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

dimscalar

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

1

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).

scipy.stats.special_ortho_group scipy.stats.unitary_group