scipy.stats.ortho_group

scipy.stats.ortho_group = <scipy.stats._multivariate.ortho_group_gen object>

A matrix-valued O(N) random variable.

Return a random orthogonal matrix, drawn from the O(N) Haar distribution (the only uniform distribution on O(N)).

The dim keyword specifies the dimension N.

Parameters:

dim : scalar

Dimension of matrices

Notes

This class is closely related to special_ortho_group.

Some care is taken to avoid numerical error, as per the paper by Mezzadri.

References

[R617]

F. Mezzadri, “How to generate random matrices from the classical compact groups”, arXiv:math-ph/0609050v2.

Examples

>>> from scipy.stats import ortho_group
>>> x = 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
>>> np.fabs(scipy.linalg.det(x))
1.0

This generates one random matrix from O(3). It is orthogonal and has a determinant of +1 or -1.

Methods

rvs(dim=None, size=1, random_state=None)

Draw random samples from O(N).