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A conforming implementation of the array API standard must provide and support the following functions adhering to the following conventions.
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- 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 function accepting positional-only parameters is called, positional arguments are mapped to these parameters based solely on their order.
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- Optional parameters must be `keyword-only <https://www.python.org/dev/peps/pep-3102/>`_ arguments.
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- Unless stated otherwise, functions must adhere to the type promotion rules defined in :ref:`type-promotion`.
Joins a sequence of arrays along an existing axis.
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Parameters
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----------
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arrays: Union[Tuple[array, ...], List[array]]
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input arrays to join. The arrays must have the same shape, except in the dimension specified by ``axis``.
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axis: Optional[int]
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axis along which the arrays will be joined. If ``axis`` is ``None``, arrays must be flattened before concatenation. If ``axis`` is negative, the function must determine the axis along which to join by counting from the last dimension. Default: ``0``.
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Returns
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-------
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out: array
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an output array containing the concatenated values. If the input arrays have different data types, normal :ref:`type-promotion` must apply. If the input arrays have the same data type, the output array must have the same data type as the input arrays.
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.. note::
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This specification leaves type promotion between data type families (i.e., ``intxx`` and ``floatxx``) unspecified.
Expands the shape of an array by inserting a new axis (dimension) of size one at the position specified by ``axis``.
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Parameters
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----------
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x: array
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input array.
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axis: int
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axis position. Must follow Python's indexing rules: zero-based and negative indices must be counted backward from the last dimension. If ``x`` has rank ``N``, a valid ``axis`` must reside on the interval ``[-N-1, N+1]``. An ``IndexError`` exception must be raised if provided an invalid ``axis`` position.
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Returns
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-------
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out: array
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an expanded output array having the same data type as ``x``.
Reverses the order of elements in an array along the given axis. The shape of the array must be preserved.
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Parameters
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----------
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x: array
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input array.
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axis: Optional[Union[int, Tuple[int, ...]]]
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axis (or axes) along which to flip. If ``axis`` is ``None``, the function must flip all input array axes. If ``axis`` is negative, the function must count from the last dimension. If provided more than one axis, the function must flip only the specified axes. Default: ``None``.
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Returns
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-------
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out: array
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an output array having the same data type and shape as ``x`` and whose elements, relative to ``x``, are reordered.
a new shape compatible with the original shape. One shape dimension is allowed to be ``-1``. When a shape dimension is ``-1``, the corresponding output array shape dimension must be inferred from the length of the array and the remaining dimensions.
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Returns
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-------
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out: array
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an output array having the same data type, elements, and underlying element order as ``x``.
Rolls array elements along a specified axis. Array elements that roll beyond the last position are re-introduced at the first position. Array elements that roll beyond the first position are re-introduced at the last position.
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Parameters
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----------
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x: array
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input array.
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shift: Union[int, Tuple[int, ...]]
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number of places by which the elements are shifted. If ``shift`` is a tuple, then ``axis`` must be a tuple of the same size, and each of the given axes must be shifted by the corresponding element in ``shift``. If ``shift`` is an ``int`` and ``axis`` a tuple, then the same ``shift`` must be used for all specified axes. If a shift is positive, then array elements must be shifted positively (toward larger indices) along the dimension of ``axis``. If a shift is negative, then array elements must be shifted negatively (toward smaller indices) along the dimension of ``axis``.
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axis: Optional[Union[int, Tuple[int, ...]]]
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axis (or axes) along which elements to shift. If ``axis`` is ``None``, the array must be flattened, shifted, and then restored to its original shape. Default: ``None``.
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Returns
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-------
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out: array
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an output array having the same data type as ``x`` and whose elements, relative to ``x``, are shifted.
input arrays to join. Each array must have the same shape.
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axis: int
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axis along which the arrays will be joined. Providing an ``axis`` specifies the index of the new axis in the dimensions of the result. For example, if ``axis`` is ``0``, the new axis will be the first dimension and the output array will have shape ``(N, A, B, C)``; if ``axis`` is ``1``, the new axis will be the second dimension and the output array will have shape ``(A, N, B, C)``; and, if ``axis`` is ``-1``, the new axis will be the last dimension and the output array will have shape ``(A, B, C, N)``. A valid ``axis`` must be on the interval ``[-N, N)``, where ``N`` is the rank (number of dimensions) of ``x``. If provided an ``axis`` outside of the required interval, the function must raise an exception. Default: ``0``.
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Returns
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--------
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out: array
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an output array having rank ``N+1``, where ``N`` is the rank (number of dimensions) of ``x``. If the input arrays have different data types, normal :ref:`type-promotion` must apply. If the input arrays have the same data type, the output array must have the same data type as the input arrays.
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.. note::
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This specification leaves type promotion between data type families (i.e., ``intxx`` and ``floatxx``) unspecified.
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