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<html lang="en">
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    <meta charset="UTF-8">
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"""Mixin classes for custom array types that don't inherit from ndarray."""
from numpy.core import umath as um


__all__ = ['NDArrayOperatorsMixin']


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:
    """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
    <https://numpy.org/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
    """
    __slots__ = ()
    # 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_