Sample uniformly from d-dimensional ball

sample_dball_uniform.py

def sample_dball_uniform(n_points=1000, n_dims=3):
    """Sample uniformly from d-dimensional ball
    
    The code is inspired by this small note:
    https://blogs.sas.com/content/iml/2016/04/06/generate-points-uniformly-in-ball.html
    https://www.sciencedirect.com/science/article/pii/S0047259X10001211
    
    Parameters
    ----------
    n_points : int
        number of samples
    n_dims : int
        number of dimensions
    Returns
    -------
    x : numpy array
        points sampled from d-ball
    """
    n_points = 10000
    #sample point from d-sphere
    x = np.random.normal(size=[n_points, n_dims])
    x_norms = np.sqrt(np.sum(np.square(x), axis=1)).reshape([-1, 1])
    x_unit = x / x_norms
    #now sample radiuses uniformly
    r = np.random.uniform(size=[n_points, 1])
    u = np.power(r, 1.0/n_dims)
    x = x_unit*u
    return x