estimates probability than random vector x in R2 (function)
function prob = montecarlo(A,b,Sigma,notrials); % with mean zero and covariance Sigma satisfies Ax <= b % % Sigma must be postive definite % % based on 100*notrials trials randn('state',0); m = size(A,1); R = chol(Sigma); % Y = R^{-T}X has covariance I X = R'*randn(2,notrials); prob = length(find(sum(A*X - b(:,ones(1,notrials)) < 0) == m))/notrials; for i=1:99 X = R'*randn(2,notrials); prob = 0.5*(prob + ... length(find(sum(A*X - b(:,ones(1,notrials)) < 0) == m))/notrials); end;