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| <div class="section"> |
| <div class="titlepage"><div><div><h2 class="title" style="clear: both"> |
| <a name="accumulators.user_s_guide"></a><a class="link" href="user_s_guide.html" title="User's Guide">User's Guide</a> |
| </h2></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework">The |
| Accumulators Framework</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library">The |
| Statistical Accumulators Library</a></span></dt> |
| </dl></div> |
| <p> |
| This section describes how to use the Boost.Accumulators framework to create |
| new accumulators and how to use the existing statistical accumulators to perform |
| incremental statistical computation. For detailed information regarding specific |
| components in Boost.Accumulators, check the <a class="link" href="reference.html#accumulators_framework_reference" title="Accumulators Framework Reference">Reference</a> |
| section. |
| </p> |
| <a name="accumulators.user_s_guide.hello__world_"></a><h3> |
| <a name="id759892"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.hello__world_">Hello, World!</a> |
| </h3> |
| <p> |
| Below is a complete example of how to use the Accumulators Framework and the |
| Statistical Accumulators to perform an incremental statistical calculation. |
| It calculates the mean and 2nd moment of a sequence of doubles. |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">iostream</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">stats</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">mean</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">moment</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="keyword">using</span> <span class="keyword">namespace</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulators</span><span class="special">;</span> |
| |
| <span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> |
| <span class="special">{</span> |
| <span class="comment">// Define an accumulator set for calculating the mean and the |
| </span> <span class="comment">// 2nd moment ... |
| </span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="comment">// push in some data ... |
| </span> <span class="identifier">acc</span><span class="special">(</span><span class="number">1.2</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.3</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">4.5</span><span class="special">);</span> |
| |
| <span class="comment">// Display the results ... |
| </span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Mean: "</span> <span class="special"><<</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"Moment: "</span> <span class="special"><<</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| |
| <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| This program displays the following: |
| </p> |
| <pre class="programlisting">Mean: 2.85 |
| Moment: 9.635 |
| </pre> |
| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework" title="The Accumulators Framework">The |
| Accumulators Framework</a> |
| </h3></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.using___accumulator_set___">Using |
| <code class="literal">accumulator_set<></code></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extracting_results">Extracting |
| Results</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.passing_optional_parameters">Passing |
| Optional Parameters</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.weighted_samples">Weighted |
| Samples</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.numeric_operators_sub_library">Numeric |
| Operators Sub-Library</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework">Extending |
| the Accumulators Framework</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts">Concepts</a></span></dt> |
| </dl></div> |
| <p> |
| The Accumulators Framework is framework for performing incremental calculations. |
| Usage of the framework follows the following pattern: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| Users build a computational object, called an <span class="emphasis"><em><code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code></em></span>, |
| by selecting the computations in which they are interested, or authoring |
| their own computational primitives which fit within the framework. |
| </li> |
| <li class="listitem"> |
| Users push data into the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| object one sample at a time. |
| </li> |
| <li class="listitem"> |
| The <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| computes the requested quantities in the most efficient method possible, |
| resolving dependencies between requested calculations, possibly cacheing |
| intermediate results. |
| </li> |
| </ul></div> |
| <p> |
| The Accumulators Framework defines the utilities needed for defining primitive |
| computational elements, called <span class="emphasis"><em>accumulators</em></span>. It also |
| provides the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| type, described above. |
| </p> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.terminology"></a><h3> |
| <a name="id760642"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.terminology">Terminology</a> |
| </h3> |
| <p> |
| The following terms are used in the rest of the documentation. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Sample</span></dt> |
| <dd> |
| <a name="sample_type"></a><p> |
| A datum that is pushed into an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| The type of the sample is the <span class="emphasis"><em>sample type</em></span>. |
| </p> |
| </dd> |
| <dt><span class="term">Weight</span></dt> |
| <dd> |
| <a name="weight_type"></a><p> |
| An optional scalar value passed along with the sample specifying the |
| weight of the sample. Conceptually, each sample is multiplied with |
| its weight. The type of the weight is the <span class="emphasis"><em>weight type</em></span>. |
| </p> |
| </dd> |
| <dt><span class="term">Feature</span></dt> |
| <dd><p> |
| An abstract primitive computational entity. When defining an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>, users specify |
| the features in which they are interested, and the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| figures out which <span class="emphasis"><em>accumulators</em></span> would best provide |
| those features. Features may depend on other features. If they do, |
| the accumulator set figures out which accumulators to add to satisfy |
| the dependencies. |
| </p></dd> |
| <dt><span class="term">Accumulator</span></dt> |
| <dd><p> |
| A concrete primitive computational entity. An accumulator is a concrete |
| implementation of a feature. It satisfies exactly one abstract feature. |
| Several different accumulators may provide the same feature, but may |
| represent different implementation strategies. |
| </p></dd> |
| <dt><span class="term">Accumulator Set</span></dt> |
| <dd><p> |
| A collection of accumulators. An accumulator set is specified with |
| a sample type and a list of features. The accumulator set uses this |
| information to generate an ordered set of accumulators depending on |
| the feature dependency graph. An accumulator set accepts samples one |
| datum at a time, propogating them to each accumulator in order. At |
| any point, results can be extracted from the accumulator set. |
| </p></dd> |
| <dt><span class="term">Extractor</span></dt> |
| <dd><p> |
| A function or function object that can be used to extract a result |
| from an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| </p></dd> |
| </dl> |
| </div> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.overview"></a><h3> |
| <a name="id760826"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.overview">Overview</a> |
| </h3> |
| <p> |
| Here is a list of the important types and functions in the Accumulator Framework |
| and a brief description of each. |
| </p> |
| <div class="table"> |
| <a name="id760844"></a><p class="title"><b>Table 1.1. Accumulators Toolbox</b></p> |
| <div class="table-contents"><table class="table" summary="Accumulators Toolbox"> |
| <colgroup> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| Tool |
| </p> |
| </th> |
| <th> |
| <p> |
| Description |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| This is the most important type in the Accumulators Framework. |
| It is a collection of accumulators. A datum pushed into an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> is forwarded |
| to each accumulator, in an order determined by the dependency relationships |
| between the accumulators. Computational results can be extracted |
| from an accumulator at any time. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/depends_on.html" title="Struct template depends_on">depends_on<></a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Used to specify which other features a feature depends on. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/feature_of.html" title="Struct template feature_of">feature_of<></a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Trait used to tell the Accumulators Framework that, for the purpose |
| of feature-based dependency resolution, one feature should be treated |
| the same as another. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/as_feature.html" title="Struct template as_feature">as_feature<></a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Used to create an alias for a feature. For example, if there are |
| two features, fast_X and accurate_X, they can be mapped to X(fast) |
| and X(accurate) with <code class="computeroutput"><a class="link" href="../boost/accumulators/as_feature.html" title="Struct template as_feature">as_feature<></a></code>. |
| This is just syntactic sugar. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/features.html" title="Struct template features">features<></a></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| An <a href="../../../libs/mpl/index.html" target="_top">MPL</a> sequence. |
| We can use <code class="computeroutput"><a class="link" href="../boost/accumulators/features.html" title="Struct template features">features<></a></code> |
| as the second template parameter when declaring an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput">external<></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| Used when declaring an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| If the weight type is specified with <code class="computeroutput">external<></code>, |
| then the weight accumulators are assumed to reside in a separate |
| accumulator set which will be passed in with a named parameter. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput">extractor<></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| A class template useful for creating an extractor function object. |
| It is parameterized on a feature, and it has member functions for |
| extracting from an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| the result corresponding to that feature. |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"><div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.using___accumulator_set___"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.using___accumulator_set___" title="Using accumulator_set<>">Using |
| <code class="literal">accumulator_set<></code></a> |
| </h4></div></div></div> |
| <p> |
| Our tour of the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| class template begins with the forward declaration: |
| </p> |
| <pre class="programlisting"><span class="keyword">template</span><span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Features</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Weight</span> <span class="special">=</span> <span class="keyword">void</span> <span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">accumulator_set</span><span class="special">;</span> |
| </pre> |
| <p> |
| The template parameters have the following meaning: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">Sample</span></code></span></dt> |
| <dd><p> |
| The type of the data that will be accumulated. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">Features</span></code></span></dt> |
| <dd><p> |
| An <a href="../../../libs/mpl/index.html" target="_top">MPL</a> sequence of |
| features to be calculated. |
| </p></dd> |
| <dt><span class="term"><code class="computeroutput"><span class="identifier">Weight</span></code></span></dt> |
| <dd><p> |
| The type of the (optional) weight paramter. |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| For example, the following line declares an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| that will accept a sequence of doubles one at a time and calculate the |
| min and mean: |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| </pre> |
| <p> |
| Notice that we use the <code class="computeroutput"><a class="link" href="../boost/accumulators/features.html" title="Struct template features">features<></a></code> |
| template to specify a list of features to be calculated. <code class="computeroutput"><a class="link" href="../boost/accumulators/features.html" title="Struct template features">features<></a></code> |
| is an MPL sequence of features. |
| </p> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/features.html" title="Struct template features">features<></a></code> is a synonym of |
| <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code>. |
| In fact, we could use <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code> or any MPL sequence if we prefer, |
| and the meaning would be the same. |
| </p></td></tr> |
| </table></div> |
| <p> |
| Once we have defined an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>, |
| we can then push data into it, and it will calculate the quantities you |
| requested, as shown below. |
| </p> |
| <pre class="programlisting"><span class="comment">// push some data into the accumulator_set ... |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">1.2</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.3</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3.4</span><span class="special">);</span> |
| </pre> |
| <p> |
| Since <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| defines its accumulate function to be the function call operator, we might |
| be tempted to use an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| as a UnaryFunction to a standard algorithm such as <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span></code>. |
| That's fine as long as we keep in mind that the standard algorithms take |
| UnaryFunction objects by value, which involves making a copy of the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> object. Consider the |
| following: |
| </p> |
| <pre class="programlisting"><span class="comment">// The data for which we wish to calculate statistical properties: |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">data</span><span class="special">(</span> <span class="comment">/* stuff */</span> <span class="special">);</span> |
| |
| <span class="comment">// The accumulator set which will calculate the properties for us: |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="comment">// Use std::for_each to accumulate the statistical properties: |
| </span><span class="identifier">acc</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span> <span class="identifier">data</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">data</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">acc</span> <span class="special">);</span> |
| </pre> |
| <p> |
| Notice how we must assign the return value of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span></code> |
| back to the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| This works, but some accumulators are not cheap to copy. For example, the |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| accumulators must store a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code>, so copying these accumulators |
| involves a dynamic allocation. We might be better off in this case passing |
| the accumulator by reference, with the help of <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">bind</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">()</span></code>. See below: |
| </p> |
| <pre class="programlisting"><span class="comment">// The data for which we wish to calculate statistical properties: |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">data</span><span class="special">(</span> <span class="comment">/* stuff */</span> <span class="special">);</span> |
| |
| <span class="comment">// The accumulator set which will calculate the properties for us: |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">4</span> <span class="special">);</span> |
| |
| <span class="comment">// Use std::for_each to accumulate the statistical properties: |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">(</span> <span class="identifier">data</span><span class="special">.</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">data</span><span class="special">.</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">bind</span><span class="special"><</span><span class="keyword">void</span><span class="special">>(</span> <span class="identifier">ref</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="identifier">_1</span> <span class="special">)</span> <span class="special">);</span> |
| </pre> |
| <p> |
| Notice now that we don't care about the return value of <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">()</span></code> anymore because <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">for_each</span><span class="special">()</span></code> is modifying <code class="computeroutput"><span class="identifier">acc</span></code> |
| directly. |
| </p> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| To use <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">bind</span><span class="special">()</span></code> |
| and <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">ref</span><span class="special">()</span></code>, |
| you must <code class="computeroutput"><span class="preprocessor">#include</span></code> |
| <code class="literal"><boost/bind.hpp></code> and <code class="literal"><boost/ref.hpp></code> |
| </p></td></tr> |
| </table></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extracting_results"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extracting_results" title="Extracting Results">Extracting |
| Results</a> |
| </h4></div></div></div> |
| <p> |
| Once we have declared an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| and pushed data into it, we need to be able to extract results from it. |
| For each feature we can add to an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>, |
| there is a corresponding extractor for fetching its result. Usually, the |
| extractor has the same name as the feature, but in a different namespace. |
| For example, if we accumulate the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span></code> |
| and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">max</span></code> features, we can extract the results |
| with the <code class="computeroutput"><span class="identifier">min</span></code> and <code class="computeroutput"><span class="identifier">max</span></code> extractors, as follows: |
| </p> |
| <pre class="programlisting"><span class="comment">// Calculate the minimum and maximum for a sequence of integers. |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">max</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="number">2</span> <span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="special">-</span><span class="number">1</span> <span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="number">1</span> <span class="special">);</span> |
| |
| <span class="comment">// This displays "(-1, 2)" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="char">'('</span> <span class="special"><<</span> <span class="identifier">min</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">)</span> <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">max</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">)</span> <span class="special"><<</span> <span class="string">")\n"</span><span class="special">;</span> |
| </pre> |
| <p> |
| The extractors are all declared in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">extract</span></code> |
| namespace, but they are brought into the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulators</span></code> |
| namespace with a <code class="computeroutput"><span class="keyword">using</span></code> declaration. |
| </p> |
| <div class="tip"><table border="0" summary="Tip"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../doc/src/images/tip.png"></td> |
| <th align="left">Tip</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| On the Windows platform, <code class="computeroutput"><span class="identifier">min</span></code> |
| and <code class="computeroutput"><span class="identifier">max</span></code> are preprocessor |
| macros defined in <code class="literal">WinDef.h</code>. To use the <code class="computeroutput"><span class="identifier">min</span></code> and <code class="computeroutput"><span class="identifier">max</span></code> |
| extractors, you should either compile with <code class="computeroutput"><span class="identifier">NOMINMAX</span></code> |
| defined, or you should invoke the extractors like: <code class="computeroutput"><span class="special">(</span><span class="identifier">min</span><span class="special">)(</span> <span class="identifier">acc</span> <span class="special">)</span></code> |
| and <code class="computeroutput"><span class="special">(</span><span class="identifier">max</span><span class="special">)(</span> <span class="identifier">acc</span> <span class="special">)</span></code>. The parentheses keep the macro from |
| being invoked. |
| </p></td></tr> |
| </table></div> |
| <p> |
| Another way to extract a result from an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| is with the <code class="computeroutput"><span class="identifier">extract_result</span><span class="special">()</span></code> function. This can be more convenient |
| if there isn't an extractor object handy for a certain feature. The line |
| above which displays results could equally be written as: |
| </p> |
| <pre class="programlisting"><span class="comment">// This displays "(-1, 2)" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="char">'('</span> <span class="special"><<</span> <span class="identifier">extract_result</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span> <span class="special">>(</span> <span class="identifier">acc</span> <span class="special">)</span> |
| <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">extract_result</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">max</span> <span class="special">>(</span> <span class="identifier">acc</span> <span class="special">)</span> <span class="special"><<</span> <span class="string">")\n"</span><span class="special">;</span> |
| </pre> |
| <p> |
| Finally, we can define our own extractor using the <code class="computeroutput">extractor<></code> |
| class template. For instance, another way to avoid the <code class="computeroutput"><span class="identifier">min</span></code> |
| / <code class="computeroutput"><span class="identifier">max</span></code> macro business would |
| be to define extractors with names that don't conflict with the macros, |
| like this: |
| </p> |
| <pre class="programlisting"><span class="identifier">extractor</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span> <span class="special">></span> <span class="identifier">min_</span><span class="special">;</span> |
| <span class="identifier">extractor</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span> <span class="special">></span> <span class="identifier">max_</span><span class="special">;</span> |
| |
| <span class="comment">// This displays "(-1, 2)" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="char">'('</span> <span class="special"><<</span> <span class="identifier">min_</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">)</span> <span class="special"><<</span> <span class="string">", "</span> <span class="special"><<</span> <span class="identifier">max_</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">)</span> <span class="special"><<</span> <span class="string">")\n"</span><span class="special">;</span> |
| </pre> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.passing_optional_parameters"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.passing_optional_parameters" title="Passing Optional Parameters">Passing |
| Optional Parameters</a> |
| </h4></div></div></div> |
| <p> |
| Some accumulators need initialization parameters. In addition, perhaps |
| some auxiliary information needs to be passed into the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| along with each sample. Boost.Accumulators handles these cases with named |
| parameters from the <a href="../../../libs/parameter/index.html" target="_top">Boost.Parameter</a> |
| library. |
| </p> |
| <p> |
| For example, consider the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> and <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| features. <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> keeps an ordered list |
| of the largest <code class="literal"><span class="emphasis"><em>N</em></span></code> samples, where |
| <code class="literal"><span class="emphasis"><em>N</em></span></code> can be specified at construction |
| time. Also, the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| feature, which depends on <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code>, keeps track of some |
| data that is covariate with the <code class="literal"><span class="emphasis"><em>N</em></span></code> |
| samples tracked by <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code>. The code below shows |
| how this all works, and is described in more detail below. |
| </p> |
| <pre class="programlisting"><span class="comment">// Define a feature for tracking covariate data |
| </span><span class="keyword">typedef</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">,</span> <span class="identifier">left</span> <span class="special">></span> <span class="identifier">my_tail_variate_tag</span><span class="special">;</span> |
| |
| <span class="comment">// This will calculate the left tail and my_tail_variate_tag for N == 2 |
| </span><span class="comment">// using the tag::tail<left>::cache_size named parameter |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">my_tail_variate_tag</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">2</span> <span class="special">);</span> |
| |
| <span class="comment">// push in some samples and some covariates by using |
| </span><span class="comment">// the covariate1 named parameter |
| </span><span class="identifier">acc</span><span class="special">(</span> <span class="number">1.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">12</span> <span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="number">2.3</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="special">-</span><span class="number">23</span> <span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="number">3.4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">34</span> <span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span> <span class="number">4.5</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="special">-</span><span class="number">45</span> <span class="special">);</span> |
| |
| <span class="comment">// Define an extractor for the my_tail_variate_tag feature |
| </span><span class="identifier">extractor</span><span class="special"><</span> <span class="identifier">my_tail_variate_tag</span> <span class="special">></span> <span class="identifier">my_tail_variate</span><span class="special">;</span> |
| |
| <span class="comment">// Write the tail statistic to std::cout. This will print "4.5, 3.4, " |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream_iterator</span><span class="special"><</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">dout</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">,</span> <span class="string">", "</span> <span class="special">);</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">copy</span><span class="special">(</span> <span class="identifier">tail</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">tail</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">dout</span> <span class="special">);</span> |
| |
| <span class="comment">// Write the tail_variate statistic to std::cout. This will print "-45, 34, " |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">ostream_iterator</span><span class="special"><</span> <span class="keyword">int</span> <span class="special">></span> <span class="identifier">iout</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span><span class="special">,</span> <span class="string">", "</span> <span class="special">);</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">copy</span><span class="special">(</span> <span class="identifier">my_tail_variate</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">begin</span><span class="special">(),</span> <span class="identifier">my_tail_variate</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">end</span><span class="special">(),</span> <span class="identifier">iout</span> <span class="special">);</span> |
| </pre> |
| <p> |
| There are several things to note about the code above. First, notice that |
| we didn't have to request that the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> feature be calculated. |
| That is implicit because the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| feature depends on the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> feature. Next, notice |
| how the <code class="computeroutput"><span class="identifier">acc</span></code> object is initialized: |
| <code class="computeroutput"><span class="identifier">acc</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> |
| <span class="number">2</span> <span class="special">)</span></code>. |
| Here, <code class="computeroutput"><span class="identifier">cache_size</span></code> is a named |
| parameter. It is used to tell the <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> and <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| accumulators how many samples and covariates to store. Conceptually, every |
| construction parameter is made available to every accumulator in an accumulator |
| set. |
| </p> |
| <p> |
| We also use a named parameter to pass covariate data into the accumulator |
| set along with the samples. As with the constructor parameters, all parameters |
| to the accumulate function are made available to all the accumulators in |
| the set. In this case, only the accumulator for the <code class="computeroutput"><span class="identifier">my_tail_variate</span></code> |
| feature would be interested in the value of the <code class="computeroutput"><span class="identifier">covariate1</span></code> |
| named parameter. |
| </p> |
| <p> |
| We can make one final observation about the example above. Since <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail.html" title="Struct template tail">tail</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/tag/tail_variate.html" title="Struct template tail_variate">tail_variate<></a></code> |
| are multi-valued features, the result we extract for them is represented |
| as an iterator range. That is why we can say <code class="computeroutput"><span class="identifier">tail</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">begin</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">tail</span><span class="special">(</span> <span class="identifier">acc</span> <span class="special">).</span><span class="identifier">end</span><span class="special">()</span></code>. |
| </p> |
| <p> |
| Even the extractors can accept named parameters. In a bit, we'll see a |
| situation where that is useful. |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.weighted_samples"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.weighted_samples" title="Weighted Samples">Weighted |
| Samples</a> |
| </h4></div></div></div> |
| <p> |
| Some accumulators, statistical accumulators in particular, deal with data |
| that are <span class="emphasis"><em>weighted</em></span>. Each sample pushed into the accumulator |
| has an associated weight, by which the sample is conceptually multiplied. |
| The Statistical Accumulators Library provides an assortment of these weighted |
| statistical accumulators. And many unweighted statistical accumulators |
| have weighted variants. For instance, the weighted variant of the <code class="computeroutput"><span class="identifier">sum</span></code> accumulator is called <code class="computeroutput"><span class="identifier">weighted_sum</span></code>, and is calculated by accumulating |
| all the samples multiplied by their weights. |
| </p> |
| <p> |
| To declare an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| that accepts weighted samples, you must specify the type of the weight |
| parameter as the 3rd template parameter, as follows: |
| </p> |
| <pre class="programlisting"><span class="comment">// 3rd template parameter 'int' means this is a weighted |
| </span><span class="comment">// accumulator set where the weights have type 'int' |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span> <span class="special">>,</span> <span class="keyword">int</span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| </pre> |
| <p> |
| When you specify a weight, all the accumulators in the set are replaced |
| with their weighted equivalents. For example, the above <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| declaration is equivalent to the following: |
| </p> |
| <pre class="programlisting"><span class="comment">// Since we specified a weight, tag::sum becomes tag::weighted_sum |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">int</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum</span> <span class="special">>,</span> <span class="keyword">int</span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| </pre> |
| <p> |
| When passing samples to the accumulator set, you must also specify the |
| weight of each sample. You can do that with the <code class="computeroutput"><span class="identifier">weight</span></code> |
| named parameter, as follows: |
| </p> |
| <pre class="programlisting"><span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">);</span> <span class="comment">// 1 * 2 |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> <span class="comment">// 2 * 4 |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">6</span><span class="special">);</span> <span class="comment">// + 3 * 6 |
| </span> <span class="comment">// ------- |
| </span> <span class="comment">// = 28 |
| </span></pre> |
| <p> |
| You can then extract the result with the <code class="computeroutput"><span class="identifier">sum</span><span class="special">()</span></code> extractor, as follows: |
| </p> |
| <pre class="programlisting"><span class="comment">// This prints "28" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| When working with weighted statistical accumulators from the Statistical |
| Accumulators Library, be sure to include the appropriate header. For |
| instance, <code class="computeroutput"><span class="identifier">weighted_sum</span></code> |
| is defined in <code class="computeroutput"><span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">statistics</span><span class="special">/</span><span class="identifier">weighted_sum</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span></code>. |
| </p></td></tr> |
| </table></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.numeric_operators_sub_library"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.numeric_operators_sub_library" title="Numeric Operators Sub-Library">Numeric |
| Operators Sub-Library</a> |
| </h4></div></div></div> |
| <p> |
| This section describes the function objects in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span></code> |
| namespace, which is a sub-library that provides function objects and meta-functions |
| corresponding to the infix operators in C++. |
| </p> |
| <p> |
| In the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span></code> namespace are additional operator |
| overloads for some useful operations not provided by the standard library, |
| such as multiplication of a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><></span></code> with a scalar. |
| </p> |
| <p> |
| In the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span></code> namespace are function object |
| equivalents of the infix operators. These function object types are heterogeneous, |
| and so are more general than the standard ones found in the <code class="literal"><functional></code> |
| header. They use the Boost.Typeof library to deduce the return types of |
| the infix expressions they evaluate. In addition, they look within the |
| <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span></code> namespace to consider any additional |
| overloads that might be defined there. |
| </p> |
| <p> |
| In the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span></code> namespace are global polymorphic |
| function objects corresponding to the function object types defined in |
| the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span></code> namespace. For example, <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">plus</span><span class="special">(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">)</span></code> is equivalent to <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">plus</span><span class="special"><</span><span class="identifier">A</span><span class="special">,</span> <span class="identifier">B</span><span class="special">>()(</span><span class="identifier">a</span><span class="special">,</span> <span class="identifier">b</span><span class="special">)</span></code>, and both are equivalent to <code class="computeroutput"><span class="keyword">using</span> <span class="keyword">namespace</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span><span class="special">;</span> |
| <span class="identifier">a</span> <span class="special">+</span> |
| <span class="identifier">b</span><span class="special">;</span></code>. |
| </p> |
| <p> |
| The Numeric Operators Sub-Library also gives several ways to sub-class |
| and a way to sub-class and specialize operations. One way uses tag dispatching |
| on the types of the operands. The other way is based on the compile-time |
| properties of the operands. |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework" title="Extending the Accumulators Framework">Extending |
| the Accumulators Framework</a> |
| </h4></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator">Defining |
| a New Accumulator</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_feature">Defining |
| a New Feature</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_extractor">Defining |
| a New Extractor</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.controlling_dependencies">Controlling |
| Dependencies</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.operators_ex">Specializing |
| Numeric Operators</a></span></dt> |
| </dl></div> |
| <p> |
| This section describes how to extend the Accumulators Framework by defining |
| new accumulators, features and extractors. Also covered are how to control |
| the dependency resolution of features within an accumulator set. |
| </p> |
| <div class="section"> |
| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator" title="Defining a New Accumulator">Defining |
| a New Accumulator</a> |
| </h5></div></div></div> |
| <p> |
| All new accumulators must satisfy the <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts.accumulator_concept">Accumulator |
| Concept</a>. Below is a sample class that satisfies the accumulator |
| concept, which simply sums the values of all samples passed into it. |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">framework</span><span class="special">/</span><span class="identifier">accumulator_base</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">accumulators</span><span class="special">/</span><span class="identifier">framework</span><span class="special">/</span><span class="identifier">parameters</span><span class="special">/</span><span class="identifier">sample</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">></span> |
| |
| <span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="comment">// Putting your accumulators in the |
| </span><span class="keyword">namespace</span> <span class="identifier">accumulators</span> <span class="special">{</span> <span class="comment">// impl namespace has some |
| </span><span class="keyword">namespace</span> <span class="identifier">impl</span> <span class="special">{</span> <span class="comment">// advantages. See below. |
| </span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Sample</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">sum_accumulator</span> <span class="comment">// All accumulators should inherit from |
| </span> <span class="special">:</span> <span class="identifier">accumulator_base</span> <span class="comment">// accumulator_base. |
| </span><span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">Sample</span> <span class="identifier">result_type</span><span class="special">;</span> <span class="comment">// The type returned by result() below. |
| </span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Args</span><span class="special">></span> <span class="comment">// The constructor takes an argument pack. |
| </span> <span class="identifier">sum_accumulator</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">args</span><span class="special">)</span> |
| <span class="special">:</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">args</span><span class="special">[</span><span class="identifier">sample</span> <span class="special">|</span> <span class="identifier">Sample</span><span class="special">()])</span> <span class="comment">// Maybe there is an initial value in the |
| </span> <span class="special">{</span> <span class="comment">// argument pack. ('sample' is defined in |
| </span> <span class="special">}</span> <span class="comment">// sample.hpp, included above.) |
| </span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Args</span><span class="special">></span> <span class="comment">// The accumulate function is the function |
| </span> <span class="keyword">void</span> <span class="keyword">operator</span> <span class="special">()(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span> <span class="identifier">args</span><span class="special">)</span> <span class="comment">// call operator, and it also accepts an |
| </span> <span class="special">{</span> <span class="comment">// argument pack. |
| </span> <span class="keyword">this</span><span class="special">-></span><span class="identifier">sum</span> <span class="special">+=</span> <span class="identifier">args</span><span class="special">[</span><span class="identifier">sample</span><span class="special">];</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">result_type</span> <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="comment">// The result function will also be passed |
| </span> <span class="special">{</span> <span class="comment">// an argument pack, but we don't use it here, |
| </span> <span class="keyword">return</span> <span class="keyword">this</span><span class="special">-></span><span class="identifier">sum</span><span class="special">;</span> <span class="comment">// so we use "dont_care" as the argument type. |
| </span> <span class="special">}</span> |
| <span class="keyword">private</span><span class="special">:</span> |
| <span class="identifier">Sample</span> <span class="identifier">sum</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="special">}}}</span> |
| </pre> |
| <p> |
| Much of the above should be pretty self-explanitory, except for the use |
| of argument packs which may be confusing if you have never used the |
| <a href="../../../libs/parameter/index.html" target="_top">Boost.Parameter</a> |
| library before. An argument pack is a cluster of values, each of which |
| can be accessed with a key. So <code class="computeroutput"><span class="identifier">args</span><span class="special">[</span><span class="identifier">sample</span><span class="special">]</span></code> extracts from the pack the value associated |
| with the <code class="computeroutput"><span class="identifier">sample</span></code> key. |
| And the cryptic <code class="computeroutput"><span class="identifier">args</span><span class="special">[</span><span class="identifier">sample</span> <span class="special">|</span> <span class="identifier">Sample</span><span class="special">()]</span></code> evaluates to the value associated |
| with the <code class="computeroutput"><span class="identifier">sample</span></code> key if |
| it exists, or a default-constructed <code class="computeroutput"><span class="identifier">Sample</span></code> |
| if it doesn't. |
| </p> |
| <p> |
| The example above demonstrates the most common attributes of an accumulator. |
| There are other optional member functions that have special meaning. |
| In particular: |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b>Optional Accumulator Member Functions</b></p> |
| <dl> |
| <dt><span class="term"><code class="literal">on_drop(Args)</code></span></dt> |
| <dd><p> |
| Defines an action to be taken when this accumulator is dropped. |
| See the section on <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.droppable_accumulators">Droppable |
| Accumulators</a>. |
| </p></dd> |
| </dl> |
| </div> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.accessing_other_accumulators_in_the_set"></a><h4> |
| <a name="id766035"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.accessing_other_accumulators_in_the_set">Accessing |
| Other Accumulators in the Set</a> |
| </h4> |
| <p> |
| Some accumulators depend on other accumulators within the same accumulator |
| set. In those cases, it is necessary to be able to access those other |
| accumulators. To make this possible, the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| passes a reference to itself when invoking the member functions of its |
| contained accumulators. It can be accessed by using the special <code class="computeroutput"><span class="identifier">accumulator</span></code> key with the argument pack. |
| Consider how we might implement <code class="computeroutput"><span class="identifier">mean_accumulator</span></code>: |
| </p> |
| <pre class="programlisting"><span class="comment">// Mean == (Sum / Count) |
| </span><span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Sample</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">mean_accumulator</span> <span class="special">:</span> <span class="identifier">accumulator_base</span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">Sample</span> <span class="identifier">result_type</span><span class="special">;</span> |
| <span class="identifier">mean_accumulator</span><span class="special">(</span><span class="identifier">dont_care</span><span class="special">)</span> <span class="special">{}</span> |
| |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Args</span><span class="special">></span> |
| <span class="identifier">result_type</span> <span class="identifier">result</span><span class="special">(</span><span class="identifier">Args</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">args</span><span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">args</span><span class="special">[</span><span class="identifier">accumulator</span><span class="special">])</span> <span class="special">/</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">args</span><span class="special">[</span><span class="identifier">accumulator</span><span class="special">]);</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| <code class="computeroutput"><span class="identifier">mean</span></code> depends on the |
| <code class="computeroutput"><span class="identifier">sum</span></code> and <code class="computeroutput"><span class="identifier">count</span></code> accumulators. (We'll see in the |
| next section how to specify these dependencies.) The result of the mean |
| accumulator is merely the result of the sum accumulator divided by the |
| result of the count accumulator. Consider how we write that: <code class="computeroutput"><span class="identifier">sum</span><span class="special">(</span><span class="identifier">args</span><span class="special">[</span><span class="identifier">accumulator</span><span class="special">])</span> |
| <span class="special">/</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">args</span><span class="special">[</span><span class="identifier">accumulator</span><span class="special">])</span></code>. The expression <code class="computeroutput"><span class="identifier">args</span><span class="special">[</span><span class="identifier">accumulator</span><span class="special">]</span></code> evaluates to a reference to the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> that contains this |
| <code class="computeroutput"><span class="identifier">mean_accumulator</span></code>. It |
| also contains the <code class="computeroutput"><span class="identifier">sum</span></code> |
| and <code class="computeroutput"><span class="identifier">count</span></code> accumulators, |
| and we can access their results with the extractors defined for those |
| features: <code class="computeroutput"><span class="identifier">sum</span></code> and <code class="computeroutput"><span class="identifier">count</span></code>. |
| </p> |
| <div class="note"><table border="0" summary="Note"> |
| <tr> |
| <td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td> |
| <th align="left">Note</th> |
| </tr> |
| <tr><td align="left" valign="top"><p> |
| Accumulators that inherit from <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_base.html" title="Struct accumulator_base">accumulator_base</a></code> get |
| an empty <code class="computeroutput"><span class="keyword">operator</span> <span class="special">()</span></code>, |
| so accumulators like <code class="computeroutput"><span class="identifier">mean_accumulator</span></code> |
| above need not define one. |
| </p></td></tr> |
| </table></div> |
| <p> |
| All the member functions that accept an argument pack have access to |
| the enclosing <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| via the <code class="computeroutput"><span class="identifier">accumulator</span></code> key, |
| including the constructor. The accumulators within the set are constructed |
| in an order determined by their interdependencies. As a result, it is |
| safe for an accumulator to access one on which it depends during construction. |
| </p> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.infix_notation_and_the_numeric_operators_sub_library"></a><h4> |
| <a name="id766588"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.infix_notation_and_the_numeric_operators_sub_library">Infix |
| Notation and the Numeric Operators Sub-Library</a> |
| </h4> |
| <p> |
| Although not necessary, it can be a good idea to put your accumulator |
| implementations in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">impl</span></code> |
| namespace. This namespace pulls in any operators defined in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span></code> namespace with a using directive. |
| The Numeric Operators Sub-Library defines some additional overloads that |
| will make your accumulators work with all sorts of data types. |
| </p> |
| <p> |
| Consider <code class="computeroutput"><span class="identifier">mean_accumulator</span></code> |
| defined above. It divides the sum of the samples by the count. The type |
| of the count is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span></code>. What if the sample type doesn't |
| define division by <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span></code>? |
| That's the case for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><></span></code>. You might think that if the |
| sample type is <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><></span></code>, |
| the code would not work, but in fact it does. That's because Numeric |
| Operators Sub-Library defines an overloaded <code class="computeroutput"><span class="keyword">operator</span><span class="special">/</span></code> for <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">complex</span><span class="special"><></span></code> and <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span></code>. |
| This operator is defined in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span></code> |
| namespace and will be found within the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">impl</span></code> |
| namespace. That's why it's a good idea to put your accumulators there. |
| </p> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.droppable_accumulators"></a><h4> |
| <a name="id766596"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_accumulator.droppable_accumulators">Droppable |
| Accumulators</a> |
| </h4> |
| <p> |
| The term "droppable" refers to an accumulator that can be removed |
| from the <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| You can request that an accumulator be made droppable by using the <code class="computeroutput">droppable<></code> class template. |
| </p> |
| <pre class="programlisting"><span class="comment">// calculate sum and count, make sum droppable: |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">count</span><span class="special">,</span> <span class="identifier">droppable</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="comment">// add some data |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">3.0</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span> |
| |
| <span class="comment">// drop the sum (sum is 5 here) |
| </span><span class="identifier">acc</span><span class="special">.</span><span class="identifier">drop</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span><span class="special">>();</span> |
| |
| <span class="comment">// add more data |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">1.0</span><span class="special">);</span> |
| |
| <span class="comment">// This will display "3" and "5" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="char">' '</span> <span class="special"><<</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span> |
| </pre> |
| <p> |
| Any accumulators that get added to an accumulator set in order to satisfy |
| dependencies on droppable accumulators are themselves droppable. Consider |
| the following accumulator: |
| </p> |
| <pre class="programlisting"><span class="comment">// Sum is not droppable. Mean is droppable. Count, brought in to |
| </span><span class="comment">// satisfy mean's dependencies, is implicitly droppable, too. |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span><span class="special">,</span> <span class="identifier">droppable</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| </pre> |
| <p> |
| <code class="computeroutput"><span class="identifier">mean</span></code> depends on <code class="computeroutput"><span class="identifier">sum</span></code> and <code class="computeroutput"><span class="identifier">count</span></code>. |
| Since <code class="computeroutput"><span class="identifier">mean</span></code> is droppable, |
| so too is <code class="computeroutput"><span class="identifier">count</span></code>. However, |
| we have explictitly requested that <code class="computeroutput"><span class="identifier">sum</span></code> |
| be not droppable, so it isn't. Had we left <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span></code> |
| out of the above declaration, the <code class="computeroutput"><span class="identifier">sum</span></code> |
| accumulator would have been implicitly droppable. |
| </p> |
| <p> |
| A droppable accumulator is reference counted, and is only really dropped |
| after all the accumulators that depend on it have been dropped. This |
| can lead to some surprising behavior in some situations. |
| </p> |
| <pre class="programlisting"><span class="comment">// calculate sum and mean, make mean droppable. |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span><span class="special">,</span> <span class="identifier">droppable</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="comment">// add some data |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">1.0</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.0</span><span class="special">);</span> |
| |
| <span class="comment">// drop the mean. mean's reference count |
| </span><span class="comment">// drops to 0, so it's really dropped. So |
| </span><span class="comment">// too, count's reference count drops to 0 |
| </span><span class="comment">// and is really dropped. |
| </span><span class="identifier">acc</span><span class="special">.</span><span class="identifier">drop</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">>();</span> |
| |
| <span class="comment">// add more data. Sum continues to accumulate! |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">3.0</span><span class="special">);</span> |
| |
| <span class="comment">// This will display "6 2 3" |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="char">' '</span> |
| <span class="special"><<</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="char">' '</span> |
| <span class="special"><<</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span> |
| </pre> |
| <p> |
| Note that at the point at which <code class="computeroutput"><span class="identifier">mean</span></code> |
| is dropped, <code class="computeroutput"><span class="identifier">sum</span></code> is 3, |
| <code class="computeroutput"><span class="identifier">count</span></code> is 2, and therefore |
| <code class="computeroutput"><span class="identifier">mean</span></code> is 1.5. But since |
| <code class="computeroutput"><span class="identifier">sum</span></code> continues to accumulate |
| even after <code class="computeroutput"><span class="identifier">mean</span></code> has been |
| dropped, the value of <code class="computeroutput"><span class="identifier">mean</span></code> |
| continues to change. If you want to remember the value of <code class="computeroutput"><span class="identifier">mean</span></code> at the point it is dropped, you |
| should save its value into a local variable. |
| </p> |
| <p> |
| The following rules more precisely specify how droppable and non-droppable |
| accumulators behave within an accumulator set. |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| There are two types of accumulators: droppable and non-droppable. |
| The default is non-droppable. |
| </li> |
| <li class="listitem"> |
| For any feature <code class="computeroutput"><span class="identifier">X</span></code>, |
| both <code class="computeroutput"><span class="identifier">X</span></code> and <code class="computeroutput"><span class="identifier">droppable</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">X</span></code> dependency. |
| </li> |
| <li class="listitem"> |
| If feature <code class="computeroutput"><span class="identifier">X</span></code> depends |
| on <code class="computeroutput"><span class="identifier">Y</span></code> and <code class="computeroutput"><span class="identifier">Z</span></code>, then <code class="computeroutput"><span class="identifier">droppable</span><span class="special"><</span><span class="identifier">X</span><span class="special">></span></code> depends on <code class="computeroutput"><span class="identifier">droppable</span><span class="special"><</span><span class="identifier">Y</span><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">droppable</span><span class="special"><</span><span class="identifier">Z</span><span class="special">></span></code>. |
| </li> |
| <li class="listitem"> |
| All accumulators have <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code> and <code class="computeroutput"><span class="identifier">drop</span><span class="special">()</span></code> member functions. |
| </li> |
| <li class="listitem"> |
| For non-droppable accumulators, <code class="computeroutput"><span class="identifier">drop</span><span class="special">()</span></code> is a no-op, and <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code> invokes <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code> on all accumulators corresponding |
| to the features upon which the current accumulator depends. |
| </li> |
| <li class="listitem"> |
| Droppable accumulators have a reference count and define <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code> |
| and <code class="computeroutput"><span class="identifier">drop</span><span class="special">()</span></code> |
| to manipulate the reference count. |
| </li> |
| <li class="listitem"> |
| For droppable accumulators, <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code> increments the accumulator's reference |
| count, and also <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code>'s the accumulators corresponding |
| to the features upon which the current accumulator depends. |
| </li> |
| <li class="listitem"> |
| For droppable accumulators, <code class="computeroutput"><span class="identifier">drop</span><span class="special">()</span></code> decrements the accumulator's reference |
| count, and also <code class="computeroutput"><span class="identifier">drop</span><span class="special">()</span></code>'s the accumulators corresponding |
| to the features upon which the current accumulator depends. |
| </li> |
| <li class="listitem"> |
| The accumulator_set constructor walks the list of <span class="bold"><strong>user-specified</strong></span> |
| features and <code class="computeroutput"><span class="identifier">add_ref</span><span class="special">()</span></code>'s the accumulator that corresponds |
| to each of them. (Note: that means that an accumulator that is not |
| user-specified but in the set merely to satisfy a dependency will |
| be dropped as soon as all its dependencies have been dropped. Ones |
| that have been user specified are not dropped until their dependencies |
| have been dropped <span class="bold"><strong>and</strong></span> the user has |
| explicitly dropped the accumulator.) |
| </li> |
| <li class="listitem"> |
| Droppable accumulators check their reference count in their accumulate |
| member function. If the reference count is 0, the function is a no-op. |
| </li> |
| <li class="listitem"> |
| Users are not allowed to drop a feature that is not user-specified |
| and marked as droppable. |
| </li> |
| </ul></div> |
| <p> |
| And as an optimization: |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| If the user specifies the non-droppable feature <code class="computeroutput"><span class="identifier">X</span></code>, |
| which depends on <code class="computeroutput"><span class="identifier">Y</span></code> |
| and <code class="computeroutput"><span class="identifier">Z</span></code>, then the accumulators |
| for <code class="computeroutput"><span class="identifier">Y</span></code> and <code class="computeroutput"><span class="identifier">Z</span></code> can be safely made non-droppable, |
| as well as any accumulators on which they depend. |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_feature"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_feature" title="Defining a New Feature">Defining |
| a New Feature</a> |
| </h5></div></div></div> |
| <p> |
| Once we have implemented an accumulator, we must define a feature for |
| it so that users can specify the feature when declaring an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. We typically put |
| the features into a nested namespace, so that later we can define an |
| extractor of the same name. All features must satisfy the <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts.feature_concept">Feature |
| Concept</a>. Using <code class="computeroutput"><a class="link" href="../boost/accumulators/depends_on.html" title="Struct template depends_on">depends_on<></a></code> |
| makes satisfying the concept simple. Below is an example of a feature |
| definition. |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">accumulators</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">tag</span> <span class="special">{</span> |
| |
| <span class="keyword">struct</span> <span class="identifier">mean</span> <span class="comment">// Features should inherit from |
| </span> <span class="special">:</span> <span class="identifier">depends_on</span><span class="special"><</span> <span class="identifier">count</span><span class="special">,</span> <span class="identifier">sum</span> <span class="special">></span> <span class="comment">// depends_on<> to specify dependencies |
| </span><span class="special">{</span> |
| <span class="comment">// Define a nested typedef called 'impl' that specifies which |
| </span> <span class="comment">// accumulator implements this feature. |
| </span> <span class="keyword">typedef</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">impl</span><span class="special">::</span><span class="identifier">mean_accumulator</span><span class="special"><</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">_1</span> <span class="special">></span> <span class="identifier">impl</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="special">}}}</span> |
| </pre> |
| <p> |
| The only two things we must do to define the <code class="computeroutput"><span class="identifier">mean</span></code> |
| feature is to specify the dependencies with <code class="computeroutput"><a class="link" href="../boost/accumulators/depends_on.html" title="Struct template depends_on">depends_on<></a></code> |
| and define the nested <code class="computeroutput"><span class="identifier">impl</span></code> |
| typedef. Even features that have no dependencies should inherit from |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/depends_on.html" title="Struct template depends_on">depends_on<></a></code>. The nested <code class="computeroutput"><span class="identifier">impl</span></code> type must be an <a href="../../../libs/mpl/doc/refmanual/lambda-expression.html" target="_top">MPL |
| Lambda Expression</a>. The result of <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">apply</span><span class="special"><</span> <span class="identifier">impl</span><span class="special">,</span> <em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em> <span class="special">>::</span><span class="identifier">type</span></code> must be be the type of the accumulator |
| that implements this feature. The use of <a href="../../../libs/mpl/index.html" target="_top">MPL</a> |
| placeholders like <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">_1</span></code> |
| make it especially easy to make a template such as <code class="computeroutput"><span class="identifier">mean_accumulator</span><span class="special"><></span></code> an <a href="../../../libs/mpl/doc/refmanual/lambda-expression.html" target="_top">MPL |
| Lambda Expression</a>. Here, <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">_1</span></code> |
| will be replaced with the sample type. Had we used <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">_2</span></code>, |
| it would have been replaced with the weight type. |
| </p> |
| <p> |
| What about accumulator types that are not templates? If you have a <code class="computeroutput"><span class="identifier">foo_accumulator</span></code> which is a plain struct |
| and not a template, you could turn it into an <a href="../../../libs/mpl/doc/refmanual/lambda-expression.html" target="_top">MPL |
| Lambda Expression</a> using <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">always</span><span class="special"><></span></code>, like this: |
| </p> |
| <pre class="programlisting"><span class="comment">// An MPL lambda expression that always evaluates to |
| </span><span class="comment">// foo_accumulator: |
| </span><span class="keyword">typedef</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">always</span><span class="special"><</span> <span class="identifier">foo_accumulator</span> <span class="special">></span> <span class="identifier">impl</span><span class="special">;</span> |
| </pre> |
| <p> |
| If you are ever unsure, or if you are not comfortable with MPL lambda |
| expressions, you could always define <code class="computeroutput"><span class="identifier">impl</span></code> |
| explicitly: |
| </p> |
| <pre class="programlisting"><span class="comment">// Same as 'typedef mpl::always< foo_accumulator > impl;' |
| </span><span class="keyword">struct</span> <span class="identifier">impl</span> |
| <span class="special">{</span> |
| <span class="keyword">template</span><span class="special"><</span> <span class="keyword">typename</span> <span class="identifier">Sample</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Weight</span> <span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">apply</span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">foo_accumulator</span> <span class="identifier">type</span><span class="special">;</span> |
| <span class="special">};</span> |
| <span class="special">};</span> |
| </pre> |
| <p> |
| Here, <code class="computeroutput"><span class="identifier">impl</span></code> is a binary |
| <a href="../../../libs/mpl/doc/refmanual/metafunction-class.html" target="_top">MPL |
| Metafunction Class</a>, which is a kind of <a href="../../../libs/mpl/doc/refmanual/lambda-expression.html" target="_top">MPL |
| Lambda Expression</a>. The nested <code class="computeroutput"><span class="identifier">apply</span><span class="special"><></span></code> template is part of the metafunction |
| class protocol and tells MPL how to to build the accumulator type given |
| the sample and weight types. |
| </p> |
| <p> |
| All features must also provide a nested <code class="computeroutput"><span class="identifier">is_weight_accumulator</span></code> |
| typedef. It must be either <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> |
| or <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code>. <code class="computeroutput"><a class="link" href="../boost/accumulators/depends_on.html" title="Struct template depends_on">depends_on<></a></code> |
| provides a default of <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code> |
| for all features that inherit from it, but that can be overridden (or |
| hidden, technically speaking) in the derived type. When the feature represents |
| an accumulation of information about the weights instead of the samples, |
| we can mark this feature as such with <code class="computeroutput"><span class="keyword">typedef</span> |
| <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span> <span class="identifier">is_weight_accumulator</span><span class="special">;</span></code>. The weight accumulators are made external |
| if the weight type is specified using the <code class="computeroutput">external<></code> |
| template. |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_extractor"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_extractor" title="Defining a New Extractor">Defining |
| a New Extractor</a> |
| </h5></div></div></div> |
| <p> |
| Now that we have an accumulator and a feature, the only thing lacking |
| is a way to get results from the accumulator set. The Accumulators Framework |
| provides the <code class="computeroutput">extractor<></code> |
| class template to make it simple to define an extractor for your feature. |
| Here's an extractor for the <code class="computeroutput"><span class="identifier">mean</span></code> |
| feature we defined above: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> |
| <span class="keyword">namespace</span> <span class="identifier">accumulators</span> <span class="special">{</span> <span class="comment">// By convention, we put extractors |
| </span><span class="keyword">namespace</span> <span class="identifier">extract</span> <span class="special">{</span> <span class="comment">// in the 'extract' namespace |
| </span> |
| <span class="identifier">extractor</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span> <span class="special">></span> <span class="keyword">const</span> <span class="identifier">mean</span> <span class="special">=</span> <span class="special">{};</span> <span class="comment">// Simply define our extractor with |
| </span> <span class="comment">// our feature tag, like this. |
| </span><span class="special">}</span> |
| <span class="keyword">using</span> <span class="identifier">extract</span><span class="special">::</span><span class="identifier">mean</span><span class="special">;</span> <span class="comment">// Pull the extractor into the |
| </span> <span class="comment">// enclosing namespace. |
| </span><span class="special">}}</span> |
| </pre> |
| <p> |
| Once defined, the <code class="computeroutput"><span class="identifier">mean</span></code> |
| extractor can be used to extract the result of the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span></code> |
| feature from an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code>. |
| </p> |
| <p> |
| Parameterized features complicate this simple picture. Consider the |
| <code class="computeroutput"><span class="identifier">moment</span></code> feature, for calculating |
| the <code class="literal"><span class="emphasis"><em>N</em></span></code>-th moment, where <code class="literal"><span class="emphasis"><em>N</em></span></code> |
| is specified as a template parameter: |
| </p> |
| <pre class="programlisting"><span class="comment">// An accumulator set for calculating the N-th moment, for N == 2 ... |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span> <span class="keyword">double</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="comment">// ... add some data ... |
| </span> |
| <span class="comment">// Display the 2nd moment ... |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special"><<</span> <span class="string">"2nd moment is "</span> <span class="special"><<</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special"><<</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span> |
| </pre> |
| <p> |
| In the expression <code class="computeroutput"><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)</span></code>, |
| what is <code class="computeroutput"><span class="identifier">moment</span></code>? It cannot |
| be an object -- the syntax of C++ will not allow it. Clearly, if we want |
| to provide this syntax, we must make <code class="computeroutput"><span class="identifier">moment</span></code> |
| a function template. Here's what the definition of the <code class="computeroutput"><span class="identifier">moment</span></code> extractor looks like: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> |
| <span class="keyword">namespace</span> <span class="identifier">accumulators</span> <span class="special">{</span> <span class="comment">// By convention, we put extractors |
| </span><span class="keyword">namespace</span> <span class="identifier">extract</span> <span class="special">{</span> <span class="comment">// in the 'extract' namespace |
| </span> |
| <span class="keyword">template</span><span class="special"><</span><span class="keyword">int</span> <span class="identifier">N</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">AccumulatorSet</span><span class="special">></span> |
| <span class="keyword">typename</span> <span class="identifier">mpl</span><span class="special">::</span><span class="identifier">apply</span><span class="special"><</span><span class="identifier">AccumulatorSet</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">>::</span><span class="identifier">type</span><span class="special">::</span><span class="identifier">result_type</span> |
| <span class="identifier">moment</span><span class="special">(</span><span class="identifier">AccumulatorSet</span> <span class="keyword">const</span> <span class="special">&</span><span class="identifier">acc</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">return</span> <span class="identifier">extract_result</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="identifier">N</span><span class="special">></span> <span class="special">>(</span><span class="identifier">acc</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="special">}</span> |
| <span class="keyword">using</span> <span class="identifier">extract</span><span class="special">::</span><span class="identifier">moment</span><span class="special">;</span> <span class="comment">// Pull the extractor into the |
| </span> <span class="comment">// enclosing namespace. |
| </span><span class="special">}}</span> |
| </pre> |
| <p> |
| The return type deserves some explanation. Every <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| type is actually a unary <a href="../../../libs/mpl/doc/refmanual/metafunction-class.html" target="_top">MPL |
| Metafunction Class</a>. When you <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">apply</span><span class="special"><></span></code> an <code class="computeroutput"><a class="link" href="../boost/accumulators/accumulator_set.html" title="Struct template accumulator_set">accumulator_set<></a></code> |
| and a feature, the result is the type of the accumulator within the set |
| that implements that feature. And every accumulator provides a nested |
| <code class="computeroutput"><span class="identifier">result_type</span></code> typedef that |
| tells what its return type is. The extractor simply delegates its work |
| to the <code class="computeroutput"><a class="link" href="reference.html#boost.accumulators.extract_result_id554849">extract_result()</a></code> |
| function. |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.controlling_dependencies"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.controlling_dependencies" title="Controlling Dependencies">Controlling |
| Dependencies</a> |
| </h5></div></div></div> |
| <p> |
| The feature-based dependency resolution of the Accumulators Framework |
| is designed to allow multiple different implementation strategies for |
| each feature. For instance, two different accumulators may calculate |
| the same quantity with different rounding modes, or using different algorithms |
| with different size/speed tradeoffs. Other accumulators that depend on |
| that quantity shouldn't care how it's calculated. The Accumulators Framework |
| handles this by allowing several different accumulators satisfy the same |
| feature. |
| </p> |
| <p> |
| <span class="bold"><strong>Aliasing feature dependencies with <code class="literal">feature_of<></code></strong></span> |
| </p> |
| <p> |
| Imagine that you would like to implement the hypothetical <span class="emphasis"><em>fubar</em></span> |
| statistic, and that you know two ways to calculate fubar on a bunch of |
| samples: an accurate but slow calculation and an approximate but fast |
| calculation. You might opt to make the accurate calculation the default, |
| so you implement two accumulators and call them <code class="computeroutput"><span class="identifier">impl</span><span class="special">::</span><span class="identifier">fubar_impl</span></code> |
| and <code class="computeroutput"><span class="identifier">impl</span><span class="special">::</span><span class="identifier">fast_fubar_impl</span></code>. You would also define |
| the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fast_fubar</span></code> |
| features as described <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.defining_a_new_feature" title="Defining a New Feature">above</a>. |
| Now, you would like to inform the Accumulators Framework that these two |
| features are the same from the point of view of dependency resolution. |
| You can do that with <code class="computeroutput"><a class="link" href="../boost/accumulators/feature_of.html" title="Struct template feature_of">feature_of<></a></code>, |
| as follows: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">accumulators</span> |
| <span class="special">{</span> |
| <span class="comment">// For the purposes of feature-based dependency resolution, |
| </span> <span class="comment">// fast_fubar provides the same feature as fubar |
| </span> <span class="keyword">template</span><span class="special"><></span> |
| <span class="keyword">struct</span> <span class="identifier">feature_of</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fast_fubar</span><span class="special">></span> |
| <span class="special">:</span> <span class="identifier">feature_of</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">></span> |
| <span class="special">{</span> |
| <span class="special">};</span> |
| <span class="special">}}</span> |
| </pre> |
| <p> |
| The above code instructs the Accumulators Framework that, if another |
| accumulator in the set depends on the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span></code> |
| feature, the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fast_fubar</span></code> feature is an acceptable |
| substitute. |
| </p> |
| <p> |
| <span class="bold"><strong>Registering feature variants with <code class="literal">as_feature<></code></strong></span> |
| </p> |
| <p> |
| You may hve noticed that some feature variants in the Accumulators Framework |
| can be specified with a nicer syntax. For instance, instead of <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">immediate_mean</span></code> |
| you can specify them with <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">lazy</span><span class="special">)</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span></code> respectively. These are merely aliases, |
| but the syntax makes the relationship between the two clearer. You can |
| create these feature aliases with the <code class="computeroutput"><a class="link" href="../boost/accumulators/as_feature.html" title="Struct template as_feature">as_feature<></a></code> |
| trait. Given the fubar example above, you might decide to alias <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">accurate</span><span class="special">)</span></code> |
| with <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">fast</span><span class="special">)</span></code> with <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fast_fubar</span></code>. |
| You would do that as follows: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">accumulators</span> |
| <span class="special">{</span> |
| <span class="keyword">struct</span> <span class="identifier">fast</span> <span class="special">{};</span> <span class="comment">// OK to leave these tags empty |
| </span> <span class="keyword">struct</span> <span class="identifier">accurate</span> <span class="special">{};</span> |
| |
| <span class="keyword">template</span><span class="special"><></span> |
| <span class="keyword">struct</span> <span class="identifier">as_feature</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">accurate</span><span class="special">)></span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span> <span class="identifier">type</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="keyword">template</span><span class="special"><></span> |
| <span class="keyword">struct</span> <span class="identifier">as_feature</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">fast</span><span class="special">)></span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">fast_fubar</span> <span class="identifier">type</span><span class="special">;</span> |
| <span class="special">};</span> |
| <span class="special">}}</span> |
| </pre> |
| <p> |
| Once you have done this, users of your fubar accumulator can request |
| the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">fast</span><span class="special">)</span></code> |
| and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">fubar</span><span class="special">(</span><span class="identifier">accurate</span><span class="special">)</span></code> |
| features when defining their <code class="computeroutput"><span class="identifier">accumulator_set</span></code>s |
| and get the correct accumulator. |
| </p> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h5 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.operators_ex"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.extending_the_accumulators_framework.operators_ex" title="Specializing Numeric Operators">Specializing |
| Numeric Operators</a> |
| </h5></div></div></div> |
| <p> |
| This section describes how to adapt third-party numeric types to work |
| with the Accumulator Framework. |
| </p> |
| <p> |
| Rather than relying on the built-in operators, the Accumulators Framework |
| relies on functions and operator overloads defined in the <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.numeric_operators_sub_library" title="Numeric Operators Sub-Library">Numeric |
| Operators Sub-Library</a> for many of its numeric operations. This |
| is so that it is possible to assign non-standard meanings to arithmetic |
| operations. For instance, when calculating an average by dividing two |
| integers, the standard integer division behavior would be mathematically |
| incorrect for most statistical quantities. So rather than use <code class="computeroutput"><span class="identifier">x</span> <span class="special">/</span> <span class="identifier">y</span></code>, the Accumulators Framework uses |
| <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">average</span><span class="special">(</span><span class="identifier">x</span><span class="special">,</span> <span class="identifier">y</span><span class="special">)</span></code>, |
| which does floating-point division even if both <code class="computeroutput"><span class="identifier">x</span></code> |
| and <code class="computeroutput"><span class="identifier">y</span></code> are integers. |
| </p> |
| <p> |
| Another example where the Numeric Operators Sub-Library is useful is |
| when a type does not define the operator overloads required to use it |
| for some statistical calculations. For instance, <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code> does not overload any arithmetic |
| operators, yet it may be useful to use <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code> as a sample or variate type. |
| The Numeric Operators Sub-Library defines the necessary operator overloads |
| in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">operators</span></code> namespace, which is brought |
| into scope by the Accumulators Framework with a using directive. |
| </p> |
| <p> |
| <span class="bold"><strong>Numeric Function Objects and Tag Dispatching</strong></span> |
| </p> |
| <p> |
| How are the numeric function object defined by the Numeric Operators |
| Sub-Library made to work with types such as <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code>? The free functions in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span></code> namespace are implemented in |
| terms of the function objects in the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span></code> |
| namespace, so to make <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">average</span><span class="special">()</span></code> do something sensible with a <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><></span></code>, |
| for instance, we'll need to partially specialize the <code class="computeroutput"><span class="identifier">boost</span><span class="special">::</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></code> function object. |
| </p> |
| <p> |
| The functional objects make use of a technique known as <a href="http://www.boost.org/community/generic_programming.html#tag_dispatching" target="_top"><span class="emphasis"><em>tag |
| dispatching</em></span></a> to select the proper implementation for |
| the given operands. It works as follows: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">functional</span> |
| <span class="special">{</span> |
| <span class="comment">// Metafunction for looking up the tag associated with |
| </span> <span class="comment">// a given numeric type T. |
| </span> <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">T</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">tag</span> |
| <span class="special">{</span> |
| <span class="comment">// by default, all types have void as a tag type |
| </span> <span class="keyword">typedef</span> <span class="keyword">void</span> <span class="identifier">type</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="comment">// Forward declaration looks up the tag types of each operand |
| </span> <span class="keyword">template</span><span class="special"><</span> |
| <span class="keyword">typename</span> <span class="identifier">Left</span> |
| <span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Right</span> |
| <span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">LeftTag</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">tag</span><span class="special"><</span><span class="identifier">Left</span><span class="special">>::</span><span class="identifier">type</span> |
| <span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">RightTag</span> <span class="special">=</span> <span class="keyword">typename</span> <span class="identifier">tag</span><span class="special"><</span><span class="identifier">Right</span><span class="special">>::</span><span class="identifier">type</span> |
| <span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">average</span><span class="special">;</span> |
| <span class="special">}}}</span> |
| </pre> |
| <p> |
| If you have some user-defined type <code class="computeroutput"><span class="identifier">MyDouble</span></code> |
| for which you would like to customimze the behavior of <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">average</span><span class="special">()</span></code>, |
| you would specialize <code class="computeroutput"><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></code> by first defining a tag type, |
| as shown below: |
| </p> |
| <pre class="programlisting"><span class="keyword">namespace</span> <span class="identifier">boost</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">numeric</span> <span class="special">{</span> <span class="keyword">namespace</span> <span class="identifier">functional</span> |
| <span class="special">{</span> |
| <span class="comment">// Tag type for MyDouble |
| </span> <span class="keyword">struct</span> <span class="identifier">MyDoubleTag</span> <span class="special">{};</span> |
| |
| <span class="comment">// Specialize tag<> for MyDouble. |
| </span> <span class="comment">// This only needs to be done once. |
| </span> <span class="keyword">template</span><span class="special"><></span> |
| <span class="keyword">struct</span> <span class="identifier">tag</span><span class="special"><</span><span class="identifier">MyDouble</span><span class="special">></span> |
| <span class="special">{</span> |
| <span class="keyword">typedef</span> <span class="identifier">MyDoubleTag</span> <span class="identifier">type</span><span class="special">;</span> |
| <span class="special">};</span> |
| |
| <span class="comment">// Specify how to divide a MyDouble by an integral count |
| </span> <span class="keyword">template</span><span class="special"><</span><span class="keyword">typename</span> <span class="identifier">Left</span><span class="special">,</span> <span class="keyword">typename</span> <span class="identifier">Right</span><span class="special">></span> |
| <span class="keyword">struct</span> <span class="identifier">average</span><span class="special"><</span><span class="identifier">Left</span><span class="special">,</span> <span class="identifier">Right</span><span class="special">,</span> <span class="identifier">MyDoubleTag</span><span class="special">,</span> <span class="keyword">void</span><span class="special">></span> |
| <span class="special">{</span> |
| <span class="comment">// Define the type of the result |
| </span> <span class="keyword">typedef</span> <span class="special">...</span> <span class="identifier">result_type</span><span class="special">;</span> |
| |
| <span class="identifier">result_type</span> <span class="keyword">operator</span><span class="special">()(</span><span class="identifier">Left</span> <span class="special">&</span> <span class="identifier">left</span><span class="special">,</span> <span class="identifier">Right</span> <span class="special">&</span> <span class="identifier">right</span><span class="special">)</span> <span class="keyword">const</span> |
| <span class="special">{</span> |
| <span class="keyword">return</span> <span class="special">...;</span> |
| <span class="special">}</span> |
| <span class="special">};</span> |
| <span class="special">}}}</span> |
| </pre> |
| <p> |
| Once you have done this, <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">average</span><span class="special">()</span></code> will use your specialization of <code class="computeroutput"><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></code> |
| when the first argument is a <code class="computeroutput"><span class="identifier">MyDouble</span></code> |
| object. All of the function objects in the Numeric Operators Sub-Library |
| can be customized in a similar fashion. |
| </p> |
| </div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.concepts"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts" title="Concepts">Concepts</a> |
| </h4></div></div></div> |
| <a name="accumulators.user_s_guide.the_accumulators_framework.concepts.accumulator_concept"></a><h3> |
| <a name="id772191"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts.accumulator_concept">Accumulator |
| Concept</a> |
| </h3> |
| <p> |
| In the following table, <code class="computeroutput"><span class="identifier">Acc</span></code> |
| is the type of an accumulator, <code class="computeroutput"><span class="identifier">acc</span></code> |
| and <code class="computeroutput"><span class="identifier">acc2</span></code> are objects of |
| type <code class="computeroutput"><span class="identifier">Acc</span></code>, and <code class="computeroutput"><span class="identifier">args</span></code> is the name of an argument pack |
| from the <a href="../../../libs/parameter/index.html" target="_top">Boost.Parameter</a> |
| library. |
| </p> |
| <div class="table"> |
| <a name="id772263"></a><p class="title"><b>Table 1.2. Accumulator Requirements</b></p> |
| <div class="table-contents"><table class="table" summary="Accumulator Requirements"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| <span class="bold"><strong>Expression</strong></span> |
| </p> |
| </th> |
| <th> |
| <p> |
| <span class="bold"><strong>Return type</strong></span> |
| </p> |
| </th> |
| <th> |
| <p> |
| <span class="bold"><strong>Assertion / Note / Pre- / Post-condition</strong></span> |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">Acc</span><span class="special">::</span><span class="identifier">result_type</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>implementation defined</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| The type returned by <code class="computeroutput"><span class="identifier">Acc</span><span class="special">::</span><span class="identifier">result</span><span class="special">()</span></code>. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">Acc</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| none |
| </p> |
| </td> |
| <td> |
| <p> |
| Construct from an argument pack. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">Acc</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| none |
| </p> |
| </td> |
| <td> |
| <p> |
| Post: <code class="computeroutput"><span class="identifier">acc</span><span class="special">.</span><span class="identifier">result</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| is equivalent to <code class="computeroutput"><span class="identifier">acc2</span><span class="special">.</span><span class="identifier">result</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">acc</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>unspecified</em></span> |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">acc</span><span class="special">.</span><span class="identifier">on_drop</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>unspecified</em></span> |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">acc</span><span class="special">.</span><span class="identifier">result</span><span class="special">(</span><span class="identifier">args</span><span class="special">)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">Acc</span><span class="special">::</span><span class="identifier">result_type</span></code> |
| </p> |
| </td> |
| <td> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"><a name="accumulators.user_s_guide.the_accumulators_framework.concepts.feature_concept"></a><h3> |
| <a name="id772725"></a> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework.concepts.feature_concept">Feature |
| Concept</a> |
| </h3> |
| <p> |
| In the following table, <code class="computeroutput"><span class="identifier">F</span></code> |
| is the type of a feature and <code class="computeroutput"><span class="identifier">S</span></code> |
| is some scalar type. |
| </p> |
| <div class="table"> |
| <a name="id772762"></a><p class="title"><b>Table 1.3. Featue Requirements</b></p> |
| <div class="table-contents"><table class="table" summary="Featue Requirements"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| <span class="bold"><strong>Expression</strong></span> |
| </p> |
| </th> |
| <th> |
| <p> |
| <span class="bold"><strong>Return type</strong></span> |
| </p> |
| </th> |
| <th> |
| <p> |
| <span class="bold"><strong>Assertion / Note / Pre- / Post-condition</strong></span> |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">F</span><span class="special">::</span><span class="identifier">dependencies</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>unspecified</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| An MPL sequence of other features on which which <code class="computeroutput"><span class="identifier">F</span></code> depends. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">F</span><span class="special">::</span><span class="identifier">is_weight_accumulator</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> or <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">true_</span></code> if the accumulator for |
| this feature should be made external when the weight type for |
| the accumulator set is <code class="computeroutput"><span class="identifier">external</span><span class="special"><</span><span class="identifier">S</span><span class="special">></span></code>, <code class="computeroutput"><span class="identifier">mpl</span><span class="special">::</span><span class="identifier">false_</span></code> |
| otherwise. |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">F</span><span class="special">::</span><span class="identifier">impl</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <span class="emphasis"><em>unspecified</em></span> |
| </p> |
| </td> |
| <td> |
| <p> |
| An <a href="../../../libs/mpl/doc/refmanual/lambda-expression.html" target="_top">MPL |
| Lambda Expression</a> that returns the type of the accumulator |
| that implements this feature when passed a sample type and a |
| weight type. |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| </div> |
| <br class="table-break"> |
| </div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library" title="The Statistical Accumulators Library">The |
| Statistical Accumulators Library</a> |
| </h3></div></div></div> |
| <div class="toc"><dl> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count">count</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.covariance">covariance</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.density">density</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.error_of_mean">error_of<mean></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square">extended_p_square</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square_quantile">extended_p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.kurtosis">kurtosis</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.max">max</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean">mean |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.median">median |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.min">min</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.moment">moment</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_cumulative_distribution">p_square_cumulative_distribution</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_quantile">p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.peaks_over_threshold">peaks_over_threshold |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile">pot_quantile |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_tail_mean">pot_tail_mean</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_count">rolling_count</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_sum">rolling_sum</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_mean">rolling_mean</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.skewness">skewness</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum">sum |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail">tail</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.coherent_tail_mean">coherent_tail_mean</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean">non_coherent_tail_mean</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_quantile">tail_quantile</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate">tail_variate</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate_means">tail_variate_means |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.variance">variance |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_covariance">weighted_covariance</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_density">weighted_density</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_extended_p_square">weighted_extended_p_square</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_kurtosis">weighted_kurtosis</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean">weighted_mean |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_median">weighted_median |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment">weighted_moment</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_cumulative_distribution">weighted_p_square_cumulative_distribution</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_quantile">weighted_p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_peaks_over_threshold">weighted_peaks_over_threshold |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_skewness">weighted_skewness</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_sum">weighted_sum |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_weighted_tail_mean">non_coherent_weighted_tail_mean</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_quantile">weighted_tail_quantile</a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_variate_means">weighted_tail_variate_means |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| <dt><span class="section"><a href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_variance">weighted_variance |
| <span class="emphasis"><em>and variants</em></span></a></span></dt> |
| </dl></div> |
| <p> |
| The Statistical Accumulators Library defines accumulators for incremental |
| statistial computations. It is built on top of <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_accumulators_framework" title="The Accumulators Framework">The |
| Accumulator Framework</a>. |
| </p> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.count"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count">count</a> |
| </h4></div></div></div> |
| <p> |
| The <code class="computeroutput"><span class="identifier">count</span></code> feature is a |
| simple counter that tracks the number of samples pushed into the accumulator |
| set. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.count_hpp" title="Header <boost/accumulators/statistics/count.hpp>">boost/accumulators/statistics/count.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">features</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">count</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> |
| <span class="identifier">assert</span><span class="special">(</span><span class="number">3</span> <span class="special">==</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/count_impl.html" title="Struct count_impl">count_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.covariance"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.covariance" title="covariance">covariance</a> |
| </h4></div></div></div> |
| <p> |
| The <code class="computeroutput"><span class="identifier">covariance</span></code> feature |
| is an iterative Monte Carlo estimator for the covariance. It is specified |
| as <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariance</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">outer_product</span><span class="special"><</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">,</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><em class="replaceable"><code>variate-type</code></em><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="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">mean</span></code> <br> <code class="computeroutput"><span class="identifier">mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_covariance</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <em class="replaceable"><code>variate-tag</code></em> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Headers</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.covariance_hpp" title="Header <boost/accumulators/statistics/covariance.hpp>">boost/accumulators/statistics/covariance.hpp</a></code><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.variates.covariate_hpp" title="Header <boost/accumulators/statistics/variates/covariate.hpp>">boost/accumulators/statistics/variates/covariate.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariance</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">2.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">4.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">6.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">assert</span><span class="special">(</span><span class="identifier">covariance</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)</span> <span class="special">==</span> <span class="special">-</span><span class="number">1.75</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/covariance_impl.html" title="Struct template covariance_impl">covariance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean" title="mean and variants"><code class="literal">mean</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.density"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.density" title="density">density</a> |
| </h4></div></div></div> |
| <p> |
| The <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">density</span></code> feature returns a histogram of |
| the sample distribution. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/density_impl.html" title="Struct template density_impl">density_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">,</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">></span> |
| <span class="special">>::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">min</span></code> <br> <code class="computeroutput"><span class="identifier">max</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">density</span><span class="special">::</span><span class="identifier">cache_size</span></code> <br> <code class="computeroutput"><span class="identifier">density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N), when N is <code class="computeroutput"><span class="identifier">density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.density_hpp" title="Header <boost/accumulators/statistics/density.hpp>">boost/accumulators/statistics/density.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Note</strong></span> |
| </p> |
| <p> |
| Results from the <code class="computeroutput"><span class="identifier">density</span></code> |
| accumulator can only be extracted after the number of samples meets or |
| exceeds the cache size. |
| </p> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/density_impl.html" title="Struct template density_impl">density_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.min" title="min"><code class="literal">min</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.max" title="max"><code class="literal">max</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.error_of_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.error_of_mean" title="error_of<mean>">error_of<mean></a> |
| </h4></div></div></div> |
| <p> |
| The <code class="computeroutput"><span class="identifier">error_of</span><span class="special"><</span><span class="identifier">mean</span><span class="special">></span></code> |
| feature calculates the error of the mean feature. It is equal to <code class="computeroutput"><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">variance</span> <span class="special">/</span> |
| <span class="special">(</span><span class="identifier">count</span> |
| <span class="special">-</span> <span class="number">1</span><span class="special">))</span></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">variance</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">error_of</span><span class="special"><</span><span class="identifier">immediate_mean</span><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.error_of_hpp" title="Header <boost/accumulators/statistics/error_of.hpp>">boost/accumulators/statistics/error_of.hpp</a></code><span class="special">></span> |
| <span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.error_of_mean_hpp" title="Header <boost/accumulators/statistics/error_of_mean.hpp>">boost/accumulators/statistics/error_of_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">error_of</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.1</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.2</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.3</span><span class="special">);</span> |
| <span class="identifier">assert</span><span class="special">(</span><span class="number">0.057735</span> <span class="special">==</span> <span class="identifier">error_of</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/error_of_mean_impl.html" title="Struct template error_of_mean_impl">error_of_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.variance" title="variance and variants"><code class="literal">variance</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square" title="extended_p_square">extended_p_square</a> |
| </h4></div></div></div> |
| <p> |
| Multiple quantile estimation with the extended <code class="literal">P^2</code> algorithm. |
| For further details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/extended_p_square_impl.html" title="Struct template extended_p_square_impl">extended_p_square_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</span> |
| <em class="replaceable"><code>implementation-defined</code></em> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.extended_p_square_hpp" title="Header <boost/accumulators/statistics/extended_p_square.hpp>">boost/accumulators/statistics/extended_p_square.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">probs</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.001</span><span class="special">,</span><span class="number">0.01</span><span class="special">,</span><span class="number">0.1</span><span class="special">,</span><span class="number">0.25</span><span class="special">,</span><span class="number">0.5</span><span class="special">,</span><span class="number">0.75</span><span class="special">,</span><span class="number">0.9</span><span class="special">,</span><span class="number">0.99</span><span class="special">,</span><span class="number">0.999</span><span class="special">};</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span> <span class="special">=</span> <span class="identifier">probs</span><span class="special">);</span> |
| |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> <span class="comment">// a random number generator |
| </span><span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">10000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">rng</span><span class="special">());</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">extended_p_square</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)[</span><span class="number">0</span><span class="special">],</span> <span class="identifier">probs</span><span class="special">[</span><span class="number">0</span><span class="special">],</span> <span class="number">25</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">extended_p_square</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)[</span><span class="number">1</span><span class="special">],</span> <span class="identifier">probs</span><span class="special">[</span><span class="number">1</span><span class="special">],</span> <span class="number">10</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">extended_p_square</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)[</span><span class="number">2</span><span class="special">],</span> <span class="identifier">probs</span><span class="special">[</span><span class="number">2</span><span class="special">],</span> <span class="number">5</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">3</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">probs</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">extended_p_square</span><span class="special">(</span><span class="identifier">acc</span><span class="special">)[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">probs</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="number">2</span><span class="special">);</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/extended_p_square_impl.html" title="Struct template extended_p_square_impl">extended_p_square_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square_quantile" title="extended_p_square_quantile and variants">extended_p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Quantile estimation using the extended <code class="literal">P^2</code> algorithm |
| for weighted and unweighted samples. By default, the calculation is linear |
| and unweighted, but quadratic and weighted variants are also provided. |
| For further implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/extended_p_square_quant_id558339.html" title="Struct template extended_p_square_quantile_impl">extended_p_square_quantile_impl</a></code>. |
| </p> |
| <p> |
| All the variants share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">quantile</span></code> |
| feature and can be extracted using the <code class="computeroutput"><span class="identifier">quantile</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| weighted variants depend on <code class="computeroutput"><span class="identifier">weighted_extended_p_square</span></code> |
| <br> unweighted variants depend on <code class="computeroutput"><span class="identifier">extended_p_square</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">extended_p_square_quantile_quadratic</span></code> |
| <br> <code class="computeroutput"><span class="identifier">weighted_extended_p_square_quantile</span></code> |
| <br> <code class="computeroutput"><span class="identifier">weighted_extended_p_square_quantile_quadratic</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> for the weighted |
| variants |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N) where N is the count of probabilities. |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.extended_p_square_quantile_hpp" title="Header <boost/accumulators/statistics/extended_p_square_quantile.hpp>">boost/accumulators/statistics/extended_p_square_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square_quantile</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">accumulator_t</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square_quantile</span><span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">accumulator_t_weighted</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">extended_p_square_quantile</span><span class="special">(</span><span class="identifier">quadratic</span><span class="special">)></span> <span class="special">></span> |
| <span class="identifier">accumulator_t_quadratic</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square_quantile</span><span class="special">(</span><span class="identifier">quadratic</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">accumulator_t_weighted_quadratic</span><span class="special">;</span> |
| |
| <span class="comment">// tolerance |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="comment">// a random number generator |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">array</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">probs</span> <span class="special">=</span> <span class="special">{</span> <span class="number">0.990</span><span class="special">,</span> <span class="number">0.991</span><span class="special">,</span> <span class="number">0.992</span><span class="special">,</span> <span class="number">0.993</span><span class="special">,</span> <span class="number">0.994</span><span class="special">,</span> |
| <span class="number">0.995</span><span class="special">,</span> <span class="number">0.996</span><span class="special">,</span> <span class="number">0.997</span><span class="special">,</span> <span class="number">0.998</span><span class="special">,</span> <span class="number">0.999</span> <span class="special">};</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">extended_p_square_probabilities</span> <span class="special">=</span> <span class="identifier">probs</span><span class="special">);</span> |
| <span class="identifier">accumulator_t_weighted</span> <span class="identifier">acc_weighted</span><span class="special">(</span><span class="identifier">extended_p_square_probabilities</span> <span class="special">=</span> <span class="identifier">probs</span><span class="special">);</span> |
| <span class="identifier">accumulator_t_quadratic</span> <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">extended_p_square_probabilities</span> <span class="special">=</span> <span class="identifier">probs</span><span class="special">);</span> |
| <span class="identifier">accumulator_t_weighted_quadratic</span> <span class="identifier">acc_weighted2</span><span class="special">(</span><span class="identifier">extended_p_square_probabilities</span> <span class="special">=</span> <span class="identifier">probs</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">10000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc_weighted</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">acc_weighted2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">probs</span><span class="special">.</span><span class="identifier">size</span><span class="special">()</span> <span class="special">-</span> <span class="number">1</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> |
| <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span><span class="special">)</span> |
| <span class="special">,</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span> |
| <span class="special">,</span> <span class="identifier">epsilon</span> |
| <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> |
| <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span><span class="special">)</span> |
| <span class="special">,</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span> |
| <span class="special">,</span> <span class="identifier">epsilon</span> |
| <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> |
| <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc_weighted</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span><span class="special">)</span> |
| <span class="special">,</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span> |
| <span class="special">,</span> <span class="identifier">epsilon</span> |
| <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> |
| <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc_weighted2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span><span class="special">)</span> |
| <span class="special">,</span> <span class="number">0.99025</span> <span class="special">+</span> <span class="identifier">i</span><span class="special">*</span><span class="number">0.001</span> |
| <span class="special">,</span> <span class="identifier">epsilon</span> |
| <span class="special">);</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/extended_p_square_quant_id558339.html" title="Struct template extended_p_square_quantile_impl">extended_p_square_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square" title="extended_p_square"><code class="literal">extended_p_square</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_extended_p_square" title="weighted_extended_p_square"><code class="literal">weighted_extended_p_square</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.kurtosis"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.kurtosis" title="kurtosis">kurtosis</a> |
| </h4></div></div></div> |
| <p> |
| The kurtosis of a sample distribution is defined as the ratio of the 4th |
| central moment and the square of the 2nd central moment (the variance) |
| of the samples, minus 3. The term <code class="literal">-3</code> is added in order |
| to ensure that the normal distribution has zero kurtosis. For more implementation |
| details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/kurtosis_impl.html" title="Struct template kurtosis_impl">kurtosis_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>sample-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">mean</span></code> <br> <code class="computeroutput"><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">moment</span><span class="special"><</span><span class="number">3</span><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">moment</span><span class="special"><</span><span class="number">4</span><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.kurtosis_hpp" title="Header <boost/accumulators/statistics/kurtosis.hpp>">boost/accumulators/statistics/kurtosis.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">kurtosis</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">7</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">9</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">5</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">159.</span><span class="special">/</span><span class="number">5.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">3</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1171.</span><span class="special">/</span><span class="number">5.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">4</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1863</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">kurtosis</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">-</span><span class="number">1.39965397924</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/kurtosis_impl.html" title="Struct template kurtosis_impl">kurtosis_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean" title="mean and variants"><code class="literal">mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.moment" title="moment"><code class="literal">moment</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.max"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.max" title="max">max</a> |
| </h4></div></div></div> |
| <p> |
| Calculates the maximum value of all the samples. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><em class="replaceable"><code>sample-type</code></em> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.max_hpp" title="Header <boost/accumulators/statistics/max.hpp>">boost/accumulators/statistics/max.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">max</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="special">(</span><span class="identifier">max</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="special">(</span><span class="identifier">max</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="special">(</span><span class="identifier">max</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/max_impl.html" title="Struct template max_impl">max_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean" title="mean and variants">mean |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Calculates the mean of samples, weights or variates. The calculation is |
| either lazy (in the result extractor), or immediate (in the accumulator). |
| The lazy implementation is the default. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/mean_impl.html" title="Struct template mean_impl">mean_impl</a></code> |
| or. <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/immediate_mean_impl.html" title="Struct template immediate_mean_impl">immediate_mean_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd><p> |
| For samples, <code class="computeroutput"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span></code> <br> For weights, |
| <code class="computeroutput"><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><em class="replaceable"><code>weight-type</code></em><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="identifier">result_type</span></code> |
| <br> For variates, <code class="computeroutput"><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><em class="replaceable"><code>variate-type</code></em><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="identifier">result_type</span></code> |
| </p></dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> The |
| lazy mean of samples depends on <code class="computeroutput"><span class="identifier">sum</span></code> |
| <br> The lazy mean of weights depends on <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| <br> The lazy mean of variates depends on <code class="computeroutput"><span class="identifier">sum_of_variates</span><span class="special"><></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">mean_of_weights</span></code> |
| <br> <code class="computeroutput"><span class="identifier">mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> <br> <code class="computeroutput"><span class="identifier">immediate_mean</span></code> |
| <br> <code class="computeroutput"><span class="identifier">immediate_mean_of_weights</span></code> |
| <br> <code class="computeroutput"><span class="identifier">immediate_mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.mean_hpp" title="Header <boost/accumulators/statistics/mean.hpp>">boost/accumulators/statistics/mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span> |
| <span class="keyword">int</span> |
| <span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean_of_weights</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> |
| <span class="special">></span> |
| <span class="special">,</span> <span class="keyword">int</span> |
| <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">0.33333333333333333</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.5</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">8</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.33333333333333333</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">20</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span> |
| <span class="keyword">int</span> |
| <span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">immediate</span><span class="special">)</span> |
| <span class="special">></span> |
| <span class="special">,</span> <span class="keyword">int</span> |
| <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">0.33333333333333333</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.5</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">8</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.33333333333333333</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="identifier">mean_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">5.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">)),</span> <span class="number">1e-5</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/mean_impl.html" title="Struct template mean_impl">mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/immediate_mean_impl.html" title="Struct template immediate_mean_impl">immediate_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.median"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.median" title="median and variants">median |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Median estimation based on the <code class="literal">P^2</code> quantile estimator, |
| the density estimator, or the <code class="literal">P^2</code> cumulative distribution |
| estimator. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/median_impl.html" title="Struct template median_impl">median_impl</a></code>, |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/with_density_median_impl.html" title="Struct template with_density_median_impl">with_density_median_impl</a></code>, |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/with_p_square_cumulativ_id560240.html" title="Struct template with_p_square_cumulative_distribution_median_impl">with_p_square_cumulative_distribution_median_impl</a></code>. |
| </p> |
| <p> |
| The three median accumulators all satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">median</span></code> |
| feature, and can all be extracted with the <code class="computeroutput"><span class="identifier">median</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">median</span></code> depends on |
| <code class="computeroutput"><span class="identifier">p_square_quantile_for_median</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_density_median</span></code> |
| depends on <code class="computeroutput"><span class="identifier">count</span></code> |
| and <code class="computeroutput"><span class="identifier">density</span></code> <br> |
| <code class="computeroutput"><span class="identifier">with_p_square_cumulative_distribution_median</span></code> |
| depends on <code class="computeroutput"><span class="identifier">p_square_cumulative_distribution</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">with_density_median</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_p_square_cumulative_distribution_median</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">with_density_median</span></code> |
| requires <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">density</span><span class="special">::</span><span class="identifier">cache_size</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_p_square_cumulative_distribution_median</span></code> |
| requires <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.median_hpp" title="Header <boost/accumulators/statistics/median.hpp>">boost/accumulators/statistics/median.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// two random number generators |
| </span><span class="keyword">double</span> <span class="identifier">mu</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma</span><span class="special">(</span><span class="identifier">mu</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> |
| <span class="identifier">normal</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">median</span><span class="special">(</span><span class="identifier">with_p_square_quantile</span><span class="special">)</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">median</span><span class="special">(</span><span class="identifier">with_density</span><span class="special">)</span> <span class="special">></span> <span class="special">></span> |
| <span class="identifier">acc_dens</span><span class="special">(</span> <span class="identifier">density_cache_size</span> <span class="special">=</span> <span class="number">10000</span><span class="special">,</span> <span class="identifier">density_num_bins</span> <span class="special">=</span> <span class="number">1000</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">median</span><span class="special">(</span><span class="identifier">with_p_square_cumulative_distribution</span><span class="special">)</span> <span class="special">></span> <span class="special">></span> |
| <span class="identifier">acc_cdist</span><span class="special">(</span> <span class="identifier">p_square_cumulative_distribution_num_cells</span> <span class="special">=</span> <span class="number">100</span> <span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">normal</span><span class="special">();</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc_dens</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc_cdist</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">median</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">median</span><span class="special">(</span><span class="identifier">acc_dens</span><span class="special">),</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">median</span><span class="special">(</span><span class="identifier">acc_cdist</span><span class="special">),</span> <span class="number">3.</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/median_impl.html" title="Struct template median_impl">median_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/with_density_median_impl.html" title="Struct template with_density_median_impl">with_density_median_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/with_p_square_cumulativ_id560240.html" title="Struct template with_p_square_cumulative_distribution_median_impl">with_p_square_cumulative_distribution_median_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_quantile" title="p_square_quantile and variants"><code class="literal">p_square_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_cumulative_distribution" title="p_square_cumulative_distribution"><code class="literal">p_square_cumulative_distribution</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.min"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.min" title="min">min</a> |
| </h4></div></div></div> |
| <p> |
| Calculates the minimum value of all the samples. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><em class="replaceable"><code>sample-type</code></em> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.min_hpp" title="Header <boost/accumulators/statistics/min.hpp>">boost/accumulators/statistics/min.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">min</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="special">(</span><span class="identifier">min</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">0</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="special">(</span><span class="identifier">min</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="special">(</span><span class="identifier">min</span><span class="special">)(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/min_impl.html" title="Struct template min_impl">min_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.moment"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.moment" title="moment">moment</a> |
| </h4></div></div></div> |
| <p> |
| Calculates the N-th moment of the samples, which is defined as the sum |
| of the N-th power of the samples over the count of samples. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.moment_hpp" title="Header <boost/accumulators/statistics/moment.hpp>">boost/accumulators/statistics/moment.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc1</span><span class="special">;</span> |
| |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> <span class="comment">// 4 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> <span class="comment">// 16 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> <span class="comment">// + 25 |
| </span> <span class="comment">// = 45 / 3 = 15 |
| </span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">15.</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">5</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> <span class="comment">// 32 |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> <span class="comment">// 243 |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> <span class="comment">// 1024 |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> <span class="comment">// + 3125 |
| </span> <span class="comment">// = 4424 / 4 = 1106 |
| </span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1106.</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">5</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/moment_impl.html" title="Struct template moment_impl">moment_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.p_square_cumulative_distribution"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_cumulative_distribution" title="p_square_cumulative_distribution">p_square_cumulative_distribution</a> |
| </h4></div></div></div> |
| <p> |
| Histogram calculation of the cumulative distribution with the <code class="literal">P^2</code> |
| algorithm. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/p_square_cumulative_dis_id560721.html" title="Struct template p_square_cumulative_distribution_impl">p_square_cumulative_distribution_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">,</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">></span> |
| <span class="special">>::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N) where N is <code class="computeroutput"><span class="identifier">num_cells</span></code> |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.p_square_cumulative_distribution_hpp" title="Header <boost/accumulators/statistics/p_square_cumulative_distribution.hpp>">boost/accumulators/statistics/p_square_cumulative_distribution.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">3</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">p_square_cumulative_distribution</span><span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span> |
| |
| <span class="comment">// two random number generators |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">normal</span><span class="special">());</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">iterator_range</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="keyword">double</span><span class="special">></span> <span class="special">>::</span><span class="identifier">iterator</span> <span class="special">></span> <span class="identifier">histogram_type</span><span class="special">;</span> |
| <span class="identifier">histogram_type</span> <span class="identifier">histogram</span> <span class="special">=</span> <span class="identifier">p_square_cumulative_distribution</span><span class="special">(</span><span class="identifier">acc</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">histogram</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">// problem with small results: epsilon is relative (in percent), not absolute! |
| </span> <span class="keyword">if</span> <span class="special">(</span> <span class="identifier">histogram</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span> <span class="special">></span> <span class="number">0.001</span> <span class="special">)</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="number">1.0</span> <span class="special">+</span> <span class="identifier">erf</span><span class="special">(</span> <span class="identifier">histogram</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">first</span> <span class="special">/</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="number">2.0</span><span class="special">)</span> <span class="special">)),</span> <span class="identifier">histogram</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/p_square_cumulative_dis_id560721.html" title="Struct template p_square_cumulative_distribution_impl">p_square_cumulative_distribution_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.p_square_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.p_square_quantile" title="p_square_quantile and variants">p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Single quantile estimation with the <code class="literal">P^2</code> algorithm. For |
| more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/p_square_quantile_impl.html" title="Struct template p_square_quantile_impl">p_square_quantile_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">p_square_quantile_for_median</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code>, |
| which defaults to <code class="computeroutput"><span class="number">0.5</span></code>. |
| (Note: for <code class="computeroutput"><span class="identifier">p_square_quantile_for_median</span></code>, |
| the <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| parameter is ignored and is always <code class="computeroutput"><span class="number">0.5</span></code>.) |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.p_square_quantile_hpp" title="Header <boost/accumulators/statistics/p_square_quantile.hpp>">boost/accumulators/statistics/p_square_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">p_square_quantile</span><span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t</span><span class="special">;</span> |
| |
| <span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="comment">// a random number generator |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.01</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.25</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc4</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.5</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc5</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.75</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc6</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc7</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc8</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc5</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc6</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc7</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc8</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">),</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">15</span><span class="special">*</span><span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">0.01</span> <span class="special">,</span> <span class="number">5</span><span class="special">*</span><span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">0.1</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">),</span> <span class="number">0.25</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">),</span> <span class="number">0.5</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc5</span><span class="special">),</span> <span class="number">0.75</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc6</span><span class="special">),</span> <span class="number">0.9</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc7</span><span class="special">),</span> <span class="number">0.99</span> <span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">p_square_quantile</span><span class="special">(</span><span class="identifier">acc8</span><span class="special">),</span> <span class="number">0.999</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/p_square_quantile_impl.html" title="Struct template p_square_quantile_impl">p_square_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.peaks_over_threshold"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.peaks_over_threshold" title="peaks_over_threshold and variants">peaks_over_threshold |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Peaks Over Threshold method for quantile and tail mean estimation. For |
| implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/peaks_over_threshold_impl.html" title="Struct template peaks_over_threshold_impl">peaks_over_threshold_impl</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/peaks_over_threshold_pr_id562190.html" title="Struct template peaks_over_threshold_prob_impl">peaks_over_threshold_prob_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special"><></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_peaks_over_threshold</span></code> feature, |
| and can be extracted with the <code class="computeroutput"><span class="identifier">peaks_over_threshold</span><span class="special">()</span></code> extractor. The result is a 3-tuple representing |
| the fit parameters <code class="computeroutput"><span class="identifier">u_bar</span></code>, |
| <code class="computeroutput"><span class="identifier">beta_bar</span></code> and <code class="computeroutput"><span class="identifier">xi_hat</span></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">tuple</span><span class="special"><</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> <span class="comment">// u_bar |
| </span> <span class="special">,</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> <span class="comment">// beta_bar |
| </span> <span class="special">,</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> <span class="comment">// xi_hat |
| </span><span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> In addtion, |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special"><></span></code> |
| depends on <code class="computeroutput"><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">peaks_over_threshold_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.peaks_over_threshold_hpp" title="Header <boost/accumulators/statistics/peaks_over_threshold.hpp>">boost/accumulators/statistics/peaks_over_threshold.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <p> |
| See example for <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile" title="pot_quantile and variants"><code class="literal">pot_quantile</code></a>. |
| </p> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/peaks_over_threshold_impl.html" title="Struct template peaks_over_threshold_impl">peaks_over_threshold_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/peaks_over_threshold_pr_id562190.html" title="Struct template peaks_over_threshold_prob_impl">peaks_over_threshold_prob_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile" title="pot_quantile and variants"><code class="literal">pot_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_tail_mean" title="pot_tail_mean"><code class="literal">pot_tail_mean</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile" title="pot_quantile and variants">pot_quantile |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Quantile estimation based on Peaks over Threshold method (for both left |
| and right tails). For implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/pot_quantile_impl.html" title="Struct template pot_quantile_impl">pot_quantile_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">quantile</span></code> feature and can be extracted |
| using the <code class="computeroutput"><span class="identifier">quantile</span><span class="special">()</span></code> |
| extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">pot_quantile</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> depends on <code class="computeroutput"><span class="identifier">peaks_over_threshold</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">pot_quantile_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| depends on <code class="computeroutput"><span class="identifier">peaks_over_threshold_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">pot_quantile_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.pot_quantile_hpp" title="Header <boost/accumulators/statistics/pot_quantile.hpp>">boost/accumulators/statistics/pot_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> |
| |
| <span class="keyword">double</span> <span class="identifier">alpha</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">threshold_probability</span> <span class="special">=</span> <span class="number">0.99</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">threshold</span> <span class="special">=</span> <span class="number">3.</span><span class="special">;</span> |
| |
| <span class="comment">// two random number generators |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">exponential_distribution</span><span class="special"><></span> <span class="identifier">lambda</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">exponential_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">exponential</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">lambda</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">>(</span><span class="identifier">with_threshold_value</span><span class="special">)></span> <span class="special">></span> <span class="identifier">acc1</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span> <span class="special">=</span> <span class="identifier">threshold</span> |
| <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">>(</span><span class="identifier">with_threshold_probability</span><span class="special">)></span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">2000</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span> <span class="special">=</span> <span class="identifier">threshold_probability</span> |
| <span class="special">);</span> |
| |
| <span class="identifier">threshold_probability</span> <span class="special">=</span> <span class="number">0.995</span><span class="special">;</span> |
| <span class="identifier">threshold</span> <span class="special">=</span> <span class="number">5.</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">>(</span><span class="identifier">with_threshold_value</span><span class="special">)></span> <span class="special">></span> <span class="identifier">acc3</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span> <span class="special">=</span> <span class="identifier">threshold</span> |
| <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">>(</span><span class="identifier">with_threshold_probability</span><span class="special">)></span> <span class="special">></span> <span class="identifier">acc4</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">2000</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span> <span class="special">=</span> <span class="identifier">threshold_probability</span> |
| <span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">normal</span><span class="special">();</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">exponential</span><span class="special">();</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="identifier">alpha</span><span class="special">),</span> <span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="identifier">alpha</span><span class="special">),</span> <span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="identifier">alpha</span><span class="special">),</span> <span class="number">6.908</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="identifier">alpha</span><span class="special">),</span> <span class="number">6.908</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/pot_quantile_impl.html" title="Struct template pot_quantile_impl">pot_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.peaks_over_threshold" title="peaks_over_threshold and variants"><code class="literal">peaks_over_threshold</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.pot_tail_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_tail_mean" title="pot_tail_mean">pot_tail_mean</a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the (coherent) tail mean based on the peaks over threshold |
| method (for both left and right tails). For inplementation details, see |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/pot_tail_mean_impl.html" title="Struct template pot_tail_mean_impl">pot_tail_mean_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_tail_mean</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">pot_tail_mean_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_mean</span></code> feature and can be extracted |
| using the <code class="computeroutput"><span class="identifier">tail_mean</span><span class="special">()</span></code> |
| extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">pot_tail_mean</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> depends on <code class="computeroutput"><span class="identifier">peaks_over_threshold</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| and <code class="computeroutput"><span class="identifier">pot_quantile</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">pot_tail_mean_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| depends on <code class="computeroutput"><span class="identifier">peaks_over_threshold_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| and <code class="computeroutput"><span class="identifier">pot_quantile_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">pot_tail_mean_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.pot_tail_mean_hpp" title="Header <boost/accumulators/statistics/pot_tail_mean.hpp>">boost/accumulators/statistics/pot_tail_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// TODO |
| </span></pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/pot_tail_mean_impl.html" title="Struct template pot_tail_mean_impl">pot_tail_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.peaks_over_threshold" title="peaks_over_threshold and variants"><code class="literal">peaks_over_threshold</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile" title="pot_quantile and variants"><code class="literal">pot_quantile</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.rolling_count"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_count" title="rolling_count">rolling_count</a> |
| </h4></div></div></div> |
| <p> |
| The rolling count is the current number of elements in the rolling window. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span></pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">rolling_window_plus1</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.rolling_count_hpp" title="Header <boost/accumulators/statistics/rolling_count.hpp>">boost/accumulators/statistics/rolling_count.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_count</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">0u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3u</span><span class="special">,</span> <span class="identifier">rolling_count</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/rolling_count_impl.html" title="Struct template rolling_count_impl">rolling_count_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.rolling_sum"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_sum" title="rolling_sum">rolling_sum</a> |
| </h4></div></div></div> |
| <p> |
| The rolling sum is the sum of the last <span class="emphasis"><em>N</em></span> samples. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><em class="replaceable"><code>sample-type</code></em></pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">rolling_window_plus1</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.rolling_sum_hpp" title="Header <boost/accumulators/statistics/rolling_sum.hpp>">boost/accumulators/statistics/rolling_sum.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_sum</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">rolling_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/rolling_sum_impl.html" title="Struct template rolling_sum_impl">rolling_sum_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.rolling_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.rolling_mean" title="rolling_mean">rolling_mean</a> |
| </h4></div></div></div> |
| <p> |
| The rolling mean is the mean over the last <span class="emphasis"><em>N</em></span> samples. |
| It is computed by dividing the rolling sum by the rolling count. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">rolling_sum</span></code> <br> |
| <code class="computeroutput"><span class="identifier">rolling_count</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.rolling_mean_hpp" title="Header <boost/accumulators/statistics/rolling_mean.hpp>">boost/accumulators/statistics/rolling_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_mean</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">rolling_window</span><span class="special">::</span><span class="identifier">window_size</span> <span class="special">=</span> <span class="number">5</span><span class="special">);</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">rolling_mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">2.0</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">6</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">7</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">rolling_mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">5.0</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/rolling_mean_impl.html" title="Struct template rolling_mean_impl">rolling_mean_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.skewness"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.skewness" title="skewness">skewness</a> |
| </h4></div></div></div> |
| <p> |
| The skewness of a sample distribution is defined as the ratio of the 3rd |
| central moment and the <code class="literal">3/2</code>-th power of the 2nd central |
| moment (the variance) of the sampless 3. For implementation details, see |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/skewness_impl.html" title="Struct template skewness_impl">skewness_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>sample-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">mean</span></code> <br> <code class="computeroutput"><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">moment</span><span class="special"><</span><span class="number">3</span><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.skewness_hpp" title="Header <boost/accumulators/statistics/skewness.hpp>">boost/accumulators/statistics/skewness.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">skewness</span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">7</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">9</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">5</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">159.</span><span class="special">/</span><span class="number">5.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">3</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1171.</span><span class="special">/</span><span class="number">5.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">skewness</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">0.406040288214</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/skewness_impl.html" title="Struct template skewness_impl">skewness_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean" title="mean and variants"><code class="literal">mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.moment" title="moment"><code class="literal">moment</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.sum"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants">sum |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| For summing the samples, weights or variates. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd><p> |
| <code class="computeroutput"><em class="replaceable"><code>sample-type</code></em></code> for summing samples <br> <code class="computeroutput"><em class="replaceable"><code>weight-type</code></em></code> for summing |
| weights <br> <code class="computeroutput"><em class="replaceable"><code>variate-type</code></em></code> for summing variates |
| </p></dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum_of_weights</span></code> |
| <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> for summing |
| weights <br> <code class="computeroutput"><em class="replaceable"><code>variate-tag</code></em></code> for summing variates |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.sum_hpp" title="Header <boost/accumulators/statistics/sum.hpp>">boost/accumulators/statistics/sum.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span> |
| <span class="keyword">int</span> |
| <span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum_of_weights</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">sum_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> |
| <span class="special">></span> |
| <span class="special">,</span> <span class="keyword">int</span> |
| <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// weighted sample = 1 * 2 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">6</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// weighted sample = 2 * 4 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">6</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">9</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">28</span><span class="special">,</span> <span class="identifier">sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// weighted sample = 3 * 6 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">18</span><span class="special">,</span> <span class="identifier">sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/sum_impl.html" title="Struct template sum_impl">sum_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.tail"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail">tail</a> |
| </h4></div></div></div> |
| <p> |
| Tracks the largest or smallest <code class="literal">N</code> values. <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code> |
| tracks the largest <code class="literal">N</code>, and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code> tracks the smallest. The parameter |
| <code class="literal">N</code> is specified with the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> initialization parameter. |
| For implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_impl.html" title="Struct template tail_impl">tail_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code> |
| and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_tail</span></code> feature and can be extracted |
| with the <code class="computeroutput"><span class="identifier">tail</span><span class="special">()</span></code> |
| extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">reverse_iterator</span><span class="special"><</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">permutation_iterator</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">>::</span><span class="identifier">const_iterator</span> <span class="comment">// samples |
| </span> <span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</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="identifier">iterator</span> <span class="comment">// indices |
| </span> <span class="special">></span> |
| <span class="special">></span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_tail</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_hpp" title="Header <boost/accumulators/statistics/tail.hpp>">boost/accumulators/statistics/tail.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <p> |
| See the Example for <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate" title="tail_variate"><code class="literal">tail_variate</code></a>. |
| </p> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_impl.html" title="Struct template tail_impl">tail_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate" title="tail_variate"><code class="literal">tail_variate</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.coherent_tail_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.coherent_tail_mean" title="coherent_tail_mean">coherent_tail_mean</a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the coherent tail mean based on order statistics (for both |
| left and right tails). The left coherent tail mean feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">coherent_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code>, |
| and the right choherent tail mean feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">coherent_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code>. They both share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_mean</span></code> feature and can be extracted |
| with the <code class="computeroutput"><span class="identifier">tail_mean</span><span class="special">()</span></code> |
| extractor. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/coherent_tail_mean_impl.html" title="Struct template coherent_tail_mean_impl">coherent_tail_mean_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">quantile</span></code> <br> <code class="computeroutput"><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_mean_hpp" title="Header <boost/accumulators/statistics/tail_mean.hpp>">boost/accumulators/statistics/tail_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <p> |
| See the example for <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean" title="non_coherent_tail_mean"><code class="literal">non_coherent_tail_mean</code></a>. |
| </p> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/coherent_tail_mean_impl.html" title="Struct template coherent_tail_mean_impl">coherent_tail_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.extended_p_square_quantile" title="extended_p_square_quantile and variants"><code class="literal">extended_p_square_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.pot_quantile" title="pot_quantile and variants"><code class="literal">pot_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_quantile" title="tail_quantile"><code class="literal">tail_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean" title="non_coherent_tail_mean"><code class="literal">non_coherent_tail_mean</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean" title="non_coherent_tail_mean">non_coherent_tail_mean</a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the (non-coherent) tail mean based on order statistics (for |
| both left and right tails). The left non-coherent tail mean feature is |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code>, |
| and the right non-choherent tail mean feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code>. They both share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_non_coherent_tail_mean</span></code> feature |
| and can be extracted with the <code class="computeroutput"><span class="identifier">non_coherent_tail_mean</span><span class="special">()</span></code> extractor. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/non_coherent_tail_mean__id564920.html" title="Struct template non_coherent_tail_mean_impl">non_coherent_tail_mean_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_non_coherent_tail_mean</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_mean_hpp" title="Header <boost/accumulators/statistics/tail_mean.hpp>">boost/accumulators/statistics/tail_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">100000</span><span class="special">;</span> <span class="comment">// number of MC steps |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">10000</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_right1</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_left1</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">coherent_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_right2</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">coherent_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_left2</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t_right1</span> <span class="identifier">acc0</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_left1</span> <span class="identifier">acc1</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_right2</span> <span class="identifier">acc2</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_left2</span> <span class="identifier">acc3</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| |
| <span class="comment">// a random number generator |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">sample</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check uniform distribution |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">),</span> <span class="number">0.975</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">0.9875</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99</span><span class="special">),</span> <span class="number">0.995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">0.9995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">),</span> <span class="number">0.025</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="number">0.0125</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.01</span><span class="special">),</span> <span class="number">0.005</span><span class="special">,</span> <span class="number">5</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="number">0.0005</span><span class="special">,</span> <span class="number">10</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">),</span> <span class="number">0.975</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">0.9875</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99</span><span class="special">),</span> <span class="number">0.995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">0.9995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">),</span> <span class="number">0.025</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="number">0.0125</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.01</span><span class="special">),</span> <span class="number">0.005</span><span class="special">,</span> <span class="number">5</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">tail_mean</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="number">0.0005</span><span class="special">,</span> <span class="number">10</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/non_coherent_tail_mean__id564920.html" title="Struct template non_coherent_tail_mean_impl">non_coherent_tail_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.tail_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_quantile" title="tail_quantile">tail_quantile</a> |
| </h4></div></div></div> |
| <p> |
| Tail quantile estimation based on order statistics (for both left and right |
| tails). The left tail quantile feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code>, and the right tail quantile feature |
| is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code>. |
| They both share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">quantile</span></code> |
| feature and can be extracted with the <code class="computeroutput"><span class="identifier">quantile</span><span class="special">()</span></code> extractor. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_quantile_impl.html" title="Struct template tail_quantile_impl">tail_quantile_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><em class="replaceable"><code>sample-type</code></em> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_quantile_hpp" title="Header <boost/accumulators/statistics/tail_quantile.hpp>">boost/accumulators/statistics/tail_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">100000</span><span class="special">;</span> <span class="comment">// number of MC steps |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">10000</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_right</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">accumulator_t_left</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t_right</span> <span class="identifier">acc0</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_right</span> <span class="identifier">acc1</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_left</span> <span class="identifier">acc2</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t_left</span> <span class="identifier">acc3</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| |
| <span class="comment">// two random number generators |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample1</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample2</span> <span class="special">=</span> <span class="identifier">normal</span><span class="special">();</span> |
| <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">sample1</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample1</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">sample2</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check uniform distribution |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.95</span> <span class="special">),</span> <span class="number">0.95</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">0.975</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99</span> <span class="special">),</span> <span class="number">0.99</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">0.999</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.05</span> <span class="special">),</span> <span class="number">0.05</span><span class="special">,</span> <span class="number">2</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="number">0.025</span><span class="special">,</span> <span class="number">2</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.01</span> <span class="special">),</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">3</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">20</span> <span class="special">);</span> |
| |
| <span class="comment">// check standard normal distribution |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="special">-</span><span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="special">-</span><span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_quantile_impl.html" title="Struct template tail_quantile_impl">tail_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate" title="tail_variate">tail_variate</a> |
| </h4></div></div></div> |
| <p> |
| Tracks the covariates of largest or smallest <code class="literal">N</code> samples. |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> <span class="identifier">right</span><span class="special">></span></code> tracks the covariate associated with |
| <em class="replaceable"><code>variate-tag</code></em> for the largest <code class="literal">N</code>, and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> |
| <span class="identifier">left</span><span class="special">></span></code> |
| for the smallest. The parameter <code class="literal">N</code> is specified with |
| the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| initialization parameter. For implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_variate_impl.html" title="Struct template tail_variate_impl">tail_variate_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> <span class="identifier">right</span><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> |
| <span class="identifier">left</span><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_tail_variate</span></code> feature and can |
| be extracted with the <code class="computeroutput"><span class="identifier">tail_variate</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">reverse_iterator</span><span class="special"><</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">permutation_iterator</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">>::</span><span class="identifier">const_iterator</span> <span class="comment">// variates |
| </span> <span class="special">,</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</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="identifier">iterator</span> <span class="comment">// indices |
| </span> <span class="special">></span> |
| <span class="special">></span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_tail_variate</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_variate_hpp" title="Header <boost/accumulators/statistics/tail_variate.hpp>">boost/accumulators/statistics/tail_variate.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">,</span> <span class="identifier">right</span><span class="special">></span> <span class="special">></span> <span class="special">></span> <span class="identifier">acc</span><span class="special">(</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">>::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">4</span> |
| <span class="special">);</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">8</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">3</span><span class="special">});</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">16</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">16</span><span class="special">,</span> <span class="number">8</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">1</span><span class="special">,</span> <span class="number">3</span><span class="special">});</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">12</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">16</span><span class="special">,</span> <span class="number">12</span><span class="special">,</span> <span class="number">8</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">1</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">3</span><span class="special">});</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">24</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">5</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">24</span><span class="special">,</span> <span class="number">16</span><span class="special">,</span> <span class="number">12</span><span class="special">,</span> <span class="number">8</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">3</span><span class="special">});</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">9</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">24</span><span class="special">,</span> <span class="number">16</span><span class="special">,</span> <span class="number">12</span><span class="special">,</span> <span class="number">8</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">3</span><span class="special">});</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">7</span><span class="special">);</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">24</span><span class="special">,</span> <span class="number">16</span><span class="special">,</span> <span class="number">12</span><span class="special">,</span> <span class="number">9</span><span class="special">});</span> |
| <span class="identifier">CHECK_RANGE_EQUAL</span><span class="special">(</span><span class="identifier">tail_variate</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">{</span><span class="number">5</span><span class="special">,</span> <span class="number">1</span><span class="special">,</span> <span class="number">4</span><span class="special">,</span> <span class="number">7</span><span class="special">});</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_variate_impl.html" title="Struct template tail_variate_impl">tail_variate_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate_means"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate_means" title="tail_variate_means and variants">tail_variate_means |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the absolute and relative tail variate means (for both left |
| and right tails). The absolute tail variate means has the feature <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">absolute_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| and the relative tail variate mean has the feature <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">relative_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> |
| <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code>. All absolute tail variate |
| mean features share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_absolute_tail_variate_means</span></code> |
| feature and can be extracted with the <code class="computeroutput"><span class="identifier">tail_variate_means</span><span class="special">()</span></code> extractor. All the relative tail variate |
| mean features share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_relative_tail_variate_means</span></code> |
| feature and can be extracted with the <code class="computeroutput"><span class="identifier">relative_tail_variate_means</span><span class="special">()</span></code> extractor. |
| </p> |
| <p> |
| For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_variate_means_impl.html" title="Struct template tail_variate_means_impl">tail_variate_means_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">non_coherent_tail_mean</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> <em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">absolute_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">relative_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.tail_variate_means_hpp" title="Header <boost/accumulators/statistics/tail_variate_means.hpp>">boost/accumulators/statistics/tail_variate_means.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">variate_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">variate_type</span><span class="special">></span> <span class="identifier">variate_set_type</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate_means</span><span class="special"><</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">relative</span><span class="special">)>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">accumulator_t1</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate_means</span><span class="special"><</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">absolute</span><span class="special">)>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">accumulator_t2</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate_means</span><span class="special"><</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">relative</span><span class="special">)>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">accumulator_t3</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail_variate_means</span><span class="special"><</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">absolute</span><span class="special">)>,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">></span> |
| <span class="identifier">accumulator_t4</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t1</span> <span class="identifier">acc1</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t2</span> <span class="identifier">acc2</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t3</span> <span class="identifier">acc3</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_t4</span> <span class="identifier">acc4</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| |
| <span class="identifier">variate_set_type</span> <span class="identifier">cov1</span><span class="special">,</span> <span class="identifier">cov2</span><span class="special">,</span> <span class="identifier">cov3</span><span class="special">,</span> <span class="identifier">cov4</span><span class="special">,</span> <span class="identifier">cov5</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">c1</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">10.</span><span class="special">,</span> <span class="number">20.</span><span class="special">,</span> <span class="number">30.</span><span class="special">,</span> <span class="number">40.</span> <span class="special">};</span> <span class="comment">// 100 |
| </span><span class="keyword">double</span> <span class="identifier">c2</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">26.</span><span class="special">,</span> <span class="number">4.</span><span class="special">,</span> <span class="number">17.</span><span class="special">,</span> <span class="number">3.</span> <span class="special">};</span> <span class="comment">// 50 |
| </span><span class="keyword">double</span> <span class="identifier">c3</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">46.</span><span class="special">,</span> <span class="number">64.</span><span class="special">,</span> <span class="number">40.</span><span class="special">,</span> <span class="number">50.</span> <span class="special">};</span> <span class="comment">// 200 |
| </span><span class="keyword">double</span> <span class="identifier">c4</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">1.</span><span class="special">,</span> <span class="number">3.</span><span class="special">,</span> <span class="number">70.</span><span class="special">,</span> <span class="number">6.</span> <span class="special">};</span> <span class="comment">// 80 |
| </span><span class="keyword">double</span> <span class="identifier">c5</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">2.</span><span class="special">,</span> <span class="number">2.</span><span class="special">,</span> <span class="number">2.</span><span class="special">,</span> <span class="number">14.</span> <span class="special">};</span> <span class="comment">// 20 |
| </span><span class="identifier">cov1</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c1</span><span class="special">,</span> <span class="identifier">c1</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c1</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov2</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c2</span><span class="special">,</span> <span class="identifier">c2</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c2</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov3</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c3</span><span class="special">,</span> <span class="identifier">c3</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c3</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov4</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c4</span><span class="special">,</span> <span class="identifier">c4</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c4</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov5</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c5</span><span class="special">,</span> <span class="identifier">c5</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c5</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc3</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc4</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="comment">// check relative risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">14.</span><span class="special">/</span><span class="number">75.</span> <span class="special">);</span> <span class="comment">// (10 + 46) / 300 = 14/75 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">7.</span><span class="special">/</span><span class="number">25.</span> <span class="special">);</span> <span class="comment">// (20 + 64) / 300 = 7/25 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">7.</span><span class="special">/</span><span class="number">30.</span> <span class="special">);</span> <span class="comment">// (30 + 40) / 300 = 7/30 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">3.</span><span class="special">/</span><span class="number">10.</span> <span class="special">);</span> <span class="comment">// (40 + 50) / 300 = 3/10 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">14.</span><span class="special">/</span><span class="number">35.</span> <span class="special">);</span> <span class="comment">// (26 + 2) / 70 = 14/35 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">3.</span><span class="special">/</span><span class="number">35.</span> <span class="special">);</span> <span class="comment">// ( 4 + 2) / 70 = 3/35 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">19.</span><span class="special">/</span><span class="number">70.</span> <span class="special">);</span> <span class="comment">// (17 + 2) / 70 = 19/70 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">17.</span><span class="special">/</span><span class="number">70.</span> <span class="special">);</span> <span class="comment">// ( 3 + 14) / 70 = 17/70 |
| </span> |
| <span class="comment">// check absolute risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">28</span> <span class="special">);</span> <span class="comment">// (10 + 46) / 2 = 28 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">42</span> <span class="special">);</span> <span class="comment">// (20 + 64) / 2 = 42 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">35</span> <span class="special">);</span> <span class="comment">// (30 + 40) / 2 = 35 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">45</span> <span class="special">);</span> <span class="comment">// (40 + 50) / 2 = 45 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">14</span> <span class="special">);</span> <span class="comment">// (26 + 2) / 2 = 14 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">3</span> <span class="special">);</span> <span class="comment">// ( 4 + 2) / 2 = 3 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span><span class="number">9.5</span> <span class="special">);</span> <span class="comment">// (17 + 2) / 2 = 9.5 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span><span class="number">8.5</span> <span class="special">);</span> <span class="comment">// ( 3 + 14) / 2 = 8.5 |
| </span> |
| <span class="comment">// check relative risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">23.</span><span class="special">/</span><span class="number">100.</span> <span class="special">);</span> <span class="comment">// 46/200 = 23/100 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">8.</span><span class="special">/</span><span class="number">25.</span> <span class="special">);</span> <span class="comment">// 64/200 = 8/25 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.</span><span class="special">/</span><span class="number">5.</span> <span class="special">);</span> <span class="comment">// 40/200 = 1/5 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">1.</span><span class="special">/</span><span class="number">4.</span> <span class="special">);</span> <span class="comment">// 50/200 = 1/4 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">1.</span><span class="special">/</span><span class="number">10.</span> <span class="special">);</span> <span class="comment">// 2/ 20 = 1/10 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">1.</span><span class="special">/</span><span class="number">10.</span> <span class="special">);</span> <span class="comment">// 2/ 20 = 1/10 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.</span><span class="special">/</span><span class="number">10.</span> <span class="special">);</span> <span class="comment">// 2/ 20 = 1/10 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">7.</span><span class="special">/</span><span class="number">10.</span> <span class="special">);</span> <span class="comment">// 14/ 20 = 7/10 |
| </span> |
| <span class="comment">// check absolute risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">46</span> <span class="special">);</span> <span class="comment">// 46 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">64</span> <span class="special">);</span> <span class="comment">// 64 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">40</span> <span class="special">);</span> <span class="comment">// 40 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">50</span> <span class="special">);</span> <span class="comment">// 50 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">2</span> <span class="special">);</span> <span class="comment">// 2 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">2</span> <span class="special">);</span> <span class="comment">// 2 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">2</span> <span class="special">);</span> <span class="comment">// 2 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">14</span> <span class="special">);</span> <span class="comment">// 14 |
| </span></pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/tail_variate_means_impl.html" title="Struct template tail_variate_means_impl">tail_variate_means_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_tail_mean" title="non_coherent_tail_mean"><code class="literal">non_coherent_tail_mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate" title="tail_variate"><code class="literal">tail_variate</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.variance"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.variance" title="variance and variants">variance |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Lazy or iterative calculation of the variance. The lazy calculation is |
| associated with the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_variance</span></code> |
| feature, and the iterative calculation with the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span></code> |
| feature. Both can be extracted using the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span><span class="special">()</span></code> extractor. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/lazy_variance_impl.html" title="Struct template lazy_variance_impl">lazy_variance_impl</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/variance_impl.html" title="Struct template variance_impl">variance_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_variance</span></code> depends on <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">mean</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span></code> |
| depends on <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">count</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">immediate_mean</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_variance</span></code> (a.k.a. <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span><span class="special">(</span><span class="identifier">lazy</span><span class="special">))</span></code> |
| <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span></code> (a.k.a. <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span></code>) |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.variance_hpp" title="Header <boost/accumulators/statistics/variance.hpp>">boost/accumulators/statistics/variance.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// lazy variance |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span><span class="special">(</span><span class="identifier">lazy</span><span class="special">)></span> <span class="special">></span> <span class="identifier">acc1</span><span class="special">;</span> |
| |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">11.</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">variance</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="comment">// immediate variance |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">variance</span><span class="special">></span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">5</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">3.</span><span class="special">,</span> <span class="identifier">mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">variance</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/lazy_variance_impl.html" title="Struct template lazy_variance_impl">lazy_variance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/variance_impl.html" title="Struct template variance_impl">variance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.mean" title="mean and variants"><code class="literal">mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.moment" title="moment"><code class="literal">moment</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_covariance"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_covariance" title="weighted_covariance">weighted_covariance</a> |
| </h4></div></div></div> |
| <p> |
| An iterative Monte Carlo estimator for the weighted covariance. The feature |
| is specified as <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_covariance</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> and |
| is extracted with the <code class="computeroutput"><span class="identifier">weighted_variate</span><span class="special">()</span></code> extractor. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_covariance_impl.html" title="Struct template weighted_covariance_impl">weighted_covariance_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">outer_product</span><span class="special"><</span> |
| <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span> |
| <em class="replaceable"><code>weight-type</code></em> |
| <span class="special">,</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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">,</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span> |
| <em class="replaceable"><code>weight-type</code></em> |
| <span class="special">,</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><em class="replaceable"><code>variate-type</code></em><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="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> <br> <code class="computeroutput"><span class="identifier">weighted_mean</span></code> <br> <code class="computeroutput"><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_weighted_covariance</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> <br> <code class="computeroutput"><em class="replaceable"><code>variate-tag</code></em></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_covariance_hpp" title="Header <boost/accumulators/statistics/weighted_covariance.hpp>">boost/accumulators/statistics/weighted_covariance.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_covariance</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">2.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">4.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3.3</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3.</span><span class="special">);</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">6.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4.4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| |
| <span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1e-6</span><span class="special">;</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">weighted_covariance</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="special">-</span><span class="number">2.39</span><span class="special">,</span> <span class="identifier">epsilon</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_covariance_impl.html" title="Struct template weighted_covariance_impl">weighted_covariance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean" title="weighted_mean and variants"><code class="literal">weighted_mean</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_density"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_density" title="weighted_density">weighted_density</a> |
| </h4></div></div></div> |
| <p> |
| The <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span></code> feature returns a histogram |
| of the weighted sample distribution. For more implementation details, see |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_density_impl.html" title="Struct template weighted_density_impl">weighted_density_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</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><em class="replaceable"><code>weight-type</code></em><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="identifier">result_type</span> |
| <span class="special">,</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><em class="replaceable"><code>weight-type</code></em><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="identifier">result_type</span> |
| <span class="special">></span> |
| <span class="special">>::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> <br> <code class="computeroutput"><span class="identifier">min</span></code> <br> <code class="computeroutput"><span class="identifier">max</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">cache_size</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N), when N is <code class="computeroutput"><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_density_hpp" title="Header <boost/accumulators/statistics/weighted_density.hpp>">boost/accumulators/statistics/weighted_density.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_density_impl.html" title="Struct template weighted_density_impl">weighted_density_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.min" title="min"><code class="literal">min</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.max" title="max"><code class="literal">max</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_extended_p_square"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_extended_p_square" title="weighted_extended_p_square">weighted_extended_p_square</a> |
| </h4></div></div></div> |
| <p> |
| Multiple quantile estimation with the extended <code class="literal">P^2</code> algorithm |
| for weighted samples. For further details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_extended_p_squ_id567805.html" title="Struct template weighted_extended_p_square_impl">weighted_extended_p_square_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</span> |
| <em class="replaceable"><code>implementation-defined</code></em> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_extended_p_square_hpp" title="Header <boost/accumulators/statistics/weighted_extended_p_square.hpp>">boost/accumulators/statistics/weighted_extended_p_square.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square</span><span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">accumulator_t</span><span class="special">;</span> |
| |
| <span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="comment">// some random number generators |
| </span><span class="keyword">double</span> <span class="identifier">mu1</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu2</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma1</span><span class="special">(</span><span class="identifier">mu1</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma2</span><span class="special">(</span><span class="identifier">mu2</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal1</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal2</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma2</span><span class="special">);</span> |
| |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="keyword">double</span><span class="special">></span> <span class="identifier">probs_uniform</span><span class="special">,</span> <span class="identifier">probs_normal1</span><span class="special">,</span> <span class="identifier">probs_normal2</span><span class="special">,</span> <span class="identifier">probs_normal_exact1</span><span class="special">,</span> <span class="identifier">probs_normal_exact2</span><span class="special">;</span> |
| |
| <span class="keyword">double</span> <span class="identifier">p1</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{/*</span><span class="number">0.001</span><span class="special">,*/</span> <span class="number">0.01</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.5</span><span class="special">,</span> <span class="number">0.9</span><span class="special">,</span> <span class="number">0.99</span><span class="special">,</span> <span class="number">0.999</span><span class="special">};</span> |
| <span class="identifier">probs_uniform</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">p1</span><span class="special">,</span> <span class="identifier">p1</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">p1</span><span class="special">)</span> <span class="special">/</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">));</span> |
| |
| <span class="keyword">double</span> <span class="identifier">p2</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.001</span><span class="special">,</span> <span class="number">0.025</span><span class="special">};</span> |
| <span class="keyword">double</span> <span class="identifier">p3</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">0.975</span><span class="special">,</span> <span class="number">0.999</span><span class="special">};</span> |
| <span class="identifier">probs_normal1</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">p2</span><span class="special">,</span> <span class="identifier">p2</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">p2</span><span class="special">)</span> <span class="special">/</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">));</span> |
| <span class="identifier">probs_normal2</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">p3</span><span class="special">,</span> <span class="identifier">p3</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">p3</span><span class="special">)</span> <span class="special">/</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">));</span> |
| |
| <span class="keyword">double</span> <span class="identifier">p4</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{-</span><span class="number">3.090232</span><span class="special">,</span> <span class="special">-</span><span class="number">1.959963</span><span class="special">};</span> |
| <span class="keyword">double</span> <span class="identifier">p5</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span><span class="number">1.959963</span><span class="special">,</span> <span class="number">3.090232</span><span class="special">};</span> |
| <span class="identifier">probs_normal_exact1</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">p4</span><span class="special">,</span> <span class="identifier">p4</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">p4</span><span class="special">)</span> <span class="special">/</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">));</span> |
| <span class="identifier">probs_normal_exact2</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">p5</span><span class="special">,</span> <span class="identifier">p5</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">p5</span><span class="special">)</span> <span class="special">/</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="keyword">double</span><span class="special">));</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc_uniform</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span> <span class="special">=</span> <span class="identifier">probs_uniform</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc_normal1</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span> <span class="special">=</span> <span class="identifier">probs_normal1</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc_normal2</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_extended_p_square</span><span class="special">::</span><span class="identifier">probabilities</span> <span class="special">=</span> <span class="identifier">probs_normal2</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">acc_uniform</span><span class="special">(</span><span class="identifier">rng</span><span class="special">(),</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| |
| <span class="keyword">double</span> <span class="identifier">sample1</span> <span class="special">=</span> <span class="identifier">normal1</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample2</span> <span class="special">=</span> <span class="identifier">normal2</span><span class="special">();</span> |
| <span class="identifier">acc_normal1</span><span class="special">(</span><span class="identifier">sample1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu1</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample1</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu1</span><span class="special">)));</span> |
| <span class="identifier">acc_normal2</span><span class="special">(</span><span class="identifier">sample2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample2</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu2</span><span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check for uniform distribution |
| </span><span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">probs_uniform</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">weighted_extended_p_square</span><span class="special">(</span><span class="identifier">acc_uniform</span><span class="special">)[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">probs_uniform</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">epsilon</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check for standard normal distribution |
| </span><span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">probs_normal1</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">weighted_extended_p_square</span><span class="special">(</span><span class="identifier">acc_normal1</span><span class="special">)[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">probs_normal_exact1</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">epsilon</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="identifier">weighted_extended_p_square</span><span class="special">(</span><span class="identifier">acc_normal2</span><span class="special">)[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">probs_normal_exact2</span><span class="special">[</span><span class="identifier">i</span><span class="special">],</span> <span class="identifier">epsilon</span><span class="special">);</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_extended_p_squ_id567805.html" title="Struct template weighted_extended_p_square_impl">weighted_extended_p_square_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_kurtosis"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_kurtosis" title="weighted_kurtosis">weighted_kurtosis</a> |
| </h4></div></div></div> |
| <p> |
| The kurtosis of a sample distribution is defined as the ratio of the 4th |
| central moment and the square of the 2nd central moment (the variance) |
| of the samples, minus 3. The term <code class="literal">-3</code> is added in order |
| to ensure that the normal distribution has zero kurtosis. For more implementation |
| details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_kurtosis_impl.html" title="Struct template weighted_kurtosis_impl">weighted_kurtosis_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">,</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_mean</span></code> <br> |
| <code class="computeroutput"><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">3</span><span class="special">></span></code> <br> <code class="computeroutput"><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">4</span><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_kurtosis_hpp" title="Header <boost/accumulators/statistics/weighted_kurtosis.hpp>">boost/accumulators/statistics/weighted_kurtosis.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_kurtosis</span><span class="special">>,</span> <span class="keyword">int</span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">7</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">42.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">212.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">3</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1350.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">4</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">9956.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_kurtosis</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">0.58137026432</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_kurtosis_impl.html" title="Struct template weighted_kurtosis_impl">weighted_kurtosis_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean" title="weighted_mean and variants"><code class="literal">weighted_mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment" title="weighted_moment"><code class="literal">weighted_moment</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean" title="weighted_mean and variants">weighted_mean |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Calculates the weighted mean of samples or variates. The calculation is |
| either lazy (in the result extractor), or immediate (in the accumulator). |
| The lazy implementation is the default. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_mean_impl.html" title="Struct template weighted_mean_impl">weighted_mean_impl</a></code> |
| or. <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/immediate_weighted_mean_id568590.html" title="Struct template immediate_weighted_mean_impl">immediate_weighted_mean_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd><p> |
| For samples, <code class="computeroutput"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span></code> <br> For variates, |
| <code class="computeroutput"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span><span class="special">,</span> |
| <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span></code> |
| </p></dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> <br> |
| The lazy mean of samples depends on <code class="computeroutput"><span class="identifier">weighted_sum</span></code> |
| <br> The lazy mean of variates depends on <code class="computeroutput"><span class="identifier">weighted_sum_of_variates</span><span class="special"><></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> <br> <code class="computeroutput"><span class="identifier">immediate_weighted_mean</span></code> |
| <br> <code class="computeroutput"><span class="identifier">immediate_weighted_mean_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_mean_hpp" title="Header <boost/accumulators/statistics/weighted_mean.hpp>">boost/accumulators/statistics/weighted_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span> |
| <span class="keyword">int</span> |
| <span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_mean</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> |
| <span class="special">></span> |
| <span class="special">,</span> <span class="keyword">int</span> |
| <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">7</span><span class="special">);</span> <span class="comment">// 20 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">8</span><span class="special">);</span> <span class="comment">// 18 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">9</span><span class="special">);</span> <span class="comment">// 16 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">5</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">6</span><span class="special">);</span> <span class="comment">//+ 30 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">14</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">//= 84 / 14 = 6 |
| </span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">6.</span><span class="special">,</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">52.</span><span class="special">/</span><span class="number">7.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc</span><span class="special">)));</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span> |
| <span class="keyword">int</span> |
| <span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span> |
| <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span> |
| <span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">immediate</span><span class="special">)</span> |
| <span class="special">></span> |
| <span class="special">,</span> <span class="keyword">int</span> |
| <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">10</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">7</span><span class="special">);</span> <span class="comment">// 20 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">8</span><span class="special">);</span> <span class="comment">// 18 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">9</span><span class="special">);</span> <span class="comment">// 16 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">// |
| </span><span class="identifier">acc2</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">5</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">6</span><span class="special">);</span> <span class="comment">//+ 30 |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">14</span><span class="special">,</span> <span class="identifier">sum_of_weights</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> <span class="comment">// |
| </span> <span class="comment">//= 84 / 14 = 6 |
| </span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">6.</span><span class="special">,</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">52.</span><span class="special">/</span><span class="number">7.</span><span class="special">,</span> <span class="special">(</span><span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_mean_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">)));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_mean_impl.html" title="Struct template weighted_mean_impl">weighted_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/immediate_weighted_mean_id568590.html" title="Struct template immediate_weighted_mean_impl">immediate_weighted_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_sum" title="weighted_sum and variants"><code class="literal">weighted_sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_median"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_median" title="weighted_median and variants">weighted_median |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Median estimation for weighted samples based on the <code class="literal">P^2</code> |
| quantile estimator, the density estimator, or the <code class="literal">P^2</code> |
| cumulative distribution estimator. For more implementation details, see |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_median_impl.html" title="Struct template weighted_median_impl">weighted_median_impl</a></code>, |
| <code class="computeroutput">with_weighted_density_median_impl</code>, |
| and <code class="computeroutput">with_weighted_p_square_cumulative_distribution_median_impl</code>. |
| </p> |
| <p> |
| The three median accumulators all satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_median</span></code> |
| feature, and can all be extracted with the <code class="computeroutput"><span class="identifier">weighted_median</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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><em class="replaceable"><code>sample-type</code></em><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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_median</span></code> depends |
| on <code class="computeroutput"><span class="identifier">weighted_p_square_quantile_for_median</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_weighted_density_median</span></code> |
| depends on <code class="computeroutput"><span class="identifier">count</span></code> |
| and <code class="computeroutput"><span class="identifier">weighted_density</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_weighted_p_square_cumulative_distribution_median</span></code> |
| depends on <code class="computeroutput"><span class="identifier">weighted_p_square_cumulative_distribution</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">with_weighted_density_median</span></code> |
| (a.k.a. <code class="computeroutput"><span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">with_weighted_density</span><span class="special">)</span></code>) <br> <code class="computeroutput"><span class="identifier">with_weighted_p_square_cumulative_distribution_median</span></code> |
| (a.k.a. <code class="computeroutput"><span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">with_weighted_p_square_cumulative_distribution</span><span class="special">)</span></code>) |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">with_weighted_density_median</span></code> |
| requires <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">cache_size</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">num_bins</span></code> |
| <br> <code class="computeroutput"><span class="identifier">with_weighted_p_square_cumulative_distribution_median</span></code> |
| requires <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_median_hpp" title="Header <boost/accumulators/statistics/weighted_median.hpp>">boost/accumulators/statistics/weighted_median.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// Median estimation of normal distribution N(1,1) using samples from a narrow normal distribution N(1,0.01) |
| </span><span class="comment">// The weights equal to the likelihood ratio of the corresponding samples |
| </span> |
| <span class="comment">// two random number generators |
| </span><span class="keyword">double</span> <span class="identifier">mu</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">sigma_narrow</span> <span class="special">=</span> <span class="number">0.01</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">sigma</span> <span class="special">=</span> <span class="number">1.</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma_narrow</span><span class="special">(</span><span class="identifier">mu</span><span class="special">,</span><span class="identifier">sigma_narrow</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal_narrow</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma_narrow</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">with_weighted_p_square_quantile</span><span class="special">)</span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">with_weighted_density</span><span class="special">)</span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc_dens</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">cache_size</span> <span class="special">=</span> <span class="number">10000</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_density</span><span class="special">::</span><span class="identifier">num_bins</span> <span class="special">=</span> <span class="number">1000</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">with_weighted_p_square_cumulative_distribution</span><span class="special">)</span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc_cdist</span><span class="special">(</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span> <span class="special">=</span> <span class="number">100</span> <span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">normal_narrow</span><span class="special">();</span> |
| <span class="identifier">acc</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(</span><span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma_narrow</span><span class="special">/</span><span class="identifier">sigma_narrow</span> <span class="special">-</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma</span><span class="special">/</span><span class="identifier">sigma</span> <span class="special">)));</span> |
| <span class="identifier">acc_dens</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(</span><span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma_narrow</span><span class="special">/</span><span class="identifier">sigma_narrow</span> <span class="special">-</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma</span><span class="special">/</span><span class="identifier">sigma</span> <span class="special">)));</span> |
| <span class="identifier">acc_cdist</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(</span><span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="identifier">mu</span><span class="special">)</span> <span class="special">*</span> <span class="special">(</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma_narrow</span><span class="special">/</span><span class="identifier">sigma_narrow</span> <span class="special">-</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">sigma</span><span class="special">/</span><span class="identifier">sigma</span> <span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">acc</span><span class="special">),</span> <span class="number">1e-1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">acc_dens</span><span class="special">),</span> <span class="number">1e-1</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weighted_median</span><span class="special">(</span><span class="identifier">acc_cdist</span><span class="special">),</span> <span class="number">1e-1</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_median_impl.html" title="Struct template weighted_median_impl">weighted_median_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput">with_weighted_density_median_impl</code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput">with_weighted_p_square_cumulative_distribution_median_impl</code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_quantile" title="weighted_p_square_quantile and variants"><code class="literal">weighted_p_square_quantile</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_cumulative_distribution" title="weighted_p_square_cumulative_distribution"><code class="literal">weighted_p_square_cumulative_distribution</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment" title="weighted_moment">weighted_moment</a> |
| </h4></div></div></div> |
| <p> |
| Calculates the N-th moment of the weighted samples, which is defined as |
| the sum of the weighted N-th power of the samples over the sum of the weights. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">,</span> <span class="identifier">weight_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_moment_hpp" title="Header <boost/accumulators/statistics/weighted_moment.hpp>">boost/accumulators/statistics/weighted_moment.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">7</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">acc7</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2.1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2.7</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">1.8</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">);</span> |
| |
| <span class="identifier">acc7</span><span class="special">(</span><span class="number">2.1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">);</span> |
| <span class="identifier">acc7</span><span class="special">(</span><span class="number">2.7</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.4</span><span class="special">);</span> |
| <span class="identifier">acc7</span><span class="special">(</span><span class="number">1.8</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">5.403</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">548.54182</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">7</span><span class="special">>(</span><span class="identifier">acc7</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_moment_impl.html" title="Struct template weighted_moment_impl">weighted_moment_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_cumulative_distribution"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_cumulative_distribution" title="weighted_p_square_cumulative_distribution">weighted_p_square_cumulative_distribution</a> |
| </h4></div></div></div> |
| <p> |
| Histogram calculation of the cumulative distribution with the <code class="literal">P^2</code> |
| algorithm for weighted samples. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_p_square_cumul_id569375.html" title="Struct template weighted_p_square_cumulative_distribution_impl">weighted_p_square_cumulative_distribution_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">iterator_range</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</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">weighted_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="identifier">result_type</span> |
| <span class="special">,</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">weighted_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="identifier">result_type</span> |
| <span class="special">></span> |
| <span class="special">>::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| where <code class="computeroutput"><span class="identifier">weighted_sample</span></code> |
| is <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span></code> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_or_weights</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N) where N is <code class="computeroutput"><span class="identifier">num_cells</span></code> |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_p_square_cumulative_distribution_hpp" title="Header <boost/accumulators/statistics/weighted_p_square_cumulative_distribution.hpp>">boost/accumulators/statistics/weighted_p_square_cumulative_distribution.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">4</span><span class="special">;</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">accumulator_t</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc_upper</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc_lower</span><span class="special">(</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">::</span><span class="identifier">num_cells</span> <span class="special">=</span> <span class="number">100</span><span class="special">);</span> |
| |
| <span class="comment">// two random number generators |
| </span><span class="keyword">double</span> <span class="identifier">mu_upper</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu_lower</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.0</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma_upper</span><span class="special">(</span><span class="identifier">mu_upper</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma_lower</span><span class="special">(</span><span class="identifier">mu_lower</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal_upper</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma_upper</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal_lower</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma_lower</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">normal_upper</span><span class="special">();</span> |
| <span class="identifier">acc_upper</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu_upper</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu_upper</span><span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">normal_lower</span><span class="special">();</span> |
| <span class="identifier">acc_lower</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu_lower</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu_lower</span><span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">typedef</span> <span class="identifier">iterator_range</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">pair</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="keyword">double</span><span class="special">></span> <span class="special">>::</span><span class="identifier">iterator</span> <span class="special">></span> <span class="identifier">histogram_type</span><span class="special">;</span> |
| <span class="identifier">histogram_type</span> <span class="identifier">histogram_upper</span> <span class="special">=</span> <span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">(</span><span class="identifier">acc_upper</span><span class="special">);</span> |
| <span class="identifier">histogram_type</span> <span class="identifier">histogram_lower</span> <span class="special">=</span> <span class="identifier">weighted_p_square_cumulative_distribution</span><span class="special">(</span><span class="identifier">acc_lower</span><span class="special">);</span> |
| |
| <span class="comment">// Note that applaying importance sampling results in a region of the distribution |
| </span><span class="comment">// to be estimated more accurately and another region to be estimated less accurately |
| </span><span class="comment">// than without importance sampling, i.e., with unweighted samples |
| </span> |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">histogram_upper</span><span class="special">.</span><span class="identifier">size</span><span class="special">();</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="comment">// problem with small results: epsilon is relative (in percent), not absolute! |
| </span> |
| <span class="comment">// check upper region of distribution |
| </span> <span class="keyword">if</span> <span class="special">(</span> <span class="identifier">histogram_upper</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span> <span class="special">></span> <span class="number">0.1</span> <span class="special">)</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="number">1.0</span> <span class="special">+</span> <span class="identifier">erf</span><span class="special">(</span> <span class="identifier">histogram_upper</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">first</span> <span class="special">/</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="number">2.0</span><span class="special">)</span> <span class="special">)),</span> <span class="identifier">histogram_upper</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="comment">// check lower region of distribution |
| </span> <span class="keyword">if</span> <span class="special">(</span> <span class="identifier">histogram_lower</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span> <span class="special"><</span> <span class="special">-</span><span class="number">0.1</span> <span class="special">)</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="number">0.5</span> <span class="special">*</span> <span class="special">(</span><span class="number">1.0</span> <span class="special">+</span> <span class="identifier">erf</span><span class="special">(</span> <span class="identifier">histogram_lower</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">first</span> <span class="special">/</span> <span class="identifier">sqrt</span><span class="special">(</span><span class="number">2.0</span><span class="special">)</span> <span class="special">)),</span> <span class="identifier">histogram_lower</span><span class="special">[</span><span class="identifier">i</span><span class="special">].</span><span class="identifier">second</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="special">}</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_p_square_cumul_id569375.html" title="Struct template weighted_p_square_cumulative_distribution_impl">weighted_p_square_cumulative_distribution_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_p_square_quantile" title="weighted_p_square_quantile and variants">weighted_p_square_quantile |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Single quantile estimation with the <code class="literal">P^2</code> algorithm. For |
| more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_p_square_quant_id569611.html" title="Struct template weighted_p_square_quantile_impl">weighted_p_square_quantile_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">count</span></code> <br> <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_p_square_quantile_for_median</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code>, |
| which defaults to <code class="computeroutput"><span class="number">0.5</span></code>. |
| (Note: for <code class="computeroutput"><span class="identifier">weighted_p_square_quantile_for_median</span></code>, |
| the <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| parameter is ignored and is always <code class="computeroutput"><span class="number">0.5</span></code>.) |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_p_square_quantile_hpp" title="Header <boost/accumulators/statistics/weighted_p_square_quantile.hpp>">boost/accumulators/statistics/weighted_p_square_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="keyword">typedef</span> <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_p_square_quantile</span><span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> <span class="identifier">accumulator_t</span><span class="special">;</span> |
| |
| <span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="comment">// some random number generators |
| </span><span class="keyword">double</span> <span class="identifier">mu4</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu5</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu6</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu7</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma4</span><span class="special">(</span><span class="identifier">mu4</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma5</span><span class="special">(</span><span class="identifier">mu5</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma6</span><span class="special">(</span><span class="identifier">mu6</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma7</span><span class="special">(</span><span class="identifier">mu7</span><span class="special">,</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal4</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma4</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal5</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma5</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal6</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma6</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal7</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma7</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc4</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc5</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc6</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">);</span> |
| <span class="identifier">accumulator_t</span> <span class="identifier">acc7</span><span class="special">(</span><span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">);</span> |
| |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">100000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="identifier">sample</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">);</span> |
| |
| <span class="keyword">double</span> <span class="identifier">sample4</span> <span class="special">=</span> <span class="identifier">normal4</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample5</span> <span class="special">=</span> <span class="identifier">normal5</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample6</span> <span class="special">=</span> <span class="identifier">normal6</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample7</span> <span class="special">=</span> <span class="identifier">normal7</span><span class="special">();</span> |
| <span class="identifier">acc4</span><span class="special">(</span><span class="identifier">sample4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu4</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample4</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu4</span><span class="special">)));</span> |
| <span class="identifier">acc5</span><span class="special">(</span><span class="identifier">sample5</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu5</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample5</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu5</span><span class="special">)));</span> |
| <span class="identifier">acc6</span><span class="special">(</span><span class="identifier">sample6</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu6</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample6</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu6</span><span class="special">)));</span> |
| <span class="identifier">acc7</span><span class="special">(</span><span class="identifier">sample7</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu7</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample7</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu7</span><span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check for uniform distribution with weight = 1 |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">),</span> <span class="number">0.001</span><span class="special">,</span> <span class="number">15</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">0.025</span><span class="special">,</span> <span class="number">5</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">0.975</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">),</span> <span class="number">0.999</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| |
| <span class="comment">// check for shifted standard normal distribution ("importance sampling") |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">),</span> <span class="special">-</span><span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc5</span><span class="special">),</span> <span class="special">-</span><span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc6</span><span class="special">),</span> <span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_p_square_quantile</span><span class="special">(</span><span class="identifier">acc7</span><span class="special">),</span> <span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_p_square_quant_id569611.html" title="Struct template weighted_p_square_quantile_impl">weighted_p_square_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_peaks_over_threshold"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_peaks_over_threshold" title="weighted_peaks_over_threshold and variants">weighted_peaks_over_threshold |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Weighted peaks over threshold method for weighted quantile and weighted |
| tail mean estimation. For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_peaks_over_thr_id569997.html" title="Struct template weighted_peaks_over_threshold_impl">weighted_peaks_over_threshold_impl</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_peaks_over_thr_id570104.html" title="Struct template weighted_peaks_over_threshold_prob_impl">weighted_peaks_over_threshold_prob_impl</a></code>. |
| </p> |
| <p> |
| Both <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_peaks_over_threshold</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_peaks_over_threshold_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| satisfy the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_peaks_over_threshold</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> feature and can be extracted using |
| the <code class="computeroutput"><span class="identifier">weighted_peaks_over_threshold</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| <code class="computeroutput"><span class="identifier">tuple</span><span class="special"><</span><span class="identifier">float_type</span><span class="special">,</span> |
| <span class="identifier">float_type</span><span class="special">,</span> |
| <span class="identifier">float_type</span><span class="special">></span></code> |
| where <code class="computeroutput"><span class="identifier">float_type</span></code> |
| is |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_peaks_over_threshold</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| depends on <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| <br> <code class="computeroutput"><span class="identifier">weighted_peaks_over_threshold_prob</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| depends on <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> |
| and <code class="computeroutput"><span class="identifier">tail_weights</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_peaks_over_threshold_prob</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold</span><span class="special">::</span><span class="identifier">threshold_value</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">peaks_over_threshold_prob</span><span class="special">::</span><span class="identifier">threshold_probability</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| TODO |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_peaks_over_threshold_hpp" title="Header <boost/accumulators/statistics/weighted_peaks_over_threshold.hpp>">boost/accumulators/statistics/weighted_peaks_over_threshold.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_peaks_over_thr_id569997.html" title="Struct template weighted_peaks_over_threshold_impl">weighted_peaks_over_threshold_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_peaks_over_thr_id570104.html" title="Struct template weighted_peaks_over_threshold_prob_impl">weighted_peaks_over_threshold_prob_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_skewness"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_skewness" title="weighted_skewness">weighted_skewness</a> |
| </h4></div></div></div> |
| <p> |
| The skewness of a sample distribution is defined as the ratio of the 3rd |
| central moment and the <code class="literal">3/2</code>-th power of the 2nd central |
| moment (the variance) of the sampless 3. The skewness estimator for weighted |
| samples is formally identical to the estimator for unweighted samples, |
| except that the weighted counterparts of all measures it depends on are |
| to be taken. |
| </p> |
| <p> |
| For implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_skewness_impl.html" title="Struct template weighted_skewness_impl">weighted_skewness_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">,</span> <span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">>::</span><span class="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weighted_mean</span></code> <br> |
| <code class="computeroutput"><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">3</span><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_skewness_hpp" title="Header <boost/accumulators/statistics/weighted_skewness.hpp>">boost/accumulators/statistics/weighted_skewness.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_skewness</span><span class="special">>,</span> <span class="keyword">int</span> <span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">7</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">9</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">42.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">212.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">3</span><span class="special">>(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1350.</span><span class="special">/</span><span class="number">11.</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">weighted_skewness</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1.30708406282</span><span class="special">,</span> <span class="number">1e-6</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_skewness_impl.html" title="Struct template weighted_skewness_impl">weighted_skewness_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean" title="weighted_mean and variants"><code class="literal">weighted_mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment" title="weighted_moment"><code class="literal">weighted_moment</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_sum"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_sum" title="weighted_sum and variants">weighted_sum |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| For summing the weighted samples or variates. All of the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum_of_variates</span><span class="special"><></span></code> |
| features can be extracted with the <code class="computeroutput"><span class="identifier">weighted_sum_of_variates</span><span class="special">()</span></code> extractor. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span></code> for summing weighted |
| samples <br> <code class="computeroutput"><span class="identifier">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span></code> |
| for summing weighted variates |
| </p></dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum_of_variates</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> <br> <code class="computeroutput"><em class="replaceable"><code>variate-tag</code></em></code> |
| for summing variates |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_sum_hpp" title="Header <boost/accumulators/statistics/weighted_sum.hpp>">boost/accumulators/statistics/weighted_sum.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_sum_of_variates</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">int</span><span class="special">></span> <span class="identifier">acc</span><span class="special">;</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weighted_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">6</span><span class="special">,</span> <span class="identifier">weighted_sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">6</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">8</span><span class="special">,</span> <span class="identifier">weighted_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">24</span><span class="special">,</span> <span class="identifier">weighted_sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| |
| <span class="identifier">acc</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">6</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="number">9</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">32</span><span class="special">,</span> <span class="identifier">weighted_sum</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">78</span><span class="special">,</span> <span class="identifier">weighted_sum_of_variates</span><span class="special">(</span><span class="identifier">acc</span><span class="special">));</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"><li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_sum_impl.html" title="Struct template weighted_sum_impl">weighted_sum_impl</a></code> |
| </li></ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_weighted_tail_mean"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_weighted_tail_mean" title="non_coherent_weighted_tail_mean">non_coherent_weighted_tail_mean</a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the (non-coherent) weighted tail mean based on order statistics |
| (for both left and right tails). The left non-coherent weighted tail mean |
| feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code>, |
| and the right non-choherent weighted tail mean feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code>. |
| They both share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_non_coherent_tail_mean</span></code> |
| feature with the unweighted non-coherent tail mean accumulators and can |
| be extracted with either the <code class="computeroutput"><span class="identifier">non_coherent_tail_mean</span><span class="special">()</span></code> or the <code class="computeroutput"><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">()</span></code> extractors. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/non_coherent_weighted_t_id570701.html" title="Struct template non_coherent_weighted_tail_mean_impl">non_coherent_weighted_tail_mean_impl</a></code>. |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> <br> |
| <code class="computeroutput"><span class="identifier">tail_weights</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">abstract_non_coherent_tail_mean</span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_tail_mean_hpp" title="Header <boost/accumulators/statistics/weighted_tail_mean.hpp>">boost/accumulators/statistics/weighted_tail_mean.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">100000</span><span class="special">;</span> <span class="comment">// number of MC steps |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">25000</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc0</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| |
| <span class="comment">// random number generators |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">smpl</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">(</span><span class="identifier">rng</span><span class="special">());</span> |
| <span class="identifier">acc0</span><span class="special">(</span><span class="identifier">smpl</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.</span><span class="special">/</span><span class="identifier">smpl</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">smpl</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">();</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">smpl</span><span class="special">*</span><span class="identifier">smpl</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">smpl</span><span class="special">);</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check uniform distribution |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.95</span><span class="special">),</span> <span class="number">0.975</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">0.9875</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.99</span><span class="special">),</span> <span class="number">0.995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc0</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">0.9995</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.05</span><span class="special">),</span> <span class="number">0.025</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="number">0.0125</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.01</span><span class="special">),</span> <span class="number">0.005</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">non_coherent_weighted_tail_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="number">0.0005</span><span class="special">,</span> <span class="number">5</span><span class="special">*</span><span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/non_coherent_weighted_t_id570701.html" title="Struct template non_coherent_weighted_tail_mean_impl">non_coherent_weighted_tail_mean_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_quantile"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_quantile" title="weighted_tail_quantile">weighted_tail_quantile</a> |
| </h4></div></div></div> |
| <p> |
| Tail quantile estimation based on order statistics of weighted samples |
| (for both left and right tails). The left weighted tail quantile feature |
| is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span></code>, |
| and the right weighted tail quantile feature is <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span></code>. They both share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">quantile</span></code> feature with the unweighted |
| tail quantile accumulators and can be extracted with either the <code class="computeroutput"><span class="identifier">quantile</span><span class="special">()</span></code> |
| or the <code class="computeroutput"><span class="identifier">weighted_tail_quantile</span><span class="special">()</span></code> extractors. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_tail_quantile__id571075.html" title="Struct template weighted_tail_quantile_impl">weighted_tail_quantile_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><em class="replaceable"><code>sample-type</code></em> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">sum_of_weights</span></code> <br> |
| <code class="computeroutput"><span class="identifier">tail_weights</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_tail_quantile_hpp" title="Header <boost/accumulators/statistics/weighted_tail_quantile.hpp>">boost/accumulators/statistics/weighted_tail_quantile.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// tolerance in % |
| </span><span class="keyword">double</span> <span class="identifier">epsilon</span> <span class="special">=</span> <span class="number">1</span><span class="special">;</span> |
| |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">n</span> <span class="special">=</span> <span class="number">100000</span><span class="special">;</span> <span class="comment">// number of MC steps |
| </span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">20000</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="keyword">double</span> <span class="identifier">mu1</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">mu2</span> <span class="special">=</span> <span class="special">-</span><span class="number">1.0</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma1</span><span class="special">(</span><span class="identifier">mu1</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma2</span><span class="special">(</span><span class="identifier">mu2</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal1</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal2</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma2</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_quantile</span><span class="special"><</span><span class="identifier">right</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_quantile</span><span class="special"><</span><span class="identifier">left</span><span class="special">></span> <span class="special">>,</span> <span class="keyword">double</span><span class="special">></span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span><span class="special">);</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special"><</span> <span class="identifier">n</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">sample1</span> <span class="special">=</span> <span class="identifier">normal1</span><span class="special">();</span> |
| <span class="keyword">double</span> <span class="identifier">sample2</span> <span class="special">=</span> <span class="identifier">normal2</span><span class="special">();</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="identifier">sample1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu1</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample1</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu1</span><span class="special">)));</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="identifier">sample2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">exp</span><span class="special">(-</span><span class="identifier">mu2</span> <span class="special">*</span> <span class="special">(</span><span class="identifier">sample2</span> <span class="special">-</span> <span class="number">0.5</span> <span class="special">*</span> <span class="identifier">mu2</span><span class="special">)));</span> |
| <span class="special">}</span> |
| |
| <span class="comment">// check standard normal distribution |
| </span><span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.975</span><span class="special">),</span> <span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.999</span><span class="special">),</span> <span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.025</span><span class="special">),</span> <span class="special">-</span><span class="number">1.959963</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span> <span class="identifier">quantile</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.001</span><span class="special">),</span> <span class="special">-</span><span class="number">3.090232</span><span class="special">,</span> <span class="identifier">epsilon</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_tail_quantile__id571075.html" title="Struct template weighted_tail_quantile_impl">weighted_tail_quantile_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.sum" title="sum and variants"><code class="literal">sum</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_variate_means"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_tail_variate_means" title="weighted_tail_variate_means and variants">weighted_tail_variate_means |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Estimation of the absolute and relative weighted tail variate means (for |
| both left and right tails) The absolute weighted tail variate means has |
| the feature <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">absolute_weighted_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> |
| <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> and the relative weighted tail |
| variate mean has the feature <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> |
| <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code>. All absolute weighted tail |
| variate mean features share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_absolute_tail_variate_means</span></code> |
| feature with their unweighted variants and can be extracted with the <code class="computeroutput"><span class="identifier">tail_variate_means</span><span class="special">()</span></code> |
| and <code class="computeroutput"><span class="identifier">weighted_tail_variate_means</span><span class="special">()</span></code> extractors. All the relative weighted |
| tail variate mean features share the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">abstract_relative_tail_variate_means</span></code> |
| feature with their unweighted variants and can be extracted with either |
| the <code class="computeroutput"><span class="identifier">relative_tail_variate_means</span><span class="special">()</span></code> or <code class="computeroutput"><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">()</span></code> extractors. |
| </p> |
| <p> |
| For more implementation details, see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_tail_variate_m_id571485.html" title="Struct template weighted_tail_variate_means_impl">weighted_tail_variate_means_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">iterator_range</span><span class="special"><</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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</span> |
| <span class="special">,</span> <em class="replaceable"><code>weight-type</code></em> |
| <span class="special">>::</span><span class="identifier">result_type</span><span class="special">::</span><span class="identifier">iterator</span> |
| <span class="special">></span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">non_coherent_weighted_tail_mean</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">tail_variate</span><span class="special"><</span><em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">,</span> <em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">tail_weights</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">absolute_weighted_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">,</span> <em class="replaceable"><code>variate-type</code></em><span class="special">,</span> <em class="replaceable"><code>variate-tag</code></em><span class="special">></span></code> |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">tail</span><span class="special"><</span><em class="replaceable"><code>left-or-right</code></em><span class="special">>::</span><span class="identifier">cache_size</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">quantile_probability</span></code> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(log N), where N is the cache size |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(N log N), where N is the cache size |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_tail_variate_means_hpp" title="Header <boost/accumulators/statistics/weighted_tail_variate_means.hpp>">boost/accumulators/statistics/weighted_tail_variate_means.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">c</span> <span class="special">=</span> <span class="number">5</span><span class="special">;</span> <span class="comment">// cache size |
| </span> |
| <span class="keyword">typedef</span> <span class="keyword">double</span> <span class="identifier">variate_type</span><span class="special">;</span> |
| <span class="keyword">typedef</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special"><</span><span class="identifier">variate_type</span><span class="special">></span> <span class="identifier">variate_set_type</span><span class="special">;</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_variate_means</span><span class="special"><</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">relative</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_variate_means</span><span class="special"><</span><span class="identifier">right</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">absolute</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="identifier">right_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_variate_means</span><span class="special"><</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">relative</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_tail_variate_means</span><span class="special"><</span><span class="identifier">left</span><span class="special">,</span> <span class="identifier">variate_set_type</span><span class="special">,</span> <span class="identifier">tag</span><span class="special">::</span><span class="identifier">covariate1</span><span class="special">>(</span><span class="identifier">absolute</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="identifier">left_tail_cache_size</span> <span class="special">=</span> <span class="identifier">c</span> <span class="special">);</span> |
| |
| <span class="identifier">variate_set_type</span> <span class="identifier">cov1</span><span class="special">,</span> <span class="identifier">cov2</span><span class="special">,</span> <span class="identifier">cov3</span><span class="special">,</span> <span class="identifier">cov4</span><span class="special">,</span> <span class="identifier">cov5</span><span class="special">;</span> |
| <span class="keyword">double</span> <span class="identifier">c1</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">10.</span><span class="special">,</span> <span class="number">20.</span><span class="special">,</span> <span class="number">30.</span><span class="special">,</span> <span class="number">40.</span> <span class="special">};</span> <span class="comment">// 100 |
| </span><span class="keyword">double</span> <span class="identifier">c2</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">26.</span><span class="special">,</span> <span class="number">4.</span><span class="special">,</span> <span class="number">17.</span><span class="special">,</span> <span class="number">3.</span> <span class="special">};</span> <span class="comment">// 50 |
| </span><span class="keyword">double</span> <span class="identifier">c3</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">46.</span><span class="special">,</span> <span class="number">64.</span><span class="special">,</span> <span class="number">40.</span><span class="special">,</span> <span class="number">50.</span> <span class="special">};</span> <span class="comment">// 200 |
| </span><span class="keyword">double</span> <span class="identifier">c4</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">1.</span><span class="special">,</span> <span class="number">3.</span><span class="special">,</span> <span class="number">70.</span><span class="special">,</span> <span class="number">6.</span> <span class="special">};</span> <span class="comment">// 80 |
| </span><span class="keyword">double</span> <span class="identifier">c5</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span> <span class="number">2.</span><span class="special">,</span> <span class="number">2.</span><span class="special">,</span> <span class="number">2.</span><span class="special">,</span> <span class="number">14.</span> <span class="special">};</span> <span class="comment">// 20 |
| </span><span class="identifier">cov1</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c1</span><span class="special">,</span> <span class="identifier">c1</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c1</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov2</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c2</span><span class="special">,</span> <span class="identifier">c2</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c2</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov3</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c3</span><span class="special">,</span> <span class="identifier">c3</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c3</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov4</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c4</span><span class="special">,</span> <span class="identifier">c4</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c4</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| <span class="identifier">cov5</span><span class="special">.</span><span class="identifier">assign</span><span class="special">(</span><span class="identifier">c5</span><span class="special">,</span> <span class="identifier">c5</span> <span class="special">+</span> <span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">c5</span><span class="special">)/</span><span class="keyword">sizeof</span><span class="special">(</span><span class="identifier">variate_type</span><span class="special">));</span> |
| |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc1</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc3</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc3</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="identifier">acc4</span><span class="special">(</span><span class="number">100.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.8</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov1</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">50.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov2</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span><span class="number">200.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.0</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov3</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">80.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.1</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov4</span><span class="special">);</span> |
| <span class="identifier">acc4</span><span class="special">(</span> <span class="number">20.</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1.2</span><span class="special">,</span> <span class="identifier">covariate1</span> <span class="special">=</span> <span class="identifier">cov5</span><span class="special">);</span> |
| |
| <span class="comment">// check relative risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">10</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">46</span><span class="special">)/(</span><span class="number">0.8</span><span class="special">*</span><span class="number">100</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">20</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">64</span><span class="special">)/(</span><span class="number">0.8</span><span class="special">*</span><span class="number">100</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">30</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">40</span><span class="special">)/(</span><span class="number">0.8</span><span class="special">*</span><span class="number">100</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">40</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">50</span><span class="special">)/(</span><span class="number">0.8</span><span class="special">*</span><span class="number">100</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">26</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/(</span><span class="number">0.9</span><span class="special">*</span><span class="number">50</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">4</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/(</span><span class="number">0.9</span><span class="special">*</span><span class="number">50</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">17</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/(</span><span class="number">0.9</span><span class="special">*</span><span class="number">50</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">3</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">14</span><span class="special">)/(</span><span class="number">0.9</span><span class="special">*</span><span class="number">50</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| |
| <span class="comment">// check absolute risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">10</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">46</span><span class="special">)/</span><span class="number">1.8</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">20</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">64</span><span class="special">)/</span><span class="number">1.8</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">30</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">40</span><span class="special">)/</span><span class="number">1.8</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.7</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="special">(</span><span class="number">0.8</span><span class="special">*</span><span class="number">40</span> <span class="special">+</span> <span class="number">1.0</span><span class="special">*</span><span class="number">50</span><span class="special">)/</span><span class="number">1.8</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">26</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/</span><span class="number">2.1</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">4</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/</span><span class="number">2.1</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">17</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">)/</span><span class="number">2.1</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.3</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="special">(</span><span class="number">0.9</span><span class="special">*</span><span class="number">3</span> <span class="special">+</span> <span class="number">1.2</span><span class="special">*</span><span class="number">14</span><span class="special">)/</span><span class="number">2.1</span> <span class="special">);</span> |
| |
| <span class="comment">// check relative risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">46</span><span class="special">/(</span><span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">64</span><span class="special">/(</span><span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">40</span><span class="special">/(</span><span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">50</span><span class="special">/(</span><span class="number">1.0</span><span class="special">*</span><span class="number">200</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/(</span><span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/(</span><span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/(</span><span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">relative_weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc3</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">14</span><span class="special">/(</span><span class="number">1.2</span><span class="special">*</span><span class="number">20</span><span class="special">)</span> <span class="special">);</span> |
| |
| <span class="comment">// check absolute risk contributions |
| </span><span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">46</span><span class="special">/</span><span class="number">1.0</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">64</span><span class="special">/</span><span class="number">1.0</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">40</span><span class="special">/</span><span class="number">1.0</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.9</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">1.0</span><span class="special">*</span><span class="number">50</span><span class="special">/</span><span class="number">1.0</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/</span><span class="number">1.2</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">1</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/</span><span class="number">1.2</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">2</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">2</span><span class="special">/</span><span class="number">1.2</span> <span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span> <span class="special">*(</span><span class="identifier">weighted_tail_variate_means</span><span class="special">(</span><span class="identifier">acc4</span><span class="special">,</span> <span class="identifier">quantile_probability</span> <span class="special">=</span> <span class="number">0.1</span><span class="special">).</span><span class="identifier">begin</span><span class="special">()</span> <span class="special">+</span> <span class="number">3</span><span class="special">),</span> <span class="number">1.2</span><span class="special">*</span><span class="number">14</span><span class="special">/</span><span class="number">1.2</span> <span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_tail_variate_m_id571485.html" title="Struct template weighted_tail_variate_means_impl">weighted_tail_variate_means_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.non_coherent_weighted_tail_mean" title="non_coherent_weighted_tail_mean"><code class="literal">non_coherent_weighted_tail_mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail_variate" title="tail_variate"><code class="literal">tail_variate</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.tail" title="tail"><code class="literal">tail</code></a> |
| </li> |
| </ul></div> |
| </div> |
| <div class="section"> |
| <div class="titlepage"><div><div><h4 class="title"> |
| <a name="accumulators.user_s_guide.the_statistical_accumulators_library.weighted_variance"></a><a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_variance" title="weighted_variance and variants">weighted_variance |
| <span class="emphasis"><em>and variants</em></span></a> |
| </h4></div></div></div> |
| <p> |
| Lazy or iterative calculation of the weighted variance. The lazy calculation |
| is associated with the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_weighted_variance</span></code> |
| feature, and the iterative calculation with the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span></code> |
| feature. Both can be extracted using the <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">()</span></code> extractor. For more implementation details, |
| see <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/lazy_weighted_variance__id572014.html" title="Struct template lazy_weighted_variance_impl">lazy_weighted_variance_impl</a></code> |
| and <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_variance_impl.html" title="Struct template weighted_variance_impl">weighted_variance_impl</a></code> |
| </p> |
| <div class="variablelist"> |
| <p class="title"><b></b></p> |
| <dl> |
| <dt><span class="term">Result Type</span></dt> |
| <dd> |
| <p> |
| |
| </p> |
| <pre class="programlisting"><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">numeric</span><span class="special">::</span><span class="identifier">functional</span><span class="special">::</span><span class="identifier">multiplies</span><span class="special"><</span><em class="replaceable"><code>sample-type</code></em><span class="special">,</span> <em class="replaceable"><code>weight-type</code></em><span class="special">>::</span><span class="identifier">result_type</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="identifier">result_type</span> |
| </pre> |
| <p> |
| </p> |
| </dd> |
| <dt><span class="term">Depends On</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_weighted_variance</span></code> depends |
| on <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">></span></code> |
| and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_mean</span></code> <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span></code> depends on <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">count</span></code> and <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">immediate_weighted_mean</span></code> |
| </p></dd> |
| <dt><span class="term">Variants</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">lazy_weighted_variance</span></code> (a.k.a. |
| <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">lazy</span><span class="special">))</span></code> |
| <br> <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span></code> (a.k.a. <code class="computeroutput"><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)</span></code>) |
| </p></dd> |
| <dt><span class="term">Initialization Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Parameters</span></dt> |
| <dd><p> |
| <code class="computeroutput"><span class="identifier">weight</span></code> |
| </p></dd> |
| <dt><span class="term">Extractor Parameters</span></dt> |
| <dd><p> |
| <span class="emphasis"><em>none</em></span> |
| </p></dd> |
| <dt><span class="term">Accumulator Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| <dt><span class="term">Extractor Complexity</span></dt> |
| <dd><p> |
| O(1) |
| </p></dd> |
| </dl> |
| </div> |
| <p> |
| <span class="bold"><strong>Header</strong></span> |
| </p> |
| <pre class="programlisting"><span class="preprocessor">#include</span> <span class="special"><</span><code class="computeroutput"><a class="link" href="reference.html#header.boost.accumulators.statistics.weighted_variance_hpp" title="Header <boost/accumulators/statistics/weighted_variance.hpp>">boost/accumulators/statistics/weighted_variance.hpp</a></code><span class="special">></span> |
| </pre> |
| <p> |
| <span class="bold"><strong>Example</strong></span> |
| </p> |
| <pre class="programlisting"><span class="comment">// lazy weighted_variance |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">lazy</span><span class="special">)>,</span> <span class="keyword">int</span><span class="special">></span> <span class="identifier">acc1</span><span class="special">;</span> |
| |
| <span class="identifier">acc1</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">);</span> <span class="comment">// 2 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> <span class="comment">// 6 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// 3 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> <span class="comment">// 16 |
| </span><span class="identifier">acc1</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> <span class="comment">// 5 |
| </span> |
| <span class="comment">// weighted_mean = (2+6+3+16+5) / (2+3+1+4+1) = 32 / 11 = 2.9090909090909090909090909090909 |
| </span> |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.9090909</span><span class="special">,</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">10.1818182</span><span class="special">,</span> <span class="identifier">accumulators</span><span class="special">::</span><span class="identifier">weighted_moment</span><span class="special"><</span><span class="number">2</span><span class="special">>(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.7190083</span><span class="special">,</span> <span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">acc1</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="comment">// immediate weighted_variance |
| </span><span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">>,</span> <span class="keyword">int</span><span class="special">></span> <span class="identifier">acc2</span><span class="special">;</span> |
| |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">2</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">2</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">3</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">3</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">4</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">4</span><span class="special">);</span> |
| <span class="identifier">acc2</span><span class="special">(</span><span class="number">5</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="number">1</span><span class="special">);</span> |
| |
| <span class="identifier">BOOST_CHECK_EQUAL</span><span class="special">(</span><span class="number">5u</span><span class="special">,</span> <span class="identifier">count</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">));</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">2.9090909</span><span class="special">,</span> <span class="identifier">weighted_mean</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.7190083</span><span class="special">,</span> <span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">acc2</span><span class="special">),</span> <span class="number">1e-5</span><span class="special">);</span> |
| |
| <span class="comment">// check lazy and immediate variance with random numbers |
| </span> |
| <span class="comment">// two random number generators |
| </span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span> <span class="identifier">rng</span><span class="special">;</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="identifier">mean_sigma</span><span class="special">(</span><span class="number">0</span><span class="special">,</span><span class="number">1</span><span class="special">);</span> |
| <span class="identifier">boost</span><span class="special">::</span><span class="identifier">variate_generator</span><span class="special"><</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">lagged_fibonacci607</span><span class="special">&,</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">normal_distribution</span><span class="special"><></span> <span class="special">></span> <span class="identifier">normal</span><span class="special">(</span><span class="identifier">rng</span><span class="special">,</span> <span class="identifier">mean_sigma</span><span class="special">);</span> |
| |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">>,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">acc_lazy</span><span class="special">;</span> |
| <span class="identifier">accumulator_set</span><span class="special"><</span><span class="keyword">double</span><span class="special">,</span> <span class="identifier">stats</span><span class="special"><</span><span class="identifier">tag</span><span class="special">::</span><span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">immediate</span><span class="special">)>,</span> <span class="keyword">double</span> <span class="special">></span> <span class="identifier">acc_immediate</span><span class="special">;</span> |
| |
| <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span><span class="special">=</span><span class="number">0</span><span class="special">;</span> <span class="identifier">i</span><span class="special"><</span><span class="number">10000</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> |
| <span class="special">{</span> |
| <span class="keyword">double</span> <span class="identifier">value</span> <span class="special">=</span> <span class="identifier">normal</span><span class="special">();</span> |
| <span class="identifier">acc_lazy</span><span class="special">(</span><span class="identifier">value</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">());</span> |
| <span class="identifier">acc_immediate</span><span class="special">(</span><span class="identifier">value</span><span class="special">,</span> <span class="identifier">weight</span> <span class="special">=</span> <span class="identifier">rng</span><span class="special">());</span> |
| <span class="special">}</span> |
| |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">acc_lazy</span><span class="special">),</span> <span class="number">1.</span><span class="special">);</span> |
| <span class="identifier">BOOST_CHECK_CLOSE</span><span class="special">(</span><span class="number">1.</span><span class="special">,</span> <span class="identifier">weighted_variance</span><span class="special">(</span><span class="identifier">acc_immediate</span><span class="special">),</span> <span class="number">1.</span><span class="special">);</span> |
| </pre> |
| <p> |
| <span class="bold"><strong>See also</strong></span> |
| </p> |
| <div class="itemizedlist"><ul class="itemizedlist" type="disc"> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/lazy_weighted_variance__id572014.html" title="Struct template lazy_weighted_variance_impl">lazy_weighted_variance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <code class="computeroutput"><a class="link" href="../boost/accumulators/impl/weighted_variance_impl.html" title="Struct template weighted_variance_impl">weighted_variance_impl</a></code> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.count" title="count"><code class="literal">count</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_mean" title="weighted_mean and variants"><code class="literal">weighted_mean</code></a> |
| </li> |
| <li class="listitem"> |
| <a class="link" href="user_s_guide.html#accumulators.user_s_guide.the_statistical_accumulators_library.weighted_moment" title="weighted_moment"><code class="literal">weighted_moment</code></a> |
| </li> |
| </ul></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> |
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