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

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.
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Last Solution submitted on Jul 19, 2024

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