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