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

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.

Methods

``rvs(dim=None, size=1, random_state=None)``

Draw random samples from U(N).

scipy.stats.ortho_group scipy.stats.random_correlation