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1"""Mixin classes for custom array types that don't inherit from ndarray.""" 

2from numpy.core import umath as um 

3 

4 

5__all__ = ['NDArrayOperatorsMixin'] 

6 

7 

8def _disables_array_ufunc(obj): 

9 """True when __array_ufunc__ is set to None.""" 

10 try: 

11 return obj.__array_ufunc__ is None 

12 except AttributeError: 

13 return False 

14 

15 

16def _binary_method(ufunc, name): 

17 """Implement a forward binary method with a ufunc, e.g., __add__.""" 

18 def func(self, other): 

19 if _disables_array_ufunc(other): 

20 return NotImplemented 

21 return ufunc(self, other) 

22 func.__name__ = '__{}__'.format(name) 

23 return func 

24 

25 

26def _reflected_binary_method(ufunc, name): 

27 """Implement a reflected binary method with a ufunc, e.g., __radd__.""" 

28 def func(self, other): 

29 if _disables_array_ufunc(other): 

30 return NotImplemented 

31 return ufunc(other, self) 

32 func.__name__ = '__r{}__'.format(name) 

33 return func 

34 

35 

36def _inplace_binary_method(ufunc, name): 

37 """Implement an in-place binary method with a ufunc, e.g., __iadd__.""" 

38 def func(self, other): 

39 return ufunc(self, other, out=(self,)) 

40 func.__name__ = '__i{}__'.format(name) 

41 return func 

42 

43 

44def _numeric_methods(ufunc, name): 

45 """Implement forward, reflected and inplace binary methods with a ufunc.""" 

46 return (_binary_method(ufunc, name), 

47 _reflected_binary_method(ufunc, name), 

48 _inplace_binary_method(ufunc, name)) 

49 

50 

51def _unary_method(ufunc, name): 

52 """Implement a unary special method with a ufunc.""" 

53 def func(self): 

54 return ufunc(self) 

55 func.__name__ = '__{}__'.format(name) 

56 return func 

57 

58 

59class NDArrayOperatorsMixin: 

60 """Mixin defining all operator special methods using __array_ufunc__. 

61 

62 This class implements the special methods for almost all of Python's 

63 builtin operators defined in the `operator` module, including comparisons 

64 (``==``, ``>``, etc.) and arithmetic (``+``, ``*``, ``-``, etc.), by 

65 deferring to the ``__array_ufunc__`` method, which subclasses must 

66 implement. 

67 

68 It is useful for writing classes that do not inherit from `numpy.ndarray`, 

69 but that should support arithmetic and numpy universal functions like 

70 arrays as described in `A Mechanism for Overriding Ufuncs 

71 <https://numpy.org/neps/nep-0013-ufunc-overrides.html>`_. 

72 

73 As an trivial example, consider this implementation of an ``ArrayLike`` 

74 class that simply wraps a NumPy array and ensures that the result of any 

75 arithmetic operation is also an ``ArrayLike`` object:: 

76 

77 class ArrayLike(np.lib.mixins.NDArrayOperatorsMixin): 

78 def __init__(self, value): 

79 self.value = np.asarray(value) 

80 

81 # One might also consider adding the built-in list type to this 

82 # list, to support operations like np.add(array_like, list) 

83 _HANDLED_TYPES = (np.ndarray, numbers.Number) 

84 

85 def __array_ufunc__(self, ufunc, method, *inputs, **kwargs): 

86 out = kwargs.get('out', ()) 

87 for x in inputs + out: 

88 # Only support operations with instances of _HANDLED_TYPES. 

89 # Use ArrayLike instead of type(self) for isinstance to 

90 # allow subclasses that don't override __array_ufunc__ to 

91 # handle ArrayLike objects. 

92 if not isinstance(x, self._HANDLED_TYPES + (ArrayLike,)): 

93 return NotImplemented 

94 

95 # Defer to the implementation of the ufunc on unwrapped values. 

96 inputs = tuple(x.value if isinstance(x, ArrayLike) else x 

97 for x in inputs) 

98 if out: 

99 kwargs['out'] = tuple( 

100 x.value if isinstance(x, ArrayLike) else x 

101 for x in out) 

102 result = getattr(ufunc, method)(*inputs, **kwargs) 

103 

104 if type(result) is tuple: 

105 # multiple return values 

106 return tuple(type(self)(x) for x in result) 

107 elif method == 'at': 

108 # no return value 

109 return None 

110 else: 

111 # one return value 

112 return type(self)(result) 

113 

114 def __repr__(self): 

115 return '%s(%r)' % (type(self).__name__, self.value) 

116 

117 In interactions between ``ArrayLike`` objects and numbers or numpy arrays, 

118 the result is always another ``ArrayLike``: 

119 

120 >>> x = ArrayLike([1, 2, 3]) 

121 >>> x - 1 

122 ArrayLike(array([0, 1, 2])) 

123 >>> 1 - x 

124 ArrayLike(array([ 0, -1, -2])) 

125 >>> np.arange(3) - x 

126 ArrayLike(array([-1, -1, -1])) 

127 >>> x - np.arange(3) 

128 ArrayLike(array([1, 1, 1])) 

129 

130 Note that unlike ``numpy.ndarray``, ``ArrayLike`` does not allow operations 

131 with arbitrary, unrecognized types. This ensures that interactions with 

132 ArrayLike preserve a well-defined casting hierarchy. 

133 

134 .. versionadded:: 1.13 

135 """ 

136 # Like np.ndarray, this mixin class implements "Option 1" from the ufunc 

137 # overrides NEP. 

138 

139 # comparisons don't have reflected and in-place versions 

140 __lt__ = _binary_method(um.less, 'lt') 

141 __le__ = _binary_method(um.less_equal, 'le') 

142 __eq__ = _binary_method(um.equal, 'eq') 

143 __ne__ = _binary_method(um.not_equal, 'ne') 

144 __gt__ = _binary_method(um.greater, 'gt') 

145 __ge__ = _binary_method(um.greater_equal, 'ge') 

146 

147 # numeric methods 

148 __add__, __radd__, __iadd__ = _numeric_methods(um.add, 'add') 

149 __sub__, __rsub__, __isub__ = _numeric_methods(um.subtract, 'sub') 

150 __mul__, __rmul__, __imul__ = _numeric_methods(um.multiply, 'mul') 

151 __matmul__, __rmatmul__, __imatmul__ = _numeric_methods( 

152 um.matmul, 'matmul') 

153 # Python 3 does not use __div__, __rdiv__, or __idiv__ 

154 __truediv__, __rtruediv__, __itruediv__ = _numeric_methods( 

155 um.true_divide, 'truediv') 

156 __floordiv__, __rfloordiv__, __ifloordiv__ = _numeric_methods( 

157 um.floor_divide, 'floordiv') 

158 __mod__, __rmod__, __imod__ = _numeric_methods(um.remainder, 'mod') 

159 __divmod__ = _binary_method(um.divmod, 'divmod') 

160 __rdivmod__ = _reflected_binary_method(um.divmod, 'divmod') 

161 # __idivmod__ does not exist 

162 # TODO: handle the optional third argument for __pow__? 

163 __pow__, __rpow__, __ipow__ = _numeric_methods(um.power, 'pow') 

164 __lshift__, __rlshift__, __ilshift__ = _numeric_methods( 

165 um.left_shift, 'lshift') 

166 __rshift__, __rrshift__, __irshift__ = _numeric_methods( 

167 um.right_shift, 'rshift') 

168 __and__, __rand__, __iand__ = _numeric_methods(um.bitwise_and, 'and') 

169 __xor__, __rxor__, __ixor__ = _numeric_methods(um.bitwise_xor, 'xor') 

170 __or__, __ror__, __ior__ = _numeric_methods(um.bitwise_or, 'or') 

171 

172 # unary methods 

173 __neg__ = _unary_method(um.negative, 'neg') 

174 __pos__ = _unary_method(um.positive, 'pos') 

175 __abs__ = _unary_method(um.absolute, 'abs') 

176 __invert__ = _unary_method(um.invert, 'invert')