Comparison of RNG streams in pbdMPI and parallel

[Martin Ivanov]

Dear all,

Please compare the following simple scripts:
script 1:

library(pbdMPI, quiet = TRUE)
init()
# here all ranks get the same RNS stream
comm.set.seed(seed=123456)
comm.print(rnorm(5), all.rank = TRUE)
comm.end.seed()
# here each rank gets a different RNG stream
comm.set.seed(seed=123456, diff = TRUE)
comm.print(rnorm(5), all.rank = TRUE)
comm.end.seed()

finalize()

and script 2:

library(parallel, quiet = TRUE)
np <- 2L;
cl <- makeCluster(spec=np, type="MPI", outfile=""); # here all processes get the same RNS stream
a <- parSapply(cl=cl, X=1:2, FUN=function(x) { set.seed(seed=123456, kind="L'Ecuyer"); print(rnorm(5));});
stopCluster(cl=cl);

cl <- makeCluster(spec=np, type="MPI", outfile="");
clusterSetRNGStream(cl=cl, iseed=123456); # here each process gets a different RNS stream
a <- parSapply(cl=cl, X=1:2, FUN=function(x) print(rnorm(5)));
stopCluster(cl=cl);
mpi.quit();

You can run script 1 with "mpirun -np 2 Rscript script1.R" and script 2 with "mpirun -np 1 Rscript script2.R".

I have the following questons:
1. In script 1, the streams are completely different when diff=TRUE from when diff=FALSE. Shouldn't one of the random vectors in the case
diff=TRUE be the same as in the case diff=FALSE? This is exactly the case in script 2.
2. Why are the random vectors generated in script 1 completely different than those generated with script 2,
despite that the seed is the same, that is seed=123456 in both script 1 and script 2?
3. Is there a better way to implement the same stream for all workers in script 2?

Best regards,

Martin Ivanov