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 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 axisb : int, optional Axis of axisc : int, optional Axis of axis : int, optional If defined, the axis of |
---|---|
Returns: |
c : ndarray Vector cross product(s). |
Raises: |
ValueError When the dimension of the vector(s) in |
New in version 1.9.0.
Supports full broadcasting of the inputs.
Vector cross-product.
>>> 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) -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]])
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Licensed under the NumPy License.
https://docs.scipy.org/doc/numpy-1.12.0/reference/generated/numpy.cross.html