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+<a name="boost.accumulators.impl.immediate_rol_idp410515456"></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 &#8212; 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: &lt;<a class="link" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.rolling_variance_hpp" title="Header &lt;boost/accumulators/statistics/rolling_variance.hpp&gt;">boost/accumulators/statistics/rolling_variance.hpp</a>&gt;
+
+</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Sample<span class="special">&gt;</span>
+<span class="keyword">struct</span> <a class="link" href="immediate_rol_idp410515456.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">&lt;</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">&gt;</span><span class="special">::</span><span class="identifier">result_type</span> <a name="boost.accumulators.impl.immediate_rol_idp410515456.result_type"></a><span class="identifier">result_type</span><span class="special">;</span>
+
+ <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#boost.accumulators.impl.immediate_rol_idp410515456construct-copy-destruct">construct/copy/destruct</a></span>
+ <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <a class="link" href="immediate_rol_idp410515456.html#idp410560832-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">&amp;</span><span class="special">)</span><span class="special">;</span>
+
+ <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#idp410555072-bb">public member functions</a></span>
+ <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410555632-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">&amp;</span><span class="special">)</span><span class="special">;</span>
+ <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a class="link" href="immediate_rol_idp410515456.html#idp410558016-bb"><span class="identifier">result</span></a><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
+
+ <span class="comment">// <a class="link" href="immediate_rol_idp410515456.html#idp410562656-bb">private member functions</a></span>
+ <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
+ <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410563232-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</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">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</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">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
+ <span class="keyword">void</span> <a class="link" href="immediate_rol_idp410515456.html#idp410566560-bb"><span class="identifier">prevent_underflow</span></a><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</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">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</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="idp110700496"></a><h2>Description</h2>
+<p>Iterative calculation of sample variance <span class="inlinemediaobject"><img src="../../../images/accumulators//form_52.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_53.png"></span>, for the first <span class="inlinemediaobject"><img src="../../../images/accumulators//form_53.png"></span> samples, the variance is computed according to the formula </p>
+<div class="equation">
+<a name="idp110709168"></a><p class="title"><b>Equation&#160;1.9.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_58.png" align="middle"></div></div>
+</div>
+<p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_59.png"></span> can be recursively computed as: </p>
+<div class="equation">
+<a name="idp110714464"></a><p class="title"><b>Equation&#160;1.10.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_60.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="idp110717472"></a><p class="title"><b>Equation&#160;1.11.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_61.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_62.png"></span> is dropped from the window. The sample variance over the window now becomes: </p>
+<div class="equation">
+<a name="idp110723040"></a><p class="title"><b>Equation&#160;1.12.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_63.png" align="middle"></div></div>
+</div>
+<p><br class="equation-break"> where the sum of squares <span class="inlinemediaobject"><img src="../../../images/accumulators//form_59.png"></span> now equals: </p>
+<div class="equation">
+<a name="idp110728448"></a><p class="title"><b>Equation&#160;1.13.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_64.png" align="middle"></div></div>
+</div>
+<p><br class="equation-break"> and the estimated mean is: </p>
+<div class="equation">
+<a name="idp110731536"></a><p class="title"><b>Equation&#160;1.14.&#160;</b></p>
+<div class="equation-contents"><div class="mediaobject" align="center"><img src="../../../images/accumulators//form_65.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_66.png"></span>. </p>
+<div class="refsect2">
+<a name="idp110737056"></a><h3>
+<a name="boost.accumulators.impl.immediate_rol_idp410515456construct-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">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <a name="idp410560832-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">&amp;</span> args<span class="special">)</span><span class="special">;</span></pre></li></ol></div>
+</div>
+<div class="refsect2">
+<a name="idp110747744"></a><h3>
+<a name="idp410555072-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">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="keyword">void</span> <a name="idp410555632-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">&amp;</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">&lt;</span><span class="keyword">typename</span> Args<span class="special">&gt;</span> <span class="identifier">result_type</span> <a name="idp410558016-bb"></a><span class="identifier">result</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&amp;</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="idp110769616"></a><h3>
+<a name="idp410562656-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">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
+ <span class="keyword">void</span> <a name="idp410563232-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</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">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</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">&lt;</span><span class="keyword">typename</span> T<span class="special">&gt;</span>
+ <span class="keyword">void</span> <a name="idp410566560-bb"></a><span class="identifier">prevent_underflow</span><span class="special">(</span><span class="identifier">T</span> <span class="special">&amp;</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">&lt;</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">is_arithmetic</span><span class="special">&lt;</span> <span class="identifier">T</span> <span class="special">&gt;</span><span class="special">,</span> <span class="identifier">T</span> <span class="special">&gt;</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>
+</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 &#169; 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_rolling_variance_impl.html"><img src="../../../../../doc/src/images/prev.png" alt="Prev"></a><a accesskey="u" href="../../../accumulators/reference.html#header.boost.accumulators.statistics.rolling_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_rolling_variance.html"><img src="../../../../../doc/src/images/next.png" alt="Next"></a>
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