scipy.stats.unitary_group

scipy.stats.unitary_group = <scipy.stats._multivariate.unitary_group_gen object>

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.

See also

ortho_group

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

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>>> 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)

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Methods

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

Draw random samples from U(N).