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 aRandomState
orGenerator
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 thervs
method ofortho_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)
>>> 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.