How can I avoid an out of memory error (correlation matrix too large) with a bivariate normal distribution?

I am trying to create a bivariate normal distribution using MATLAB,

The two well known and easy methods are:

Y = mvnrnd(Mu , Sigma*CorrelationMatrix , Simulations);

or

Y = randn(Simulations,size)*chol(Sigma*CorrelationMatrix );

I am getting an out of memory message since the CM (CorrelationMatrix) is too large.

Attempts to solve the problem: (with no luck so far)

- I tried to do matrix partitioning, i.e. partition the CM into n*m blocks and using the following technique:

Y = randn(Simulations,size)*chol(Sigma*CorrelationMatrix );

However "chol" complains about CM not being a positive definite matrix, which makes sense.

- Using "sparse" I was able to push the size a bit up before getting the "Out of Memory" error,

- Using "single" instead of "double" seem to do better than "sparse" but it is still way far from the target size.

Is there any other way to handle large matrices problem?

Answer 1

[Daniel Shub]

More RAM.

[SM]

Thank you Daniel for the reply,

I have 8G of ram, the max my mac BP can take,