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 - RandomStateinstance is used, seeded with seed. If seed is already a- RandomStateor- Generatorinstance, 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 - rvsmethod 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- rvsmethod 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) - >>> 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.