reduceDimensions

Generate a seven-dimensional Sobol point set and scramble the points.

p = sobolset(7);
ps = scramble(p,'MatousekAffineOwen')

ps = 
Sobol point set in 7 dimensions (9007199254740992 points)

Properties:
              Skip : 0
              Leap : 0
    ScrambleMethod : MatousekAffineOwen
        PointOrder : standard

Split the first 7168 points in ps into seven levels of 1024 points each. Reduce the first 1024 points to be one-dimensional, the second 1024 points to be two-dimensional, and so on. For each level, compute the variance of the point values in each dimension.

variance = NaN(7);
for level = 1:7
    pr = reduceDimensions(ps,level);
    pr.Skip = (level-1)*1024;
    pts = pr(1:1024,:);
    variance(level,1:level) = var(pts);
end

Plot the variances. The dark blue bars show the variance of the points in the first dimension, the dark orange bars show the variance of the points in the second dimension, and so on.

bar(variance)
xlabel('Level')
ylabel('Variances')