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<title>Addability, Subtractability and Aggregate on Overlap</title>
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<div class="section boost_icl_concepts_aggrovering" lang="en">
<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"><a class="link" href="../../boost/icl/inverse.html" title="Struct template inverse">inverse</a></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"><a class="link" href="../../boost/icl/inverse.html" title="Struct template inverse">inverse</a></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"><a class="link" href="../../boost/icl/inverse.html" title="Struct template inverse">inverse</a></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>
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<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>)
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