Difference between mvnrnd(,sigma) and randn()*chol(sigma)

I would like to create correlated multivariate normal random numbers. It is my understanding that this can either be done using the Statistic Toolbox function mvrnd or by using randn with a Cholesky decomposition of the covariance matrix (sigma).

rng('default')

sigma = [1 .5;0.5 1];

R = mvnrnd(zeros(100,2),sigma);
R2 = randn(100,2)*chol(sigma);

corrcoef(R)
corrcoef(R2)

However, above code gives me different random numbers (although they do exhibit the desired correlation). Why is this the case? Is their a difference between using mvnrnd() and randn()*chol()?

Best regards, Florian

Answer 1

[Peter Perkins]

Did you forget to reset the random number generator between the two calls? mvnrnd and randn draw random values from the same stream.

[Florian]

Yes, that was it. If I put rng('default') after

    R = mvnrnd(zeros(100,2),sigma);

I get the same results!