scipy.stats.unitary_group#
- scipy.stats.unitary_group = <scipy.stats._multivariate.unitary_group_gen object>[source]#
A matrix-valued U(N) random variable.
Return a random unitary matrix.
The dim keyword specifies the dimension N.
- Parameters:
- dimscalar
Dimension of matrices, must be greater than 1.
- 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 U(N).
See also
Notes
This class is similar to
ortho_group
.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 unitary_group >>> x = unitary_group.rvs(3)
>>> np.dot(x, x.conj().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]])
This generates one random matrix from U(3). The dot product confirms that it is unitary up to machine precision.
Alternatively, the object may be called (as a function) to fix the dim parameter, return a “frozen” unitary_group random variable:
>>> rv = unitary_group(5)