| import numpy as np | |
| def point_on_hypersphere(n, theta): | |
| """Unit vector on n-sphere using angle theta in first two dimensions.""" | |
| v = np.zeros(n) | |
| v[0] = np.cos(theta) | |
| v[1] = np.sin(theta) | |
| return v | |
| def normalize(v): | |
| norm = np.linalg.norm(v) | |
| return v if norm < 1e-12 else v / norm | |