In order to improve this specific issue, I got familiar with some multi-threading possibilities in Python. Now, there are some deep issues related to the way Python threads are actually implemented and especially the issues with thread locking known as GIL. Related stuff has been completely chewed in here. In order to avoid facing GIL-related issues, another way is to use Python multiprocessing, which allows the programmer to fully leverage multiple processors on a given machine. Moreover, separate processes are completely separate and one process cannot affect another's variables.
Comparison statistics
Again, I simulated term structure up to 30 years with daily time step, using 10000 paths. I did some quick profiling, in order to find the bottlenecks in the original program (sequential). By looking the column task share, we can see, that there are two tasks, which are consuming the most part of the complete running time: path generations (~54%) and path integrations (~46%). After this, I isolated these two parts and processed these by using multiprocessing scheme.
By using multiprocessing (two configured processes), I managed to decrease the complete running time from 163 seconds to 107 seconds. In general, for all those parts which were enjoying the benefits of multiprocessing, improvement ratio (multiprocessing per sequential) is around 0.65.
CPU puzzle
In order to understand the reason for this improvement, let us take a look at processor architecture in my laptop. First, let us check the "Grand Promise" made by System Monitor.
Based on this view, I actually expected to have four CPU for processing. I was then really surprised, that adding third and fourth process was not decreasing running time any further, than having just two processes. After some usual Stackoverflow gymnastics, I finally got the definition to calculate the real number of CPU available in my laptop.
CPU available is "Core(s) per socket * Socket(s)", which is 2 * 1 in my laptop. So, all in all I have only two CPU available for processing, not four as was shown in that System Monitor. This means, that having more than two CPU available in a laptop, one should expect even better improvement ratio than reported in my statistics here.
Wrapper method
In order to avoid code duplication and to come up with something a bit more generic, I started to dream about the possibility to create a mechanism for applying multiprocessing for any given method, if so desired. Such solution is possible by using Python lambda methods.
# method for executing given lambdas in parallel def MultiprocessingWrapper(targetFunctionList): processList = [] aggregatedResults = [] queue = mp.Manager().Queue() # execute lambda from a given list based on a given index # storing results into queue def Worker(index): result = targetFunctionList[index]() queue.put(result) # start processes, call worker method with index number for i in range(len(targetFunctionList)): process = mp.Process(target = Worker, args = (i,)) processList.append(process) process.start() # join processes, extract queue into results list for process in processList: process.join() aggregatedResults.append(queue.get()) # return list of results for a client return aggregatedResults
Previous method is receiving a list of lambda methods as its argument. The idea is, that there would be always one lambda method for each process to be started. Why? We might face a situation, in which different set of parameters would be required for each lambda (say, all lambdas would be using the same uniform random generator, but with a different values for seeding the generator). In wrapper method, process is then created to start each configured lambda method. Results calculated by given lambda will be stored into queue. Finally, all results will be imported from queue into result list and returned for a client.
As concrete example, the following program segment is first creating two lambda methods for starting GeneratePaths method, but with different seed value for both processes. After this, wrapper method is then fed with the list of lambdas and processed paths will be received into list of results.
# task of generating paths is highly time critical # use multiprocessing for path generation # create lambdas for multiprocessing wrapper # target signature: def GeneratePaths(seed, process, timeGrid, n) nPaths = 10000 nProcesses = 2 seeds = [1834, 66023] nPathsPerProcess = int(nPaths / nProcesses) target_1 = lambda:GeneratePaths(seeds[0], HW1F, grid.GetTimeGrid(), nPathsPerProcess) target_2 = lambda:GeneratePaths(seeds[1], HW1F, grid.GetTimeGrid(), nPathsPerProcess) targetFunctionList = [target_1, target_2] results = MultiprocessingWrapper(targetFunctionList)
The complete program can be found in my GitHub repository. Finally, a couple of discussion threads, which may be useful in order to understand some QuantLib-related issues, are given in here and here. Thanks for reading my blog and again, Merry Christmas for everyone.
-Mike
