jax.random.orthogonal

jax.random.orthogonal(key, n, shape=(), dtype=<class 'float'>)

Sample uniformly from the orthogonal group O(n).

If the dtype is complex, sample uniformly from the unitary group U(n).

Parameters:

• key (ArrayLike) – a PRNG key used as the random key.

• n (int) – an integer indicating the resulting dimension.

• shape (Shape) – optional, the batch dimensions of the result. Default ().

• dtype (DTypeLikeFloat) – optional, a float dtype for the returned values (default float64 if jax_enable_x64 is true, otherwise float32).

Returns:

A random array of shape (*shape, n, n) and specified dtype.

Return type:

Array

References

[1]

Mezzadri, Francesco. (2007). “How to generate random matrices from the classical compact groups”. Notices of the American Mathematical Society, 54(5), 592-604. https://arxiv.org/abs/math-ph/0609050.