Coulomb Particle Optimization

Produce quasi-uniform distributions with minimum potential energy of N samples in P dimensions as per Coulomb's law, within the [0, 1] range

Description

[x,e] = coulomb(n,p): Returns a point cloud x with n samples and p dimensions that have minimum potential energy in the [0,1] range and thus approximating a uniform distribution. Passing the parameter e returns the potential energy of the system x.

The optimizer runs 'A' cycles of 'B' iterations per cycle, seeking the minimun total potential energy in the resulting point cloud. It uses a constant 'C' to scale down the inverse squared distance calculations

Examples

% 1D generation
[x1,e1] = coulomb(12,1);
figure
plot(x1,'o')

% 2D generation
[x2,e2] = coulomb(70,2);
figure
plot(x2(:,1),x2(:,2),'o')

% 3D generation
[x3,e3] = coulomb(100,3);
figure
plot3(x3(:,1),x3(:,2),x3(:,3),'o')

% Multidimensional
[xN,eN] = coulomb(40,5);
figure
hist(xN)

Miguel Moreno, June 2024