Module « scipy.stats »

Fonction special_ortho_group - module scipy.stats

Signature de la fonction special_ortho_group

def special_ortho_group(dim=None, seed=None) 

Description

special_ortho_group.__doc__

A matrix-valued SO(N) random variable.

    Return a random rotation matrix, drawn from the Haar distribution
    (the only uniform distribution on SO(n)).

    The `dim` keyword specifies the dimension N.

    Methods
    -------
    ``rvs(dim=None, size=1, random_state=None)``
        Draw random samples from SO(N).

    Parameters
    ----------
    dim : scalar
        Dimension of matrices

    Notes
    -----
    This class is wrapping the random_rot code from the MDP Toolkit,
    https://github.com/mdp-toolkit/mdp-toolkit

    Return a random rotation matrix, drawn from the Haar distribution
    (the only uniform distribution on SO(n)).
    The algorithm is described in the paper
    Stewart, G.W., "The efficient generation of random orthogonal
    matrices with an application to condition estimators", SIAM Journal
    on Numerical Analysis, 17(3), pp. 403-409, 1980.
    For more information see
    https://en.wikipedia.org/wiki/Orthogonal_matrix#Randomization

    See also the similar `ortho_group`. For a random rotation in three
    dimensions, see `scipy.spatial.transform.Rotation.random`.

    Examples
    --------
    >>> from scipy.stats import special_ortho_group
    >>> x = special_ortho_group.rvs(3)

    >>> np.dot(x, x.T)
    array([[  1.00000000e+00,   1.13231364e-17,  -2.86852790e-16],
           [  1.13231364e-17,   1.00000000e+00,  -1.46845020e-16],
           [ -2.86852790e-16,  -1.46845020e-16,   1.00000000e+00]])

    >>> import scipy.linalg
    >>> scipy.linalg.det(x)
    1.0

    This generates one random matrix from SO(3). It is orthogonal and
    has a determinant of 1.

    See Also
    --------
    ortho_group, scipy.spatial.transform.Rotation.random