Source code for toqito.rand.random_orthonormal_basis

"""Generates a random orthonormal basis."""

import numpy as np

from toqito.rand import random_unitary




def random_orthonormal_basis(dim: int, is_real: bool = False, seed: int | None = None) -> list[np.ndarray]:
    r"""Generate a real random orthonormal basis of given dimension \(d\).

    The basis is generated from the columns of a random unitary matrix of the same dimension
    as the columns of a unitary matrix typically form an orthonormal basis [@SE_1688950].

    Examples:
        To generate a random orthonormal basis of dimension \(4\),

        ```python exec="1" source="above"
        from toqito.rand import random_orthonormal_basis

        print(random_orthonormal_basis(4, is_real = True))
        ```

        It is also possible to add a seed for reproducibility.

        ```python exec="1" source="above"
        from toqito.rand import random_orthonormal_basis

        print(random_orthonormal_basis(2, is_real=True, seed=42))
        ```

    Args:
        dim: Number of elements in the random orthonormal basis.
        is_real: Bool
        seed: A seed used to instantiate numpy's random number generator.

    """
    random_mat = random_unitary(dim, is_real, seed)
    return [random_mat[:, i] for i in range(dim)]