As a part of my research studies, I have developed a code which is essentially based on random generation of numbers. The first version of the code was written in MATLAB, however, for some reasons I transferred it to Mathematica for further development. In order to assure the correctness of my code in Mathematica, I decided to compare the corresponding results with those from MATLAB. It happened that I was not able to carry out my comparison quantitatively, as I couldn't tweak the random number generators to give the same quantities.
As written in the Mathematica documentation, the possible random number generation methods are as follows:
On the other hand, the MATLAB documentation reads
So as it appears, the Mersenne Twister is the only common algorithm between MATLAB and Mathematica, but, as shown below, it does not generate the same number in the two environments.
What is the reason for this?