Generate a point cloud named `Simplex-Lattice Design` - MATLAB Cody - MATLAB Central

Problem 60441. Generate a point cloud named `Simplex-Lattice Design`

Difficulty:
(8)
Rate
The input is the number of dimensions M and the parameter H.
The output is a point cloud W involving N points.
W is N uniformly distributed points with M dimensions on the unit hyperplane.
The relationship between M, H and point cloud size N is as follows.
In the case of M=3 dimensions, the results for cases where H is 1 to 6 are as follows.
Ex)
  • [W,N] = SLD(M=3,H=2) -> W = [0 0 1; 0 .5 .5; 0 1 0; .5 0 .5; .5 .5 0; 1 0 0]; N = 6;
  • [W,N] = SLD(M=5,H=2) -> W = [0 0 0 0 1; 0 0 0 .5 .5; 0 0 0 1 0; 0 0 .5 0 .5; 0 0 .5 .5 0; 0 0 1 0 0; 0 .5 0 0 .5; 0 .5 0 .5 0; 0 .5 .5 0 0; 0 1 0 0 0; .5 0 0 0 .5; .5 0 0 .5 0; .5 0 .5 0 0; .5 .5 0 0 0; 1 0 0 0 0]; N = 15;
Reference
  • H. Scheffé, “Experiments with mixtures," Journal of the Royal Statistical Society: Series B (Methodological), Vol. 20, No. 2, pp. 344–360, 1958.
  • I. Das and J. E. Dennis, “Normal-boundary intersection: A new method for generating the Pareto surface in nonlinear multicriteria optimization problems," SIAM Journal on Optimization, Vol. 8, No. 3, pp. 631–657, 1998.
Solve

Solution Stats

45.83% Correct | 54.17% Incorrect
Last Solution submitted on Apr 26, 2025

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers8

Suggested Problems

More from this Author10

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!