cross

→Tensor

cross(x: Tensor, y: Tensor, dim: int = -1)

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Compute the cross product of two 3-D vectors.

Returns the standard 3-D vector cross product

x \times y \,=\, \big(x_2 y_3 - x_3 y_2,\; x_3 y_1 - x_1 y_3,\; x_1 y_2 - x_2 y_1\big).

Parameters

xTensor

First operand. Must have size 3 along dim.

yTensor

Second operand. Same shape as x.

dimint= -1

Axis along which the 3 components are stored. Default -1.

Returns

Tensor

Cross product, same shape as inputs.

Notes

Implemented via gather + element-wise products so that autograd flows through naturally. Recall that $x \times y$ is orthogonal to both $x$ and $y$ , with magnitude $\|x\|\,\|y\|\,\sin\theta$ .

Examples

>>> import lucid
>>> from lucid.linalg import cross
>>> cross(lucid.tensor([1.0, 0.0, 0.0]), lucid.tensor([0.0, 1.0, 0.0]))
Tensor([0.0000, 0.0000, 1.0000])