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Add support for broadcasting to linalg.cross (#417)
* Make explicit that broadcasting only applies to non-compute dimensions in vecdot
* Add support for broadcasting to `linalg.cross`
* Update copy
* Update copy
* Fix spacing
Returns the cross product of 3-element vectors. If ``x1`` and ``x2`` are multi-dimensional arrays (i.e., both have a rank greater than ``1``), then the cross-product of each pair of corresponding 3-element vectors is independently computed.
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Returns the cross product of 3-element vectors.
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If ``x1`` and/or ``x2`` are multi-dimensional arrays (i.e., the broadcasted result has a rank greater than ``1``), then the cross-product of each pair of corresponding 3-element vectors is independently computed.
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Parameters
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----------
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x1: array
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first input array. Should have a real-valued data type.
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x2: array
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second input array. Must have the same shape as ``x1``. Should have a real-valued data type.
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second input array. Must be compatible with ``x1`` for all non-compute axes (see :ref:`broadcasting`). The size of the axis over which to compute the cross product must be the same size as the respective axis in ``x1``. Should have a real-valued data type.
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.. note::
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The compute axis (dimension) must not be broadcasted.
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axis: int
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the axis (dimension) of ``x1`` and ``x2`` containing the vectors for which to compute the cross product. If set to ``-1``, the function computes the cross product for vectors defined by the last axis (dimension). Default: ``-1``.
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the axis (dimension) of ``x1`` and ``x2`` containing the vectors for which to compute the cross product. Must be an integer on the interval ``[-N, N)``, where ``N`` is the rank (number of dimensions) of the shape determined according to :ref:`broadcasting`. If specified as a negative integer, the function must determine the axis along which to compute the cross product by counting backward from the last dimension (where ``-1`` refers to the last dimension). By default, the function must compute the cross product over the last axis. Default: ``-1``.
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Returns
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-------
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out: array
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an array containing the cross products. The returned array must have a data type determined by :ref:`type-promotion`.
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**Raises**
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- if provided an invalid ``axis``.
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- if the size of the axis over which to compute the cross product is not equal to ``3``.
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- if the size of the axis over which to compute the cross product is not the same (before broadcasting) for both ``x1`` and ``x2``.
first input array. Should have a real-valued data type.
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x2: array
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second input array. Should have a real-valued data type. Corresponding contracted axes of ``x1`` and ``x2`` must be equal.
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second input array. Must be compatible with ``x1`` for all non-contracted axes (see :ref:`broadcasting`). The size of the axis over which to compute the dot product must be the same size as the respective axis in ``x1``. Should have a real-valued data type.
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.. note::
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Contracted axes (dimensions) must not be broadcasted.
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The contracted axis (dimension) must not be broadcasted.
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axis:int
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axis:int
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axis over which to compute the dot product. Must be an integer on the interval ``[-N, N)``, where ``N`` is the rank (number of dimensions) of the shape determined according to :ref:`broadcasting`. If specified as a negative integer, the function must determine the axis along which to compute the dot product by counting backward from the last dimension (where ``-1`` refers to the
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last dimension). By default, the function must compute the dot product over the last axis. Default: ``-1``.
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