Move 2021.12 docs to respective sub-folders

Author: honno

spec/2021.12/API_specification/array_object.rst

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+.. _array-object:
+
+Array object
+============
+
+    Array API specification for array object attributes and methods.
+
+A conforming implementation of the array API standard must provide and support an array object having the following attributes and methods adhering to the following conventions.
+
+*   Positional parameters must be `positional-only <https://www.python.org/dev/peps/pep-0570/>`_ parameters. Positional-only parameters have no externally-usable name. When a method accepting positional-only parameters is called, positional arguments are mapped to these parameters based solely on their order.
+*   Optional parameters must be `keyword-only <https://www.python.org/dev/peps/pep-3102/>`_ arguments.
+*   Broadcasting semantics must follow the semantics defined in :ref:`broadcasting`.
+*   Unless stated otherwise, methods must support the data types defined in :ref:`data-types`.
+*   Unless stated otherwise, methods must adhere to the type promotion rules defined in :ref:`type-promotion`.
+*   Unless stated otherwise, floating-point operations must adhere to IEEE 754-2019.
+
+Furthermore, a conforming implementation of the array API standard must support array objects of arbitrary rank ``N`` (i.e., number of dimensions), where ``N`` is greater than or equal to zero.
+
+.. note::
+    Conforming implementations must support zero-dimensional arrays.
+
+    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.
+
+    *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.*
+
+-------------------------------------------------
+
+.. _operators:
+
+Operators
+---------
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following Python operators.
+
+Arithmetic Operators
+~~~~~~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following Python arithmetic operators.
+
+-   ``+x``: :meth:`.array.__pos__`
+
+    -   `operator.pos(x) <https://docs.python.org/3/library/operator.html#operator.pos>`_
+    -   `operator.__pos__(x) <https://docs.python.org/3/library/operator.html#operator.__pos__>`_
+
+-   `-x`: :meth:`.array.__neg__`
+
+    -   `operator.neg(x) <https://docs.python.org/3/library/operator.html#operator.neg>`_
+    -   `operator.__neg__(x) <https://docs.python.org/3/library/operator.html#operator.__neg__>`_
+
+-   `x1 + x2`: :meth:`.array.__add__`
+
+    -   `operator.add(x1, x2) <https://docs.python.org/3/library/operator.html#operator.add>`_
+    -   `operator.__add__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__add__>`_
+
+-   `x1 - x2`: :meth:`.array.__sub__`
+
+    -   `operator.sub(x1, x2) <https://docs.python.org/3/library/operator.html#operator.sub>`_
+    -   `operator.__sub__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__sub__>`_
+
+-   `x1 * x2`: :meth:`.array.__mul__`
+
+    -   `operator.mul(x1, x2) <https://docs.python.org/3/library/operator.html#operator.mul>`_
+    -   `operator.__mul__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__mul__>`_
+
+-   `x1 / x2`: :meth:`.array.__truediv__`
+
+    -   `operator.truediv(x1,x2) <https://docs.python.org/3/library/operator.html#operator.truediv>`_
+    -   `operator.__truediv__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__truediv__>`_
+
+-   `x1 // x2`: :meth:`.array.__floordiv__`
+
+    -   `operator.floordiv(x1, x2) <https://docs.python.org/3/library/operator.html#operator.floordiv>`_
+    -   `operator.__floordiv__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__floordiv__>`_
+
+-   `x1 % x2`: :meth:`.array.__mod__`
+
+    -   `operator.mod(x1, x2) <https://docs.python.org/3/library/operator.html#operator.mod>`_
+    -   `operator.__mod__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__mod__>`_
+
+-   `x1 ** x2`: :meth:`.array.__pow__`
+
+    -   `operator.pow(x1, x2) <https://docs.python.org/3/library/operator.html#operator.pow>`_
+    -   `operator.__pow__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__pow__>`_
+
+Arithmetic operators should be defined for arrays having real-valued data types.
+
+Array Operators
+~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following Python array operators.
+
+-   `x1 @ x2`: :meth:`.array.__matmul__`
+
+    -   `operator.matmul(x1, x2) <https://docs.python.org/3/library/operator.html#operator.matmul>`_
+    -   `operator.__matmul__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__matmul__>`_
+
+The matmul ``@`` operator should be defined for arrays having real-valued data types.
+
+Bitwise Operators
+~~~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following Python bitwise operators.
+
+-   `~x`: :meth:`.array.__invert__`
+
+    -   `operator.inv(x) <https://docs.python.org/3/library/operator.html#operator.inv>`_
+    -   `operator.invert(x) <https://docs.python.org/3/library/operator.html#operator.invert>`_
+    -   `operator.__inv__(x) <https://docs.python.org/3/library/operator.html#operator.__inv__>`_
+    -   `operator.__invert__(x) <https://docs.python.org/3/library/operator.html#operator.__invert__>`_
+
+-   `x1 & x2`: :meth:`.array.__and__`
+
+    -   `operator.and(x1, x2) <https://docs.python.org/3/library/operator.html#operator.and>`_
+    -   `operator.__and__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__and__>`_
+
+-   `x1 | x2`: :meth:`.array.__or__`
+
+    -   `operator.or(x1, x2) <https://docs.python.org/3/library/operator.html#operator.or>`_
+    -   `operator.__or__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__or__>`_
+
+-   `x1 ^ x2`: :meth:`.array.__xor__`
+
+    -   `operator.xor(x1, x2) <https://docs.python.org/3/library/operator.html#operator.xor>`_
+    -   `operator.__xor__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__xor__>`_
+
+-   `x1 << x2`: :meth:`.array.__lshift__`
+
+    -   `operator.lshift(x1, x2) <https://docs.python.org/3/library/operator.html#operator.lshift>`_
+    -   `operator.__lshift__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__lshift__>`_
+
+-   `x1 >> x2`: :meth:`.array.__rshift__`
+
+    -   `operator.rshift(x1, x2) <https://docs.python.org/3/library/operator.html#operator.rshift>`_
+    -   `operator.__rshift__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__rshift__>`_
+
+Bitwise operators should be defined for arrays having integer and boolean data types.
+
+Comparison Operators
+~~~~~~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following Python comparison operators.
+
+-   `x1 < x2`: :meth:`.array.__lt__`
+
+    -   `operator.lt(x1, x2) <https://docs.python.org/3/library/operator.html#operator.lt>`_
+    -   `operator.__lt__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__lt__>`_
+
+-   `x1 <= x2`: :meth:`.array.__le__`
+
+    -   `operator.le(x1, x2) <https://docs.python.org/3/library/operator.html#operator.le>`_
+    -   `operator.__le__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__le__>`_
+
+-   `x1 > x2`: :meth:`.array.__gt__`
+
+    -   `operator.gt(x1, x2) <https://docs.python.org/3/library/operator.html#operator.gt>`_
+    -   `operator.__gt__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__gt__>`_
+
+-   `x1 >= x2`: :meth:`.array.__ge__`
+
+    -   `operator.ge(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ge>`_
+    -   `operator.__ge__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ge__>`_
+
+-   `x1 == x2`: :meth:`.array.__eq__`
+
+    -   `operator.eq(x1, x2) <https://docs.python.org/3/library/operator.html#operator.eq>`_
+    -   `operator.__eq__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__eq__>`_
+
+-   `x1 != x2`: :meth:`.array.__ne__`
+
+    -   `operator.ne(x1, x2) <https://docs.python.org/3/library/operator.html#operator.ne>`_
+    -   `operator.__ne__(x1, x2) <https://docs.python.org/3/library/operator.html#operator.__ne__>`_
+
+Comparison operators should be defined for arrays having any data type.
+
+In-place Operators
+~~~~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following in-place Python operators.
+
+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`.
+
+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``.
+
+.. note::
+    In-place operators must be supported as discussed in :ref:`copyview-mutability`.
+
+Arithmetic Operators
+""""""""""""""""""""
+
+-   ``+=``. May be implemented via ``__iadd__``.
+-   ``-=``. May be implemented via ``__isub__``.
+-   ``*=``. May be implemented via ``__imul__``.
+-   ``/=``. May be implemented via ``__itruediv__``.
+-   ``//=``. May be implemented via ``__ifloordiv__``.
+-   ``**=``. May be implemented via ``__ipow__``.
+-   ``%=``. May be implemented via ``__imod__``.
+
+Array Operators
+"""""""""""""""
+
+-   ``@=``. May be implemented via ``__imatmul__``.
+
+Bitwise Operators
+"""""""""""""""""
+
+-   ``&=``. May be implemented via ``__iand__``.
+-   ``|=``. May be implemented via ``__ior__``.
+-   ``^=``. May be implemented via ``__ixor__``.
+-   ``<<=``. May be implemented via ``__ilshift__``.
+-   ``>>=``. May be implemented via ``__irshift__``.
+
+Reflected Operators
+~~~~~~~~~~~~~~~~~~~
+
+A conforming implementation of the array API standard must provide and support an array object supporting the following reflected operators.
+
+The results of applying reflected operators must match their non-reflected equivalents.
+
+.. note::
+    All operators for which ``array <op> scalar`` is implemented must have an equivalent reflected operator implementation.
+
+Arithmetic Operators
+""""""""""""""""""""
+
+-   ``__radd__``
+-   ``__rsub__``
+-   ``__rmul__``
+-   ``__rtruediv__``
+-   ``__rfloordiv__``
+-   ``__rpow__``
+-   ``__rmod__``
+
+Array Operators
+"""""""""""""""
+
+-   ``__rmatmul__``
+
+Bitwise Operators
+"""""""""""""""""
+
+-   ``__rand__``
+-   ``__ror__``
+-   ``__rxor__``
+-   ``__rlshift__``
+-   ``__rrshift__``
+
+-------------------------------------------------
+
+.. currentmodule:: array_api
+
+Attributes
+----------
+..
+  NOTE: please keep the attributes in alphabetical order
+
+
+.. autosummary::
+   :toctree: generated
+   :template: property.rst
+
+   array.dtype
+   array.device
+   array.mT
+   array.ndim
+   array.shape
+   array.size
+   array.T
+
+-------------------------------------------------
+
+Methods
+-------
+..
+  NOTE: please keep the methods in alphabetical order
+
+
+.. autosummary::
+   :toctree: generated
+   :template: property.rst
+
+   array.__abs__
+   array.__add__
+   array.__and__
+   array.__array_namespace__
+   array.__bool__
+   array.__dlpack__
+   array.__dlpack_device__
+   array.__eq__
+   array.__float__
+   array.__floordiv__
+   array.__ge__
+   array.__getitem__
+   array.__gt__
+   array.__index__
+   array.__int__
+   array.__invert__
+   array.__le__
+   array.__lshift__
+   array.__lt__
+   array.__matmul__
+   array.__mod__
+   array.__mul__
+   array.__ne__
+   array.__neg__
+   array.__or__
+   array.__pos__
+   array.__pow__
+   array.__rshift__
+   array.__setitem__
+   array.__sub__
+   array.__truediv__
+   array.__xor__
+   array.to_device