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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My code is size 94.
Misleading graphical problem description.
Inadequate verbal problem description.
Am I just supposed to keep pushing buttons until it works?
I get this all the time IRL, but it's disappointing to find it here.
The graphic makes it look like we are painting a corner, that is, that the points all have at least one zero value. But it again appears that this is a constituency problem, that is, the sum of every row is one, or in dimensions, every point falls in the plane where the sum of all of the Cartesian coordinates is one. I first encountered these as the sand-silt-clay triangle in the eighties, unless Dennis showed them to me in the seventies and I forgot. But Dennis is big on rocks not soil, so probably not.