array_object.rst

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 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 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.

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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)
  • operator.__pos__(x)
• -x: :meth:`.array.__neg__`
  • operator.neg(x)
  • operator.__neg__(x)
• x1 + x2: :meth:`.array.__add__`
  • operator.add(x1, x2)
  • operator.__add__(x1, x2)
• x1 - x2: :meth:`.array.__sub__`
  • operator.sub(x1, x2)
  • operator.__sub__(x1, x2)
• x1 * x2: :meth:`.array.__mul__`
  • operator.mul(x1, x2)
  • operator.__mul__(x1, x2)
• x1 / x2: :meth:`.array.__truediv__`
  • operator.truediv(x1,x2)
  • operator.__truediv__(x1, x2)
• x1 // x2: :meth:`.array.__floordiv__`
  • operator.floordiv(x1, x2)
  • operator.__floordiv__(x1, x2)
• x1 % x2: :meth:`.array.__mod__`
  • operator.mod(x1, x2)
  • operator.__mod__(x1, x2)
• x1 ** x2: :meth:`.array.__pow__`
  • operator.pow(x1, x2)
  • operator.__pow__(x1, x2)

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)
  • operator.__matmul__(x1, x2)

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)
  • operator.invert(x)
  • operator.__inv__(x)
  • operator.__invert__(x)
• x1 & x2: :meth:`.array.__and__`
  • operator.and(x1, x2)
  • operator.__and__(x1, x2)
• x1 | x2: :meth:`.array.__or__`
  • operator.or(x1, x2)
  • operator.__or__(x1, x2)
• x1 ^ x2: :meth:`.array.__xor__`
  • operator.xor(x1, x2)
  • operator.__xor__(x1, x2)
• x1 << x2: :meth:`.array.__lshift__`
  • operator.lshift(x1, x2)
  • operator.__lshift__(x1, x2)
• x1 >> x2: :meth:`.array.__rshift__`
  • operator.rshift(x1, x2)
  • operator.__rshift__(x1, x2)

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)
  • operator.__lt__(x1, x2)
• x1 <= x2: :meth:`.array.__le__`
  • operator.le(x1, x2)
  • operator.__le__(x1, x2)
• x1 > x2: :meth:`.array.__gt__`
  • operator.gt(x1, x2)
  • operator.__gt__(x1, x2)
• x1 >= x2: :meth:`.array.__ge__`
  • operator.ge(x1, x2)
  • operator.__ge__(x1, x2)
• x1 == x2: :meth:`.array.__eq__`
  • operator.eq(x1, x2)
  • operator.__eq__(x1, x2)
• x1 != x2: :meth:`.array.__ne__`
  • operator.ne(x1, x2)
  • operator.__ne__(x1, x2)

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

.. autosummary::
   :toctree: generated
   :template: property.rst

   array.dtype
   array.device
   array.mT
   array.ndim
   array.shape
   array.size
   array.T

---

Methods

.. autosummary::
   :toctree: generated
   :template: property.rst

   array.__abs__
   array.__add__
   array.__and__
   array.__array_namespace__
   array.__bool__
   array.__complex__
   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