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Re: Generate random numbers with fixed sum and different constraints
Posted:
Nov 18, 2012 1:46 PM
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I have not fully tested, but it should go like this:
% lower + upper bounds
lo = [1 0 2 1 0];
up = [5 6 4 4 2];
% target sum
s = 15;
% number of samples
n = 1000;
m = length(lo);
slo = sum(lo);
sup = sum(up);
x0 = interp1([slo; sup], [lo; up], s);
if any(isnan(x0))
error('no solution exists')
end
x0 = x0(:);
B = null(ones(size(lo)));
A = [-B; B];
b = [x0-lo(:); up(:)-x0];
% FEX: http://www.mathworks.com/matlabcentral/fileexchange/30892
% Thank you Matt
[V,nr,nre] = lcon2vert(A,b,[],[],tol);
T = delaunayn(V);
P = V(T,:);
P = reshape(P, [size(T) m-1]);
P = permute(P, [3 2 1]);
np = size(P,3);
% http://www.mathworks.com/matlabcentral/fileexchange/9700
% % Thank you Roger
Q = bsxfun(@minus, P, P(:,end,:));
Q(:,end,:) = [];
vol = arrayfun(@(k) det(Q(:,:,k)), 1:np);
vol = abs(vol);
w = randfixedsum(m,n,1,0,1);
% generate n samples of v with probability vol
vol = vol / sum(vol);
c = cumsum(vol); c(end)=1;
[~, i] = histc(rand(1,n),[0 c]);
V = P(:,:,i);
y = zeros(m-1, n);
for k=1:n
y(:,k) = V(:,:,k)*w(:,k);
end
x = bsxfun(@plus, x0, B*y);
% Bruno
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