`numpy:cross`

source: /numpy/_core/numeric.py :1567

Signature

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

Summary

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

Extended Summary

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 : array_like: Components of the first vector(s).
b : array_like: 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 : ndarray: Vector cross product(s).

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.

Dimension-2 input arrays were deprecated in 2.0.0. If you do need this functionality, you can use

def cross2d(x, y):
    return x[..., 0] * y[..., 1] - x[..., 1] * y[..., 0]

Examples

Vector cross-product.

import numpy as np
x = [1, 2, 3]
y = [4, 5, 6]
np.cross(x, y)

✓

One vector with dimension 2.

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

✓

Equivalently:

x = [1, 2, 0]
y = [4, 5, 6]
np.cross(x, y)

✓

Both vectors with dimension 2.

x = [1,2]
y = [4,5]
np.cross(x, y)

✓

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)

✓

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

np.cross(x, y, axisc=0)

✓

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)
np.cross(x, y, axisa=0, axisb=0)

`numpy:cross`

Signature

Summary

Extended Summary

Parameters

Returns

Raises

Notes

Examples

See also

Aliases

Referenced by

This package