`scipy.stats._multivariate:special_ortho_group_gen`

source: /scipy/stats/_multivariate.py :4282

Signature

class special_ortho_group_gen ( seed = None )

Members

Summary

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

Extended Summary

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

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.

Methods

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

Notes

The rvs method returns a random rotation matrix drawn from the Haar distribution, the only uniform distribution on SO(N). The algorithm generates a Haar-distributed orthogonal matrix in O(N) using the rvs method of ortho_group, then adjusts the matrix to ensure that the determinant is +1.

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)

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np.dot(x, x.T)

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import scipy.linalg

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scipy.linalg.det(x)

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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)

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Aliases

scipy.stats._multivariate.special_ortho_group_gen