ParallelTable running on outermost index only

Question

I need to run a simple ParallelTable:

ParallelTable[
  {tab1[[i1]], tab2[[i2]], tab3[[i3]], tab4[[i4]],
   fun[tab1[[i1]],tab2[[i2]],tab3[[i3]],tab4[[i4]]]
  }, 
  {i1, 1, n1}, {i2, 1, n2}, {i3, 1,n3}, {i4, 1, n4}
]

The computation, however, is parallelized only on the outermost index i1 and not on all of them. The problem is that I have more cores than n1 and so I'm not computing this table as fast as I had hoped. Is there a simple way to run on as many cores as possible without having to rewrite the table in a flattened version?

Answer 1

If you don't need a high-dimensional tensor as the output (from the code it seems you don't, since you're including all parameters in each output), I recommend you use a flattened table instead. This will make sure that the available cores can be used optimally.

Tuples gives you an easy way to parallelize this calculation. Assuming that the length of tab1 is n1, etc.,

ParallelMap[Append[#, fun @@ #]&, Tuples[{tab1, tab2, tab3, tab4}]]

will do what you need.

I typically use this approach (though I like to define fun to take a list as one argument instead of a number of arguments).

Answer 2

One solution that I can see is nesting a ParallelTable inside a Table.

Original code (I have four cores, so I let the loop index stop at 3 for this demo):

ParallelTable[Labeled[Framed[{i, j}], $KernelID], {i, 3}, {j, 6}]// TableForm

Indeed, only 3 cores have been used

Table[ParallelTable[Labeled[Framed[{i, j}], $KernelID], {j, 6}], {i, 3}] // TableForm

Now all four are used.