generate random numbers with a given correlation in matlab

Q. How to generate random numbers with a pre specified correlation in Matlab?

Ans. Use mvnrnd() function.This function takes mean (vector of 1xk), covariance (matrix of k x k), number of points (n). The output is an nxk matrix which corresponds to the multivariate normal distribution with the specified mean, covariance.

>> n=1000; mu=[-2,2]; sigma=[1 0.5; 0.5 1]; X = mvnrnd(mu, sigma, n);
>> size(X)
ans =
        1000           2

>> mean(X)
ans =
   -2.0350    2.0157

>> cov(X)
ans =
    0.9950    0.4898
    0.4898    0.9894

>> plot(X(:,1), X(:,2), '.')
>> grid

The problem is underspecified if only the correlation matrix is known. In this case, set the mean to a zero vector, covariance to the given correlation matrix.

Tested in MATLAB 7.14.0.739 (R2012a),  Octave 3.6.2