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Update: In MATLAB R2017a the function got introduced. For a better experience simulating models in parallel, we recommend using PARSIM instead of SIM inside parfor. See the more recent blog post for more details. If you have to run thousands of simulations, you will probably want to do it as quickly as possibly. While in some cases this means looking for more efficient modeling techniques, or buying a more powerful computer, in this post I want to show how to run thousands of simulations in parallel across all available MATLAB workers. Specifically, this post is about how to use the, and with Simulink.
Embarrassingly Parallel Problems PARFOR is the parallel for-loop construct in MATLAB. Using the Parallel Computing toolbox, you can start a local pool of MATLAB Workers, or connect to a cluster running the. Once connected, these PARFOR loops are automatically split from serial execution into parallel execution. PARFOR enables parallelization of what are often referred to as embarrassingly parallel problems. Each iteration of the loop must be able to run independent of every other iteration of the loop. There can be no dependency of the variables in one loop on the results of a previous loop.
Some examples of this in Simulink are problems where you need to perform a parameter sweep, or running simulations of a large number of models just to generate the data output for later analysis. Computing the Basin of Attraction To illustrate an embarrassingly parallel problem, I will look at computing the basin of attraction for a simple differential equation. (Thanks to my colleague Ned for giving me this example.) The equation is from an article about. When the system is integrated forward, the state will approach one of two attractors. Which attractor it approaches depends on the initial conditions of and its derivative,. The Scholarpedia article shows the following image as the fractal basin of attraction for this equation.
(picture made by H.E. Nusse) Each of the thousands of pixels in that plot is the result of a simulation. So, to make that plot you need to run thousands of simulations. Forced Damped Pendulum Model Here is my version of that differential equation in Simulink. Opensystem( 'ForcedDampedPendulum') To see how evolves over time, here is a plot of 100 seconds of simulation. (Notice, I'm using the.) simOut = sim( 'ForcedDampedPendulum', 'StopTime', '100'); y = simOut.get( 'yout'); t = simOut.get( 'tout'); plot(t,y) hold on Nested FOR loops Using nested for loops, we can sweep over a range of values for.
If we add that to the plot above, you can visualize the attractors at. I can use a grayscale colorbar to indicate the final value of at the end of the simulation to make a basin of attraction image. N = 5; thetaRange = linspace(-pi,pi,n); thetadotRange = linspace(-5,5,n); tic; for i = 1:n for j = 1:n thetaX0 = thetaRange(i); thetadotX0 = thetadotRange(j); simOut = sim( 'ForcedDampedPendulum', 'StopTime', '100'); y = simOut.get( 'yout'); t = simOut.get( 'tout'); plot(t,y) end end t1 = toc; colormap gray colorbar I have added TIC/ TOC timing to the code to measure the time spent running these simulations, and from this we can figure out the time required per simulation. T1PerSim = t1/n^2; disp( 'Time per simulation with nested FOR loops = ' num2str(t1PerSim)) Time per simulation with nested FOR loops = 0.11862 During the loops, I iterate over each combination of values only once. This represents simulations that need to be run. Because the simulations are all independent of each other, this is a perfect candidate for distribution to parallel MATLABs. Converting to a PARFOR loop PARFOR loops can not be nested, so the iteration across the initial conditions needs to be rewritten as a single loop.
For this problem I can re-imagine the output image as a grid of pixels. If I create a corresponding thetaX0 and thetadotX0 matrix, I will be able to loop over the elements in a PARFOR loop. An easy way to do this is with MESHGRID.
Another important change to the loop is using the ASSIGNIN function to set the initial values of the states. Within PARFOR, the 'base' workspace refers to the MATLAB workers, where the simulation is run. N = 20; thetaMat,thetadotMat = meshgrid(linspace(-pi,pi,n),linspace(-5,5,n)); map = zeros(n,n); tic; parfor i = 1:n^2 assignin( 'base', 'thetaX0',thetaMat(i)); assignin( 'base', 'thetadotX0',thetadotMat(i)); simOut = sim( 'ForcedDampedPendulum', 'StopTime', '100'); y = simOut.get( 'yout'); map(i)=y(end); end t2 = toc; I can use a scaled image to display the basin of attraction. (Of course, this is verly low resolution.) clf imagesc(-pi,pi,-5,5,map) colormap(gray), axis xy square The PARFOR loop acts as a normal for-loop when there are no MATLAB workers. We can see this from the timing analysis. T2PerSim = t2/n^2; disp( 'Time per simulation with PARFOR loop = ' num2str(t2PerSim)) Time per simulation with PARFOR loop = 0.13012 Local MATLAB Workers Most computers today have multiple processors, or multi-core architectures.
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To take advantage of all the cores on this computer, I can use the MATLABPOOL command to start a local MATLAB pool of workers. Matlabpool open local nWorkers3 = matlabpool( 'size'); Starting matlabpool using the 'local' configuration.
Connected to 4 labs. In order to remove any first time effects from my timing analysis, I can run commands using pctRunOnAll to load the model and simulate it. PctRunOnAll( 'loadsystem('ForcedDampedPendulum')')% warm-up pctRunOnAll( 'sim('ForcedDampedPendulum')')% warm-up Now, let's measure the PARFOR loop again, using the full power of all the cores on this computer. N = 20; thetaMat,thetadotMat = meshgrid(linspace(-pi,pi,n),linspace(-5,5,n)); map = zeros(n,n); tic; parfor i = 1:n^2 assignin( 'base', 'thetaX0',thetaMat(i)); assignin( 'base', 'thetadotX0',thetadotMat(i)); simOut = sim( 'ForcedDampedPendulum', 'StopTime', '100'); y = simOut.get( 'yout'); map(i)=y(end); end t3=toc; t3PerSim = t3/n^2; disp( 'Time per simulation with PARFOR and ' num2str(nWorkers3). ' workers = ' num2str(t3PerSim)) disp( 'Speed up factor = ' num2str(t1PerSim/t3PerSim)) Time per simulation with PARFOR and 4 workers = 0.025087 Speed up factor = 4.7285 Now that I am done with the local MATLAB Workers, I can issue a command to close them. Matlabpool close Sending a stop signal to all the labs. Connecting to a Cluster I am fortunate enough to have access to a small distributed computing cluster, configured with MATLAB Distributed Computing Server.
The cluster consists of four, quad-core computers with 6 GB of memory. It is configured to start one MATLAB worker for each core, giving a 16 node cluster.
I can repeat my timing experiments here. Matlabpool open Cluster16 nWorkers4 = matlabpool( 'size'); pctRunOnAll( 'loadsystem('ForcedDampedPendulum')')% warm-up pctRunOnAll( 'sim('ForcedDampedPendulum')')% warm-up Starting matlabpool using the 'Cluster16' configuration. Connected to 16 labs. N = 20; thetaMat,thetadotMat = meshgrid(linspace(-pi,pi,n),linspace(-5,5,n)); map = zeros(n,n); tic; parfor i = 1:n^2 assignin( 'base', 'thetaX0',thetaMat(i)); assignin( 'base', 'thetadotX0',thetadotMat(i)); simOut = sim( 'ForcedDampedPendulum', 'StopTime', '100'); y = simOut.get( 'yout'); map(i)=y(end); end t4 = toc; t4PerSim = t4/n^2; disp( 'Time per simulation with PARFOR and ' num2str(nWorkers4).
' workers = ' num2str(t4PerSim)) disp( 'Speed up factor = ' num2str(t1PerSim/t4PerSim)) Time per simulation with PARFOR and 16 workers = 0.0064637 Speed up factor = 18.3521 matlabpool close Sending a stop signal to all the labs. Timing Summary Here is a summary of the timing measurements: disp( 'Time per simulation with nested FOR loops = ' num2str(t1PerSim)) disp( 'Time per simulation with PARFOR loop = ' num2str(t2PerSim)) disp( 'Time per simulation with PARFOR and ' num2str(nWorkers3). ' workers = ' num2str(t3PerSim)) disp( 'Speed up factor for ' num2str(nWorkers3). ' local workers = ' num2str(t1PerSim/t3PerSim)) disp( 'Time per simulation with PARFOR and ' num2str(nWorkers4). ' workers = ' num2str(t4PerSim)) disp( 'Speed up factor for ' num2str(nWorkers4).
' workers on the cluster = ' num2str(t1PerSim/t4PerSim)) Time per simulation with nested FOR loops = 0.11862 Time per simulation with PARFOR loop = 0.13012 Time per simulation with PARFOR and 4 workers = 0.025087 Speed up factor for 4 local workers = 4.7285 Time per simulation with PARFOR and 16 workers = 0.0064637 Speed up factor for 16 workers on the cluster = 18.3521 A Quarter Million Simulations Many months ago I tinkered with this problem, using a high performance desktop machine with 4 local workers, and generated the following graph. This represents 250,000 simulations. Performance Increase There are many factors that contribute to the performance of parallel code execution. Breaking up the loop and distributing it across workers represents some amount of overhead. For some, smaller problems with a small number of workers, this overhead can swamp the problem. Another major factor to consider is data transfer and network speed; transferring large amounts of data adds overhead that doesn't normally exist in MATLAB.
Now it's your turn Do you have a problem that could benefit from a PARFOR loop and a cluster of MATLAB Workers? Leave a and tell us all about it. Published with MATLAB® 7.11.
Teja replied on: 1 of 11 Seth, Thank you for a very informative post. I had been trying to do this exact same thing earlier today, but distributing simulation parameters to the local workspaces was throwing me off. I see you have to use 'assignin' to get it to work properly (this was somewhat unintuitive). Can you explain why it is possible to get a faster than linear speedup when running Simulink models in parallel? In other words, why is running it on N processors more than N times as fast as running it on one? Mike Thomas replied on: 2 of 11 Hi, I haven't done any parallel simulations in MatLab yet, but we have a 5.0 GHz Intel Core i7-980X with 6 processing cores. All 6 cores are at 5.0 GHz.
I am wondering what hardware you have there at MatLab, and if you'd be interested in testing your sims on our machines to measure the performance gains? We have the following available for testing: 3.9 GHz i7-860 x 4 cores 4.0 GHz AMD 1055T x 6 cores 4.3 GHz i7-975 Extreme x 4 cores 5.0 GHz i7-980X Gulftown x 6 cores We have MatLab installed on just the 3.9 GHz system right now. You can call (610) 818-5063 for more information. I look forward to hearing from you.
Seth replied on: 3 of 11 @Teja - I noticed that too, but didn't comment on it. I believe this was due to graphics overhead associated with the interactive session of MATLAB, versus the 'headless MATLAB' workers. ALSO, notice that I only used LOADSYSTEM on the parallel timing calculations. I could have also done this during the interactive session to just run the simulations without displaying the model. @Mike Thomas - Thanks for the offer. Those computers seem pretty fast. I bet you can heat a small home with those overclocked systems!
Paul Metcalf replied on: 4 of 11 Thanks for the post, however could you please clarify what the performance implications are for running the parallel toolbox (and compatible toolboxes such as Simulink Design Optimisation) on the new Xeon processors with hyper-threading technology? It is not at all clear what the performance implications are of running say a Dual Processor machine with hyper-threading chips compared to previous generation Xeon's without hyper-threading. Since the parallel toolbox maxes out at 8 local workers (and there doesn't seem to be a plan to expand this count any time soon according to Jack himself in the virtual conference) my guess is that performance on the new chipsets will be significantly worse. Please comment. And please consider increasing the number of workers supported by the parallel toolbox, since this is an artificial limitation designed to sell more Distributed Computing Server licenses.
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Paul Mathworks License Admin. Vesh replied on: 5 of 11 Hi Seth, I am running a Monte Carlo simulation that includes as a part the evaluation of infinite sums (approximated by a certain number of terms say, 40).
The simulation needs to be run for about 10^6 times in order to get the desired accuracy in my case. But even running it 10^5 times is taking almost a whole day. I am using the parfor command in breaking up the work across two workers. I am still not satified with the time it is taking. Do you have any suggestions regarding this? I have several nested for loops inside that parfor loop.
Venkatesh replied on: 7 of 11 I have a complex simulink module. It takes about more than 1 hour to run on my local computer and even i tried running it through high computing computer but still it takes the same time. Question1: Is parallel computing the only solution for that? If so, how to do that for a power system network model. Can you provide an example by performing parallel computing on a sample network provided in simpowersystems?
Question2: how to store the results/graphs after running the simulations (automatically) in simulink? (Please provide appropriate commands so that i need not wait till the simulation is done).