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diff --git a/doc/html/boost/accumulators/impl/variance_impl.html b/doc/html/boost/accumulators/impl/variance_impl.html new file mode 100755 index 0000000000..1b125cc2ae --- /dev/null +++ b/doc/html/boost/accumulators/impl/variance_impl.html @@ -0,0 +1,101 @@ +<html> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=US-ASCII"> +<title>Struct template variance_impl</title> +<link rel="stylesheet" href="../../../../../doc/src/boostbook.css" type="text/css"> +<meta name="generator" content="DocBook XSL Stylesheets V1.76.1"> +<link rel="home" href="../../../index.html" title="The Boost C++ Libraries BoostBook Documentation Subset"> +<link rel="up" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.variance_hpp" title="Header <boost/accumulators/statistics/variance.hpp>"> +<link rel="prev" href="lazy_variance_impl.html" title="Struct template lazy_variance_impl"> +<link rel="next" href="../tag/lazy_variance.html" title="Struct lazy_variance"> 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<boost/accumulators/statistics/variance.hpp>">boost/accumulators/statistics/variance.hpp</a>> + +</span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Sample<span class="special">,</span> <span class="keyword">typename</span> MeanFeature<span class="special">,</span> <span class="keyword">typename</span> Tag<span class="special">></span> +<span class="keyword">struct</span> <a class="link" href="variance_impl.html" title="Struct template variance_impl">variance_impl</a> <span class="special">{</span> + <span class="comment">// types</span> + <span class="keyword">typedef</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">average</span><span class="special"><</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="special">></span><span class="special">::</span><span class="identifier">result_type</span> <a name="boost.accumulators.impl.variance_impl.result_type"></a><span class="identifier">result_type</span><span class="special">;</span> + + <span class="comment">// <a class="link" href="variance_impl.html#boost.accumulators.impl.variance_implconstruct-copy-destruct">construct/copy/destruct</a></span> + <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <a class="link" href="variance_impl.html#id571763-bb"><span class="identifier">variance_impl</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> + + <span class="comment">// <a class="link" href="variance_impl.html#id571726-bb">public member functions</a></span> + <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="keyword">void</span> <a class="link" href="variance_impl.html#id571729-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span><span class="special">)</span><span class="special">;</span> + <span class="identifier">result_type</span> <a class="link" href="variance_impl.html#id571750-bb"><span class="identifier">result</span></a><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span> +<span class="special">}</span><span class="special">;</span></pre></div> +<div class="refsect1"> +<a name="id950473"></a><h2>Description</h2> +<p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators/form_75.png"></span> according to the formula </p> +<div class="equation"> +<a name="id950500"></a><p class="title"><b>Equation 1.23. </b></p> +<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators/form_76.png" align="middle"></div></div> +</div> +<p><br class="equation-break"> where </p> +<div class="equation"> +<a name="id950526"></a><p class="title"><b>Equation 1.24. </b></p> +<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators/form_74.png" align="middle"></div></div> +</div> +<p><br class="equation-break"> is the estimate of the sample mean and <span class="inlinemediaobject"><img src="../../../images/accumulators/form_60.png"></span> is the number of samples.</p> +<p>Note that the sample variance is not defined for <span class="inlinemediaobject"><img src="../../../images/accumulators/form_77.png"></span>.</p> +<p>A simplification can be obtained by the approximate recursion </p> +<div class="equation"> +<a name="id950596"></a><p class="title"><b>Equation 1.25. </b></p> +<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators/form_78.png" align="middle"></div></div> +</div> +<p><br class="equation-break"> because the difference </p> +<div class="equation"> +<a name="id950622"></a><p class="title"><b>Equation 1.26. </b></p> +<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators/form_79.png" align="middle"></div></div> +</div> +<p><br class="equation-break"> converges to zero as <span class="inlinemediaobject"><img src="../../../images/accumulators/form_80.png"></span>. However, for small <span class="inlinemediaobject"><img src="../../../images/accumulators/form_17.png"></span> the difference can be non-negligible. </p> +<div class="refsect2"> +<a name="id950689"></a><h3> +<a name="boost.accumulators.impl.variance_implconstruct-copy-destruct"></a><code class="computeroutput">variance_impl</code> + public + construct/copy/destruct</h3> +<div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <a name="id571763-bb"></a><span class="identifier">variance_impl</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> args<span class="special">)</span><span class="special">;</span></pre></li></ol></div> +</div> +<div class="refsect2"> +<a name="id950776"></a><h3> +<a name="id571726-bb"></a><code class="computeroutput">variance_impl</code> public member functions</h3> +<div class="orderedlist"><ol class="orderedlist" type="1"> +<li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="keyword">void</span> <a name="id571729-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> args<span class="special">)</span><span class="special">;</span></pre></li> +<li class="listitem"><pre class="literallayout"><span class="identifier">result_type</span> <a name="id571750-bb"></a><span class="identifier">result</span><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre></li> +</ol></div> +</div> +</div> +</div> +<table xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" width="100%"><tr> +<td align="left"></td> +<td align="right"><div class="copyright-footer">Copyright © 2005, 2006 Eric Niebler<p> + Distributed under the Boost Software License, Version 1.0. (See accompanying + file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>) + </p> +</div></td> +</tr></table> +<hr> +<div class="spirit-nav"> +<a accesskey="p" href="lazy_variance_impl.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.variance_hpp"><img src="../../../../../doc/src/images/up.png" alt="Up"></a><a accesskey="h" href="../../../index.html"><img src="../../../../../doc/src/images/home.png" alt="Home"></a><a accesskey="n" href="../tag/lazy_variance.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a> +</div> +</body> +</html> |