numpy.cross

语法

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

功能

Return the cross product of two (arrays of) vectors. The cross product of a and b in :math: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.

计算两个向量（向量数组）的叉乘。叉乘返回的数组既垂直于a，又垂直于b。如果a,b是向量数组，则向量在最后一维定义。该维度可以为2，也可以为3. 为2的时候会自动将第三个分量视作0补充进去计算。

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.

axisa, axisb, axisc 分别指定两个输入和输出c的向量所在的维度。而axis则可以覆盖前三个参数，为全局指定向量所在维度。

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.

当向量所在axis的dimension不为2或者3时，raise ValueError.

Notes

.. versionadded:: 1.9.0 Supports full broadcasting of the inputs. 支持广播。

Examples


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)
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]])