mxnet.np.cross

cross(a, b, axisa=-1, axisb=-1, axisc=-1, axis=None)

Return the cross product of two (arrays of) vectors.

The cross product of a and b in \(R^3\) is a vector perpendicular to both a and b. If a and b are arrays of vectors, the vectors are defined by the last axis of a and b by default, and these axes can have dimensions 2 or 3. Where the dimension of either a or b is 2, the third component of the input vector is assumed to be zero and the cross product calculated accordingly. In cases where both input vectors have dimension 2, the z-component of the cross product is returned.

Parameters

  • a (ndarray) – Components of the first vector(s).

  • b (ndarray) – Components of the second vector(s).

  • axisa (int, optional) – Axis of a that defines the vector(s). By default, the last axis.

  • axisb (int, optional) – Axis of b that defines the vector(s). By default, the last axis.

  • axisc (int, optional) – Axis of c containing the cross product vector(s). Ignored if both input vectors have dimension 2, as the return is scalar. By default, the last axis.

  • axis (int, optional) – If defined, the axis of a, b and c that defines the vector(s) and cross product(s). Overrides axisa, axisb and axisc.

Returns

c – Vector cross product(s).

Return type

ndarray

Raises

ValueError – When the dimension of the vector(s) in a and/or b does not equal 2 or 3.

Notes

Supports full broadcasting of the inputs.

Examples

Vector cross-product.

>>> x = np.array([1., 2., 3.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([-3.,  6., -3.])

One vector with dimension 2.

>>> x = np.array([1., 2.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([12., -6., -3.])

Equivalently:

>>> x = np.array([1., 2., 0.])
>>> y = np.array([4., 5., 6.])
>>> np.cross(x, y)
array([12., -6., -3.])

Both vectors with dimension 2.

>>> x = np.array([1., 2.])
>>> y = np.array([4., 5.])
>>> np.cross(x, y)
array(-3.)

Multiple vector cross-products. Note that the direction of the cross product vector is defined by the right-hand rule.

>>> x = np.array([[1., 2., 3.], [4., 5., 6.]])
>>> y = np.array([[4., 5., 6.], [1., 2., 3.]])
>>> np.cross(x, y)
array([[-3.,  6., -3.],
       [ 3., -6.,  3.]])

The orientation of c can be changed using the axisc keyword.

>>> np.cross(x, y, axisc=0)
array([[-3.,  3.],
       [ 6., -6.],
       [-3.,  3.]])

Change the vector definition of x and y using axisa and axisb.

>>> x = np.array([[1., 2., 3.], [4., 5., 6.], [7., 8., 9.]])
>>> y = np.array([[7., 8., 9.], [4., 5., 6.], [1., 2., 3.]])
>>> np.cross(x, y)
array([[ -6.,  12.,  -6.],
       [  0.,   0.,   0.],
       [  6., -12.,   6.]])
>>> np.cross(x, y, axisa=0, axisb=0)
array([[-24.,  48., -24.],
       [-30.,  60., -30.],
       [-36.,  72., -36.]])