nengolib.stats.random_orthogonal

nengolib.stats.random_orthogonal(d, rng=None)

Returns a random orthogonal matrix.

Parameters:

d : integer

Positive dimension of returned matrix.

rng : numpy.random.RandomState or None, optional

Random number generator state.

Returns:

samples : (d, d) np.array

Random orthogonal matrix (an orthonormal basis); linearly transforms any vector into a uniformly sampled vector on the d–ball with the same L2 norm.

See also

ScatteredHypersphere

Examples

>>> from nengolib.stats import random_orthogonal, sphere
>>> rng = np.random.RandomState(seed=0)
>>> u = sphere.sample(1000, 3, rng=rng)
>>> u[:, 0] = 0
>>> v = u.dot(random_orthogonal(3, rng=rng))

>>> import matplotlib.pyplot as plt
>>> from mpl_toolkits.mplot3d import Axes3D
>>> ax = plt.subplot(111, projection='3d')
>>> ax.scatter(*u.T, alpha=.5, label="u")
>>> ax.scatter(*v.T, alpha=.5, label="v")
>>> ax.patch.set_facecolor('white')
>>> ax.set_xlim3d(-1, 1)
>>> ax.set_ylim3d(-1, 1)
>>> ax.set_zlim3d(-1, 1)
>>> plt.legend()
>>> plt.show()

(Source code)