dpnp.linalg.matrix_norm

dpnp.linalg.matrix_norm(x, /, *, keepdims=False, ord='fro')[source]

Computes the matrix norm of a matrix (or a stack of matrices) x.

This function is Array API compatible.

For full documentation refer to numpy.linalg.matrix_norm.

Parameters:

x ({dpnp.ndarray, usm_ndarray}) -- Input array having shape (..., M, N) and whose two innermost dimensions form MxN matrices.
keepdims ({None, 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.
ord ({None, 1, -1, 2, -2, dpnp.inf, -dpnp.inf, 'fro', 'nuc'}, optional) --
The order of the norm. For details see the table under Notes section in dpnp.linalg.norm.

Default: "fro".

Returns:

out -- Norm of the matrix.

Return type:

dpnp.ndarray

See also

dpnp.linalg.norm: Generic norm function.

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.matrix_norm(b)
array(7.74596669)
>>> np.linalg.matrix_norm(b, ord='fro')
array(7.74596669)
>>> np.linalg.matrix_norm(b, ord=np.inf)
array(9.)
>>> np.linalg.matrix_norm(b, ord=-np.inf)
array(2.)

>>> np.linalg.matrix_norm(b, ord=1)
array(7.)
>>> np.linalg.matrix_norm(b, ord=-1)
array(6.)
>>> np.linalg.matrix_norm(b, ord=2)
array(7.34846923)
>>> np.linalg.matrix_norm(b, ord=-2)
array(4.35106603e-18) # may vary