Thanks for adding your thoughts. You are correct that the best solution depends on what your circumstances are, and that for the Minit to work, I am assuming they are indices.

–Loren

It should be noted that the vecIM solution creates an array imap that is as large (in length) as the biggest element in a. This will slow down the computation by memory hogging.

The best solution is (as always in Matlab) dependent on your particular application and size of matrices.

With the same a and Minit that you created, try the following:
% Same size of matrices but scaled values
a=a*1000000;
Minit=Minit*1000000;

and rerun your timing experiment.

Due to better hardware since 2006 i also added a larger value of N
N = [1 10 100 1000 10000 100000 1000000];

I also want to point out that you left out the important requirement that the values in a and Minit need to be integers for the loopFR and vecIM to work since they rely on indexing.

Try
% Non integer values
a=a+.1;
Minit=Minit+.1;

Regards
/K