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.
Solution Stats
Problem Comments
Solution Comments
Show commentsProblem Recent Solvers6
Suggested Problems
-
Replace NaNs with the number that appears to its left in the row.
3012 Solvers
-
9477 Solvers
-
Getting the indices from a matrix
656 Solvers
-
4684 Solvers
-
Matlab Basics - Switching Assignments
313 Solvers
More from this Author9
Problem Tags
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!