scipy.stats.unitary_group — SciPy v1.15.2 Manual (original) (raw)

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 a RandomState or Generator instance, then that object is used. Default is None.

Notes

This class is similar to ortho_group.

References

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]]) # may vary

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