Function get_projections_sphere

ot/sliced.py:291–333

r""" Generates n_projections samples from the uniform distribution on the Stiefel manifold of dimension :math:`d\times 2`: :math:`\mathbb{V}_{d,2}=\{X \in \mathbb{R}^{d\times 2}, X^TX=I_2\}` Parameters ---------- d : int dimension of the space n_projections : int

(d, n_projections, seed=None, backend=None, type_as=None)

def get_projections_sphere(d, n_projections, seed=None, backend=None, type_as=None):
    r"""
    Generates n_projections samples from the uniform distribution on the Stiefel manifold of dimension :math:`d\times 2`: :math:`\mathbb{V}_{d,2}=\{X \in \mathbb{R}^{d\times 2}, X^TX=I_2\}`

    Parameters
    ----------
    d : int
        dimension of the space
    n_projections : int
        number of samples requested
    seed: int or RandomState, optional
        Seed used for numpy random number generator
    backend:
        Backend to use for random generation
    type_as: optional
        Type to use for random generation

    Returns
    -------
    out: ndarray, shape (n_projections, d, 2)

    Examples
    --------
    >>> n_projections = 100
    >>> d = 5
    >>> projs = get_projections_sphere(d, n_projections)
    >>> np.allclose(np.einsum("nij, nik -> njk", projs, projs), np.eye(2))  # doctest: +NORMALIZE_WHITESPACE
    True
    """
    if backend is None:
        nx = NumpyBackend()
    else:
        nx = backend

    if isinstance(seed, np.random.RandomState) and str(nx) == "numpy":
        Z = seed.randn(n_projections, d, 2)
    else:
        if seed is not None:
            nx.seed(seed)
        Z = nx.randn(n_projections, d, 2, type_as=type_as)

    projections, _ = nx.qr(Z)
    return projections


def projection_sphere_to_circle(