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<section id="putting-the-inner-loop-in-cython">
<h1>Putting the inner loop in Cython<a class="headerlink" href="#putting-the-inner-loop-in-cython" title="Link to this heading">#</a></h1>
<p>Those who want really good performance out of their low level operations
should strongly consider directly using the iteration API provided
in C, but for those who are not comfortable with C or C++, Cython
is a good middle ground with reasonable performance tradeoffs. For
the <a class="reference internal" href="generated/numpy.nditer.html#numpy.nditer" title="numpy.nditer"><code class="xref py py-class docutils literal notranslate"><span class="pre">nditer</span></code></a> object, this means letting the iterator take care
of broadcasting, dtype conversion, and buffering, while giving the inner
loop to Cython.</p>
<p>For our example, we’ll create a sum of squares function. To start,
let’s implement this function in straightforward Python. We want to
support an ‘axis’ parameter similar to the numpy <a class="reference external" href="https://docs.python.org/3/library/functions.html#sum" title="(in Python v3.13)"><code class="xref py py-func docutils literal notranslate"><span class="pre">sum</span></code></a> function,
so we will need to construct a list for the <em class="xref py py-obj">op_axes</em> parameter.
Here’s how this looks.</p>
<div class="admonition-example admonition">
<p class="admonition-title">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="k">def</span><span class="w"> </span><span class="nf">axis_to_axeslist</span><span class="p">(</span><span class="n">axis</span><span class="p">,</span> <span class="n">ndim</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">if</span> <span class="n">axis</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">return</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">ndim</span>
<span class="gp">... </span> <span class="k">else</span><span class="p">:</span>
<span class="gp">... </span> <span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">axis</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">tuple</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">axis</span> <span class="o">=</span> <span class="p">(</span><span class="n">axis</span><span class="p">,)</span>
<span class="gp">... </span> <span class="n">axeslist</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">ndim</span>
<span class="gp">... </span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">axis</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="gp">... </span> <span class="n">ax</span> <span class="o">=</span> <span class="mi">0</span>
<span class="gp">... </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="n">ndim</span><span class="p">):</span>
<span class="gp">... </span> <span class="k">if</span> <span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">ax</span>
<span class="gp">... </span> <span class="n">ax</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">axeslist</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="k">def</span><span class="w"> </span><span class="nf">sum_squares_py</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">axis</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="gp">... </span> <span class="n">axeslist</span> <span class="o">=</span> <span class="n">axis_to_axeslist</span><span class="p">(</span><span class="n">axis</span><span class="p">,</span> <span class="n">arr</span><span class="o">.</span><span class="n">ndim</span><span class="p">)</span>
<span class="gp">... </span> <span class="n">it</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nditer</span><span class="p">([</span><span class="n">arr</span><span class="p">,</span> <span class="n">out</span><span class="p">],</span> <span class="n">flags</span><span class="o">=</span><span class="p">[</span><span class="s1">'reduce_ok'</span><span class="p">,</span>
<span class="gp">... </span> <span class="s1">'buffered'</span><span class="p">,</span> <span class="s1">'delay_bufalloc'</span><span class="p">],</span>
<span class="gp">... </span> <span class="n">op_flags</span><span class="o">=</span><span class="p">[[</span><span class="s1">'readonly'</span><span class="p">],</span> <span class="p">[</span><span class="s1">'readwrite'</span><span class="p">,</span> <span class="s1">'allocate'</span><span class="p">]],</span>
<span class="gp">... </span> <span class="n">op_axes</span><span class="o">=</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="n">axeslist</span><span class="p">],</span>
<span class="gp">... </span> <span class="n">op_dtypes</span><span class="o">=</span><span class="p">[</span><span class="s1">'float64'</span><span class="p">,</span> <span class="s1">'float64'</span><span class="p">])</span>
<span class="gp">... </span> <span class="k">with</span> <span class="n">it</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">it</span><span class="o">.</span><span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="o">...</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="gp">... </span> <span class="n">it</span><span class="o">.</span><span class="n">reset</span><span class="p">()</span>
<span class="gp">... </span> <span class="k">for</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">it</span><span class="p">:</span>
<span class="gp">... </span> <span class="n">y</span><span class="p">[</span><span class="o">...</span><span class="p">]</span> <span class="o">+=</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span>
<span class="gp">... </span> <span class="k">return</span> <span class="n">it</span><span class="o">.</span><span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
<span class="gp">...</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sum_squares_py</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">array(55.)</span>
<span class="gp">>>> </span><span class="n">sum_squares_py</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">array([ 5., 50.])</span>
</pre></div>
</div>
</div>
<p>To Cython-ize this function, we replace the inner loop (y[…] += x*x) with
Cython code that’s specialized for the float64 dtype. With the
‘external_loop’ flag enabled, the arrays provided to the inner loop will
always be one-dimensional, so very little checking needs to be done.</p>
<p>Here’s the listing of sum_squares.pyx:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span><span class="w"> </span><span class="nn">numpy</span><span class="w"> </span><span class="k">as</span><span class="w"> </span><span class="nn">np</span>
<span class="n">cimport</span> <span class="n">numpy</span> <span class="k">as</span> <span class="n">np</span>
<span class="n">cimport</span> <span class="n">cython</span>
<span class="k">def</span><span class="w"> </span><span class="nf">axis_to_axeslist</span><span class="p">(</span><span class="n">axis</span><span class="p">,</span> <span class="n">ndim</span><span class="p">):</span>
<span class="k">if</span> <span class="n">axis</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">return</span> <span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">ndim</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">axis</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="nb">tuple</span><span class="p">:</span>
<span class="n">axis</span> <span class="o">=</span> <span class="p">(</span><span class="n">axis</span><span class="p">,)</span>
<span class="n">axeslist</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">ndim</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">axis</span><span class="p">:</span>
<span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="mi">1</span>
<span class="n">ax</span> <span class="o">=</span> <span class="mi">0</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="n">ndim</span><span class="p">):</span>
<span class="k">if</span> <span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">!=</span> <span class="o">-</span><span class="mi">1</span><span class="p">:</span>
<span class="n">axeslist</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">ax</span>
<span class="n">ax</span> <span class="o">+=</span> <span class="mi">1</span>
<span class="k">return</span> <span class="n">axeslist</span>
<span class="nd">@cython</span><span class="o">.</span><span class="n">boundscheck</span><span class="p">(</span><span class="kc">False</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">sum_squares_cy</span><span class="p">(</span><span class="n">arr</span><span class="p">,</span> <span class="n">axis</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">cdef</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">[</span><span class="n">double</span><span class="p">]</span> <span class="n">x</span>
<span class="n">cdef</span> <span class="n">np</span><span class="o">.</span><span class="n">ndarray</span><span class="p">[</span><span class="n">double</span><span class="p">]</span> <span class="n">y</span>
<span class="n">cdef</span> <span class="nb">int</span> <span class="n">size</span>
<span class="n">cdef</span> <span class="n">double</span> <span class="n">value</span>
<span class="n">axeslist</span> <span class="o">=</span> <span class="n">axis_to_axeslist</span><span class="p">(</span><span class="n">axis</span><span class="p">,</span> <span class="n">arr</span><span class="o">.</span><span class="n">ndim</span><span class="p">)</span>
<span class="n">it</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">nditer</span><span class="p">([</span><span class="n">arr</span><span class="p">,</span> <span class="n">out</span><span class="p">],</span> <span class="n">flags</span><span class="o">=</span><span class="p">[</span><span class="s1">'reduce_ok'</span><span class="p">,</span> <span class="s1">'external_loop'</span><span class="p">,</span>
<span class="s1">'buffered'</span><span class="p">,</span> <span class="s1">'delay_bufalloc'</span><span class="p">],</span>
<span class="n">op_flags</span><span class="o">=</span><span class="p">[[</span><span class="s1">'readonly'</span><span class="p">],</span> <span class="p">[</span><span class="s1">'readwrite'</span><span class="p">,</span> <span class="s1">'allocate'</span><span class="p">]],</span>
<span class="n">op_axes</span><span class="o">=</span><span class="p">[</span><span class="kc">None</span><span class="p">,</span> <span class="n">axeslist</span><span class="p">],</span>
<span class="n">op_dtypes</span><span class="o">=</span><span class="p">[</span><span class="s1">'float64'</span><span class="p">,</span> <span class="s1">'float64'</span><span class="p">])</span>
<span class="k">with</span> <span class="n">it</span><span class="p">:</span>
<span class="n">it</span><span class="o">.</span><span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="o">...</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">it</span><span class="o">.</span><span class="n">reset</span><span class="p">()</span>
<span class="k">for</span> <span class="n">xarr</span><span class="p">,</span> <span class="n">yarr</span> <span class="ow">in</span> <span class="n">it</span><span class="p">:</span>
<span class="n">x</span> <span class="o">=</span> <span class="n">xarr</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">yarr</span>
<span class="n">size</span> <span class="o">=</span> <span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</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="n">size</span><span class="p">):</span>
<span class="n">value</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
<span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">value</span> <span class="o">*</span> <span class="n">value</span>
<span class="k">return</span> <span class="n">it</span><span class="o">.</span><span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
</pre></div>
</div>
<p>On this machine, building the .pyx file into a module looked like the
following, but you may have to find some Cython tutorials to tell you
the specifics for your system configuration.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>$ cython sum_squares.pyx
$ gcc -shared -pthread -fPIC -fwrapv -O2 -Wall -I/usr/include/python2.7 -fno-strict-aliasing -o sum_squares.so sum_squares.c
</pre></div>
</div>
<p>Running this from the Python interpreter produces the same answers
as our native Python/NumPy code did.</p>
<div class="admonition-example admonition">
<p class="admonition-title">Example</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">sum_squares</span><span class="w"> </span><span class="kn">import</span> <span class="n">sum_squares_cy</span>
<span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sum_squares_cy</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="go">array(55.0)</span>
<span class="gp">>>> </span><span class="n">sum_squares_cy</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">array([ 5., 50.])</span>
</pre></div>
</div>
</div>
<p>Doing a little timing in IPython shows that the reduced overhead and
memory allocation of the Cython inner loop is providing a very nice
speedup over both the straightforward Python code and an expression
using NumPy’s built-in sum function.:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1000</span><span class="p">,</span><span class="mi">1000</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">timeit</span> <span class="n">sum_squares_py</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">10 loops, best of 3: 37.1 ms per loop</span>
<span class="gp">>>> </span><span class="n">timeit</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">a</span><span class="o">*</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">10 loops, best of 3: 20.9 ms per loop</span>
<span class="gp">>>> </span><span class="n">timeit</span> <span class="n">sum_squares_cy</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span>
<span class="go">100 loops, best of 3: 11.8 ms per loop</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">sum_squares_cy</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">a</span><span class="o">*</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">))</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">sum_squares_py</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">)</span> <span class="o">==</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">a</span><span class="o">*</span><span class="n">a</span><span class="p">,</span> <span class="n">axis</span><span class="o">=-</span><span class="mi">1</span><span class="p">))</span>
<span class="go">True</span>
</pre></div>
</div>
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