Add random module

We could add functions that uniformly sample the bloch sphere, randomly
generate unitaries, etc.

README.md

@@ -35,3 +35,6 @@ for i in qutil.ui.progressbar(range(n)):
 
 ## qutil.qi
 In this module there are some quantities and functions related to quantum information, like the Pauli matrices in different data types.
+
+## qutil.random
+Here we collect functions for random numbers like `random_hermitian` to generate random Hermitian matrices.

qutil/__init__.py

-from . import const, linalg, matlab, plotting, ui, qi
+from . import const, linalg, matlab, plotting, ui, qi, random
 
 __version__ = '0.1'
 
-__all__ = ['const', 'linalg', 'matlab', 'ui', 'plotting', 'qi']
+__all__ = ['const', 'linalg', 'matlab', 'ui', 'plotting', 'qi', 'random']

qutil/random.py

+"""
+This module contains random functions
+"""
+import numpy as np
+from numpy import ndarray
+
+
+def random_hermitian(d: int = 2, n: int = 1, std: float = 1,
+                     mean: float = 0) -> ndarray:
+    r"""
+    Generate *n* random Hermitian matrices of dimension *d* drawn from a
+    Gaussian ensemble :math:`~\mathcal{N}(\mu, \sigma^2)`.
+    """
+    H_ii = np.random.randn(n, d)*std
+    H_ij = np.random.randn(2, n, (d**2 - d)//2)*std/np.sqrt(2)
+    H = np.empty((n, d, d), dtype=complex)
+    H[:, range(d), range(d)] = H_ii
+    H[:, ~np.tri(d, k=0, dtype=bool)] = H_ij[0] + 1j*H_ij[1]
+    H[:, np.tri(d, k=-1, dtype=bool)] = H_ij[0] - 1j*H_ij[1]
+    return H.squeeze() + mean