# scipy.stats.special_ortho_group#

scipy.stats.special_ortho_group = <scipy.stats._multivariate.special_ortho_group_gen object>[source]#

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.

Parameters:
dimscalar

Dimension of matrices

seed{None, int, np.random.RandomState, np.random.Generator}, optional

Used for drawing random variates. If seed is None, the 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.

Methods

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

Notes

This class is wrapping the random_rot code from the MDP Toolkit, 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.
```