Parallel Programming in Mathematica

Question

I am interested in running the same function that does some monte carlo evaluations with different values of the arguments on mulitple kernels in a parallel fashion. I also want to ensure that entire function runs on the same kernel, without the computations within the function being distributed across kernels. For example, suppose I have a function (deliberately simplified)

f[a_, b_] := Module[{}, RandomReal[{a, b}]]


In[1]:= LaunchKernels[]

Out[1]= {KernelObject[1, "local"], KernelObject[2, "local"], 
 KernelObject[3, "local"], KernelObject[4, "local"], 
 KernelObject[5, "local"], KernelObject[6, "local"], 
 KernelObject[7, "local"]}

SeedRandom[795132, Method -> "ParallelGenerator"];

m1 = 1; m2 = 2; m3 = 3; m4 = 4; m5 = 5; m6 = 6; m7 = 7; m8 = 8;

DistributeDefinitions[f, m1, m2, m3, m4, m5, m6, m7, m8];

I now want to run f[m1, m2], f[m3, m4], f[m5, m6], f[m7, m8] f[m9, m10] on five different kernels with no information transfer across these kernels, i.e, with a separate stream of random numbers across the different kernels.

How can one do this within Mathematica?

Answer 1

Perhaps you can seed individual kernels with $KernelID and $ProcessID?

ParallelEvaluate[
 Print[$KernelID $ProcessID];
 SeedRandom[$KernelID $ProcessID]
]

And this should go to five different kernels (the FinestGrained option takes every evaluation to a new kernel):

ParallelTable[$KernelID -> f[2 i - 1, 2 i], {i, 5}, Method -> "FinestGrained"]

When i (max 5) is greater than the number of kernels (8), this is going to run into issues though, i.e. f[13,14] may use the same seed as f[2,3].