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

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)
```

Methods

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