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+"""Mixin classes for custom array types that don't inherit from ndarray."""
+from __future__ import division, absolute_import, print_function
+
+import sys
+
+from numpy.core import umath as um
+
+# Nothing should be exposed in the top-level NumPy module.
+__all__ = []
+
+
+def _disables_array_ufunc(obj):
+ """True when __array_ufunc__ is set to None."""
+ try:
+ return obj.__array_ufunc__ is None
+ except AttributeError:
+ return False
+
+
+def _binary_method(ufunc, name):
+ """Implement a forward binary method with a ufunc, e.g., __add__."""
+ def func(self, other):
+ if _disables_array_ufunc(other):
+ return NotImplemented
+ return ufunc(self, other)
+ func.__name__ = '__{}__'.format(name)
+ return func
+
+
+def _reflected_binary_method(ufunc, name):
+ """Implement a reflected binary method with a ufunc, e.g., __radd__."""
+ def func(self, other):
+ if _disables_array_ufunc(other):
+ return NotImplemented
+ return ufunc(other, self)
+ func.__name__ = '__r{}__'.format(name)
+ return func
+
+
+def _inplace_binary_method(ufunc, name):
+ """Implement an in-place binary method with a ufunc, e.g., __iadd__."""
+ def func(self, other):
+ return ufunc(self, other, out=(self,))
+ func.__name__ = '__i{}__'.format(name)
+ return func
+
+
+def _numeric_methods(ufunc, name):
+ """Implement forward, reflected and inplace binary methods with a ufunc."""
+ return (_binary_method(ufunc, name),
+ _reflected_binary_method(ufunc, name),
+ _inplace_binary_method(ufunc, name))
+
+
+def _unary_method(ufunc, name):
+ """Implement a unary special method with a ufunc."""
+ def func(self):
+ return ufunc(self)
+ func.__name__ = '__{}__'.format(name)
+ return func
+
+
+class NDArrayOperatorsMixin(object):
+ """Mixin defining all operator special methods using __array_ufunc__.
+
+ This class implements the special methods for almost all of Python's
+ builtin operators defined in the `operator` module, including comparisons
+ (``==``, ``>``, etc.) and arithmetic (``+``, ``*``, ``-``, etc.), by
+ deferring to the ``__array_ufunc__`` method, which subclasses must
+ implement.
+
+ It is useful for writing classes that do not inherit from `numpy.ndarray`,
+ but that should support arithmetic and numpy universal functions like
+ arrays as described in `A Mechanism for Overriding Ufuncs
+ <../../neps/nep-0013-ufunc-overrides.html>`_.
+
+ As an trivial example, consider this implementation of an ``ArrayLike``
+ class that simply wraps a NumPy array and ensures that the result of any
+ arithmetic operation is also an ``ArrayLike`` object::
+
+ class ArrayLike(np.lib.mixins.NDArrayOperatorsMixin):
+ def __init__(self, value):
+ self.value = np.asarray(value)
+
+ # One might also consider adding the built-in list type to this
+ # list, to support operations like np.add(array_like, list)
+ _HANDLED_TYPES = (np.ndarray, numbers.Number)
+
+ def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+ out = kwargs.get('out', ())
+ for x in inputs + out:
+ # Only support operations with instances of _HANDLED_TYPES.
+ # Use ArrayLike instead of type(self) for isinstance to
+ # allow subclasses that don't override __array_ufunc__ to
+ # handle ArrayLike objects.
+ if not isinstance(x, self._HANDLED_TYPES + (ArrayLike,)):
+ return NotImplemented
+
+ # Defer to the implementation of the ufunc on unwrapped values.
+ inputs = tuple(x.value if isinstance(x, ArrayLike) else x
+ for x in inputs)
+ if out:
+ kwargs['out'] = tuple(
+ x.value if isinstance(x, ArrayLike) else x
+ for x in out)
+ result = getattr(ufunc, method)(*inputs, **kwargs)
+
+ if type(result) is tuple:
+ # multiple return values
+ return tuple(type(self)(x) for x in result)
+ elif method == 'at':
+ # no return value
+ return None
+ else:
+ # one return value
+ return type(self)(result)
+
+ def __repr__(self):
+ return '%s(%r)' % (type(self).__name__, self.value)
+
+ In interactions between ``ArrayLike`` objects and numbers or numpy arrays,
+ the result is always another ``ArrayLike``:
+
+ >>> x = ArrayLike([1, 2, 3])
+ >>> x - 1
+ ArrayLike(array([0, 1, 2]))
+ >>> 1 - x
+ ArrayLike(array([ 0, -1, -2]))
+ >>> np.arange(3) - x
+ ArrayLike(array([-1, -1, -1]))
+ >>> x - np.arange(3)
+ ArrayLike(array([1, 1, 1]))
+
+ Note that unlike ``numpy.ndarray``, ``ArrayLike`` does not allow operations
+ with arbitrary, unrecognized types. This ensures that interactions with
+ ArrayLike preserve a well-defined casting hierarchy.
+
+ .. versionadded:: 1.13
+ """
+ # Like np.ndarray, this mixin class implements "Option 1" from the ufunc
+ # overrides NEP.
+
+ # comparisons don't have reflected and in-place versions
+ __lt__ = _binary_method(um.less, 'lt')
+ __le__ = _binary_method(um.less_equal, 'le')
+ __eq__ = _binary_method(um.equal, 'eq')
+ __ne__ = _binary_method(um.not_equal, 'ne')
+ __gt__ = _binary_method(um.greater, 'gt')
+ __ge__ = _binary_method(um.greater_equal, 'ge')
+
+ # numeric methods
+ __add__, __radd__, __iadd__ = _numeric_methods(um.add, 'add')
+ __sub__, __rsub__, __isub__ = _numeric_methods(um.subtract, 'sub')
+ __mul__, __rmul__, __imul__ = _numeric_methods(um.multiply, 'mul')
+ __matmul__, __rmatmul__, __imatmul__ = _numeric_methods(
+ um.matmul, 'matmul')
+ if sys.version_info.major < 3:
+ # Python 3 uses only __truediv__ and __floordiv__
+ __div__, __rdiv__, __idiv__ = _numeric_methods(um.divide, 'div')
+ __truediv__, __rtruediv__, __itruediv__ = _numeric_methods(
+ um.true_divide, 'truediv')
+ __floordiv__, __rfloordiv__, __ifloordiv__ = _numeric_methods(
+ um.floor_divide, 'floordiv')
+ __mod__, __rmod__, __imod__ = _numeric_methods(um.remainder, 'mod')
+ __divmod__ = _binary_method(um.divmod, 'divmod')
+ __rdivmod__ = _reflected_binary_method(um.divmod, 'divmod')
+ # __idivmod__ does not exist
+ # TODO: handle the optional third argument for __pow__?
+ __pow__, __rpow__, __ipow__ = _numeric_methods(um.power, 'pow')
+ __lshift__, __rlshift__, __ilshift__ = _numeric_methods(
+ um.left_shift, 'lshift')
+ __rshift__, __rrshift__, __irshift__ = _numeric_methods(
+ um.right_shift, 'rshift')
+ __and__, __rand__, __iand__ = _numeric_methods(um.bitwise_and, 'and')
+ __xor__, __rxor__, __ixor__ = _numeric_methods(um.bitwise_xor, 'xor')
+ __or__, __ror__, __ior__ = _numeric_methods(um.bitwise_or, 'or')
+
+ # unary methods
+ __neg__ = _unary_method(um.negative, 'neg')
+ __pos__ = _unary_method(um.positive, 'pos')
+ __abs__ = _unary_method(um.absolute, 'abs')
+ __invert__ = _unary_method(um.invert, 'invert')