scipy.stats.ortho_group#
- scipy.stats.ortho_group = <scipy.stats._multivariate.ortho_group_gen object>[source]#
- An Orthogonal matrix (O(N)) random variable. - 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:
- 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 O(N). - See also - Notes - This class is closely related to - special_ortho_group.- Some care is taken to avoid numerical error, as per the paper by Mezzadri. - References [1]- F. Mezzadri, “How to generate random matrices from the classical compact groups”, arXiv:math-ph/0609050v2. - Examples - >>> import numpy as np >>> from scipy.stats import ortho_group >>> x = 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 >>> np.fabs(scipy.linalg.det(x)) 1.0 - 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) >>> # Frozen object with the same methods but holding the >>> # dimension parameter fixed.