dpnp.linalg.norm

dpnp.linalg.norm(x, ord=None, axis=None, keepdims=False)[source]

Matrix or vector norm.

For full documentation refer to numpy.linalg.norm.

Parameters:

x ({dpnp.ndarray, usm_ndarray}) -- Input array. If axis is None, x must be 1-D or 2-D, unless ord is None. If both axis and ord are None, the 2-norm of x.ravel will be returned.
ord ({int, float, inf, -inf, "fro", "nuc"}, optional) -- Norm type. inf means dpnp's inf object. The default is None.
axis ({None, int, 2-tuple of ints}, optional) -- If axis is an integer, it specifies the axis of x along which to compute the vector norms. If axis is a 2-tuple, it specifies the axes that hold 2-D matrices, and the matrix norms of these matrices are computed. If axis is None then either a vector norm (when x is 1-D) or a matrix norm (when x is 2-D) is returned. Default: False.
keepdims (bool, optional) -- If this is set to True, the axes which are normed over are left in the result as dimensions with size one. With this option the result will broadcast correctly against the original x. Default: False.

Returns:

out -- Norm of the matrix or vector(s).

Return type:

dpnp.ndarray

Examples

>>> import dpnp as np
>>> a = np.arange(9) - 4
>>> a
array([-4, -3, -2, -1,  0,  1,  2,  3,  4])
>>> b = a.reshape((3, 3))
>>> b
array([[-4, -3, -2],
       [-1,  0,  1],
       [ 2,  3,  4]])

>>> np.linalg.norm(a)
array(7.74596669)
>>> np.linalg.norm(b)
array(7.74596669)
>>> np.linalg.norm(b, 'fro')
array(7.74596669)
>>> np.linalg.norm(a, np.inf)
array(4.)
>>> np.linalg.norm(b, np.inf)
array(9.)
>>> np.linalg.norm(a, -np.inf)
array(0.)
>>> np.linalg.norm(b, -np.inf)
array(2.)

>>> np.linalg.norm(a, 1)
array(20.)
>>> np.linalg.norm(b, 1)
array(7.)
>>> np.linalg.norm(a, -1)
array(0.)
>>> np.linalg.norm(b, -1)
array(6.)
>>> np.linalg.norm(a, 2)
array(7.74596669)
>>> np.linalg.norm(b, 2)
array(7.34846923)

>>> np.linalg.norm(a, -2)
array(0.)
>>> np.linalg.norm(b, -2)
array(4.35106603e-18) # may vary
>>> np.linalg.norm(a, 3)
array(5.84803548) # may vary
>>> np.linalg.norm(a, -3)
array(0.)

Using the axis argument to compute vector norms:

>>> c = np.array([[ 1, 2, 3],
...               [-1, 1, 4]])
>>> np.linalg.norm(c, axis=0)
array([ 1.41421356,  2.23606798,  5.        ])
>>> np.linalg.norm(c, axis=1)
array([ 3.74165739,  4.24264069])
>>> np.linalg.norm(c, ord=1, axis=1)
array([ 6.,  6.])

Using the axis argument to compute matrix norms:

>>> m = np.arange(8).reshape(2,2,2)
>>> np.linalg.norm(m, axis=(1,2))
array([  3.74165739,  11.22497216])
>>> np.linalg.norm(m[0, :, :]), np.linalg.norm(m[1, :, :])
(array(3.74165739), array(11.22497216))