el" href="classbdm_1_1RV.html">RV</a> &amp;rv0)</td></tr>
+
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f8e3798150b42fd1f3e16ddbbe0e7045"></a><!-- doxytag: member="bdm::mgamma_fix::isnamed" ref="f8e3798150b42fd1f3e16ddbbe0e7045" args="()" -->
+bool&nbsp;</td><td class="memItemRight" valign="bottom"><b>isnamed</b> ()</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="1eb701506aabb2e6af007e487212d6fa"></a><!-- doxytag: member="bdm::mgamma_fix::l" ref="1eb701506aabb2e6af007e487212d6fa" args="" -->
@@ -116 +128 @@
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">Constant <img class="formulaInl" alt="$k$" src="form_41.png">. <br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="f6a652ce70fa2eb4d2c7ba6d5a6ae343"></a><!-- doxytag: member="bdm::mgamma_fix::_beta" ref="f6a652ce70fa2eb4d2c7ba6d5a6ae343" args="" -->
-vec *&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#f6a652ce70fa2eb4d2c7ba6d5a6ae343">_beta</a></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="3d95f4dde9214ff6dba265e18af60312"></a><!-- doxytag: member="bdm::mgamma_fix::_beta" ref="3d95f4dde9214ff6dba265e18af60312" args="" -->
+vec &amp;&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mgamma.html#3d95f4dde9214ff6dba265e18af60312">_beta</a></td></tr>
 
 <tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">cache of epdf.beta <br></td></tr>
-<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="9bcfb45435d30983f436d41c298cbb51"></a><!-- doxytag: member="bdm::mgamma_fix::rv" ref="9bcfb45435d30983f436d41c298cbb51" args="" -->
-<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>
-
-<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">modeled random variable <br></td></tr>
+<tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="7c1900976ff13dbc09c9729b3bbff9e6"></a><!-- doxytag: member="bdm::mgamma_fix::dimc" ref="7c1900976ff13dbc09c9729b3bbff9e6" args="" -->
+int&nbsp;</td><td class="memItemRight" valign="bottom"><a class="el" href="classbdm_1_1mpdf.html#7c1900976ff13dbc09c9729b3bbff9e6">dimc</a></td></tr>
+
+<tr><td class="mdescLeft">&nbsp;</td><td class="mdescRight">dimension of the condition <br></td></tr>
 <tr><td class="memItemLeft" nowrap align="right" valign="top"><a class="anchor" name="5a5f08950daa08b85b01ddf4e1c36288"></a><!-- doxytag: member="bdm::mgamma_fix::rvc" ref="5a5f08950daa08b85b01ddf4e1c36288" args="" -->
 <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>
@@ -133 +145 @@
 <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>
 </table>
-<hr><a name="_details"></a><h2>Detailed Description</h2>
-Gamma random walk around a fixed point. 
-<p>
-Mean 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">
-<img class="formulaDsp" alt="\[ \mu = \mu_{t-1} ^{l} p^{1-l}\]" src="form_18.png">
-<p>
-<p>
-Standard 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>
-The standard deviation of the walk is then: <img class="formulaInl" alt="$\mu/\sqrt(k)$" src="form_13.png">. <hr><h2>Member Function Documentation</h2>
+<hr><h2>Member Function Documentation</h2>
 <a class="anchor" name="f0c1db6fcbb3aae2dd6123884457a367"></a><!-- doxytag: member="bdm::mgamma_fix::samplecond" ref="f0c1db6fcbb3aae2dd6123884457a367" args="(const vec &amp;cond)" -->
 <div class="memitem">
@@ -167 +171 @@
 </dl>
 
-<p>References <a class="el" href="libBM_8h-source.html#l00250">bdm::mpdf::condition()</a>, <a class="el" href="libBM_8h-source.html#l00233">bdm::mpdf::ep</a>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
+<p>References <a class="el" href="libBM_8h-source.html#l00315">bdm::mpdf::condition()</a>, <a class="el" href="libBM_8h-source.html#l00288">bdm::mpdf::ep</a>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
 
 <p>Referenced by <a class="el" href="libPF_8h-source.html#l00143">bdm::MPF&lt; BM_T &gt;::bayes()</a>, <a class="el" href="libPF_8cpp-source.html#l00007">bdm::PF::bayes()</a>, and <a class="el" href="libDS_8cpp-source.html#l00044">bdm::ArxDS::step()</a>.</p>
@@ -173 +177 @@
 </div>
 </div><p>
-<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)" -->
+<a class="anchor" name="afe4185b26baeb03688202e254d3b005"></a><!-- doxytag: member="bdm::mgamma_fix::samplecond_m" ref="afe4185b26baeb03688202e254d3b005" args="(const vec &amp;cond, int N)" -->
 <div class="memitem">
 <div class="memproto">
@@ -182 +186 @@
           <td class="paramtype">const vec &amp;&nbsp;</td>
           <td class="paramname"> <em>cond</em>, </td>
-        </tr>
-        <tr>
-          <td class="paramkey"></td>
-          <td></td>
-          <td class="paramtype">vec &amp;&nbsp;</td>
-          <td class="paramname"> <em>ll</em>, </td>
         </tr>
         <tr>
@@ -215 +213 @@
 </dl>
 
-<p>References <a class="el" href="libBM_8h-source.html#l00250">bdm::mpdf::condition()</a>, <a class="el" href="libBM_8h-source.html#l00086">bdm::RV::count()</a>, <a class="el" href="libBM_8h-source.html#l00233">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#l00229">bdm::mpdf::rv</a>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
+<p>References <a class="el" href="libBM_8h-source.html#l00315">bdm::mpdf::condition()</a>, <a class="el" href="libBM_8h-source.html#l00272">bdm::epdf::dimension()</a>, <a class="el" href="libBM_8h-source.html#l00288">bdm::mpdf::ep</a>, and <a class="el" href="classbdm_1_1epdf.html#09721eb148bc49d6ec2f1956039f3a10">bdm::epdf::sample()</a>.</p>
 
 </div>
@@ -222 +220 @@
 <li><a class="el" href="libEF_8h-source.html">libEF.h</a></ul>
 </div>
-<hr size="1"><address style="text-align: right;"><small>Generated on Wed Feb 11 10:21:07 2009 for mixpp by&nbsp;
+<hr size="1"><address style="text-align: right;"><small>Generated on Wed Feb 11 23:34:07 2009 for mixpp by&nbsp;
 <a href="http://www.doxygen.org/index.html">
 <img src="doxygen.png" alt="doxygen" align="middle" border="0"></a> 1.5.6 </small></address>