reverse_normalised_kronecker.py

def normalise(vec: numpy.ndarray) -> numpy.ndarray:
    norm = numpy.linalg.norm(vec)
    if norm > numpy.finfo(float).eps:
        return vec / norm
    return vec

def reverse_normalised_kronecker(vec: numpy.ndarray, *sizes: int, under_is_zero: float = 1e-10):
    """Reverse a kronecker product of normalised vectors.

    :param vec: The full vector, result of the kronecker product.
    :param sizes: The sizes of the vectors that have been composed with kronecker
        product to give vec.
    :return:
    """
    assert vec.size == numpy.product(sizes)
    if len(sizes) == 1:
        return [normalise(vec)]

    first_size = sizes[0]
    remaining_size = numpy.product(sizes[1:]).astype(int)

    matrix = vec.reshape((first_size, remaining_size))
    first_vec, other_vecs = None, None
    for column in range(remaining_size):
        if numpy.linalg.norm(matrix[:, column]) > under_is_zero:
            first_vec = normalise(matrix[:, column])
            break
    for row in range(first_size):
        if numpy.linalg.norm(matrix[row, :]) > under_is_zero:
            other_vecs = reverse_normalised_kronecker(matrix[row, :], *sizes[1:])
            break
    if first_vec is None or other_vecs is None:
        raise RuntimeError(
            "Can't reverse this kronecker product because one of the "
            + "given dimension is the zero vector (and so cannot be "
            + "normalised). A norm below {}".format(under_is_zero)
            + " is considered as 0."
        )
    return [first_vec] + other_vecs