Source code for toqito.matrix_props.kp_norm

"""Computes the Kp-norm for matrices or vectors."""

import numpy as np




def kp_norm(mat: np.ndarray, k: int, p: int) -> float | np.floating:
    r"""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

        ```python exec="1" source="above"
        import numpy as np
        from toqito.states import bell
        from toqito.matrix_props import kp_norm

        print(np.around(kp_norm(bell(0), 1, np.inf), decimals=2))
        ```



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

        ```python exec="1" source="above"
        import numpy as np
        from toqito.matrix_props import kp_norm
        from toqito.rand import random_unitary

        print(np.around(kp_norm(random_unitary(5), 5, 2), decimals=2))
        ```



    Args:
        mat: 2D numpy ndarray
        k: The number of singular values to take.
        p: The order of the norm.

    Returns:
        The kp-norm of a matrix.

    """
    dim = min(mat.shape)

    # If the requested norm is the Frobenius norm, compute it using numpy's
    # built-in Frobenius norm calculation, which is significantly faster than
    # computing singular values.
    if k >= dim and p == 2:
        return np.linalg.norm(mat, ord="fro")

    s_vals = np.linalg.svd(mat, compute_uv=False)
    return np.linalg.norm(s_vals[:k], ord=p)