How can I generate the same random number in Mathematica and MATLAB?

Question

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?

Answer 1

If it is solely for regression testing, the quality of the random numbers doesn't matter very much. You can substitute a better random number generator once you know the Mathematica version matches the MATLAB version.

In which case, you might use something like

Mathematica

Module[{seed = 123456789},
 random := With[{a = 69069, b = 1},
   seed = Mod[a seed + b, 2^32];
   N[seed/2^32]
   ]
 ]

    Table[random, {5}]
(* {0.355504, 0.286935, 0.320493, 0.135751,0.213987} *)

Octave

function u = Random
  persistent seed
  if isempty(seed)
    seed = uint64(123456789);
  end

  a = uint64(69069);
  b = uint64(1);
  seed = mod(a * seed + b, 2^32);
  u = (2^-32) * double(seed);
end

Octave:> [Random, Random, Random, Random, Random]
ans =

   0.35550   0.28694   0.32049   0.13575   0.21399