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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

help(scipy.stats.special_ortho_group)

A Special Orthogonal matrix (SO(N)) random variable.

Return a random rotation matrix, drawn from the Haar distribution
(the only uniform distribution on SO(N)) with a determinant of +1.

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
seed : {None, int, np.random.RandomState, np.random.Generator}, optional
    Used for drawing random variates.
    If `seed` is `None`, the `~np.random.RandomState` singleton is used.
    If `seed` is an int, a new ``RandomState`` instance is used, seeded
    with seed.
    If `seed` is already a ``RandomState`` or ``Generator`` instance,
    then that object is used.
    Default is `None`.

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
--------
>>> import numpy as np
>>> 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.

Alternatively, the object may be called (as a function) to fix the `dim`
parameter, returning a "frozen" special_ortho_group random variable:

>>> rv = special_ortho_group(5)
>>> # Frozen object with the same methods but holding the
>>> # dimension parameter fixed.

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

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