[Numpy-discussion] Revised NEP-18, __array_function__ protocol

Hameer Abbasi einstein.edison at gmail.com
Wed Jun 27 02:27:06 EDT 2018

On 27. Jun 2018 at 07:48, Stephan Hoyer <shoyer at gmail.com> wrote:

After much discussion (and the addition of three new co-authors!), I’m
pleased to present a significantly revision of NumPy Enhancement Proposal
18: A dispatch mechanism for NumPy's high level array functions:

The full text is also included below.


A dispatch mechanism for NumPy's high level array functions

:Author: Stephan Hoyer <shoyer at google.com>
:Author: Matthew Rocklin <mrocklin at gmail.com>
:Author: Marten van Kerkwijk <mhvk at astro.utoronto.ca>
:Author: Hameer Abbasi <hameerabbasi at yahoo.com>
:Author: Eric Wieser <wieser.eric at gmail.com>
:Status: Draft
:Type: Standards Track
:Created: 2018-05-29


We propose the ``__array_function__`` 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

Detailed description

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.

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
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

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.

For example, we would like for the following code example to work
equally well with any NumPy-like array object:

.. code:: python

    def f(x):
        y = np.tensordot(x, x.T)
        return np.mean(np.exp(y))

Some of this is possible today with various protocol mechanisms within

-  The ``np.exp`` function checks the ``__array_ufunc__`` protocol
-  The ``.T`` method works using Python's method dispatch
-  The ``np.mean`` function explicitly checks for a ``.mean`` method on
   the argument

However other functions, like ``np.tensordot`` do not dispatch, and
instead are likely to coerce to a NumPy array (using the ``__array__``)
protocol, or err outright. To achieve enough coverage of the NumPy API
to support downstream projects like XArray and autograd we want to
support *almost all* functions within NumPy, which calls for a more
reaching protocol than just ``__array_ufunc__``. 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.


We propose adding support for a new protocol in NumPy,

This protocol is intended to be a catch-all for NumPy functionality that
is not covered by the ``__array_ufunc__`` protocol for universal functions
(like ``np.exp``). The semantics are very similar to ``__array_ufunc__``,
the operation is specified by an arbitrary callable object rather than a
instance and method.

A prototype implementation can be found in
`this notebook <

The interface

We propose the following signature for implementations of

.. code-block:: python

    def __array_function__(self, func, types, args, kwargs)

-  ``func`` is an arbitrary callable exposed by NumPy's public API,
   which was called in the form ``func(*args, **kwargs)``.
-  ``types`` is a ``frozenset`` of unique argument types from the original
   function call that implement ``__array_function__``.
-  The tuple ``args`` and dict ``kwargs`` are directly passed on from the
   original call.

Unlike ``__array_ufunc__``, there are no high-level guarantees about the
type of ``func``, or about which of ``args`` and ``kwargs`` may contain
implementing the array API.

As a convenience for ``__array_function__`` implementors, ``types``
provides all
argument types with an ``'__array_function__'`` attribute. This
allows downstream implementations to quickly determine if they are likely
to support the operation. A ``frozenset`` is used to ensure that
``__array_function__`` implementations cannot rely on the iteration order of
``types``, which would facilitate violating the well-defined "Type casting
hierarchy" described in
`NEP-13 <https://www.numpy.org/neps/nep-0013-ufunc-overrides.html>`_.

Example for a project implementing the NumPy API

Most implementations of ``__array_function__`` will start with two

1.  Is the given function something that we know how to overload?
2.  Are all arguments of a type that we know how to handle?

If these conditions hold, ``__array_function__`` should return
the result from calling its implementation for ``func(*args, **kwargs)``.
Otherwise, it should return the sentinel value ``NotImplemented``,
that the function is not implemented by these types. This is preferable to
raising ``TypeError`` directly, because it gives *other* arguments the
opportunity to define the operations.

There are no general requirements on the return value from
``__array_function__``, although most sensible implementations should
return array(s) with the same type as one of the function's arguments.
If/when Python gains
`typing support for protocols <https://www.python.org/dev/peps/pep-0544/>`_
and NumPy adds static type annotations, the ``@overload`` implementation
for ``SupportsArrayFunction`` will indicate a return type of ``Any``.

It may also be convenient to define a custom decorators (``implements``
for registering ``__array_function__`` implementations.

.. code:: python


    class MyArray:
        def __array_function__(self, func, types, args, kwargs):
            if func not in HANDLED_FUNCTIONS:
                return NotImplemented
            # Note: this allows subclasses that don't override
            # __array_function__ to handle MyArray objects
            if not all(issubclass(t, MyArray) for t in types):
                return NotImplemented
            return HANDLED_FUNCTIONS[func](*args, **kwargs)

    def implements(numpy_function):
        """Register an __array_function__ implementation for MyArray
        def decorator(func):
            HANDLED_FUNCTIONS[numpy_function] = func
            return func
        return decorator

    def concatenate(arrays, axis=0, out=None):
        ...  # implementation of concatenate for MyArray objects

    def broadcast_to(array, shape):
        ...  # implementation of broadcast_to for MyArray objects

Note that it is not required for ``__array_function__`` implementations to
include *all* of the corresponding NumPy function's optional arguments
(e.g., ``broadcast_to`` above omits the irrelevant ``subok`` argument).
Optional arguments are only passed in to ``__array_function__`` if they
were explicitly used in the NumPy function call.

Necessary changes within the NumPy codebase itself

This will require two changes within the NumPy codebase:

1. A function to inspect available inputs, look for the
   ``__array_function__`` 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 `np.concatenate`).

   This is one additional function of moderate complexity.
2. Calling this function within all relevant NumPy functions.

   This affects many parts of the NumPy codebase, although with very low

Finding and calling the right ``__array_function__``

Given a NumPy function, ``*args`` and ``**kwargs`` inputs, we need to
search through ``*args`` and ``**kwargs`` for all appropriate inputs
that might have the ``__array_function__`` attribute. Then we need to
select among those possible methods and execute the right one.
Negotiating between several possible implementations can be complex.

Finding arguments

Valid arguments may be directly in the ``*args`` and ``**kwargs``, such
as in the case for ``np.tensordot(left, right, out=out)``, or they may
be nested within lists or dictionaries, such as in the case of
``np.concatenate([x, y, z])``. This can be problematic for two reasons:

1. Some functions are given long lists of values, and traversing them
   might be prohibitively expensive.
2. Some functions may have arguments that we don't want to inspect, even
   if they have the ``__array_function__`` method.

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
``array_like`` or ``ndarray``.

We propose to do so by writing "dispatcher" functions for each overloaded
NumPy function:

- These functions will be called with the exact same arguments that were
  into the NumPy function (i.e., ``dispatcher(*args, **kwargs)``), and
  return an iterable of arguments to check for overrides.
- Dispatcher functions are required to share the exact same positional,
  optional and keyword-only arguments as their corresponding NumPy
  Otherwise, valid invocations of a NumPy function could result in an error
  calling its dispatcher.
- Because default *values* for keyword arguments do not have
  ``__array_function__`` attributes, by convention we set all default
  values to ``None``. 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.

An example of the dispatcher for ``np.concatenate`` may be instructive:

.. code:: python

    def _concatenate_dispatcher(arrays, axis=None, out=None):
        for array in arrays:
            yield array
        if out is not None:
            yield out

The concatenate dispatcher is written as generator function, which allows it
to potentially include the value of the optional ``out`` argument without
needing to create a new sequence with the (potentially long) list of objects
to be concatenated.

Trying ``__array_function__`` methods until the right one works

Many arguments may implement the ``__array_function__`` 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?

For the most part, the rules for dispatch with ``__array_function__``
match those for ``__array_ufunc__`` (see
`NEP-13 <https://www.numpy.org/neps/nep-0013-ufunc-overrides.html>`_).
In particular:

-  NumPy will gather implementations of ``__array_function__`` 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
   `current behavior <https://bugs.python.org/issue30140>`_ of Python.
-  Implementations of ``__array_function__`` indicate that they can
   handle the operation by returning any value other than
-  If all ``__array_function__`` methods return ``NotImplemented``,
   NumPy will raise ``TypeError``.

One deviation from the current behavior of ``__array_ufunc__`` is that NumPy
will only call ``__array_function__`` on the *first* argument of each unique
type. This matches Python's
`rule for calling reflected methods <
and this ensures that checking overloads has acceptable performance even
there are a large number of overloaded arguments. To avoid long-term
between these two dispatch protocols, we should
`also update <https://github.com/numpy/numpy/issues/11306>`_
``__array_ufunc__`` to match this behavior.

Special handling of ``numpy.ndarray``

The use cases for subclasses with ``__array_function__`` are the same as
with ``__array_ufunc__``, so ``numpy.ndarray`` should also define a
``__array_function__`` method mirroring ``ndarray.__array_ufunc__``:

.. code:: python

    def __array_function__(self, func, types, args, kwargs):
        # Cannot handle items that have __array_function__ other than our
        for t in types:
            if (hasattr(t, '__array_function__') and
                    t.__array_function__ is not ndarray.__array_function__):
                return NotImplemented

        # Arguments contain no overrides, so we can safely call the
        # overloaded function again.
        return func(*args, **kwargs)

To avoid infinite recursion, the dispatch rules for ``__array_function__``
also the same special case they have for ``__array_ufunc__``: any arguments
an ``__array_function__`` method that is identical to
``numpy.ndarray.__array_function__`` are not be called as
``__array_function__`` implementations.

Changes within NumPy functions

Given a function defining the above behavior, for now call it
``try_array_function_override``, 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 ``__array_function__``

In most cases, these functions should written using the
``array_function_dispatch`` decorator, which also associates dispatcher

.. code:: python

    def array_function_dispatch(dispatcher):
        """Wrap a function for dispatch with the __array_function__
        def decorator(func):
            def new_func(*args, **kwargs):
                relevant_arguments = dispatcher(*args, **kwargs)
                success, value = try_array_function_override(
                    new_func, relevant_arguments, args, kwargs)
                if success:
                    return value
                return func(*args, **kwargs)
            return new_func
        return decorator

    # example usage
    def _broadcast_to_dispatcher(array, shape, subok=None,
        return (array,)

    def broadcast_to(array, shape, subok=False):
        ...  # existing definition of np.broadcast_to

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., ``sum`` and ``prod``).
For such functions, the largest change could be adding a few lines to the
docstring to note which arguments are checked for overloads.

It's particularly worth calling out the decorator's use of

- This ensures that the wrapped function has the same name and docstring as
  the wrapped NumPy function.
- On Python 3, it also ensures that the decorator function copies the
  function signature, which is important for introspection based tools such
  auto-complete. If we care about preserving function signatures on Python
  for the `short while longer <
  that NumPy supports Python 2.7, we do could do so by adding a vendored
  dependency on the (single-file, BSD licensed)
  `decorator library <https://github.com/micheles/decorator>`_.
- Finally, it ensures that the wrapped function
  `can be pickled <

In a few cases, it would not make sense to use the
decorator directly, but override implementation in terms of
``try_array_function_override`` should still be straightforward.

- Functions written entirely in C (e.g., ``np.concatenate``) can't use
  decorators, but they could still use a C equivalent of
  ``try_array_function_override``. If performance is not a concern, they
  also be easily wrapped with a small Python wrapper.
- The ``__call__`` method of ``np.vectorize`` can't be decorated with
<p style="margin:0px;font-stretch:normal;font-size:17.4px;line-

NumPy-Discussion mailing list
NumPy-Discussion at python.org

I would like to propose that we use `__array_function` in the following
manner for functions that create arrays:

   - `array_reference` for indicating the “reference array” whose
   `__array_function__` implementation will be called. For example,
   `np.arange(5, array_reference=some_dask_array)`.
   - I use a reference in the design rather than a type because for some
   arrays (such as Dask), chunk sizes or other reference data is needed to
   make this work.

I realise that this is a big design decision, so I welcome any input!

Best Regards,
Hameer Abbasi
Sent from Astro <https://www.helloastro.com> for Mac
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