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<title>Struct template immediate_rolling_variance_impl</title>
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<a name="boost.accumulators.impl.immediate_roll_idp66209616"></a><div class="titlepage"></div>
<div class="refnamediv">
<h2><span class="refentrytitle">Struct template immediate_rolling_variance_impl</span></h2>
<p>boost::accumulators::impl::immediate_rolling_variance_impl — Iterative calculation of the rolling variance. </p>
</div>
<h2 xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv-title">Synopsis</h2>
<div xmlns:rev="http://www.cs.rpi.edu/~gregod/boost/tools/doc/revision" class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: <<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.rolling_variance_hpp" title="Header <boost/accumulators/statistics/rolling_variance.hpp>">boost/accumulators/statistics/rolling_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">struct</span> <a class="link" href="immediate_roll_idp66209616.html" title="Struct template immediate_rolling_variance_impl">immediate_rolling_variance_impl</a> <span class="special">:</span> <span class="keyword">public</span> <span class="identifier">accumulator_base</span> <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">fdiv</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.immediate_roll_idp66209616.result_type"></a><span class="identifier">result_type</span><span class="special">;</span>
<span class="comment">// <a class="link" href="immediate_roll_idp66209616.html#boost.accumulators.impl.immediate_roll_idp66209616construct-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="immediate_roll_idp66209616.html#idp66255856-bb"><span class="identifier">immediate_rolling_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="immediate_roll_idp66209616.html#idp66250096-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="immediate_roll_idp66209616.html#idp66250656-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="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="identifier">result_type</span> <a class="link" href="immediate_roll_idp66209616.html#idp66253040-bb"><span class="identifier">result</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="keyword">const</span><span class="special">;</span>
<span class="comment">// <a class="link" href="immediate_roll_idp66209616.html#idp66257680-bb">private member functions</a></span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span>
<span class="keyword">void</span> <a class="link" href="immediate_roll_idp66209616.html#idp66258256-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">enable_if</span><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special"><</span> <span class="identifier">T</span> <span class="special">></span><span class="special">,</span> <span class="identifier">T</span> <span class="special">></span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span>
<span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span>
<span class="keyword">void</span> <a class="link" href="immediate_roll_idp66209616.html#idp66261664-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&</span><span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">disable_if</span><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special"><</span> <span class="identifier">T</span> <span class="special">></span><span class="special">,</span> <span class="identifier">T</span> <span class="special">></span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span>
<span class="special">}</span><span class="special">;</span></pre></div>
<div class="refsect1">
<a name="idp105025472"></a><h2>Description</h2>
<p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators//form_61.png"></span> is done as follows, see also <a href="http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance" target="_top">http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance</a>. For a rolling window of size <span class="inlinemediaobject"><img src="../../../images/accumulators//form_70.png"></span>, for the first <span class="inlinemediaobject"><img src="../../../images/accumulators//form_70.png"></span> samples, the variance is computed according to the formula </p>
<div class="equation">
<a name="idp105034224"></a><p class="title"><b>Equation 1.9. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_75.png" align="middle"></div></div>
</div>
<p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_76.png"></span> can be recursively computed as: </p>
<div class="equation">
<a name="idp105039616"></a><p class="title"><b>Equation 1.10. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_77.png" align="middle"></div></div>
</div>
<p><br class="equation-break"> and the estimate of the sample mean as: </p>
<div class="equation">
<a name="idp105042624"></a><p class="title"><b>Equation 1.11. </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"> For further samples, when the rolling window is fully filled with data, one has to take into account that the oldest sample <span class="inlinemediaobject"><img src="../../../images/accumulators//form_79.png"></span> is dropped from the window. The sample variance over the window now becomes: </p>
<div class="equation">
<a name="idp105048192"></a><p class="title"><b>Equation 1.12. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_80.png" align="middle"></div></div>
</div>
<p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_76.png"></span> now equals: </p>
<div class="equation">
<a name="idp105053600"></a><p class="title"><b>Equation 1.13. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_81.png" align="middle"></div></div>
</div>
<p><br class="equation-break"> and the estimated mean is: </p>
<div class="equation">
<a name="idp105056688"></a><p class="title"><b>Equation 1.14. </b></p>
<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_82.png" align="middle"></div></div>
</div>
<p><br class="equation-break"></p>
<p>Note that the sample variance is not defined for <span class="inlinemediaobject"><img src="../../../images/accumulators//form_63.png"></span>. </p>
<div class="refsect2">
<a name="idp105062208"></a><h3>
<a name="boost.accumulators.impl.immediate_roll_idp66209616construct-copy-destruct"></a><code class="computeroutput">immediate_rolling_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="idp66255856-bb"></a><span class="identifier">immediate_rolling_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="idp105072960"></a><h3>
<a name="idp66250096-bb"></a><code class="computeroutput">immediate_rolling_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="idp66250656-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="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> Args<span class="special">></span> <span class="identifier">result_type</span> <a name="idp66253040-bb"></a><span class="identifier">result</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="keyword">const</span><span class="special">;</span></pre></li>
</ol></div>
</div>
<div class="refsect2">
<a name="idp105094768"></a><h3>
<a name="idp66257680-bb"></a><code class="computeroutput">immediate_rolling_variance_impl</code> private 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> T<span class="special">></span>
<span class="keyword">void</span> <a name="idp66258256-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&</span> non_negative_number<span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">enable_if</span><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special"><</span> <span class="identifier">T</span> <span class="special">></span><span class="special">,</span> <span class="identifier">T</span> <span class="special">></span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span></pre></li>
<li class="listitem"><pre class="literallayout"><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> T<span class="special">></span>
<span class="keyword">void</span> <a name="idp66261664-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&</span> non_arithmetic_quantity<span class="special">,</span>
<span class="keyword">typename</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">disable_if</span><span class="special"><</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special"><</span> <span class="identifier">T</span> <span class="special">></span><span class="special">,</span> <span class="identifier">T</span> <span class="special">></span><span class="special">::</span><span class="identifier">type</span> <span class="special">*</span> <span class="special">=</span> <span class="number">0</span><span class="special">)</span><span class="special">;</span></pre></li>
</ol></div>
</div>
</div>
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<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>)
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