numpy.cross¶

numpy.
cross
(a, b, axisa=1, axisb=1, axisc=1, axis=None)[source]¶ Return the cross product of two (arrays of) vectors.
The cross product of a and b in 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 zcomponent 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
New in version 1.9.0.
Supports full broadcasting of the inputs.
Examples
Vector crossproduct.
>>> x = [1, 2, 3] >>> y = [4, 5, 6] >>> np.cross(x, y) array([3, 6, 3])
One vector with dimension 2.
>>> x = [1, 2] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, 6, 3])
Equivalently:
>>> x = [1, 2, 0] >>> y = [4, 5, 6] >>> np.cross(x, y) array([12, 6, 3])
Both vectors with dimension 2.
>>> x = [1,2] >>> y = [4,5] >>> np.cross(x, y) array(3)
Multiple vector crossproducts. Note that the direction of the cross product vector is defined by the righthand 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]])