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Add complex number support to tensordot #558

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Dec 14, 2022
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Add complex number support to tensordot #558

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11 changes: 9 additions & 2 deletions spec/API_specification/array_api/linear_algebra_functions.py
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Expand Up @@ -56,12 +56,15 @@ def tensordot(x1: array, x2: array, /, *, axes: Union[int, Tuple[Sequence[int],
"""
Returns a tensor contraction of ``x1`` and ``x2`` over specific axes.

.. note::
The ``tensordot`` function corresponds to the generalized matrix product.

Parameters
----------
x1: array
first input array. Should have a real-valued data type.
first input array. Should have a numeric data type.
x2: array
second input array. Should have a real-valued data type. Corresponding contracted axes of ``x1`` and ``x2`` must be equal.
second input array. Should have a numeric data type. Corresponding contracted axes of ``x1`` and ``x2`` must be equal.

.. note::
Contracted axes (dimensions) must not be broadcasted.
Expand All @@ -77,6 +80,10 @@ def tensordot(x1: array, x2: array, /, *, axes: Union[int, Tuple[Sequence[int],

If ``axes`` is a tuple of two sequences ``(x1_axes, x2_axes)``, the first sequence must apply to ``x`` and the second sequence to ``x2``. Both sequences must have the same length. Each axis (dimension) ``x1_axes[i]`` for ``x1`` must have the same size as the respective axis (dimension) ``x2_axes[i]`` for ``x2``. Each sequence must consist of unique (nonnegative) integers that specify valid axes for each respective array.


.. note::
If either ``x1`` or ``x2`` has a complex floating-point data type, neither argument must be complex-conjugated or transposed. If conjugation and/or transposition is desired, these operations should be explicitly performed prior to computing the generalized matrix product.

Returns
-------
out: array
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