dpnp.cross

dpnp.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 \(R^3\) 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.

For full documentation refer to numpy.cross.

Parameters:

a ({dpnp.ndarray, usm_ndarray}) -- First input array.
b ({dpnp.ndarray, usm_ndarray}) -- Second input array.
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, None}, optional) -- If defined, the axis of a, b and c that defines the vector(s) and cross product(s). Overrides axisa, axisb and axisc. Default: None.

Returns:

out -- Vector cross product(s).

Return type:

dpnp.ndarray

See also

dpnp.linalg.cross: Array API compatible version.
dpnp.inner: Inner product.
dpnp.outer: Outer product.

Examples

Vector cross-product.

>>> import dpnp as np
>>> 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]])