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<title>NEP 18 — A dispatch mechanism for NumPy’s high level array functions — NumPy Enhancement Proposals</title>
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<section id="nep-18-a-dispatch-mechanism-for-numpy-s-high-level-array-functions">
<span id="nep18"></span><h1>NEP 18 — A dispatch mechanism for NumPy’s high level array functions<a class="headerlink" href="#nep-18-a-dispatch-mechanism-for-numpy-s-high-level-array-functions" 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>Stephan Hoyer <<a class="reference external" href="mailto:shoyer%40google.com">shoyer<span>@</span>google<span>.</span>com</a>></p>
</dd>
<dt class="field-even">Author<span class="colon">:</span></dt>
<dd class="field-even"><p>Matthew Rocklin <<a class="reference external" href="mailto:mrocklin%40gmail.com">mrocklin<span>@</span>gmail<span>.</span>com</a>></p>
</dd>
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Marten van Kerkwijk <<a class="reference external" href="mailto:mhvk%40astro.utoronto.ca">mhvk<span>@</span>astro<span>.</span>utoronto<span>.</span>ca</a>></p>
</dd>
<dt class="field-even">Author<span class="colon">:</span></dt>
<dd class="field-even"><p>Hameer Abbasi <<a class="reference external" href="mailto:hameerabbasi%40yahoo.com">hameerabbasi<span>@</span>yahoo<span>.</span>com</a>></p>
</dd>
<dt class="field-odd">Author<span class="colon">:</span></dt>
<dd class="field-odd"><p>Eric Wieser <<a class="reference external" href="mailto:wieser.eric%40gmail.com">wieser<span>.</span>eric<span>@</span>gmail<span>.</span>com</a>></p>
</dd>
<dt class="field-even">Status<span class="colon">:</span></dt>
<dd class="field-even"><p>Final</p>
</dd>
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Standards Track</p>
</dd>
<dt class="field-even">Created<span class="colon">:</span></dt>
<dd class="field-even"><p>2018-05-29</p>
</dd>
<dt class="field-odd">Updated<span class="colon">:</span></dt>
<dd class="field-odd"><p>2019-05-25</p>
</dd>
<dt class="field-even">Resolution<span class="colon">:</span></dt>
<dd class="field-even"><p><a class="reference external" href="https://mail.python.org/pipermail/numpy-discussion/2018-August/078493.html">https://mail.python.org/pipermail/numpy-discussion/2018-August/078493.html</a></p>
</dd>
</dl>
<section id="abstract">
<h2>Abstract<a class="headerlink" href="#abstract" title="Link to this heading">#</a></h2>
<p>We propose the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol, to allow arguments of NumPy
functions to define how that function operates on them. This will allow
using NumPy as a high level API for efficient multi-dimensional array
operations, even with array implementations that differ greatly from
<code class="docutils literal notranslate"><span class="pre">numpy.ndarray</span></code>.</p>
</section>
<section id="detailed-description">
<h2>Detailed description<a class="headerlink" href="#detailed-description" title="Link to this heading">#</a></h2>
<p>NumPy’s high level ndarray API has been implemented several times
outside of NumPy itself for different architectures, such as for GPU
arrays (CuPy), Sparse arrays (scipy.sparse, pydata/sparse) and parallel
arrays (Dask array) as well as various NumPy-like implementations in the
deep learning frameworks, like TensorFlow and PyTorch.</p>
<p>Similarly there are many projects that build on top of the NumPy API
for labeled and indexed arrays (XArray), automatic differentiation
(Autograd, Tangent), masked arrays (numpy.ma), physical units (astropy.units,
pint, unyt), etc. that add additional functionality on top of the NumPy API.
Most of these project also implement a close variation of NumPy’s level high
API.</p>
<p>We would like to be able to use these libraries together, for example we
would like to be able to place a CuPy array within XArray, or perform
automatic differentiation on Dask array code. This would be easier to
accomplish if code written for NumPy ndarrays could also be used by
other NumPy-like projects.</p>
<p>For example, we would like for the following code example to work
equally well with any NumPy-like array object:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">f</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
<span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="n">y</span><span class="p">))</span>
</pre></div>
</div>
<p>Some of this is possible today with various protocol mechanisms within
NumPy.</p>
<ul class="simple">
<li><p>The <code class="docutils literal notranslate"><span class="pre">np.exp</span></code> function checks the <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> protocol</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">.T</span></code> method works using Python’s method dispatch</p></li>
<li><p>The <code class="docutils literal notranslate"><span class="pre">np.mean</span></code> function explicitly checks for a <code class="docutils literal notranslate"><span class="pre">.mean</span></code> method on
the argument</p></li>
</ul>
<p>However other functions, like <code class="docutils literal notranslate"><span class="pre">np.tensordot</span></code> do not dispatch, and
instead are likely to coerce to a NumPy array (using the <code class="docutils literal notranslate"><span class="pre">__array__</span></code>)
protocol, or err outright. To achieve enough coverage of the NumPy API
to support downstream projects like XArray and autograd we want to
support <em>almost all</em> functions within NumPy, which calls for a more
reaching protocol than just <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code>. We would like a
protocol that allows arguments of a NumPy function to take control and
divert execution to another function (for example a GPU or parallel
implementation) in a way that is safe and consistent across projects.</p>
</section>
<section id="implementation">
<h2>Implementation<a class="headerlink" href="#implementation" title="Link to this heading">#</a></h2>
<p>We propose adding support for a new protocol in NumPy,
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>.</p>
<p>This protocol is intended to be a catch-all for NumPy functionality that
is not covered by the <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> protocol for universal functions
(like <code class="docutils literal notranslate"><span class="pre">np.exp</span></code>). The semantics are very similar to <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code>, except
the operation is specified by an arbitrary callable object rather than a ufunc
instance and method.</p>
<p>A prototype implementation can be found in
<a class="reference external" href="https://nbviewer.jupyter.org/gist/shoyer/1f0a308a06cd96df20879a1ddb8f0006">this notebook</a>.</p>
<div class="admonition warning">
<p class="admonition-title">Warning</p>
<p>The <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol, and its use on particular functions,
is <em>experimental</em>. We plan to retain an interface that makes it possible
to override NumPy functions, but the way to do so for particular functions
<strong>can and will change</strong> with little warning. If such reduced backwards
compatibility guarantees are not accepted to you, do not rely upon overrides
of NumPy functions for non-NumPy arrays. See “Non-goals” below for more
details.</p>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Dispatch with the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol has been implemented but is
not yet enabled by default:</p>
<ul class="simple">
<li><p>In NumPy 1.16, you need to set the environment variable
<code class="docutils literal notranslate"><span class="pre">NUMPY_EXPERIMENTAL_ARRAY_FUNCTION=1</span></code> before importing NumPy to test
NumPy function overrides.</p></li>
<li><p>In NumPy 1.17, the protocol will be enabled by default, but can be disabled
with <code class="docutils literal notranslate"><span class="pre">NUMPY_EXPERIMENTAL_ARRAY_FUNCTION=0</span></code>.</p></li>
<li><p>Eventually, expect to <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> to always be enabled.</p></li>
</ul>
</div>
<section id="the-interface">
<h3>The interface<a class="headerlink" href="#the-interface" title="Link to this heading">#</a></h3>
<p>We propose the following signature for implementations of
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">__array_function__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
</pre></div>
</div>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">func</span></code> is an arbitrary callable exposed by NumPy’s public API,
which was called in the form <code class="docutils literal notranslate"><span class="pre">func(*args,</span> <span class="pre">**kwargs)</span></code>.</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">types</span></code> is a <a class="reference external" href="https://docs.python.org/3/library/collections.abc.html#collections.abc.Collection">collection</a>
of unique argument types from the original NumPy function call that
implement <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>.</p></li>
<li><p>The tuple <code class="docutils literal notranslate"><span class="pre">args</span></code> and dict <code class="docutils literal notranslate"><span class="pre">kwargs</span></code> are directly passed on from the
original call.</p></li>
</ul>
<p>Unlike <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code>, there are no high-level guarantees about the
type of <code class="docutils literal notranslate"><span class="pre">func</span></code>, or about which of <code class="docutils literal notranslate"><span class="pre">args</span></code> and <code class="docutils literal notranslate"><span class="pre">kwargs</span></code> may contain objects
implementing the array API.</p>
<p>As a convenience for <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> implementers, <code class="docutils literal notranslate"><span class="pre">types</span></code> provides all
argument types with an <code class="docutils literal notranslate"><span class="pre">'__array_function__'</span></code> attribute. This
allows implementers to quickly identify cases where they should defer to
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> implementations on other arguments.
The type of <code class="docutils literal notranslate"><span class="pre">types</span></code> is intentionally vague:
<code class="docutils literal notranslate"><span class="pre">frozenset</span></code> would most closely match intended use, but we may use <code class="docutils literal notranslate"><span class="pre">tuple</span></code>
instead for performance reasons. In any case, <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>
implementations should not rely on the iteration order of <code class="docutils literal notranslate"><span class="pre">types</span></code>, which
would violate a well-defined “Type casting hierarchy” (as described in
<a class="reference internal" href="nep-0013-ufunc-overrides.html#nep13"><span class="std std-ref">NEP-13</span></a>).</p>
</section>
<section id="example-for-a-project-implementing-the-numpy-api">
<h3>Example for a project implementing the NumPy API<a class="headerlink" href="#example-for-a-project-implementing-the-numpy-api" title="Link to this heading">#</a></h3>
<p>Most implementations of <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> will start with two
checks:</p>
<ol class="arabic simple">
<li><p>Is the given function something that we know how to overload?</p></li>
<li><p>Are all arguments of a type that we know how to handle?</p></li>
</ol>
<p>If these conditions hold, <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> should return
the result from calling its implementation for <code class="docutils literal notranslate"><span class="pre">func(*args,</span> <span class="pre">**kwargs)</span></code>.
Otherwise, it should return the sentinel value <code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code>, indicating
that the function is not implemented by these types. This is preferable to
raising <code class="docutils literal notranslate"><span class="pre">TypeError</span></code> directly, because it gives <em>other</em> arguments the
opportunity to define the operations.</p>
<p>There are no general requirements on the return value from
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>, although most sensible implementations should probably
return array(s) with the same type as one of the function’s arguments.
If/when Python gains
<a class="reference external" href="https://www.python.org/dev/peps/pep-0544/">typing support for protocols</a>
and NumPy adds static type annotations, the <code class="docutils literal notranslate"><span class="pre">@overload</span></code> implementation
for <code class="docutils literal notranslate"><span class="pre">SupportsArrayFunction</span></code> will indicate a return type of <code class="docutils literal notranslate"><span class="pre">Any</span></code>.</p>
<p>It may also be convenient to define a custom decorators (<code class="docutils literal notranslate"><span class="pre">implements</span></code> below)
for registering <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> implementations.</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="n">HANDLED_FUNCTIONS</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">class</span><span class="w"> </span><span class="nc">MyArray</span><span class="p">:</span>
<span class="k">def</span><span class="w"> </span><span class="nf">__array_function__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">):</span>
<span class="k">if</span> <span class="n">func</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">HANDLED_FUNCTIONS</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">NotImplemented</span>
<span class="c1"># Note: this allows subclasses that don't override</span>
<span class="c1"># __array_function__ to handle MyArray objects</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">MyArray</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">):</span>
<span class="k">return</span> <span class="bp">NotImplemented</span>
<span class="k">return</span> <span class="n">HANDLED_FUNCTIONS</span><span class="p">[</span><span class="n">func</span><span class="p">](</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">implements</span><span class="p">(</span><span class="n">numpy_function</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Register an __array_function__ implementation for MyArray objects."""</span>
<span class="k">def</span><span class="w"> </span><span class="nf">decorator</span><span class="p">(</span><span class="n">func</span><span class="p">):</span>
<span class="n">HANDLED_FUNCTIONS</span><span class="p">[</span><span class="n">numpy_function</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span>
<span class="k">return</span> <span class="n">func</span>
<span class="k">return</span> <span class="n">decorator</span>
<span class="nd">@implements</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">concatenate</span><span class="p">(</span><span class="n">arrays</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">out</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="o">...</span> <span class="c1"># implementation of concatenate for MyArray objects</span>
<span class="nd">@implements</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">broadcast_to</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">broadcast_to</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="n">shape</span><span class="p">):</span>
<span class="o">...</span> <span class="c1"># implementation of broadcast_to for MyArray objects</span>
</pre></div>
</div>
<p>Note that it is not required for <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> implementations to
include <em>all</em> of the corresponding NumPy function’s optional arguments
(e.g., <code class="docutils literal notranslate"><span class="pre">broadcast_to</span></code> above omits the irrelevant <code class="docutils literal notranslate"><span class="pre">subok</span></code> argument).
Optional arguments are only passed in to <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> if they
were explicitly used in the NumPy function call.</p>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Just like the case for builtin special methods like <code class="docutils literal notranslate"><span class="pre">__add__</span></code>, properly
written <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> methods should always return
<code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code> when an unknown type is encountered. Otherwise, it will
be impossible to correctly override NumPy functions from another object
if the operation also includes one of your objects.</p>
</div>
</section>
<section id="necessary-changes-within-the-numpy-codebase-itself">
<h3>Necessary changes within the NumPy codebase itself<a class="headerlink" href="#necessary-changes-within-the-numpy-codebase-itself" title="Link to this heading">#</a></h3>
<p>This will require two changes within the NumPy codebase:</p>
<ol class="arabic">
<li><p>A function to inspect available inputs, look for the
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> attribute on those inputs, and call those
methods appropriately until one succeeds. This needs to be fast in the
common all-NumPy case, and have acceptable performance (no worse than
linear time) even if the number of overloaded inputs is large (e.g.,
as might be the case for <cite>np.concatenate</cite>).</p>
<p>This is one additional function of moderate complexity.</p>
</li>
<li><p>Calling this function within all relevant NumPy functions.</p>
<p>This affects many parts of the NumPy codebase, although with very low
complexity.</p>
</li>
</ol>
<section id="finding-and-calling-the-right-array-function">
<h4>Finding and calling the right <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code><a class="headerlink" href="#finding-and-calling-the-right-array-function" title="Link to this heading">#</a></h4>
<p>Given a NumPy function, <code class="docutils literal notranslate"><span class="pre">*args</span></code> and <code class="docutils literal notranslate"><span class="pre">**kwargs</span></code> inputs, we need to
search through <code class="docutils literal notranslate"><span class="pre">*args</span></code> and <code class="docutils literal notranslate"><span class="pre">**kwargs</span></code> for all appropriate inputs
that might have the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> attribute. Then we need to
select among those possible methods and execute the right one.
Negotiating between several possible implementations can be complex.</p>
<section id="finding-arguments">
<h5>Finding arguments<a class="headerlink" href="#finding-arguments" title="Link to this heading">#</a></h5>
<p>Valid arguments may be directly in the <code class="docutils literal notranslate"><span class="pre">*args</span></code> and <code class="docutils literal notranslate"><span class="pre">**kwargs</span></code>, such
as in the case for <code class="docutils literal notranslate"><span class="pre">np.tensordot(left,</span> <span class="pre">right,</span> <span class="pre">out=out)</span></code>, or they may
be nested within lists or dictionaries, such as in the case of
<code class="docutils literal notranslate"><span class="pre">np.concatenate([x,</span> <span class="pre">y,</span> <span class="pre">z])</span></code>. This can be problematic for two reasons:</p>
<ol class="arabic simple">
<li><p>Some functions are given long lists of values, and traversing them
might be prohibitively expensive.</p></li>
<li><p>Some functions may have arguments that we don’t want to inspect, even
if they have the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> method.</p></li>
</ol>
<p>To resolve these issues, NumPy functions should explicitly indicate which
of their arguments may be overloaded, and how these arguments should be
checked. As a rule, this should include all arguments documented as either
<code class="docutils literal notranslate"><span class="pre">array_like</span></code> or <code class="docutils literal notranslate"><span class="pre">ndarray</span></code>.</p>
<p>We propose to do so by writing “dispatcher” functions for each overloaded
NumPy function:</p>
<ul class="simple">
<li><p>These functions will be called with the exact same arguments that were passed
into the NumPy function (i.e., <code class="docutils literal notranslate"><span class="pre">dispatcher(*args,</span> <span class="pre">**kwargs)</span></code>), and should
return an iterable of arguments to check for overrides.</p></li>
<li><p>Dispatcher functions are required to share the exact same positional,
optional and keyword-only arguments as their corresponding NumPy functions.
Otherwise, valid invocations of a NumPy function could result in an error when
calling its dispatcher.</p></li>
<li><p>Because default <em>values</em> for keyword arguments do not have
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> attributes, by convention we set all default argument
values to <code class="docutils literal notranslate"><span class="pre">None</span></code>. This reduces the likelihood of signatures falling out
of sync, and minimizes extraneous information in the dispatcher.
The only exception should be cases where the argument value in some way
effects dispatching, which should be rare.</p></li>
</ul>
<p>An example of the dispatcher for <code class="docutils literal notranslate"><span class="pre">np.concatenate</span></code> may be instructive:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">_concatenate_dispatcher</span><span class="p">(</span><span class="n">arrays</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="k">for</span> <span class="n">array</span> <span class="ow">in</span> <span class="n">arrays</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">array</span>
<span class="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">yield</span> <span class="n">out</span>
</pre></div>
</div>
<p>The concatenate dispatcher is written as generator function, which allows it
to potentially include the value of the optional <code class="docutils literal notranslate"><span class="pre">out</span></code> argument without
needing to create a new sequence with the (potentially long) list of objects
to be concatenated.</p>
</section>
<section id="trying-array-function-methods-until-the-right-one-works">
<h5>Trying <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> methods until the right one works<a class="headerlink" href="#trying-array-function-methods-until-the-right-one-works" title="Link to this heading">#</a></h5>
<p>Many arguments may implement the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol. Some
of these may decide that, given the available inputs, they are unable to
determine the correct result. How do we call the right one? If several
are valid then which has precedence?</p>
<p>For the most part, the rules for dispatch with <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>
match those for <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> (see
<a class="reference internal" href="nep-0013-ufunc-overrides.html#nep13"><span class="std std-ref">NEP-13</span></a>).
In particular:</p>
<ul class="simple">
<li><p>NumPy will gather implementations of <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> from all
specified inputs and call them in order: subclasses before
superclasses, and otherwise left to right. Note that in some edge cases
involving subclasses, this differs slightly from the
<a class="reference external" href="https://bugs.python.org/issue30140">current behavior</a> of Python.</p></li>
<li><p>Implementations of <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> indicate that they can
handle the operation by returning any value other than
<code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code>.</p></li>
<li><p>If all <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> methods return <code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code>,
NumPy will raise <code class="docutils literal notranslate"><span class="pre">TypeError</span></code>.</p></li>
</ul>
<p>If no <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> methods exist, NumPy will default to calling its
own implementation, intended for use on NumPy arrays. This case arises, for
example, when all array-like arguments are Python numbers or lists.
(NumPy arrays do have a <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> method, given below, but it
always returns <code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code> if any argument other than a NumPy array
subclass implements <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>.)</p>
<p>One deviation from the current behavior of <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> is that NumPy
will only call <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> on the <em>first</em> argument of each unique
type. This matches Python’s
<a class="reference external" href="https://docs.python.org/3/reference/datamodel.html#object.__ror__">rule for calling reflected methods</a>,
and this ensures that checking overloads has acceptable performance even when
there are a large number of overloaded arguments. To avoid long-term divergence
between these two dispatch protocols, we should
<a class="reference external" href="https://github.com/numpy/numpy/issues/11306">also update</a>
<code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> to match this behavior.</p>
</section>
<section id="the-array-function-method-on-numpy-ndarray">
<h5>The <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> method on <code class="docutils literal notranslate"><span class="pre">numpy.ndarray</span></code><a class="headerlink" href="#the-array-function-method-on-numpy-ndarray" title="Link to this heading">#</a></h5>
<p>The use cases for subclasses with <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> are the same as those
with <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code>, so <code class="docutils literal notranslate"><span class="pre">numpy.ndarray</span></code> also defines a
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> method:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">__array_function__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">types</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">):</span>
<span class="k">if</span> <span class="ow">not</span> <span class="nb">all</span><span class="p">(</span><span class="nb">issubclass</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">ndarray</span><span class="p">)</span> <span class="k">for</span> <span class="n">t</span> <span class="ow">in</span> <span class="n">types</span><span class="p">):</span>
<span class="c1"># Defer to any non-subclasses that implement __array_function__</span>
<span class="k">return</span> <span class="bp">NotImplemented</span>
<span class="c1"># Use NumPy's private implementation without __array_function__</span>
<span class="c1"># dispatching</span>
<span class="k">return</span> <span class="n">func</span><span class="o">.</span><span class="n">_implementation</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
</pre></div>
</div>
<p>This method matches NumPy’s dispatching rules, so for most part it is
possible to pretend that <code class="docutils literal notranslate"><span class="pre">ndarray.__array_function__</span></code> does not exist.
The private <code class="docutils literal notranslate"><span class="pre">_implementation</span></code> attribute, defined below in the
<code class="docutils literal notranslate"><span class="pre">array_function_dispatch</span></code> decorator, allows us to avoid the special cases for
NumPy arrays that were needed in the <code class="docutils literal notranslate"><span class="pre">__array_ufunc__</span></code> protocol.</p>
<p>The <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol always calls subclasses before
superclasses, so if any <code class="docutils literal notranslate"><span class="pre">ndarray</span></code> subclasses are involved in an operation,
they will get the chance to override it, just as if any other argument
overrides <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>. But the default behavior in an operation
that combines a base NumPy array and a subclass is different: if the subclass
returns <code class="docutils literal notranslate"><span class="pre">NotImplemented</span></code>, NumPy’s implementation of the function will be
called instead of raising an exception. This is appropriate since subclasses
are <a class="reference external" href="https://en.wikipedia.org/wiki/Liskov_substitution_principle">expected to be substitutable</a>.</p>
<p>We still caution authors of subclasses to exercise caution when relying
upon details of NumPy’s internal implementations. It is not always possible to
write a perfectly substitutable ndarray subclass, e.g., in cases involving the
creation of new arrays, not least because NumPy makes use of internal
optimizations specialized to base NumPy arrays, e.g., code written in C. Even
if NumPy’s implementation happens to work today, it may not work in the future.
In these cases, your recourse is to re-implement top-level NumPy functions via
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> on your subclass.</p>
</section>
</section>
<section id="changes-within-numpy-functions">
<h4>Changes within NumPy functions<a class="headerlink" href="#changes-within-numpy-functions" title="Link to this heading">#</a></h4>
<p>Given a function defining the above behavior, for now call it
<code class="docutils literal notranslate"><span class="pre">implement_array_function</span></code>, we now need to call that
function from within every relevant NumPy function. This is a pervasive change,
but of fairly simple and innocuous code that should complete quickly and
without effect if no arguments implement the <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>
protocol.</p>
<p>To achieve this, we define a <code class="docutils literal notranslate"><span class="pre">array_function_dispatch</span></code> decorator to rewrite
NumPy functions. The basic implementation is as follows:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">array_function_dispatch</span><span class="p">(</span><span class="n">dispatcher</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="w"> </span><span class="sd">"""Wrap a function for dispatch with the __array_function__ protocol."""</span>
<span class="k">def</span><span class="w"> </span><span class="nf">decorator</span><span class="p">(</span><span class="n">implementation</span><span class="p">):</span>
<span class="nd">@functools</span><span class="o">.</span><span class="n">wraps</span><span class="p">(</span><span class="n">implementation</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">public_api</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
<span class="n">relevant_args</span> <span class="o">=</span> <span class="n">dispatcher</span><span class="p">(</span><span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
<span class="k">return</span> <span class="n">implement_array_function</span><span class="p">(</span>
<span class="n">implementation</span><span class="p">,</span> <span class="n">public_api</span><span class="p">,</span> <span class="n">relevant_args</span><span class="p">,</span> <span class="n">args</span><span class="p">,</span> <span class="n">kwargs</span><span class="p">)</span>
<span class="k">if</span> <span class="n">module</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="n">public_api</span><span class="o">.</span><span class="vm">__module__</span> <span class="o">=</span> <span class="n">module</span>
<span class="c1"># for ndarray.__array_function__</span>
<span class="n">public_api</span><span class="o">.</span><span class="n">_implementation</span> <span class="o">=</span> <span class="n">implementation</span>
<span class="k">return</span> <span class="n">public_api</span>
<span class="k">return</span> <span class="n">decorator</span>
<span class="c1"># example usage</span>
<span class="k">def</span><span class="w"> </span><span class="nf">_broadcast_to_dispatcher</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">subok</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">return</span> <span class="p">(</span><span class="n">array</span><span class="p">,)</span>
<span class="nd">@array_function_dispatch</span><span class="p">(</span><span class="n">_broadcast_to_dispatcher</span><span class="p">,</span> <span class="n">module</span><span class="o">=</span><span class="s1">'numpy'</span><span class="p">)</span>
<span class="k">def</span><span class="w"> </span><span class="nf">broadcast_to</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">subok</span><span class="o">=</span><span class="kc">False</span><span class="p">):</span>
<span class="o">...</span> <span class="c1"># existing definition of np.broadcast_to</span>
</pre></div>
</div>
<p>Using a decorator is great! We don’t need to change the definitions of
existing NumPy functions, and only need to write a few additional lines
for the dispatcher function. We could even reuse a single dispatcher for
families of functions with the same signature (e.g., <code class="docutils literal notranslate"><span class="pre">sum</span></code> and <code class="docutils literal notranslate"><span class="pre">prod</span></code>).
For such functions, the largest change could be adding a few lines to the
docstring to note which arguments are checked for overloads.</p>
<p>It’s particularly worth calling out the decorator’s use of
<code class="docutils literal notranslate"><span class="pre">functools.wraps</span></code>:</p>
<ul class="simple">
<li><p>This ensures that the wrapped function has the same name and docstring as
the wrapped NumPy function.</p></li>
<li><p>On Python 3, it also ensures that the decorator function copies the original
function signature, which is important for introspection based tools such as
auto-complete.</p></li>
<li><p>Finally, it ensures that the wrapped function
<a class="reference external" href="http://gael-varoquaux.info/programming/decoration-in-python-done-right-decorating-and-pickling.html">can be pickled</a>.</p></li>
</ul>
<p>The example usage illustrates several best practices for writing dispatchers
relevant to NumPy contributors:</p>
<ul>
<li><p>We passed the <code class="docutils literal notranslate"><span class="pre">module</span></code> argument, which in turn sets the <code class="docutils literal notranslate"><span class="pre">__module__</span></code>
attribute on the generated function. This is for the benefit of better error
messages, here for errors raised internally by NumPy when no implementation
is found, e.g.,
<code class="docutils literal notranslate"><span class="pre">TypeError:</span> <span class="pre">no</span> <span class="pre">implementation</span> <span class="pre">found</span> <span class="pre">for</span> <span class="pre">'numpy.broadcast_to'</span></code>. Setting
<code class="docutils literal notranslate"><span class="pre">__module__</span></code> to the canonical location in NumPy’s public API encourages
users to use NumPy’s public API for identifying functions in
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>.</p></li>
<li><p>The dispatcher is a function that returns a tuple, rather than an equivalent
(and equally valid) generator using <code class="docutils literal notranslate"><span class="pre">yield</span></code>:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="c1"># example usage</span>
<span class="k">def</span><span class="w"> </span><span class="nf">broadcast_to</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">subok</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
<span class="k">yield</span> <span class="n">array</span>
</pre></div>
</div>
<p>This is no accident: NumPy’s implementation of dispatch for
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> is fastest when dispatcher functions return a builtin
sequence type (<code class="docutils literal notranslate"><span class="pre">tuple</span></code> or <code class="docutils literal notranslate"><span class="pre">list</span></code>).</p>
<p>On a related note, it’s perfectly fine for dispatchers to return arguments
even if in some cases you <em>know</em> that they cannot have an
<code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> method. This can arise for functions with default
arguments (e.g., <code class="docutils literal notranslate"><span class="pre">None</span></code>) or complex signatures. NumPy’s dispatching logic
sorts out these cases very quickly, so it generally is not worth the trouble
of parsing them on your own.</p>
</li>
</ul>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>The code for <code class="docutils literal notranslate"><span class="pre">array_function_dispatch</span></code> above has been updated from the
original version of this NEP to match the actual
<a class="reference external" href="https://github.com/numpy/numpy/blob/e104f03ac8f65ae5b92a9b413b0fa639f39e6de2/numpy/core/overrides.py">implementation in NumPy</a>.</p>
</div>
</section>
</section>
<section id="extensibility">
<h3>Extensibility<a class="headerlink" href="#extensibility" title="Link to this heading">#</a></h3>
<p>An important virtue of this approach is that it allows for adding new
optional arguments to NumPy functions without breaking code that already
relies on <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code>.</p>
<p>This is not a theoretical concern. NumPy’s older, haphazard implementation of
overrides <em>within</em> functions like <code class="docutils literal notranslate"><span class="pre">np.sum()</span></code> necessitated some awkward
gymnastics when we decided to add new optional arguments, e.g., the new
<code class="docutils literal notranslate"><span class="pre">keepdims</span></code> argument is only passed in cases where it is used:</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">sum</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="o">...</span><span class="p">,</span> <span class="n">keepdims</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">_NoValue</span><span class="p">):</span>
<span class="n">kwargs</span> <span class="o">=</span> <span class="p">{}</span>
<span class="k">if</span> <span class="n">keepdims</span> <span class="ow">is</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">_NoValue</span><span class="p">:</span>
<span class="n">kwargs</span><span class="p">[</span><span class="s1">'keepdims'</span><span class="p">]</span> <span class="o">=</span> <span class="n">keepdims</span>
<span class="k">return</span> <span class="n">array</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="o">...</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
</pre></div>
</div>
<p>For <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> implementers, this also means that it is possible
to implement even existing optional arguments incrementally, and only in cases
where it makes sense. For example, a library implementing immutable arrays
would not be required to explicitly include an unsupported <code class="docutils literal notranslate"><span class="pre">out</span></code> argument in
the function signature. This can be somewhat onerous to implement properly,
e.g.,</p>
<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="k">def</span><span class="w"> </span><span class="nf">my_sum</span><span class="p">(</span><span class="n">array</span><span class="p">,</span> <span class="o">...</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="k">if</span> <span class="n">out</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
<span class="k">raise</span> <span class="ne">TypeError</span><span class="p">(</span><span class="s1">'out argument is not supported'</span><span class="p">)</span>
<span class="o">...</span>
</pre></div>
</div>
<p>We thus avoid encouraging the tempting shortcut of adding catch-all
<code class="docutils literal notranslate"><span class="pre">**ignored_kwargs</span></code> to the signatures of functions called by NumPy, which fails
silently for misspelled or ignored arguments.</p>
</section>
<section id="performance">
<h3>Performance<a class="headerlink" href="#performance" title="Link to this heading">#</a></h3>
<p>Performance is always a concern with NumPy, even though NumPy users have
already prioritized usability over pure speed with their choice of the Python
language itself. It’s important that this new <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol
not impose a significant cost in the typical case of NumPy functions acting
on NumPy arrays.</p>
<p>Our <a class="reference external" href="https://nbviewer.jupyter.org/gist/shoyer/1f0a308a06cd96df20879a1ddb8f0006">microbenchmark results</a>
show that a pure Python implementation of the override machinery described
above adds roughly 2-3 microseconds of overhead to each NumPy function call
without any overloaded arguments. For context, typical NumPy functions on small
arrays have a runtime of 1-10 microseconds, mostly determined by what fraction
of the function’s logic is written in C. For example, one microsecond is about
the difference in speed between the <code class="docutils literal notranslate"><span class="pre">ndarray.sum()</span></code> method (1.6 us) and
<code class="docutils literal notranslate"><span class="pre">numpy.sum()</span></code> function (2.6 us).</p>
<p>Fortunately, we expect significantly less overhead with a C implementation of
<code class="docutils literal notranslate"><span class="pre">implement_array_function</span></code>, which is where the bulk of the
runtime is. This would leave the <code class="docutils literal notranslate"><span class="pre">array_function_dispatch</span></code> decorator and
dispatcher function on their own adding about 0.5 microseconds of overhead,
for perhaps ~1 microsecond of overhead in the typical case.</p>
<p>In our view, this level of overhead is reasonable to accept for code written
in Python. We’re pretty sure that the vast majority of NumPy users aren’t
concerned about performance differences measured in microsecond(s) on NumPy
functions, because it’s difficult to do <em>anything</em> in Python in less than a
microsecond.</p>
</section>
<section id="use-outside-of-numpy">
<h3>Use outside of NumPy<a class="headerlink" href="#use-outside-of-numpy" title="Link to this heading">#</a></h3>
<p>Nothing about this protocol that is particular to NumPy itself. Should
we encourage use of the same <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> protocol third-party
libraries for overloading non-NumPy functions, e.g., for making
array-implementation generic functionality in SciPy?</p>
<p>This would offer significant advantages (SciPy wouldn’t need to invent
its own dispatch system) and no downsides that we can think of, because
every function that dispatches with <code class="docutils literal notranslate"><span class="pre">__array_function__</span></code> already needs
to be explicitly recognized. Libraries like Dask, CuPy, and Autograd
already wrap a limited subset of SciPy functionality (e.g.,
<code class="docutils literal notranslate"><span class="pre">scipy.linalg</span></code>) similarly to how they wrap NumPy.</p>
<p>If we want to do this, we should expose at least the decorator
<code class="docutils literal notranslate"><span class="pre">array_function_dispatch()</span></code> and possibly also the lower level
<code class="docutils literal notranslate"><span class="pre">implement_array_function()</span></code> as part of NumPy’s public API.</p>
</section>