parallel python, or MPI?

Question

I have a code with heavy symbolic calculations (many multiple symbolic integrals). Also I have access to both an 8-core cpu computer (with 18 GB RAM) and a small 32 cpu cluster. I prefer to remain on my professor's 8-core pc rather than to go to another professor's lab using his cluster in a more limited time, however, I'm not sure it will work on the SMP system, so I am looking for a parallel tool in Python that can be used on both SMP and Clusters and of course prefer the codes on one system to be easily and with least effort modifiable for use on the other system.

So far, I have found Parallel Python (PP) promising for my need, but I have recently told that MPI also does the same (pyMPI or MPI4py). I couldn't approve this as seemingly very little is discussed about this on the web, only here it is stated that MPI (both pyMPI or MPI4py) is usable for clusters only, if I am right about that "only"!

Is "Parallel Python" my only choice, or I can also happily use MPI based solutions? Which one is more promising for my needs?

PS. It seems none of them have very comprehensive documentations so if you know some links to other than their official websites that can help a newbie in parallel computation I will be so grateful if you would also mention them in your answer :)

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Edit.

My code has two loops one inside the other, the outer loop cannot be parallelized as it is an iteration method (a recursive solution) each step depending on the values calculated within its previous step. The outer loop contains the inner loop alongside 3 extra equations whose calculations depend on the whole results of the inner loop. However, the inner loop (which contains 9 out of 12 equations computable at each step) can be safely parallelized, all 3*3 equations are independent w.r.t each other, only depending on the previous step. All my equations are so computationally heavy as each contains many multiple symbolic integrals. Seemingly I can parallelize both the inner loop's 9 equations and the integration calculations in each of these 9 equation separately, and also parallelize all the integrations in other 3 equations alongside the inner loop. You can find my code here if it can help you better understand my need, it is written inside SageMath.

Answer 1

I would look in to multiprocessing (doc) which provides a bunch of nice tools for spawning and working with sub-processes.

To quote the documentation:

multiprocessing is a package that supports spawning processes using an API similar to the threading module. The multiprocessing package offers both local and remote concurrency, effectively side-stepping the Global Interpreter Lock by using subprocesses instead of threads.

From the comments I think the Pool and it's map would serve your purposes (doc).

def work_done_in_inner_loop(arg):
    # put your work code here
    pass

p = Pool(9)
for o in outer_loop:
     # what ever else you do
     list_of_args = [...] # what your inner loop currently loops over
     res = p.map(work_done_in_inner_loop,list_of_args])
     # rest of code

Answer 2

It seems like there are a few reasonable ways to design this.

Let me refer to your jobs as the main job, the 9 intermediate jobs, and the many inner jobs the intermediate jobs can spin off. I'm assuming the intermediate jobs have a "merge" step after the inner jobs all finish, and the same for the outer job.

The simplest design is that the main job fires off the intermediate jobs and then waits for them all to finish before doings its merge step. Then intermediate jobs then fire off the inner jobs and wait for them all to finish before doing their merge steps.

This can work with a single shared queue, but you need a queue that doesn't block the worker pool while waiting, and I don't think multiprocessing's Pool and Queue can do that out of the box. As soon as you've got all of your processes waiting to join their children, nothing gets done.

One way around that is to change to a continuation-passing style. If you know which one of the intermediate jobs will finish last, you can pass it the handles to the other intermediate jobs and have it join on them and do the merge, instead of the outer job. And the intermediate similarly pass off the merge to their last inner job.

The problem is that you usually have no way of knowing what's going to finish last, even without scheduling issues. So that means you need some form of either sharing (e.g., a semaphore) or message passing between the jobs to negotiate that among themselves. You can do that on top of multiprocessing. The only problem is that it destroys the independence of your jobs, and you're suddenly dealing with all the annoying problems of shared concurrency.

A different alternative is to have separate pools and queues for each intermediate job, and some kind of load balancing between the pools that can ensure that each core is running one active process.

Or, of course, a single pool with a more complicated implementation than multiprocessing's, which does either load balancing or cooperative scheduling, so a joiner doesn't block a core.

Or a super-simple solution: Overschedule, and pay a little cost in context switching for simplicity. For example, you can run 32 workers even though you've only got 8 cores, so you've got 22 active workers and 10 waiting. Each core has 2 or 3 active workers, which will slow things down a bit, but maybe not too badly—and at least nobody's idle, and you didn't have to write any code beyond passing a different parameter to the multiprocessing.Pool constructor.

At any rate, multiprocessing is very simple, and it has almost no extra concepts that won't apply to other solutions. So it may take less time to play with it until you run into a brick wall or don't, than to try to figure out in advance whether it'll work for you.