mirror of
https://github.com/PiBrewing/craftbeerpi4.git
synced 2024-11-27 17:28:02 +01:00
272 lines
9.8 KiB
Python
272 lines
9.8 KiB
Python
|
""".. _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 interfaces ``__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>`_.
|
||
|
|
"""
|