Problem 59581. Generate a point cloud named `Incremental 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] = ILD(M=3,H=1) -> W = [1/3 1/3 1/3; 0 0 1; 0 1 0; 1 0 0]; N = 4;
  • [W,N] = ILD(M=4,H=2) -> W = [0 0 0 1; 0 0 1/2 1/2; 0 0 1 0; 0 1/2 0 1/2; 0 1/2 1/2 0; 0 1 0 0; 1/8 1/8 1/8 5/8; 1/8 1/8 5/8 1/8; 1/8 5/8 1/8 1/8; 1/4 1/4 1/4 1/4; 1/2 0 0 1/2; 1/2 0 1/2 0; 1/2 1/2 0 0; 5/8 1/8 1/8 1/8; 1 0 0 0]; N = 15;
Reference
  • https://github.com/tomtkg/ILD
  • Tomoaki Takagi, Keiki Takadama, and Hiroyuki Sato, Incremental Lattice Design of Weight Vector Set, Proc. of the 2020 Genetic and Evolutionary Computation Conference (GECCO2020), pp. 1486-1494, 2020. DOI.
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80.0% Correct | 20.0% Incorrect
Last Solution submitted on Jul 19, 2024

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