""".. _dispatch_mechanism:

Numpy's dispatch mechanism, introduced in numpy version v1.16 is the
recommended approach for writing custom N-dimensional array containers that are
compatible with the numpy API and provide custom implementations of numpy
functionality. Applications include `dask <http://dask.pydata.org>`_ arrays, an
N-dimensional array distributed across multiple nodes, and `cupy
<https://docs-cupy.chainer.org/en/stable/>`_ arrays, an N-dimensional array on
a GPU.

To get a feel for writing custom array containers, we'll begin with a simple
example that has rather narrow utility but illustrates the concepts involved.

>>> import numpy as np
>>> class DiagonalArray:
...     def __init__(self, N, value):
...         self._N = N
...         self._i = value
...     def __repr__(self):
...         return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
...     def __array__(self):
...         return self._i * np.eye(self._N)
...

Our custom array can be instantiated like:

>>> arr = DiagonalArray(5, 1)
>>> arr
DiagonalArray(N=5, value=1)

We can convert to a numpy array using :func:`numpy.array` or
:func:`numpy.asarray`, which will call its ``__array__`` method to obtain a
standard ``numpy.ndarray``.

>>> np.asarray(arr)
array([[1., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0.],
       [0., 0., 1., 0., 0.],
       [0., 0., 0., 1., 0.],
       [0., 0., 0., 0., 1.]])

If we operate on ``arr`` with a numpy function, numpy will again use the
``__array__`` interface to convert it to an array and then apply the function
in the usual way.

>>> np.multiply(arr, 2)
array([[2., 0., 0., 0., 0.],
       [0., 2., 0., 0., 0.],
       [0., 0., 2., 0., 0.],
       [0., 0., 0., 2., 0.],
       [0., 0., 0., 0., 2.]])


Notice that the return type is a standard ``numpy.ndarray``.

>>> type(arr)
numpy.ndarray

How can we pass our custom array type through this function? Numpy allows a
class to indicate that it would like to handle computations in a custom-defined
way through the interaces ``__array_ufunc__`` and ``__array_function__``. Let's
take one at a time, starting with ``_array_ufunc__``. This method covers
:ref:`ufuncs`, a class of functions that includes, for example,
:func:`numpy.multiply` and :func:`numpy.sin`.

The ``__array_ufunc__`` receives:

- ``ufunc``, a function like ``numpy.multiply``
- ``method``, a string, differentiating between ``numpy.multiply(...)`` and
  variants like ``numpy.multiply.outer``, ``numpy.multiply.accumulate``, and so
  on.  For the common case, ``numpy.multiply(...)``, ``method == '__call__'``.
- ``inputs``, which could be a mixture of different types
- ``kwargs``, keyword arguments passed to the function

For this example we will only handle the method ``__call__``.

>>> from numbers import Number
>>> class DiagonalArray:
...     def __init__(self, N, value):
...         self._N = N
...         self._i = value
...     def __repr__(self):
...         return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
...     def __array__(self):
...         return self._i * np.eye(self._N)
...     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
...         if method == '__call__':
...             N = None
...             scalars = []
...             for input in inputs:
...                 if isinstance(input, Number):
...                     scalars.append(input)
...                 elif isinstance(input, self.__class__):
...                     scalars.append(input._i)
...                     if N is not None:
...                         if N != self._N:
...                             raise TypeError("inconsistent sizes")
...                     else:
...                         N = self._N
...                 else:
...                     return NotImplemented
...             return self.__class__(N, ufunc(*scalars, **kwargs))
...         else:
...             return NotImplemented
...

Now our custom array type passes through numpy functions.

>>> arr = DiagonalArray(5, 1)
>>> np.multiply(arr, 3)
DiagonalArray(N=5, value=3)
>>> np.add(arr, 3)
DiagonalArray(N=5, value=4)
>>> np.sin(arr)
DiagonalArray(N=5, value=0.8414709848078965)

At this point ``arr + 3`` does not work.

>>> arr + 3
TypeError: unsupported operand type(s) for *: 'DiagonalArray' and 'int'

To support it, we need to define the Python interfaces ``__add__``, ``__lt__``,
and so on to dispatch to the corresponding ufunc. We can achieve this
conveniently by inheriting from the mixin
:class:`~numpy.lib.mixins.NDArrayOperatorsMixin`.

>>> import numpy.lib.mixins
>>> class DiagonalArray(numpy.lib.mixins.NDArrayOperatorsMixin):
...     def __init__(self, N, value):
...         self._N = N
...         self._i = value
...     def __repr__(self):
...         return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
...     def __array__(self):
...         return self._i * np.eye(self._N)
...     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
...         if method == '__call__':
...             N = None
...             scalars = []
...             for input in inputs:
...                 if isinstance(input, Number):
...                     scalars.append(input)
...                 elif isinstance(input, self.__class__):
...                     scalars.append(input._i)
...                     if N is not None:
...                         if N != self._N:
...                             raise TypeError("inconsistent sizes")
...                     else:
...                         N = self._N
...                 else:
...                     return NotImplemented
...             return self.__class__(N, ufunc(*scalars, **kwargs))
...         else:
...             return NotImplemented
...

>>> arr = DiagonalArray(5, 1)
>>> arr + 3
DiagonalArray(N=5, value=4)
>>> arr > 0
DiagonalArray(N=5, value=True)

Now let's tackle ``__array_function__``. We'll create dict that maps numpy
functions to our custom variants.

>>> HANDLED_FUNCTIONS = {}
>>> class DiagonalArray(numpy.lib.mixins.NDArrayOperatorsMixin):
...     def __init__(self, N, value):
...         self._N = N
...         self._i = value
...     def __repr__(self):
...         return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
...     def __array__(self):
...         return self._i * np.eye(self._N)
...     def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
...         if method == '__call__':
...             N = None
...             scalars = []
...             for input in inputs:
...                 # In this case we accept only scalar numbers or DiagonalArrays.
...                 if isinstance(input, Number):
...                     scalars.append(input)
...                 elif isinstance(input, self.__class__):
...                     scalars.append(input._i)
...                     if N is not None:
...                         if N != self._N:
...                             raise TypeError("inconsistent sizes")
...                     else:
...                         N = self._N
...                 else:
...                     return NotImplemented
...             return self.__class__(N, ufunc(*scalars, **kwargs))
...         else:
...             return NotImplemented
...    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 DiagonalArray objects.
...        if not all(issubclass(t, self.__class__) for t in types):
...            return NotImplemented
...        return HANDLED_FUNCTIONS[func](*args, **kwargs)
...

A convenient pattern is to define a decorator ``implements`` that can be used
to add functions to ``HANDLED_FUNCTIONS``.

>>> def implements(np_function):
...    "Register an __array_function__ implementation for DiagonalArray objects."
...    def decorator(func):
...        HANDLED_FUNCTIONS[np_function] = func
...        return func
...    return decorator
...

Now we write implementations of numpy functions for ``DiagonalArray``.
For completeness, to support the usage ``arr.sum()`` add a method ``sum`` that
calls ``numpy.sum(self)``, and the same for ``mean``.

>>> @implements(np.sum)
... def sum(arr):
...     "Implementation of np.sum for DiagonalArray objects"
...     return arr._i * arr._N
...
>>> @implements(np.mean)
... def mean(arr):
...     "Implementation of np.mean for DiagonalArray objects"
...     return arr._i / arr._N
...
>>> arr = DiagonalArray(5, 1)
>>> np.sum(arr)
5
>>> np.mean(arr)
0.2

If the user tries to use any numpy functions not included in
``HANDLED_FUNCTIONS``, a ``TypeError`` will be raised by numpy, indicating that
this operation is not supported. For example, concatenating two
``DiagonalArrays`` does not produce another diagonal array, so it is not
supported.

>>> np.concatenate([arr, arr])
TypeError: no implementation found for 'numpy.concatenate' on types that implement __array_function__: [<class '__main__.DiagonalArray'>]

Additionally, our implementations of ``sum`` and ``mean`` do not accept the
optional arguments that numpy's implementation does.

>>> np.sum(arr, axis=0)
TypeError: sum() got an unexpected keyword argument 'axis'

The user always has the option of converting to a normal ``numpy.ndarray`` with
:func:`numpy.asarray` and using standard numpy from there.

>>> np.concatenate([np.asarray(arr), np.asarray(arr)])
array([[1., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0.],
       [0., 0., 1., 0., 0.],
       [0., 0., 0., 1., 0.],
       [0., 0., 0., 0., 1.],
       [1., 0., 0., 0., 0.],
       [0., 1., 0., 0., 0.],
       [0., 0., 1., 0., 0.],
       [0., 0., 0., 1., 0.],
       [0., 0., 0., 0., 1.]])

Refer to the `dask source code <https://github.com/dask/dask>`_ and
`cupy source code <https://github.com/cupy/cupy>`_  for more fully-worked
examples of custom array containers.

See also `NEP 18 <http://www.numpy.org/neps/nep-0018-array-function-protocol.html>`_.
"""