matrix_props.kp_norm

Computes the Kp-norm for matrices or vectors.

Functions

kp_norm(mat, k, p)

Compute the kp_norm of vector or matrix.

Module Contents

matrix_props.kp_norm.kp_norm(mat, k, p)

Compute the kp_norm of vector or matrix.

Calculate the p-norm of a vector or the k-largest singular values of a matrix.

Examples

To compute the p-norm of a vector:

>>> import numpy as np
>>> from toqito.matrix_props import kp_norm
>>> from toqito.states import bell
>>> np.around(kp_norm(bell(0), 1, np.inf), decimals=2)
np.float64(1.0)

To compute the k-largest singular values of a matrix:

>>> import numpy as np
>>> from toqito.matrix_props import kp_norm
>>> from toqito.rand import random_unitary
>>> np.around(kp_norm(random_unitary(5), 5, 2), decimals=2)
np.float64(2.24)
Parameters:

  • mat (numpy.ndarray) – 2D numpy ndarray

  • k (int) – The number of singular values to take.

  • p (int) – The order of the norm.

Returns:

The kp-norm of a matrix.

Return type:

float