Files
mlpack/doc/html/randomized__svd_8hpp_source.html
T

126 lines
21 KiB
HTML

<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="Content-Type" content="text/xhtml;charset=UTF-8"/>
<meta http-equiv="X-UA-Compatible" content="IE=9"/>
<meta name="generator" content="Doxygen 1.8.11"/>
<title>mlpack: src/mlpack/methods/randomized_svd/randomized_svd.hpp Source File</title>
<link href="tabs.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="jquery.js"></script>
<script type="text/javascript" src="dynsections.js"></script>
<link href="search/search.css" rel="stylesheet" type="text/css"/>
<script type="text/javascript" src="search/searchdata.js"></script>
<script type="text/javascript" src="search/search.js"></script>
<script type="text/javascript">
$(document).ready(function() { init_search(); });
</script>
<link href="doxygen.css" rel="stylesheet" type="text/css" />
<link href="extra-stylesheet.css" rel="stylesheet" type="text/css"/>
</head>
<body>
<div id="top"><!-- do not remove this div, it is closed by doxygen! -->
<div id="titlearea">
<table cellspacing="0" cellpadding="0">
<tbody>
<tr style="height: 56px;">
<td id="projectalign" style="padding-left: 0.5em;">
<div id="projectname">mlpack
&#160;<span id="projectnumber">master</span>
</div>
</td>
</tr>
</tbody>
</table>
</div>
<!-- end header part -->
<!-- Generated by Doxygen 1.8.11 -->
<script type="text/javascript">
var searchBox = new SearchBox("searchBox", "search",false,'Search');
</script>
<div id="navrow1" class="tabs">
<ul class="tablist">
<li><a href="index.html"><span>Main&#160;Page</span></a></li>
<li><a href="pages.html"><span>Related&#160;Pages</span></a></li>
<li><a href="namespaces.html"><span>Namespaces</span></a></li>
<li><a href="annotated.html"><span>Classes</span></a></li>
<li class="current"><a href="files.html"><span>Files</span></a></li>
<li>
<div id="MSearchBox" class="MSearchBoxInactive">
<span class="left">
<img id="MSearchSelect" src="search/mag_sel.png"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
alt=""/>
<input type="text" id="MSearchField" value="Search" accesskey="S"
onfocus="searchBox.OnSearchFieldFocus(true)"
onblur="searchBox.OnSearchFieldFocus(false)"
onkeyup="searchBox.OnSearchFieldChange(event)"/>
</span><span class="right">
<a id="MSearchClose" href="javascript:searchBox.CloseResultsWindow()"><img id="MSearchCloseImg" border="0" src="search/close.png" alt=""/></a>
</span>
</div>
</li>
</ul>
</div>
<div id="navrow2" class="tabs2">
<ul class="tablist">
<li><a href="files.html"><span>File&#160;List</span></a></li>
<li><a href="globals.html"><span>File&#160;Members</span></a></li>
</ul>
</div>
<!-- window showing the filter options -->
<div id="MSearchSelectWindow"
onmouseover="return searchBox.OnSearchSelectShow()"
onmouseout="return searchBox.OnSearchSelectHide()"
onkeydown="return searchBox.OnSearchSelectKey(event)">
</div>
<!-- iframe showing the search results (closed by default) -->
<div id="MSearchResultsWindow">
<iframe src="javascript:void(0)" frameborder="0"
name="MSearchResults" id="MSearchResults">
</iframe>
</div>
<div id="nav-path" class="navpath">
<ul>
<li class="navelem"><a class="el" href="dir_68267d1309a1af8e8297ef4c3efbcdba.html">src</a></li><li class="navelem"><a class="el" href="dir_44a936ef30fc126706c6284a2fc0c990.html">mlpack</a></li><li class="navelem"><a class="el" href="dir_3cfbf900288ec2fe8dd2c2c8482f216e.html">methods</a></li><li class="navelem"><a class="el" href="dir_2fc1595eb878e336b6604e9b96f83670.html">randomized_svd</a></li> </ul>
</div>
</div><!-- top -->
<div class="header">
<div class="headertitle">
<div class="title">randomized_svd.hpp</div> </div>
</div><!--header-->
<div class="contents">
<a href="randomized__svd_8hpp.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span>&#160;</div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160;<span class="preprocessor">#ifndef MLPACK_METHODS_RANDOMIZED_SVD_RANDOMIZED_SVD_HPP</span></div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="preprocessor">#define MLPACK_METHODS_RANDOMIZED_SVD_RANDOMIZED_SVD_HPP</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160;</div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="preprocessor">#include &lt;<a class="code" href="prereqs_8hpp.html">mlpack/prereqs.hpp</a>&gt;</span></div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacemlpack.html">mlpack</a> {</div><div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;<span class="keyword">namespace </span>svd {</div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;</div><div class="line"><a name="l00066"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html"> 66</a></span>&#160;<span class="keyword">class </span><a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html">RandomizedSVD</a></div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160;{</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; <span class="keyword">public</span>:</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a8ce931925a0625f40d2271506fb24ab7">RandomizedSVD</a>(<span class="keyword">const</span> arma::mat&amp; data,</div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; arma::mat&amp; u,</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; arma::vec&amp; s,</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; arma::mat&amp; v,</div><div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">iteratedPower</a> = 0,</div><div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">maxIterations</a> = 2,</div><div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; <span class="keyword">const</span> <span class="keywordtype">size_t</span> rank = 0,</div><div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">eps</a> = 1e-7);</div><div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160;</div><div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a8ce931925a0625f40d2271506fb24ab7">RandomizedSVD</a>(<span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">iteratedPower</a> = 0,</div><div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keyword">const</span> <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">maxIterations</a> = 2,</div><div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">eps</a> = 1e-7);</div><div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160;</div><div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keywordtype">void</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a6956d9a633c8b11f3ece411808d346f7">Apply</a>(<span class="keyword">const</span> arma::mat&amp; data,</div><div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; arma::mat&amp; u,</div><div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; arma::vec&amp; s,</div><div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; arma::mat&amp; v,</div><div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="keyword">const</span> <span class="keywordtype">size_t</span> rank);</div><div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160;</div><div class="line"><a name="l00124"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a184b9b07dc065737b2d293e7b7f82b00"> 124</a></span>&#160; <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a184b9b07dc065737b2d293e7b7f82b00">IteratedPower</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">iteratedPower</a>; }</div><div class="line"><a name="l00126"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ac183fa54a6e9dc6b175a5390bca63a0f"> 126</a></span>&#160; <span class="keywordtype">size_t</span>&amp; <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ac183fa54a6e9dc6b175a5390bca63a0f">IteratedPower</a>() { <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">iteratedPower</a>; }</div><div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160;</div><div class="line"><a name="l00129"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ae95613dfd1b7c9a8bf0bc24a846be969"> 129</a></span>&#160; <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ae95613dfd1b7c9a8bf0bc24a846be969">MaxIterations</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">maxIterations</a>; }</div><div class="line"><a name="l00131"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#aa7e2301ec004ef067ad990a1ad6cbd26"> 131</a></span>&#160; <span class="keywordtype">size_t</span>&amp; <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#aa7e2301ec004ef067ad990a1ad6cbd26">MaxIterations</a>() { <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">maxIterations</a>; }</div><div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160;</div><div class="line"><a name="l00134"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#afec19c9ed1b260e5892c5595242844c8"> 134</a></span>&#160; <span class="keywordtype">double</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#afec19c9ed1b260e5892c5595242844c8">Epsilon</a>()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">eps</a>; }</div><div class="line"><a name="l00136"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a53fefe22486542d7921648e20369f5ff"> 136</a></span>&#160; <span class="keywordtype">double</span>&amp; <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a53fefe22486542d7921648e20369f5ff">Epsilon</a>() { <span class="keywordflow">return</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">eps</a>; }</div><div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160;</div><div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; <span class="keyword">private</span>:</div><div class="line"><a name="l00140"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9"> 140</a></span>&#160; <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">iteratedPower</a>;</div><div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160;</div><div class="line"><a name="l00143"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884"> 143</a></span>&#160; <span class="keywordtype">size_t</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">maxIterations</a>;</div><div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;</div><div class="line"><a name="l00146"></a><span class="lineno"><a class="line" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac"> 146</a></span>&#160; <span class="keywordtype">double</span> <a class="code" href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">eps</a>;</div><div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;};</div><div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;</div><div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;} <span class="comment">// namespace svd</span></div><div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;} <span class="comment">// namespace mlpack</span></div><div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;</div><div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;<span class="preprocessor">#endif</span></div><div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_ab80fc947e7ce20772539bebae51bc884"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#ab80fc947e7ce20772539bebae51bc884">mlpack::svd::RandomizedSVD::maxIterations</a></div><div class="ttdeci">size_t maxIterations</div><div class="ttdoc">Locally stored number of iterations for the power method. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00143">randomized_svd.hpp:143</a></div></div>
<div class="ttc" id="namespacemlpack_html"><div class="ttname"><a href="namespacemlpack.html">mlpack</a></div><div class="ttdoc">Linear algebra utility functions, generally performed on matrices or vectors. </div><div class="ttdef"><b>Definition:</b> <a href="binarize_8hpp_source.html#l00018">binarize.hpp:18</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a184b9b07dc065737b2d293e7b7f82b00"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a184b9b07dc065737b2d293e7b7f82b00">mlpack::svd::RandomizedSVD::IteratedPower</a></div><div class="ttdeci">size_t IteratedPower() const </div><div class="ttdoc">Get the size of the normalized power iterations. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00124">randomized_svd.hpp:124</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a6956d9a633c8b11f3ece411808d346f7"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a6956d9a633c8b11f3ece411808d346f7">mlpack::svd::RandomizedSVD::Apply</a></div><div class="ttdeci">void Apply(const arma::mat &amp;data, arma::mat &amp;u, arma::vec &amp;s, arma::mat &amp;v, const size_t rank)</div><div class="ttdoc">Apply Principal Component Analysis to the provided data set using the randomized SVD. </div></div>
<div class="ttc" id="prereqs_8hpp_html"><div class="ttname"><a href="prereqs_8hpp.html">prereqs.hpp</a></div><div class="ttdoc">The core includes that mlpack expects; standard C++ includes and Armadillo. </div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_ae95613dfd1b7c9a8bf0bc24a846be969"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#ae95613dfd1b7c9a8bf0bc24a846be969">mlpack::svd::RandomizedSVD::MaxIterations</a></div><div class="ttdeci">size_t MaxIterations() const </div><div class="ttdoc">Get the number of iterations for the power method. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00129">randomized_svd.hpp:129</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a327ded7a6390da4eda87420505fc83ac"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a327ded7a6390da4eda87420505fc83ac">mlpack::svd::RandomizedSVD::eps</a></div><div class="ttdeci">double eps</div><div class="ttdoc">The value used for numerical stability. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00146">randomized_svd.hpp:146</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a8ce931925a0625f40d2271506fb24ab7"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a8ce931925a0625f40d2271506fb24ab7">mlpack::svd::RandomizedSVD::RandomizedSVD</a></div><div class="ttdeci">RandomizedSVD(const arma::mat &amp;data, arma::mat &amp;u, arma::vec &amp;s, arma::mat &amp;v, const size_t iteratedPower=0, const size_t maxIterations=2, const size_t rank=0, const double eps=1e-7)</div><div class="ttdoc">Create object for the randomized SVD method. </div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_aa7e2301ec004ef067ad990a1ad6cbd26"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#aa7e2301ec004ef067ad990a1ad6cbd26">mlpack::svd::RandomizedSVD::MaxIterations</a></div><div class="ttdeci">size_t &amp; MaxIterations()</div><div class="ttdoc">Modify the number of iterations for the power method. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00131">randomized_svd.hpp:131</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a53fefe22486542d7921648e20369f5ff"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a53fefe22486542d7921648e20369f5ff">mlpack::svd::RandomizedSVD::Epsilon</a></div><div class="ttdeci">double &amp; Epsilon()</div><div class="ttdoc">Modify the value used for decomposition stability. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00136">randomized_svd.hpp:136</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html">mlpack::svd::RandomizedSVD</a></div><div class="ttdoc">Randomized SVD is a matrix factorization that is based on randomized matrix approximation techniques...</div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00066">randomized_svd.hpp:66</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_ac183fa54a6e9dc6b175a5390bca63a0f"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#ac183fa54a6e9dc6b175a5390bca63a0f">mlpack::svd::RandomizedSVD::IteratedPower</a></div><div class="ttdeci">size_t &amp; IteratedPower()</div><div class="ttdoc">Modify the size of the normalized power iterations. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00126">randomized_svd.hpp:126</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_a7bcf1e679819fb35932e47538b94c7c9"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#a7bcf1e679819fb35932e47538b94c7c9">mlpack::svd::RandomizedSVD::iteratedPower</a></div><div class="ttdeci">size_t iteratedPower</div><div class="ttdoc">Locally stored size of the normalized power iterations. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00140">randomized_svd.hpp:140</a></div></div>
<div class="ttc" id="classmlpack_1_1svd_1_1RandomizedSVD_html_afec19c9ed1b260e5892c5595242844c8"><div class="ttname"><a href="classmlpack_1_1svd_1_1RandomizedSVD.html#afec19c9ed1b260e5892c5595242844c8">mlpack::svd::RandomizedSVD::Epsilon</a></div><div class="ttdeci">double Epsilon() const </div><div class="ttdoc">Get the value used for decomposition stability. </div><div class="ttdef"><b>Definition:</b> <a href="randomized__svd_8hpp_source.html#l00134">randomized_svd.hpp:134</a></div></div>
</div><!-- fragment --></div><!-- contents -->
<!-- start footer part -->
<hr class="footer"/><address class="footer"><small>
Generated by &#160;<a href="http://www.doxygen.org/index.html">
<img class="footer" src="doxygen.png" alt="doxygen"/>
</a> 1.8.11
</small></address>
</body>
<script type="text/javascript">
var x = document.getElementsByClassName("formulaDsp");
var i;
for (i = 0; i < x.length; i++)
{
x[i].width /= 4;
}
</script>
</html>