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
- 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.
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
>>> 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)
Methods
rvs(dim=None, size=1, random_state=None)
Draw random samples from U(N).