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Python Pool Multiprocessing Poor CPU Usage

I have a bunch of independent N body sims I want to run in parallel in python. The walltime for individual sims is going to vary dramatically depending on the parameters of the bodies in the sims. It seemed like the best way to do this would be to build pool of processes with the multiprocessing module, give them the sim jobs with the starmap() function, and have them save the results to separate files based on the process ID. However, I've getting awful parallel performance. There is no speedup between 2 and 4 processes (I have 4 CPU on my laptop) and the unix time utility seems to think that the CPU usage percentage is ~150% which is terrible. Below is my code:
import rebound
import numpy as np
import multiprocessing as mp
def two_orbits_one_pool(orbit1, orbit2):
#######################################
print('process number', mp.current_process().name)
#######################################
# build simulation
sim = rebound.Simulation()
# add sun
sim.add(m=1.)
# add two overlapping orbits
sim.add(primary=sim.particles[0], m=orbit1['m'], a=orbit1['a'], e=orbit1['e'], inc=orbit1['i'], \
pomega=orbit1['lop'], Omega=orbit1['lan'], M=orbit1['M'])
sim.add(primary=sim.particles[0], m=orbit2['m'], a=orbit2['a'], e=orbit2['e'], inc=orbit2['i'], \
pomega=orbit2['lop'], Omega=orbit2['lan'], M=orbit2['M'])
sim.move_to_com()
# integrate for 10 orbits of orbit1
P = 2.*np.pi * np.sqrt(orbit1['a']**3)
sim.automateSimulationArchive("archive-{}.bin".format(mp.current_process().name), interval=P)
sim.integrate(10.*P)
if __name__ == "__main__":
# orbit definitions
N_M = 10
N_lop = 10
m = 1e-6
a, e = 1., 0.3
inc, lop, lan = 0., 0., 0.
M = np.linspace(0., 2*np.pi, endpoint=False, num=N_M)
dlop = np.linspace(0., 0.05, num=N_lop)
# orbit dictionaries
args = []
for i in range(dlop.shape[0]):
for j in range(M.shape[0]):
for k in range(M.shape[0]):
args.append( ( {'m':m, 'a':a, 'e':e, 'i':inc, \
'lop':lop, 'lan':lan, 'M':M[j]},
{'m':m, 'a':a, 'e':e, 'i':inc, \
'lop':lop+dlop[i], 'lan':lan, 'M':M[k]} ) )
# fill the pool with orbit jobs
with mp.Pool() as pool:
pool.starmap(two_orbits_one_pool, args)
Could someone explain why this is performing so poorly? I'm much more used to OpenMP and MPI; I'm not that familiar with parallel programming in Python. Overall, I've been quite disappointed in the multiprocessing module. I think maybe I should try using the numba module instead?
EDIT:
In response to Roland Smith's response, I profiled the integration and save time for my code. Here is a stripplot showing the results. As you can see, both Roland Smith's and J_H's suggestions were true. There is a subset of initial conditions that result in extremely long integration times due to close encounters between the bodes. However, in general, the save time was about 5 times longer than the integration time. The job suffers from stragglers and is disk i/o bound.

If there is no discernable speedup, then probably your code is not CPU-bound.
In general, writing to a disk (even an SSD) is much slower than running code on the CPU.
If several worker processes are writing significant amounts of data to disk, that might be the bottleneck.
To diagnose the problem, you have to measure.
You should separate the calculations from the saving of the data; e.g. run sim.integrate() followed by sim.simulationarchive_snapshot() 10 times, and sandwich each of those calls between time.monotonic() calls. Then return the average time of the integration step and the snapshot steps as shown below.
import time
def two_orbits_one_pool(orbit1, orbit2):
#######################################
print('process number', mp.current_process().name)
#######################################
# build simulation
sim = rebound.Simulation()
# add sun
sim.add(m=1.)
# add two overlapping orbits
sim.add(primary=sim.particles[0], m=orbit1['m'], a=orbit1['a'], e=orbit1['e'], inc=orbit1['i'], \
pomega=orbit1['lop'], Omega=orbit1['lan'], M=orbit1['M'])
sim.add(primary=sim.particles[0], m=orbit2['m'], a=orbit2['a'], e=orbit2['e'], inc=orbit2['i'], \
pomega=orbit2['lop'], Omega=orbit2['lan'], M=orbit2['M'])
sim.move_to_com()
# integrate for 10 orbits of orbit1
P = 2.*np.pi * np.sqrt(orbit1['a']**3)
arname = "archive-{}.bin".format(mp.current_process().name)
itime, stime = 0.0, 0.0
for k in range(10):
start = time.monotonic()
sim.integrate(P)
itime += time.monotonic() - start
start = time.monotonic()
sim.simulationarchive_snapshot(arname)
stime += time.monotonic() - start
return (mp.current_process().name, itime/10, stime/10)
# Run the calculations
with mp.Pool() as pool:
data = pool.starmap(two_orbits_one_pool, args)
# Print the times that it took.
for name, itime, stime in data:
print(f"worker {name}: itime {itime} s, stime {stime} s")
That should tell you what the bottleneck is.
Possible solutions if writing to disk is the bottleneck;
Use an SSD to store the simulation results.
Use a RAM-disk to store the simulation results. (Although compared to an SSD not a huge performance boost.)
Check if you can tune your OS for maximum write performance.
Edit1: Given your measurement result, the obvious performance improvement is to save less often.
Another option that might be worth looking at is staggering the writes. That only makes sense if there is significant overlap between the writes from different processes, and if those concurrent writes can saturate the disk I/O subsystem. So you'd have to measure that first.
If there is overlap, create a Lock object in the parent process. Then acquire the lock before (explicitly) saving, and release it after. This won't work with automateSimulationArchive.
A last option is to write your own save function using mmap. Using mmap is somewhat clunky compared to normal file handling in Python. But it can significantly improve performance. However I am unsure that the gains justify the effort in this case.

The straggler effect can have a big impact on such jobs.
straggler effect
Suppose you have N tasks for N cores,
and each task has a different duration.
Order by duration to find min_time and max_time.
All N cores will be busy up through min_time,
but then they go idle, one by one.
Just before max_time, only a single "straggler" core is being used.
predictions
If you can make a decent guess about task duration beforehand,
use that to sort them in descending order.
For T tasks > N cores, schedule the long tasks first.
Then N tasks run for a while, the shortest of those completes,
and the now-idle core picks up a task of "medium" duration.
By the time we get to the T-th task, each core has a random
amount of work still to do, and we're scheduling a "short" task.
So cores are mostly busy doing useful work, right up till near the end.
logging
If you cannot make a useful duration estimate a priori,
at least record the start times and durations.
Use that to figure out whether stragglers are causing you grief,
or if it's something else like L3 cache thrashing.

numpy.random.normal() in multithreaded environment

I was trying to parallelize the generation of normally-distributed random arrays with the numpy.random.normal() function but it looks like the calls from the threads are executed sequentially instead.
import numpy as np
start = time.time()
active_threads = 0
for i in range(100000):
t = threading.Thread(target=lambda x : np.random.normal(0,2,4000), args = [0])
t.start()
while active_threads >= 12:
time.sleep(0.1)
continue
end = time.time()
print(str(end-start))
If i measure the time for a 1 thread process i get the same result as the 12 thread one.
I know this kind of parallelization suffers from a lot of overhead, but even then it should still get some time off with the multithread version.

np.random.normal use a seed variable internally. This variable is retrieved from default_rng() and it is certainly shared between thread so it is not safe to call it using multiple threads (due to possible race conditions). In fact, the documentation provides examples for such a case (see here and there). Alternatively, you can use multiple processes (you need to configure the seed to get different results in different processes). Another solution is to use custom random number generators (RNG) so to use a different RNG object in each thread.

Why is multiprocessing slower here?

I am trying to speed up some code with multiprocessing in Python, but I cannot understand one point. Assume I have the following dumb function:
import time
from multiprocessing.pool import Pool
def foo(_):
for _ in range(100000000):
a = 3
When I run this code without using multiprocessing (see the code below) on my laptop (Intel - 8 cores cpu) time taken is ~2.31 seconds.
t1 = time.time()
foo(1)
print(f"Without multiprocessing {time.time() - t1}")
Instead, when I run this code by using Python multiprocessing library (see the code below) time taken is ~6.0 seconds.
pool = Pool(8)
t1 = time.time()
pool.map(foo, range(8))
print(f"Sample multiprocessing {time.time() - t1}")
From the best of my knowledge, I understand that when using multiprocessing there is some time overhead mainly caused by the need to spawn the new processes and to copy the memory state. However, this operation should be performed just once when the processed are initially spawned at the very beginning and should not be that huge.
So what I am missing here? Is there something wrong in my reasoning?
Edit: I think it is better to be more explicit on my question. What I expected here was the multiprocessed code to be slightly slower than the sequential one. It is true that I don't split the whole work across the 8 cores, but I am using 8 cores in parallel to do the same job (hence in an ideal world the processing time should more or less stay the same). Considering the overhead of spawning new processes, I expected a total increase in time of some (not too big) percentage, but not of a ~2.60x increase as I got here.

Well, multiprocessing can't possibly make this faster: you're not dividing the work across 8 processes, you're asking each of 8 processes to do the entire thing. Each process will take at least as long as your code doing it just once without using multiprocessing.
So if multiprocessing weren't helping at all, you'd expect it to take about 8 times as long (it's doing 8x the work!) as your single-processor run. But you said it's not taking 2.31 * 8 ~= 18.5 seconds, but "only" about 6. So you're getting better than a factor of 3 speedup.
Why not more than that? Can't guess from here. That will depend on how many physical cores your machine has, and how much other stuff you're running at the same time. Each process will be 100% CPU-bound for this specific function, so the number of "logical" cores is pretty much irrelevant - there's scant opportunity for processor hyper-threading to help. So I'm guessing you have 4 physical cores.
On my box
Sample timing on my box, which has 8 logical cores but only 4 physical cores, and otherwise left the box pretty quiet:
Without multiprocessing 2.468580484390259
Sample multiprocessing 4.78624415397644
As above, none of that surprises me. In fact, I was a little surprised (but pleasantly) at how effectively the program used up the machine's true capacity.

#TimPeters already answered that you are actually just running the job 8 times across the 8 Pool subprocesses, so it is slower not faster.
That answers the issue but does not really answer what your real underlying question was. It is clear from your surprise at this result, that you were expecting that the single job to somehow be automatically split up and run in parts across the 8 Pool processes. That is not the way that it works. You have to build in/tell it how to split up the work.
Different kinds of jobs needs need to be subdivided in different ways, but to continue with your example you might do something like this:
import time
from multiprocessing.pool import Pool
def foo(_):
for _ in range(100000000):
a = 3
def foo2(job_desc):
start, stop = job_desc
print(f"{start}, {stop}")
for _ in range(start, stop):
a = 3
def main():
t1 = time.time()
foo(1)
print(f"Without multiprocessing {time.time() - t1}")
pool_size = 8
pool = Pool(pool_size)
t1 = time.time()
top_num = 100000000
size = top_num // pool_size
job_desc_list = [[size * j, size * (j+1)] for j in range(pool_size)]
# this is in case the the upper bound is not a multiple of pool_size
job_desc_list[-1][-1] = top_num
pool.map(foo2, job_desc_list)
print(f"Sample multiprocessing {time.time() - t1}")
if __name__ == "__main__":
main()
Which results in:
Without multiprocessing 3.080709171295166
0, 12500000
12500000, 25000000
25000000, 37500000
37500000, 50000000
50000000, 62500000
62500000, 75000000
75000000, 87500000
87500000, 100000000
Sample multiprocessing 1.5312283039093018
As this shows, splitting the job up does allow it to take less time. The speedup will depend on the number of CPUs. In a CPU bound job you should try to limit it the pool size to the number of CPUs. My laptop has plenty more CPU's but some of the benefit is lost to the overhead. If the jobs were longer this should look more useful.

Multiprocessing in Python. Why is there no speed-up?

I am trying to get to grips with multiprocessing in Python. I started by creating this code. It simply computes cos(i) for integers i and measures the time taken when one uses multiprocessing and when one does not. I am not observing any time difference. Here is my code:
import multiprocessing
from multiprocessing import Pool
import numpy as np
import time
def tester(num):
return np.cos(num)
if __name__ == '__main__':
starttime1 = time.time()
pool_size = multiprocessing.cpu_count()
pool = multiprocessing.Pool(processes=pool_size,
)
pool_outputs = pool.map(tester, range(5000000))
pool.close()
pool.join()
endtime1 = time.time()
timetaken = endtime1 - starttime1
starttime2 = time.time()
for i in range(5000000):
tester(i)
endtime2 = time.time()
timetaken2 = timetaken = endtime2 - starttime2
print( 'The time taken with multiple processes:', timetaken)
print( 'The time taken the usual way:', timetaken2)
I am observing no (or very minimal) difference between the two times measured. I am using a machine with 8 cores, so this is surprising. What have I done incorrectly in my code?
Note that I learned all of this from this.
http://pymotw.com/2/multiprocessing/communication.html
I understand that "joblib" might be more convenient for an example like this, but the ultimate thing that this needs to be applied to does not work with "joblib".

Your job seems the computation of a single cos value. This is going to be basically unnoticeable compared to the time of communicating with the slave.
Try making 5 computations of 1000000 cos values and you should see them going in parallel.

First, you wrote :
timetaken2 = timetaken = endtime2 - starttime2
So it is normal if you have the same times displayed. But this is not the important part.
I ran your code on my computer (i7, 4 cores), and I get :
('The time taken with multiple processes:', 14.95710802078247)
('The time taken the usual way:', 6.465447902679443)
The multiprocessed loop is slower than doing the for loop. Why?
The multiprocessing module can use multiple processes, but still has to work with the Python Global Interpreter Lock, wich means you can't share memory between your processes. So when you try to launch a Pool, you need to copy useful variables, process your calculation, and retrieve the result. This cost you a little time for every process, and makes you less effective.
But this happens because you do a very small computation : multiprocessing is only useful for larger calculation, when the memory copying and results retrieving is cheaper (in time) than the calculation.
I tried with following tester, which is much more expensive, on 2000 runs:
def expenser_tester(num):
A=np.random.rand(10*num) # creation of a random Array 1D
for k in range(0,len(A)-1): # some useless but costly operation
A[k+1]=A[k]*A[k+1]
return A
('The time taken with multiple processes:', 4.030329942703247)
('The time taken the usual way:', 8.180987119674683)
You can see that on an expensive calculation, it is more efficient with the multiprocessing, even if you don't always have what you could expect (I could have a x4 speedup, but I only got x2)
Keep in mind that Pool has to duplicate every bit of memory used in calculation, so it may be memory expensive.
If you really want to improve a small calculation like your example, make it big by grouping and sending a list of variable to the pool instead of one variable by process.
You should also know that numpy and scipy have a lot of expensive function written in C/Fortran and already parallelized, so you can't do anything much to speed them.

If the problem is cpu bounded then you should see the required speed-up (if the operation is long enough and overhead is not significant). But when multiprocessing (because memory is not shared between processes) it's easier to have a memory bound problem.

Inefficient multiprocessing of numpy-based calculations

I'm trying to parallelize some calculations that use numpy with the help of Python's multiprocessing module. Consider this simplified example:
import time
import numpy
from multiprocessing import Pool
def test_func(i):
a = numpy.random.normal(size=1000000)
b = numpy.random.normal(size=1000000)
for i in range(2000):
a = a + b
b = a - b
a = a - b
return 1
t1 = time.time()
test_func(0)
single_time = time.time() - t1
print("Single time:", single_time)
n_par = 4
pool = Pool()
t1 = time.time()
results_async = [
pool.apply_async(test_func, [i])
for i in range(n_par)]
results = [r.get() for r in results_async]
multicore_time = time.time() - t1
print("Multicore time:", multicore_time)
print("Efficiency:", single_time / multicore_time)
When I execute it, the multicore_time is roughly equal to single_time * n_par, while I would expect it to be close to single_time. Indeed, if I replace numpy calculations with just time.sleep(10), this is what I get — perfect efficiency. But for some reason it does not work with numpy. Can this be solved, or is it some internal limitation of numpy?
Some additional info which may be useful:
I'm using OSX 10.9.5, Python 3.4.2 and the CPU is Core i7 with (as reported by the system info) 4 cores (although the above program only takes 50% of CPU time in total, so the system info may not be taking into account hyperthreading).
when I run this I see n_par processes in top working at 100% CPU
if I replace numpy array operations with a loop and per-index operations, the efficiency rises significantly (to about 75% for n_par = 4).

It looks like the test function you're using is memory bound. That means that the run time you're seeing is limited by how fast the computer can pull the arrays from memory into cache. For example, the line a = a + b is actually using 3 arrays, a, b and a new array that will replace a. These three arrays are about 8MB each (1e6 floats * 8 bytes per floats). I believe the different i7s have something like 3MB - 8MB of shared L3 cache so you cannot fit all 3 arrays in cache at once. Your cpu adds the floats faster than the array can be loaded into cache so most of the time is spent waiting on the array to be read from memory. Because the cache is shared between the cores, you don't see any speedup by spreading the work onto multiple cores.
Memory bound operations are an issue for numpy in general and the only way I know to deal with them is to use something like cython or numba.

One easy thing that should bump efficiency up should be to do in-place array operations, if possible -- so add(a,b,a) will not create a new array, while a = a + b will. If your for loop over numpy arrays could be rewritten as vector operations, that should be more efficient as well. Another possibility would be to use numpy.ctypeslib to enable shared memory numpy arrays (see: https://stackoverflow.com/a/5550156/2379433).

I have been programming numerical methods for mathematics and having the same problem: I wasn't seeing any speed-up for a supposedly cpu bounded problem. It turns out my problem was reaching the CPU cache memory limit.
I have been using Intel PCM (Intel® Performance Counter Monitor) to see how the cpu cache memory was behaving (displaying it inside Linux ksysguard). I also disabled 2 of my processors to have clearer results (2 are active).
Here is what I have found out with this code:
def somethinglong(b):
n=200000
m=5000
shared=np.arange(n)
for i in np.arange(m):
0.01*shared
pool = mp.Pool(2)
jobs = [() for i in range(8)]
for i in range(5):
timei = time.time()
pool.map(somethinglong, jobs , chunksize=1)
#for job in jobs:
#somethinglong(job)
print(time.time()-timei)
Example that doesn't reach the cache memory limit:
n=10000
m=100000
Sequential execution: 15s
2 processor pool no cache memory limit: 8s
It can be seen that there is no cache misses (all cache hits), therefore the speed-up is almost perfect: 15/8.
Memory cache hits 2 pool
Example that reaches the cache memory limit:
n=200000
m=5000
Sequential execution: 14s
2 processor pool cache memory limit: 14s
In this case, I increased the size of the vector onto which we operate (and decreased the loop size, to see reasonable execution times). In this case we can see that the memory gets full and the processes always miss the cache memory. Therefore not getting any speedup: 15/15.
Memory cache misses 2 pool
Observation: assigning an operation to a variable (aux = 0.01*shared) also uses the cache memory and can bound the problem by memory (without increasing any vector size).