Random number generation

Function which generation n random numbers between 0 and 1

Description

Function which generation n random numbers between 0 and 1 using the formula ri = (177786 ri-1 + 64654 ri-6) mod (2^31-1)

• MATLAB release: MATLAB 7.0.1 (R14SP1)

[John D'Errico]

If you care even remotely about speed of execution, this is not the code you wish to use.

>> tic,r = prng(10000,6);toc
Elapsed time is 2.749655 seconds.
>> tic,r = rand(1,10000);toc
Elapsed time is 0.001816 seconds.

Who cares if the period of this RNG is as large as the author claims? As slow as this code is, you will never come close to that period.

I'd suggest using Matlab's builtin rand. If you prefer the Twister algorithm, it too is available now in matlab. Older Matlab releases can use Peter's code from the file exchange.

http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=6614&objectType=file

[Paul de Wit]

Attempted to decrease the time of execution

tic,r = prng(10000,6);toc
Elapsed time is 0.033910 seconds.
tic,r = rand(1,10000);toc
Elapsed time is 0.000387 seconds.

Unfortuately still no where near as good as Matlab please suggest any further improvements

[John D'Errico]

This seems quite a bit better for speed now. Its still not as fast as the builtin rand, but I imagine to get maximum speed from this you would need carefully written compiled code. Thanks for the improvement.

I've noticed one other point since - if you call this repeatedly with the same starting integer, you get the same exact pseudo-random sequence.

If you call it repeatedly with a different starting point, then the sequence is the same for the for the first few values. Changing the starting point introduces an offset.

>> r = prng(10,7)'
r =
        0.763
      0.20333
      0.40782
      0.48588
     0.076487
      0.13995
       0.4621
      0.27007
      0.67838
       0.2846

>> r = prng(10,8)'
r =
      0.20333
      0.40782
      0.48588
     0.076487
      0.13995
      0.86102
        0.669
     0.077306
      0.68352
      0.91051

So, if you need many random numbers, generate the entire set of numbers that you will ever need in one call.

To repair this, can this RNG be set to pick up where the last call left off? Could you use a persistent variable to have it remember the final state of the RNG?

[Paul Connelly]

How can I backtrack a PRN. I'm trying to find an algorithm that I can scramble and then unscramble with PRN. Any ideas pointers?