Roger Stafford

@Joel: det(u*v') can also be -1.

Nice. I'm trying to generate random data within a simplex defined by linear inequality constraints.

Lets say I already have the N vertices of the simplex defined by the inequalities. Is it then correct to first generate a random sample in the interval [0,1] with a sum equal to 1, and then take the inner product of this sample with the vector of vertices?

Something along the lines of:

X = rand(6,2);
k = convhull(X);
plot(X(k,1),X(k,2),'b'), hold on
nv = numel(k)-1; % Nmuber of vertices
X = X(k(1:end-1),:); % Remove repeated first vertex
L = randfixedsum(size(X,1),1000,1,0,1);
Y = L'*X;
plot(Y(:,1),Y(:,2),'r.'), hold off

Maybe I shouldn't trust my vision on this, but the samples don't really look uniformly spread within the simplex. For some reason they only seem to do for a triangle.

Any thoughts?

Thanks

Christophe

Hi!

Thank you for sharing this neat function! I was wondering if you could give me any reference explaining the theoretical concepts underlying this script?

Thanks,
Vincent