scipy.stats.special_ortho_group¶
- scipy.stats.special_ortho_group = <scipy.stats._multivariate.special_ortho_group_gen object at 0x2b23194db310>[source]¶
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.
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 http://en.wikipedia.org/wiki/Orthogonal_matrix#Randomization
See also the similar ortho_group.
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.
Methods
rvs(dim=None, size=1, random_state=None) Draw random samples from SO(N).