`scipy.stats._multivariate:ortho_group_gen`

source: build-install/usr/lib/python3.14/site-packages/scipy/stats/_multivariate.py:4426

Signature

class ortho_group_gen(seed = None)

Members

Summary

An Orthogonal matrix (O(N)) random variable.

Extended Summary

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
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 O(N).

Notes

This class is closely related to special_ortho_group.

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

Examples

import numpy as np
from scipy.stats import ortho_group
x = ortho_group.rvs(3)

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np.dot(x, x.T)

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array([[ 1.,  0.,  0.],
       [ 0.,  1., -0.],
       [ 0., -0.,  1.]])

import scipy.linalg

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np.fabs(scipy.linalg.det(x))

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np.float64(0.9999999999999998)

This generates one random matrix from O(3). It is orthogonal and has a determinant of +1 or -1. Alternatively, the object may be called (as a function) to fix the `dim` parameter, returning a "frozen" ortho_group random variable:

rv = ortho_group(5)

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Aliases

scipy.stats._multivariate.ortho_group_gen