| 
 | 1 | +.. _array-object:  | 
 | 2 | + | 
 | 3 | +Array object  | 
 | 4 | +============  | 
 | 5 | + | 
 | 6 | +    Array API specification for array object attributes and methods.  | 
 | 7 | + | 
 | 8 | +A conforming implementation of the array API standard must provide and support an array object having the following attributes and methods.  | 
 | 9 | + | 
 | 10 | +Furthermore, a conforming implementation of the array API standard must support, at minimum, array objects of rank (i.e., number of dimensions) ``0``, ``1``, ``2``, ``3``, and ``4`` and must explicitly document their maximum supported rank ``N``.  | 
 | 11 | + | 
 | 12 | +.. note::  | 
 | 13 | +    Conforming implementations must support zero-dimensional arrays.  | 
 | 14 | + | 
 | 15 | +    Apart from array object attributes, such as ``ndim``, ``device``, and ``dtype``, all operations in this standard return arrays (or tuples of arrays), including those operations, such as ``mean``, ``var``, and ``std``, from which some common array libraries (e.g., NumPy) return scalar values.  | 
 | 16 | + | 
 | 17 | +    *Rationale: always returning arrays is necessary to (1) support accelerator libraries where non-array return values could force device synchronization and (2) support delayed execution models where an array represents a future value.*  | 
 | 18 | + | 
 | 19 | +-------------------------------------------------  | 
 | 20 | + | 
 | 21 | +.. _operators:  | 
 | 22 | + | 
 | 23 | +Operators  | 
 | 24 | +---------  | 
 | 25 | + | 
 | 26 | +A conforming implementation of the array API standard must provide and support an array object supporting the following Python operators.  | 
 | 27 | + | 
 | 28 | +Arithmetic Operators  | 
 | 29 | +~~~~~~~~~~~~~~~~~~~~  | 
 | 30 | + | 
 | 31 | +A conforming implementation of the array API standard must provide and support an array object supporting the following Python arithmetic operators.  | 
 | 32 | + | 
 | 33 | +-   ``+x``: :meth:`.array.__pos__`  | 
 | 34 | + | 
 | 35 | +    -   `operator.pos(x) <https://docs.python.org/3/library/operator.html#operator.pos>`_  | 
 | 36 | +    -   `operator.__pos__(x) <https://docs.python.org/3/library/operator.html#operator.__pos__>`_  | 
 | 37 | + | 
 | 38 | +-   `-x`: :meth:`.array.__neg__`  | 
 | 39 | + | 
 | 40 | +    -   `operator.neg(x) <https://docs.python.org/3/library/operator.html#operator.neg>`_  | 
 | 41 | +    -   `operator.__neg__(x) <https://docs.python.org/3/library/operator.html#operator.__neg__>`_  | 
 | 42 | + | 
 | 43 | +-   `x1 + x2`: :meth:`.array.__add__`  | 
 | 44 | + | 
 | 45 | +    -   `operator.add(x1, x2) <https://docs.python.org/3/library/operator.html#operator.add>`_  | 
 | 46 | +    -   `operator.__add__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__add__>`_  | 
 | 47 | + | 
 | 48 | +-   `x1 - x2`: :meth:`.array.__sub__`  | 
 | 49 | + | 
 | 50 | +    -   `operator.sub(x1, x2) <https://docs.python.org/3/library/operator.html#operator.sub>`_  | 
 | 51 | +    -   `operator.__sub__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__sub__>`_  | 
 | 52 | + | 
 | 53 | +-   `x1 * x2`: :meth:`.array.__mul__`  | 
 | 54 | + | 
 | 55 | +    -   `operator.mul(x1, x2) <https://docs.python.org/3/library/operator.html#operator.mul>`_  | 
 | 56 | +    -   `operator.__mul__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__mul__>`_  | 
 | 57 | + | 
 | 58 | +-   `x1 / x2`: :meth:`.array.__truediv__`  | 
 | 59 | + | 
 | 60 | +    -   `operator.truediv(x1,x2) <https://docs.python.org/3/library/operator.html#operator.truediv>`_  | 
 | 61 | +    -   `operator.__truediv__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__truediv__>`_  | 
 | 62 | + | 
 | 63 | +-   `x1 // x2`: :meth:`.array.__floordiv__`  | 
 | 64 | + | 
 | 65 | +    -   `operator.floordiv(x1, x2) <https://docs.python.org/3/library/operator.html#operator.floordiv>`_  | 
 | 66 | +    -   `operator.__floordiv__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__floordiv__>`_  | 
 | 67 | + | 
 | 68 | +-   `x1 % x2`: :meth:`.array.__mod__`  | 
 | 69 | + | 
 | 70 | +    -   `operator.mod(x1, x2) <https://docs.python.org/3/library/operator.html#operator.mod>`_  | 
 | 71 | +    -   `operator.__mod__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__mod__>`_  | 
 | 72 | + | 
 | 73 | +-   `x1 ** x2`: :meth:`.array.__pow__`  | 
 | 74 | + | 
 | 75 | +    -   `operator.pow(x1, x2) <https://docs.python.org/3/library/operator.html#operator.pow>`_  | 
 | 76 | +    -   `operator.__pow__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__pow__>`_  | 
 | 77 | + | 
 | 78 | +Arithmetic operators should be defined for arrays having real-valued data types.  | 
 | 79 | + | 
 | 80 | +Array Operators  | 
 | 81 | +~~~~~~~~~~~~~~~  | 
 | 82 | + | 
 | 83 | +A conforming implementation of the array API standard must provide and support an array object supporting the following Python array operators.  | 
 | 84 | + | 
 | 85 | +-   `x1 @ x2`: :meth:`.array.__matmul__`  | 
 | 86 | + | 
 | 87 | +    -   `operator.matmul(x1, x2) <https://docs.python.org/3/library/operator.html#operator.matmul>`_  | 
 | 88 | +    -   `operator.__matmul__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__matmul__>`_  | 
 | 89 | + | 
 | 90 | +The matmul ``@`` operator should be defined for arrays having real-valued data types.  | 
 | 91 | + | 
 | 92 | +Bitwise Operators  | 
 | 93 | +~~~~~~~~~~~~~~~~~  | 
 | 94 | + | 
 | 95 | +A conforming implementation of the array API standard must provide and support an array object supporting the following Python bitwise operators.  | 
 | 96 | + | 
 | 97 | +-   `~x`: :meth:`.array.__invert__`  | 
 | 98 | + | 
 | 99 | +    -   `operator.inv(x) <https://docs.python.org/3/library/operator.html#operator.inv>`_  | 
 | 100 | +    -   `operator.invert(x) <https://docs.python.org/3/library/operator.html#operator.invert>`_  | 
 | 101 | +    -   `operator.__inv__(x) <https://docs.python.org/3/library/operator.html#operator.__inv__>`_  | 
 | 102 | +    -   `operator.__invert__(x) <https://docs.python.org/3/library/operator.html#operator.__invert__>`_  | 
 | 103 | + | 
 | 104 | +-   `x1 & x2`: :meth:`.array.__and__`  | 
 | 105 | + | 
 | 106 | +    -   `operator.and(x1, x2) <https://docs.python.org/3/library/operator.html#operator.and>`_  | 
 | 107 | +    -   `operator.__and__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__and__>`_  | 
 | 108 | + | 
 | 109 | +-   `x1 | x2`: :meth:`.array.__or__`  | 
 | 110 | + | 
 | 111 | +    -   `operator.or(x1, x2) <https://docs.python.org/3/library/operator.html#operator.or>`_  | 
 | 112 | +    -   `operator.__or__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__or__>`_  | 
 | 113 | + | 
 | 114 | +-   `x1 ^ x2`: :meth:`.array.__xor__`  | 
 | 115 | + | 
 | 116 | +    -   `operator.xor(x1, x2) <https://docs.python.org/3/library/operator.html#operator.xor>`_  | 
 | 117 | +    -   `operator.__xor__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__xor__>`_  | 
 | 118 | + | 
 | 119 | +-   `x1 << x2`: :meth:`.array.__lshift__`  | 
 | 120 | + | 
 | 121 | +    -   `operator.lshift(x1, x2) <https://docs.python.org/3/library/operator.html#operator.lshift>`_  | 
 | 122 | +    -   `operator.__lshift__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__lshift__>`_  | 
 | 123 | + | 
 | 124 | +-   `x1 >> x2`: :meth:`.array.__rshift__`  | 
 | 125 | + | 
 | 126 | +    -   `operator.rshift(x1, x2) <https://docs.python.org/3/library/operator.html#operator.rshift>`_  | 
 | 127 | +    -   `operator.__rshift__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__rshift__>`_  | 
 | 128 | + | 
 | 129 | +Bitwise operators should be defined for arrays having integer and boolean data types.  | 
 | 130 | + | 
 | 131 | +Comparison Operators  | 
 | 132 | +~~~~~~~~~~~~~~~~~~~~  | 
 | 133 | + | 
 | 134 | +A conforming implementation of the array API standard must provide and support an array object supporting the following Python comparison operators.  | 
 | 135 | + | 
 | 136 | +-   `x1 < x2`: :meth:`.array.__lt__`  | 
 | 137 | + | 
 | 138 | +    -   `operator.lt(x1, x2) <https://docs.python.org/3/library/operator.html#operator.lt>`_  | 
 | 139 | +    -   `operator.__lt__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__lt__>`_  | 
 | 140 | + | 
 | 141 | +-   `x1 <= x2`: :meth:`.array.__le__`  | 
 | 142 | + | 
 | 143 | +    -   `operator.le(x1, x2) <https://docs.python.org/3/library/operator.html#operator.le>`_  | 
 | 144 | +    -   `operator.__le__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__le__>`_  | 
 | 145 | + | 
 | 146 | +-   `x1 > x2`: :meth:`.array.__gt__`  | 
 | 147 | + | 
 | 148 | +    -   `operator.gt(x1, x2) <https://docs.python.org/3/library/operator.html#operator.gt>`_  | 
 | 149 | +    -   `operator.__gt__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__gt__>`_  | 
 | 150 | + | 
 | 151 | +-   `x1 >= x2`: :meth:`.array.__ge__`  | 
 | 152 | + | 
 | 153 | +    -   `operator.ge(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ge>`_  | 
 | 154 | +    -   `operator.__ge__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ge__>`_  | 
 | 155 | + | 
 | 156 | +-   `x1 == x2`: :meth:`.array.__eq__`  | 
 | 157 | + | 
 | 158 | +    -   `operator.eq(x1, x2) <https://docs.python.org/3/library/operator.html#operator.eq>`_  | 
 | 159 | +    -   `operator.__eq__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__eq__>`_  | 
 | 160 | + | 
 | 161 | +-   `x1 != x2`: :meth:`.array.__ne__`  | 
 | 162 | + | 
 | 163 | +    -   `operator.ne(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ne>`_  | 
 | 164 | +    -   `operator.__ne__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ne__>`_  | 
 | 165 | + | 
 | 166 | +:meth:`.array.__lt__`, :meth:`.array.__le__`, :meth:`.array.__gt__`, :meth:`.array.__ge__` are only defined for arrays having real-valued data types. Other comparison operators should be defined for arrays having any data type.  | 
 | 167 | +For backward compatibility, conforming implementations may support complex numbers; however, inequality comparison of complex numbers is unspecified and thus implementation-dependent (see :ref:`complex-number-ordering`).  | 
 | 168 | + | 
 | 169 | +In-place Operators  | 
 | 170 | +~~~~~~~~~~~~~~~~~~  | 
 | 171 | + | 
 | 172 | +A conforming implementation of the array API standard must provide and support an array object supporting the following in-place Python operators.  | 
 | 173 | + | 
 | 174 | +An in-place operation must not change the data type or shape of the in-place array as a result of :ref:`type-promotion` or :ref:`broadcasting`.  | 
 | 175 | + | 
 | 176 | +An in-place operation must have the same behavior (including special cases) as its respective binary (i.e., two operand, non-assignment) operation. For example, after in-place addition ``x1 += x2``, the modified array ``x1`` must always equal the result of the equivalent binary arithmetic operation ``x1 = x1 + x2``.  | 
 | 177 | + | 
 | 178 | +.. note::  | 
 | 179 | +    In-place operators must be supported as discussed in :ref:`copyview-mutability`.  | 
 | 180 | + | 
 | 181 | +Arithmetic Operators  | 
 | 182 | +""""""""""""""""""""  | 
 | 183 | + | 
 | 184 | +-   ``+=``. May be implemented via ``__iadd__``.  | 
 | 185 | +-   ``-=``. May be implemented via ``__isub__``.  | 
 | 186 | +-   ``*=``. May be implemented via ``__imul__``.  | 
 | 187 | +-   ``/=``. May be implemented via ``__itruediv__``.  | 
 | 188 | +-   ``//=``. May be implemented via ``__ifloordiv__``.  | 
 | 189 | +-   ``**=``. May be implemented via ``__ipow__``.  | 
 | 190 | +-   ``%=``. May be implemented via ``__imod__``.  | 
 | 191 | + | 
 | 192 | +Array Operators  | 
 | 193 | +"""""""""""""""  | 
 | 194 | + | 
 | 195 | +-   ``@=``. May be implemented via ``__imatmul__``.  | 
 | 196 | + | 
 | 197 | +Bitwise Operators  | 
 | 198 | +"""""""""""""""""  | 
 | 199 | + | 
 | 200 | +-   ``&=``. May be implemented via ``__iand__``.  | 
 | 201 | +-   ``|=``. May be implemented via ``__ior__``.  | 
 | 202 | +-   ``^=``. May be implemented via ``__ixor__``.  | 
 | 203 | +-   ``<<=``. May be implemented via ``__ilshift__``.  | 
 | 204 | +-   ``>>=``. May be implemented via ``__irshift__``.  | 
 | 205 | + | 
 | 206 | +Reflected Operators  | 
 | 207 | +~~~~~~~~~~~~~~~~~~~  | 
 | 208 | + | 
 | 209 | +A conforming implementation of the array API standard must provide and support an array object supporting the following reflected operators.  | 
 | 210 | + | 
 | 211 | +The results of applying reflected operators must match their non-reflected equivalents.  | 
 | 212 | + | 
 | 213 | +.. note::  | 
 | 214 | +    All operators for which ``array <op> scalar`` is implemented must have an equivalent reflected operator implementation.  | 
 | 215 | + | 
 | 216 | +Arithmetic Operators  | 
 | 217 | +""""""""""""""""""""  | 
 | 218 | + | 
 | 219 | +-   ``__radd__``  | 
 | 220 | +-   ``__rsub__``  | 
 | 221 | +-   ``__rmul__``  | 
 | 222 | +-   ``__rtruediv__``  | 
 | 223 | +-   ``__rfloordiv__``  | 
 | 224 | +-   ``__rpow__``  | 
 | 225 | +-   ``__rmod__``  | 
 | 226 | + | 
 | 227 | +Array Operators  | 
 | 228 | +"""""""""""""""  | 
 | 229 | + | 
 | 230 | +-   ``__rmatmul__``  | 
 | 231 | + | 
 | 232 | +Bitwise Operators  | 
 | 233 | +"""""""""""""""""  | 
 | 234 | + | 
 | 235 | +-   ``__rand__``  | 
 | 236 | +-   ``__ror__``  | 
 | 237 | +-   ``__rxor__``  | 
 | 238 | +-   ``__rlshift__``  | 
 | 239 | +-   ``__rrshift__``  | 
 | 240 | + | 
 | 241 | +-------------------------------------------------  | 
 | 242 | + | 
 | 243 | +.. currentmodule:: array_api  | 
 | 244 | + | 
 | 245 | +Attributes  | 
 | 246 | +----------  | 
 | 247 | +..  | 
 | 248 | +  NOTE: please keep the attributes in alphabetical order  | 
 | 249 | +
  | 
 | 250 | + | 
 | 251 | +.. autosummary::  | 
 | 252 | +   :toctree: generated  | 
 | 253 | +   :template: property.rst  | 
 | 254 | + | 
 | 255 | +   array.dtype  | 
 | 256 | +   array.device  | 
 | 257 | +   array.mT  | 
 | 258 | +   array.ndim  | 
 | 259 | +   array.shape  | 
 | 260 | +   array.size  | 
 | 261 | +   array.T  | 
 | 262 | + | 
 | 263 | +-------------------------------------------------  | 
 | 264 | + | 
 | 265 | +Methods  | 
 | 266 | +-------  | 
 | 267 | +..  | 
 | 268 | +  NOTE: please keep the methods in alphabetical order  | 
 | 269 | +
  | 
 | 270 | + | 
 | 271 | +.. autosummary::  | 
 | 272 | +   :toctree: generated  | 
 | 273 | +   :template: property.rst  | 
 | 274 | + | 
 | 275 | +   array.__abs__  | 
 | 276 | +   array.__add__  | 
 | 277 | +   array.__and__  | 
 | 278 | +   array.__array_namespace__  | 
 | 279 | +   array.__bool__  | 
 | 280 | +   array.__complex__  | 
 | 281 | +   array.__dlpack__  | 
 | 282 | +   array.__dlpack_device__  | 
 | 283 | +   array.__eq__  | 
 | 284 | +   array.__float__  | 
 | 285 | +   array.__floordiv__  | 
 | 286 | +   array.__ge__  | 
 | 287 | +   array.__getitem__  | 
 | 288 | +   array.__gt__  | 
 | 289 | +   array.__index__  | 
 | 290 | +   array.__int__  | 
 | 291 | +   array.__invert__  | 
 | 292 | +   array.__le__  | 
 | 293 | +   array.__lshift__  | 
 | 294 | +   array.__lt__  | 
 | 295 | +   array.__matmul__  | 
 | 296 | +   array.__mod__  | 
 | 297 | +   array.__mul__  | 
 | 298 | +   array.__ne__  | 
 | 299 | +   array.__neg__  | 
 | 300 | +   array.__or__  | 
 | 301 | +   array.__pos__  | 
 | 302 | +   array.__pow__  | 
 | 303 | +   array.__rshift__  | 
 | 304 | +   array.__setitem__  | 
 | 305 | +   array.__sub__  | 
 | 306 | +   array.__truediv__  | 
 | 307 | +   array.__xor__  | 
 | 308 | +   array.to_device  | 
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