Equally-Spaced Points

Optimal space filling design in an arbitrary number of dimensions. Fixed or preexisting data points can be specified.

Syntax

osf

osf(x)

osf(n,p)

osf(x,i,j)

osf(n,p,i,j)

osf(settings)

Where:

n Number of samples

p Number of dimensions

i Number of cycles

j Number of iterations

x Initial solution state

settings

settings.num Number of samples (n)

settings.dim Number of dimensions (p)

settings.cyc Number of cycles (i)

settings.itr Number of iterations (j)

settings.ini Initial solution state (x)

settings.fix Fixed data points (f)

settings.lim Limit for dimension range (r)

settings.fig Produce output figure (0 or 1)

Description

Generates n uniformly-sampled points in p dimensions by repeating i cycles of j iterations each. In each iteration, each point's position is altered based on its nearest-neighbour information, seeking to minimise the potential energy between points (assumed to be proportional to the inverse of their squared pointwise distance).

It is advised that the user sets the parameter h to 0 when convenient, and to note that the brute-force nearest neighbour search is slow for larger sample sizes and dimensions. A k-d tree, pre-defined distance matrices or approximate nearest-neighbour search algorithms can be more efficient for those cases.

Examples

% Demo uses of the function (Cases 1-5)

for i = 1:5

osf;

end

% Function with (N, P) and with (N, P, I, J) (Cases 6-7)

osf(40,2);

osf(12,2,10,700);

% Optimise a LHS and an OSF solution (Cases 8-9)

x = osf(lhsdesign(12,2));

osf(x,40,1000);

% Explore a pre-existing design space region (Case 10)

settings.num = 5;

settings.dim = 2;

settings.cyc = 12;

settings.itr = 1000;

settings.ini = [];

settings.fix = x;

settings.lim = [0.5,1; 0.5,1];

settings.fig = 1;

osf(settings);