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272 lines
9.8 KiB
Python
272 lines
9.8 KiB
Python
""".. _dispatch_mechanism:
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Numpy's dispatch mechanism, introduced in numpy version v1.16 is the
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recommended approach for writing custom N-dimensional array containers that are
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compatible with the numpy API and provide custom implementations of numpy
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functionality. Applications include `dask <http://dask.pydata.org>`_ arrays, an
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N-dimensional array distributed across multiple nodes, and `cupy
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<https://docs-cupy.chainer.org/en/stable/>`_ arrays, an N-dimensional array on
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a GPU.
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To get a feel for writing custom array containers, we'll begin with a simple
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example that has rather narrow utility but illustrates the concepts involved.
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>>> import numpy as np
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>>> class DiagonalArray:
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... def __init__(self, N, value):
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... self._N = N
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... self._i = value
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... def __repr__(self):
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... return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
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... def __array__(self):
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... return self._i * np.eye(self._N)
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...
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Our custom array can be instantiated like:
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>>> arr = DiagonalArray(5, 1)
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>>> arr
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DiagonalArray(N=5, value=1)
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We can convert to a numpy array using :func:`numpy.array` or
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:func:`numpy.asarray`, which will call its ``__array__`` method to obtain a
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standard ``numpy.ndarray``.
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>>> np.asarray(arr)
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array([[1., 0., 0., 0., 0.],
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[0., 1., 0., 0., 0.],
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[0., 0., 1., 0., 0.],
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[0., 0., 0., 1., 0.],
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[0., 0., 0., 0., 1.]])
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If we operate on ``arr`` with a numpy function, numpy will again use the
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``__array__`` interface to convert it to an array and then apply the function
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in the usual way.
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>>> np.multiply(arr, 2)
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array([[2., 0., 0., 0., 0.],
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[0., 2., 0., 0., 0.],
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[0., 0., 2., 0., 0.],
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[0., 0., 0., 2., 0.],
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[0., 0., 0., 0., 2.]])
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Notice that the return type is a standard ``numpy.ndarray``.
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>>> type(arr)
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numpy.ndarray
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How can we pass our custom array type through this function? Numpy allows a
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class to indicate that it would like to handle computations in a custom-defined
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way through the interaces ``__array_ufunc__`` and ``__array_function__``. Let's
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take one at a time, starting with ``_array_ufunc__``. This method covers
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:ref:`ufuncs`, a class of functions that includes, for example,
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:func:`numpy.multiply` and :func:`numpy.sin`.
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The ``__array_ufunc__`` receives:
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- ``ufunc``, a function like ``numpy.multiply``
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- ``method``, a string, differentiating between ``numpy.multiply(...)`` and
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variants like ``numpy.multiply.outer``, ``numpy.multiply.accumulate``, and so
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on. For the common case, ``numpy.multiply(...)``, ``method == '__call__'``.
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- ``inputs``, which could be a mixture of different types
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- ``kwargs``, keyword arguments passed to the function
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For this example we will only handle the method ``'__call__``.
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>>> from numbers import Number
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>>> class DiagonalArray:
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... def __init__(self, N, value):
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... self._N = N
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... self._i = value
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... def __repr__(self):
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... return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
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... def __array__(self):
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... return self._i * np.eye(self._N)
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... def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
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... if method == '__call__':
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... N = None
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... scalars = []
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... for input in inputs:
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... if isinstance(input, Number):
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... scalars.append(input)
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... elif isinstance(input, self.__class__):
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... scalars.append(input._i)
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... if N is not None:
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... if N != self._N:
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... raise TypeError("inconsistent sizes")
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... else:
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... N = self._N
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... else:
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... return NotImplemented
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... return self.__class__(N, ufunc(*scalars, **kwargs))
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... else:
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... return NotImplemented
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...
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Now our custom array type passes through numpy functions.
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>>> arr = DiagonalArray(5, 1)
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>>> np.multiply(arr, 3)
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DiagonalArray(N=5, value=3)
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>>> np.add(arr, 3)
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DiagonalArray(N=5, value=4)
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>>> np.sin(arr)
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DiagonalArray(N=5, value=0.8414709848078965)
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At this point ``arr + 3`` does not work.
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>>> arr + 3
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TypeError: unsupported operand type(s) for *: 'DiagonalArray' and 'int'
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To support it, we need to define the Python interfaces ``__add__``, ``__lt__``,
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and so on to dispatch to the corresponding ufunc. We can achieve this
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conveniently by inheriting from the mixin
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:class:`~numpy.lib.mixins.NDArrayOperatorsMixin`.
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>>> import numpy.lib.mixins
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>>> class DiagonalArray(numpy.lib.mixins.NDArrayOperatorsMixin):
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... def __init__(self, N, value):
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... self._N = N
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... self._i = value
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... def __repr__(self):
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... return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
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... def __array__(self):
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... return self._i * np.eye(self._N)
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... def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
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... if method == '__call__':
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... N = None
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... scalars = []
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... for input in inputs:
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... if isinstance(input, Number):
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... scalars.append(input)
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... elif isinstance(input, self.__class__):
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... scalars.append(input._i)
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... if N is not None:
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... if N != self._N:
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... raise TypeError("inconsistent sizes")
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... else:
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... N = self._N
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... else:
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... return NotImplemented
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... return self.__class__(N, ufunc(*scalars, **kwargs))
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... else:
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... return NotImplemented
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...
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>>> arr = DiagonalArray(5, 1)
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>>> arr + 3
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DiagonalArray(N=5, value=4)
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>>> arr > 0
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DiagonalArray(N=5, value=True)
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Now let's tackle ``__array_function__``. We'll create dict that maps numpy
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functions to our custom variants.
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>>> HANDLED_FUNCTIONS = {}
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>>> class DiagonalArray(numpy.lib.mixins.NDArrayOperatorsMixin):
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... def __init__(self, N, value):
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... self._N = N
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... self._i = value
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... def __repr__(self):
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... return f"{self.__class__.__name__}(N={self._N}, value={self._i})"
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... def __array__(self):
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... return self._i * np.eye(self._N)
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... def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
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... if method == '__call__':
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... N = None
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... scalars = []
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... for input in inputs:
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... # In this case we accept only scalar numbers or DiagonalArrays.
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... if isinstance(input, Number):
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... scalars.append(input)
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... elif isinstance(input, self.__class__):
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... scalars.append(input._i)
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... if N is not None:
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... if N != self._N:
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... raise TypeError("inconsistent sizes")
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... else:
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... N = self._N
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... else:
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... return NotImplemented
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... return self.__class__(N, ufunc(*scalars, **kwargs))
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... else:
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... return NotImplemented
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... def __array_function__(self, func, types, args, kwargs):
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... if func not in HANDLED_FUNCTIONS:
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... return NotImplemented
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... # Note: this allows subclasses that don't override
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... # __array_function__ to handle DiagonalArray objects.
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... if not all(issubclass(t, self.__class__) for t in types):
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... return NotImplemented
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... return HANDLED_FUNCTIONS[func](*args, **kwargs)
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...
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A convenient pattern is to define a decorator ``implements`` that can be used
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to add functions to ``HANDLED_FUNCTIONS``.
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>>> def implements(np_function):
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... "Register an __array_function__ implementation for DiagonalArray objects."
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... def decorator(func):
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... HANDLED_FUNCTIONS[np_function] = func
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... return func
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... return decorator
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...
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Now we write implementations of numpy functions for ``DiagonalArray``.
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For completeness, to support the usage ``arr.sum()`` add a method ``sum`` that
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calls ``numpy.sum(self)``, and the same for ``mean``.
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>>> @implements(np.sum)
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... def sum(a):
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... "Implementation of np.sum for DiagonalArray objects"
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... return arr._i * arr._N
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...
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>>> @implements(np.mean)
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... def mean(arr):
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... "Implementation of np.mean for DiagonalArray objects"
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... return arr._i / arr._N
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...
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>>> arr = DiagonalArray(5, 1)
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>>> np.sum(arr)
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5
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>>> np.mean(arr)
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0.2
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If the user tries to use any numpy functions not included in
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``HANDLED_FUNCTIONS``, a ``TypeError`` will be raised by numpy, indicating that
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this operation is not supported. For example, concatenating two
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``DiagonalArrays`` does not produce another diagonal array, so it is not
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supported.
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>>> np.concatenate([arr, arr])
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TypeError: no implementation found for 'numpy.concatenate' on types that implement __array_function__: [<class '__main__.DiagonalArray'>]
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Additionally, our implementations of ``sum`` and ``mean`` do not accept the
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optional arguments that numpy's implementation does.
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>>> np.sum(arr, axis=0)
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TypeError: sum() got an unexpected keyword argument 'axis'
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The user always has the option of converting to a normal ``numpy.ndarray`` with
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:func:`numpy.asarray` and using standard numpy from there.
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>>> np.concatenate([np.asarray(arr), np.asarray(arr)])
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array([[1., 0., 0., 0., 0.],
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[0., 1., 0., 0., 0.],
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[0., 0., 1., 0., 0.],
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[0., 0., 0., 1., 0.],
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[0., 0., 0., 0., 1.],
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[1., 0., 0., 0., 0.],
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[0., 1., 0., 0., 0.],
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[0., 0., 1., 0., 0.],
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[0., 0., 0., 1., 0.],
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[0., 0., 0., 0., 1.]])
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Refer to the `dask source code <https://github.com/dask/dask>`_ and
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`cupy source code <https://github.com/cupy/cupy>`_ for more fully-worked
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examples of custom array containers.
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See also `NEP 18 <http://www.numpy.org/neps/nep-0018-array-function-protocol.html>`_.
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"""
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