sambal

sambal provides functions to

• uniformly sample a sphere
• uniformly sample a spherical cap of a sphere

Usage

Random vector on sphere

Generate a random vector on a 100-dimensional unit sphere.

import numpy as np
from sambal import random_on_sphere

dim = 100
print(random_on_sphere(dim))

The same as above, but with a random number generator seeded to 0.

import numpy as np
from sambal import random_on_sphere

dim = 100
rng = np.random.default_rng(0)
print(random_on_sphere(dim, rng))

Random vector on spherical cap

Generate a 100-dimensional random vector on a spherical cap whose central axis is [1, 1, 1, ..., 1] / sqrt(100) and whose maximum planar angle is pi/3.

import numpy as np
from sambal import random_on_cap

dim = 100
axis = np.ones(dim)
axis = axis / np.linalg.norm(axis)
max_planar_angle = np.pi/3
print(random_on_cap(axis, max_planar_angle))

The same as above, but with a random number generator seeded to 0.

import numpy as np
from sambal import random_on_cap

rng = np.random.default_rng(0)
dim = 100
axis = np.ones(dim)
axis = axis / np.linalg.norm(axis)
max_planar_angle = np.pi/3
print(random_on_cap(axis, max_planar_angle, rng))

Citing

If you use this code for your research, please cite the paper An O(n) algorithm for generating uniform random vectors in n-dimensional cones.

License

sambal is free software released under the terms of the GNU General Public License, either version 3 of the License, or (at your option) any later version.