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| <div class="titlepage"><div><div><h3 class="title"> |
| <a name="boost_icl.concepts.aggrovering"></a><a class="link" href="aggrovering.html" title="Addability, Subtractability and Aggregate on Overlap"> Addability, Subtractability |
| and Aggregate on Overlap</a> |
| </h3></div></div></div> |
| <p> |
| While <span class="emphasis"><em><span class="bold"><strong>addition</strong></span></em></span> and |
| <span class="emphasis"><em><span class="bold"><strong>subtraction</strong></span></em></span> on <code class="computeroutput"><span class="identifier">Sets</span></code> are implemented as <span class="emphasis"><em><span class="bold"><strong>set union</strong></span></em></span> and <span class="emphasis"><em><span class="bold"><strong>set |
| difference</strong></span></em></span>, for <code class="computeroutput"><span class="identifier">Maps</span></code> |
| we want to implement <span class="emphasis"><em><span class="bold"><strong>aggregation</strong></span></em></span> |
| on the associated values for the case of collision (of key elements) or overlap |
| (of key intervals), which has been refered to as <span class="emphasis"><em><span class="bold"><strong>aggregate |
| on overlap</strong></span></em></span> above. This kind of <code class="computeroutput"><span class="identifier">Addability</span></code> |
| and <code class="computeroutput"><span class="identifier">Subtractability</span></code> allows |
| to compute a lot of useful aggregation results on an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map's</a></code> |
| associated values, just by adding and subtracting value pairs. Various examples |
| of <span class="emphasis"><em><span class="bold"><strong>aggregate on overlap</strong></span></em></span> |
| are given in <a class="link" href="../examples.html" title="Examples">section examples</a>. |
| In addition, this concept of <code class="computeroutput"><span class="identifier">Addability</span></code> |
| and <code class="computeroutput"><span class="identifier">Subtractability</span></code> contains |
| the classical <code class="computeroutput"><span class="identifier">Insertability</span></code> |
| and <code class="computeroutput"><span class="identifier">Erasability</span></code> of key value |
| pairs as a special case so it provides a broader new semantics without loss |
| of the <span class="emphasis"><em>classical</em></span> one. |
| </p> |
| <p> |
| Aggregation is implemented for functions <code class="computeroutput"><span class="identifier">add</span></code> |
| and <code class="computeroutput"><span class="identifier">subtract</span></code> by propagating |
| a <code class="computeroutput"><span class="identifier">Combiner</span></code> functor to combine |
| associated values of type <code class="computeroutput"><span class="identifier">CodomainT</span></code>. |
| The standard <code class="computeroutput"><span class="identifier">Combiner</span></code> is |
| set as default template parameter <code class="computeroutput"><span class="keyword">template</span><span class="special"><</span><span class="keyword">class</span><span class="special">></span><span class="keyword">class</span> <span class="identifier">Combine</span> <span class="special">=</span> <span class="identifier">inplace_plus</span></code>, which is again generically |
| implemented by <code class="computeroutput"><span class="keyword">operator</span> <span class="special">+=</span></code> |
| for all Addable types. |
| </p> |
| <p> |
| For <code class="computeroutput"><span class="identifier">Combine</span></code> functors, the |
| Icl provides an <code class="computeroutput">inverse</code> |
| functor. |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| <code class="computeroutput"><span class="identifier">Combine</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="computeroutput"><span class="identifier">inverse</span><span class="special"><</span><span class="identifier">Combine</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> |
| <span class="special">>::</span><span class="identifier">type</span></code> |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_plus.html" title="Struct template inplace_plus">inplace_plus</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_minus.html" title="Struct template inplace_minus">inplace_minus</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_et.html" title="Struct template inplace_et">inplace_et</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_caret.html" title="Struct template inplace_caret">inplace_caret</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_star.html" title="Struct template inplace_star">inplace_star</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_slash.html" title="Struct template inplace_slash">inplace_slash</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_max.html" title="Struct template inplace_max">inplace_max</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_min.html" title="Struct template inplace_min">inplace_min</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_identity.html" title="Struct template inplace_identity">inplace_identity</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_erasure.html" title="Struct template inplace_erasure">inplace_erasure</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">Functor</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><a class="link" href="../../boost/icl/inplace_erasure.html" title="Struct template inplace_erasure">inplace_erasure</a></code><code class="computeroutput"><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code> |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <p> |
| The meta function <code class="computeroutput">inverse</code> |
| is mutually implemented for all but the default functor <code class="computeroutput"><span class="identifier">Functor</span></code> |
| such that e.g. <code class="computeroutput"><span class="identifier">inverse</span><span class="special"><</span><span class="identifier">inplace_minus</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span> <span class="special">>::</span><span class="identifier">type</span></code> |
| yields <code class="computeroutput"><span class="identifier">inplace_plus</span><span class="special"><</span><span class="identifier">T</span><span class="special">></span></code>. |
| Not in every case, e.g. <code class="computeroutput"><span class="identifier">max</span><span class="special">/</span><span class="identifier">min</span></code>, does |
| the <code class="computeroutput">inverse</code> functor invert |
| the effect of it's antetype. But for the default it does: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="computeroutput"><span class="identifier">_add</span><span class="special"><</span><span class="identifier">Combine</span><span class="special"><</span><span class="identifier">CodomainT</span><span class="special">></span> |
| <span class="special">>((</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">x</span><span class="special">))</span></code> |
| </p> |
| </th> |
| <th> |
| <p> |
| <code class="computeroutput"><span class="identifier">_subtract</span><span class="special"><</span><span class="identifier">inverse</span><span class="special"><</span><span class="identifier">Combine</span><span class="special"><</span><span class="identifier">CodomainT</span><span class="special">></span> |
| <span class="special">>::</span><span class="identifier">type</span><span class="special">>((</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">x</span><span class="special">))</span></code> |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| Instance |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">_add</span><span class="special"><</span><span class="identifier">inplace_plus</span><span class="special"><</span><span class="keyword">int</span><span class="special">></span> |
| <span class="special">>((</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">x</span><span class="special">))</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">_subtract</span><span class="special"><</span><span class="identifier">inplace_minus</span><span class="special"><</span><span class="keyword">int</span><span class="special">></span> |
| <span class="special">>((</span><span class="identifier">k</span><span class="special">,</span><span class="identifier">x</span><span class="special">))</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| Inversion |
| </p> |
| </td> |
| <td> |
| <p> |
| adds <code class="computeroutput"><span class="identifier">x</span></code> on overlap. |
| This inverts a preceding <code class="computeroutput"><span class="identifier">subtract</span></code> |
| of <code class="computeroutput"><span class="identifier">x</span></code> on <code class="computeroutput"><span class="identifier">k</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| subtracts <code class="computeroutput"><span class="identifier">x</span></code> on overlap. |
| This inverts a preceding <code class="computeroutput"><span class="identifier">add</span></code> |
| of <code class="computeroutput"><span class="identifier">x</span></code> on <code class="computeroutput"><span class="identifier">k</span></code> |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <p> |
| As already mentioned aggregating <code class="computeroutput"><span class="identifier">Addability</span></code> |
| and <code class="computeroutput"><span class="identifier">Subtractability</span></code> on <code class="computeroutput"><span class="identifier">Maps</span></code> contains the <span class="emphasis"><em>classical</em></span> |
| <code class="computeroutput"><span class="identifier">Insertability</span></code> and <code class="computeroutput"><span class="identifier">Erasability</span></code> of key value pairs as a special |
| case: |
| </p> |
| <div class="informaltable"><table class="table"> |
| <colgroup> |
| <col> |
| <col> |
| </colgroup> |
| <thead><tr> |
| <th> |
| <p> |
| aggregating function |
| </p> |
| </th> |
| <th> |
| <p> |
| equivalent <span class="emphasis"><em>classical</em></span> function |
| </p> |
| </th> |
| </tr></thead> |
| <tbody> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">_add</span><span class="special"><</span><span class="identifier">inplace_identity</span><span class="special"><</span><span class="identifier">CodomainT</span><span class="special">></span> |
| <span class="special">>(</span><span class="keyword">const</span> |
| <span class="identifier">value_type</span><span class="special">&)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">insert</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&)</span></code> |
| </p> |
| </td> |
| </tr> |
| <tr> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">_subtract</span><span class="special"><</span><span class="identifier">inplace_erasure</span><span class="special"><</span><span class="identifier">CodomainT</span><span class="special">></span> |
| <span class="special">>(</span><span class="keyword">const</span> |
| <span class="identifier">value_type</span><span class="special">&)</span></code> |
| </p> |
| </td> |
| <td> |
| <p> |
| <code class="computeroutput"><span class="identifier">erase</span><span class="special">(</span><span class="keyword">const</span> <span class="identifier">value_type</span><span class="special">&)</span></code> |
| </p> |
| </td> |
| </tr> |
| </tbody> |
| </table></div> |
| <p> |
| The aggregating member function templates <code class="computeroutput"><span class="identifier">_add</span></code> |
| and <code class="computeroutput"><span class="identifier">_subtract</span></code> are not in |
| the public interface of <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_maps</a></code>, |
| because the <code class="computeroutput"><span class="identifier">Combine</span></code> functor |
| is intended to be an invariant of <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_map's</a></code> |
| template instance to avoid, that clients spoil the aggregation by accidentally |
| calling varying aggregation functors. But you could instantiate an <code class="computeroutput"><a class="link" href="../../boost/icl/interval_map.html" title="Class template interval_map">interval_map</a></code> to have <code class="computeroutput"><span class="identifier">insert</span><span class="special">/</span><span class="identifier">erase</span></code> semantics this way: |
| </p> |
| <pre class="programlisting"><span class="identifier">interval_map</span><span class="special"><</span><span class="keyword">int</span><span class="special">,</span><span class="keyword">int</span><span class="special">,</span><span class="identifier">partial_absorber</span><span class="special">,</span> |
| <span class="identifier">std</span><span class="special">::</span><span class="identifier">less</span><span class="special">,</span> |
| <span class="identifier">inplace_identity</span> <span class="comment">//Combine parameter specified |
| </span> <span class="special">></span> <span class="identifier">m</span><span class="special">;</span> |
| <span class="identifier">interval</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">type</span> <span class="identifier">itv</span> <span class="special">=</span> <span class="identifier">interval</span><span class="special"><</span><span class="keyword">int</span><span class="special">>::</span><span class="identifier">rightopen</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="identifier">m</span><span class="special">.</span><span class="identifier">add</span><span class="special">(</span><span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">itv</span><span class="special">,</span><span class="number">42</span><span class="special">));</span> <span class="comment">//same as insert |
| </span><span class="identifier">m</span><span class="special">.</span><span class="identifier">subtract</span><span class="special">(</span><span class="identifier">make_pair</span><span class="special">(</span><span class="identifier">itv</span><span class="special">,</span><span class="number">42</span><span class="special">));</span> <span class="comment">//same as erase |
| </span></pre> |
| <p> |
| </p> |
| <p> |
| This is, of course, only a clarifying example. Member functions <code class="computeroutput"><span class="identifier">insert</span></code> and <code class="computeroutput"><span class="identifier">erase</span></code> |
| are available in <code class="computeroutput"><a class="link" href="../../boost/icl/interval_base_map.html" title="Class template interval_base_map">interval_map's</a></code> |
| interface so they can be called directly. |
| </p> |
| </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 © 2007 -2010 Joachim Faulhaber<br>Copyright © 1999 -2006 Cortex Software GmbH<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> |
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