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<section id="nep-8-a-proposal-for-adding-groupby-functionality-to-numpy">
<span id="nep08"></span><h1>NEP 8 — A proposal for adding groupby functionality to NumPy<a class="headerlink" href="#nep-8-a-proposal-for-adding-groupby-functionality-to-numpy" title="Link to this heading">#</a></h1>
<dl class="field-list simple">
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Travis Oliphant</p>
</dd>
<dt class="field-even">Contact<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="mailto:oliphant%40enthought.com">oliphant<span>@</span>enthought<span>.</span>com</a></p>
</dd>
<dt class="field-odd">Date<span class="colon">:</span></dt>
<dd class="field-odd"><p>2010-04-27</p>
</dd>
<dt class="field-even">Status<span class="colon">:</span></dt>
<dd class="field-even"><p>Deferred</p>
</dd>
</dl>
<section id="executive-summary">
<h2>Executive summary<a class="headerlink" href="#executive-summary" title="Link to this heading">#</a></h2>
<p>NumPy provides tools for handling data and doing calculations in much
the same way as relational algebra allows. However, the common group-by
functionality is not easily handled. The reduce methods of NumPy’s
ufuncs are a natural place to put this groupby behavior. This NEP
describes two additional methods for ufuncs (reduceby and reducein) and
two additional functions (segment and edges) which can help add this
functionality.</p>
</section>
<section id="example-use-case">
<h2>Example use case<a class="headerlink" href="#example-use-case" title="Link to this heading">#</a></h2>
<p>Suppose you have a NumPy structured array containing information about
the number of purchases at several stores over multiple days. To be clear, the
structured array data-type is:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">dt</span> <span class="o">=</span> <span class="p">[(</span><span class="s1">'year'</span><span class="p">,</span> <span class="n">i2</span><span class="p">),</span> <span class="p">(</span><span class="s1">'month'</span><span class="p">,</span> <span class="n">i1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'day'</span><span class="p">,</span> <span class="n">i1</span><span class="p">),</span> <span class="p">(</span><span class="s1">'time'</span><span class="p">,</span> <span class="nb">float</span><span class="p">),</span>
<span class="p">(</span><span class="s1">'store'</span><span class="p">,</span> <span class="n">i4</span><span class="p">),</span> <span class="p">(</span><span class="s1">'SKU'</span><span class="p">,</span> <span class="s1">'S6'</span><span class="p">),</span> <span class="p">(</span><span class="s1">'number'</span><span class="p">,</span> <span class="n">i4</span><span class="p">)]</span>
</pre></div>
</div>
<p>Suppose there is a 1-d NumPy array of this data-type and you would like
to compute various statistics (max, min, mean, sum, etc.) on the number
of products sold, by product, by month, by store, etc.</p>
<p>Currently, this could be done by using reduce methods on the number
field of the array, coupled with in-place sorting, unique with
return_inverse=True and bincount, etc. However, for such a common
data-analysis need, it would be nice to have standard and more direct
ways to get the results.</p>
</section>
<section id="ufunc-methods-proposed">
<h2>Ufunc methods proposed<a class="headerlink" href="#ufunc-methods-proposed" title="Link to this heading">#</a></h2>
<p>It is proposed to add two new reduce-style methods to the ufuncs:
reduceby and reducein. The reducein method is intended to be a simpler
to use version of reduceat, while the reduceby method is intended to
provide group-by capability on reductions.</p>
<p>reducein:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o"><</span><span class="n">ufunc</span><span class="o">>.</span><span class="n">reducein</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">indices</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
<span class="n">Perform</span> <span class="n">a</span> <span class="n">local</span> <span class="n">reduce</span> <span class="k">with</span> <span class="n">slices</span> <span class="n">specified</span> <span class="n">by</span> <span class="n">pairs</span> <span class="n">of</span> <span class="n">indices</span><span class="o">.</span>
<span class="n">The</span> <span class="n">reduction</span> <span class="n">occurs</span> <span class="n">along</span> <span class="n">the</span> <span class="n">provided</span> <span class="n">axis</span><span class="p">,</span> <span class="n">using</span> <span class="n">the</span> <span class="n">provided</span>
<span class="n">data</span><span class="o">-</span><span class="nb">type</span> <span class="n">to</span> <span class="n">calculate</span> <span class="n">intermediate</span> <span class="n">results</span><span class="p">,</span> <span class="n">storing</span> <span class="n">the</span> <span class="n">result</span> <span class="n">into</span>
<span class="n">the</span> <span class="n">array</span> <span class="n">out</span> <span class="p">(</span><span class="k">if</span> <span class="n">provided</span><span class="p">)</span><span class="o">.</span>
<span class="n">The</span> <span class="n">indices</span> <span class="n">array</span> <span class="n">provides</span> <span class="n">the</span> <span class="n">start</span> <span class="ow">and</span> <span class="n">end</span> <span class="n">indices</span> <span class="k">for</span> <span class="n">the</span>
<span class="n">reduction</span><span class="o">.</span> <span class="n">If</span> <span class="n">the</span> <span class="n">length</span> <span class="n">of</span> <span class="n">the</span> <span class="n">indices</span> <span class="n">array</span> <span class="ow">is</span> <span class="n">odd</span><span class="p">,</span> <span class="n">then</span> <span class="n">the</span>
<span class="n">final</span> <span class="n">index</span> <span class="n">provides</span> <span class="n">the</span> <span class="n">beginning</span> <span class="n">point</span> <span class="k">for</span> <span class="n">the</span> <span class="n">final</span> <span class="n">reduction</span>
<span class="ow">and</span> <span class="n">the</span> <span class="n">ending</span> <span class="n">point</span> <span class="ow">is</span> <span class="n">the</span> <span class="n">end</span> <span class="n">of</span> <span class="n">arr</span><span class="o">.</span>
<span class="n">This</span> <span class="n">generalizes</span> <span class="n">along</span> <span class="n">the</span> <span class="n">given</span> <span class="n">axis</span><span class="p">,</span> <span class="n">the</span> <span class="n">behavior</span><span class="p">:</span>
<span class="p">[</span><span class="o"><</span><span class="n">ufunc</span><span class="o">>.</span><span class="n">reduce</span><span class="p">(</span><span class="n">arr</span><span class="p">[</span><span class="n">indices</span><span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">i</span><span class="p">]:</span><span class="n">indices</span><span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">i</span><span class="o">+</span><span class="mi">1</span><span class="p">]])</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">indices</span><span class="p">)</span><span class="o">/</span><span class="mi">2</span><span class="p">)]</span>
<span class="n">This</span> <span class="n">assumes</span> <span class="n">indices</span> <span class="ow">is</span> <span class="n">of</span> <span class="n">even</span> <span class="n">length</span>
<span class="n">Example</span><span class="p">:</span>
<span class="o">>>></span> <span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">9</span><span class="p">,</span><span class="mi">10</span><span class="p">]</span>
<span class="o">>>></span> <span class="n">add</span><span class="o">.</span><span class="n">reducein</span><span class="p">(</span><span class="n">a</span><span class="p">,[</span><span class="mi">0</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">5</span><span class="p">,</span><span class="o">-</span><span class="mi">2</span><span class="p">])</span>
<span class="p">[</span><span class="mi">3</span><span class="p">,</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">19</span><span class="p">]</span>
<span class="n">Notice</span> <span class="n">that</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">3</span><span class="p">])</span> <span class="o">=</span> <span class="mi">3</span><span class="p">;</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">5</span><span class="p">])</span> <span class="o">=</span> <span class="mi">11</span><span class="p">;</span> <span class="ow">and</span> <span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="o">-</span><span class="mi">2</span><span class="p">:])</span> <span class="o">=</span> <span class="mi">19</span>
</pre></div>
</div>
<p>reduceby:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o"><</span><span class="n">ufunc</span><span class="o">>.</span><span class="n">reduceby</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">by</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="n">out</span><span class="o">=</span><span class="kc">None</span><span class="p">)</span>
<span class="n">Perform</span> <span class="n">a</span> <span class="n">reduction</span> <span class="ow">in</span> <span class="n">arr</span> <span class="n">over</span> <span class="n">unique</span> <span class="n">non</span><span class="o">-</span><span class="n">negative</span> <span class="n">integers</span> <span class="ow">in</span> <span class="n">by</span><span class="o">.</span>
<span class="n">Let</span> <span class="n">N</span><span class="o">=</span><span class="n">arr</span><span class="o">.</span><span class="n">ndim</span> <span class="ow">and</span> <span class="n">M</span><span class="o">=</span><span class="n">by</span><span class="o">.</span><span class="n">ndim</span><span class="o">.</span> <span class="n">Then</span><span class="p">,</span> <span class="n">by</span><span class="o">.</span><span class="n">shape</span><span class="p">[:</span><span class="n">N</span><span class="p">]</span> <span class="o">==</span> <span class="n">arr</span><span class="o">.</span><span class="n">shape</span><span class="o">.</span>
<span class="n">In</span> <span class="n">addition</span><span class="p">,</span> <span class="n">let</span> <span class="n">I</span> <span class="n">be</span> <span class="n">an</span> <span class="n">N</span><span class="o">-</span><span class="n">length</span> <span class="n">index</span> <span class="nb">tuple</span><span class="p">,</span> <span class="n">then</span> <span class="n">by</span><span class="p">[</span><span class="n">I</span><span class="p">]</span>
<span class="n">contains</span> <span class="n">the</span> <span class="n">location</span> <span class="ow">in</span> <span class="n">the</span> <span class="n">output</span> <span class="n">array</span> <span class="k">for</span> <span class="n">the</span> <span class="n">reduction</span> <span class="n">to</span>
<span class="n">be</span> <span class="n">stored</span><span class="o">.</span> <span class="n">Notice</span> <span class="n">that</span> <span class="k">if</span> <span class="n">N</span> <span class="o">==</span> <span class="n">M</span><span class="p">,</span> <span class="n">then</span> <span class="n">by</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="ow">is</span> <span class="n">a</span> <span class="n">non</span><span class="o">-</span><span class="n">negative</span>
<span class="n">integer</span><span class="p">,</span> <span class="k">while</span> <span class="k">if</span> <span class="n">N</span> <span class="o"><</span> <span class="n">M</span><span class="p">,</span> <span class="n">then</span> <span class="n">by</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="ow">is</span> <span class="n">an</span> <span class="n">array</span> <span class="n">of</span> <span class="n">indices</span> <span class="n">into</span>
<span class="n">the</span> <span class="n">output</span> <span class="n">array</span><span class="o">.</span>
<span class="n">The</span> <span class="n">reduction</span> <span class="ow">is</span> <span class="n">computed</span> <span class="n">on</span> <span class="n">groups</span> <span class="n">specified</span> <span class="n">by</span> <span class="n">unique</span> <span class="n">indices</span>
<span class="n">into</span> <span class="n">the</span> <span class="n">output</span> <span class="n">array</span><span class="o">.</span> <span class="n">The</span> <span class="n">index</span> <span class="ow">is</span> <span class="n">either</span> <span class="n">the</span> <span class="n">single</span>
<span class="n">non</span><span class="o">-</span><span class="n">negative</span> <span class="n">integer</span> <span class="k">if</span> <span class="n">N</span> <span class="o">==</span> <span class="n">M</span> <span class="ow">or</span> <span class="k">if</span> <span class="n">N</span> <span class="o"><</span> <span class="n">M</span><span class="p">,</span> <span class="n">the</span> <span class="n">entire</span>
<span class="p">(</span><span class="n">M</span><span class="o">-</span><span class="n">N</span><span class="o">+</span><span class="mi">1</span><span class="p">)</span><span class="o">-</span><span class="n">length</span> <span class="n">index</span> <span class="n">by</span><span class="p">[</span><span class="n">I</span><span class="p">]</span> <span class="n">considered</span> <span class="k">as</span> <span class="n">a</span> <span class="n">whole</span><span class="o">.</span>
</pre></div>
</div>
</section>
<section id="functions-proposed">
<h2>Functions proposed<a class="headerlink" href="#functions-proposed" title="Link to this heading">#</a></h2>
<ul class="simple">
<li><p>segment</p></li>
<li><p>edges</p></li>
</ul>
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