Modeling and Simulating Social Systems with MATLAB

Transcription

1 Modeling and Simulating Social Systems with MATLAB Lecture 6 Optimization and Parallelization Olivia Woolley, Tobias Kuhn, Dario Biasini, Dirk Helbing Chair of Sociology, in particular of Modeling and Simulation ETH Zürich

2 Schedule of the course Introduction to MATLAB Working on projects (seminar thesis) Introduction to social-science modeling and simulations Handing in seminar thesis and giving a presentation canceled Modeling and Simulating Social Systems with MATLAB 2

3 How to Optimize your Program General Remarks: Carefully plan the workflow of your program Store intermediate results and re-use them Do not visualize in real time if not necessary Modeling and Simulating Social Systems with MATLAB 3

4 How to Optimize your Program Strategy: The design and structure of your program is the place to most easily gain performance - Try to have an overall plan of your code before you start writing in Matlab Use matlab functions to run your program, they are best performance-optimized - Make your code as modular as possible. Divide it into independent functions and put these together to generate your simulation. In a second step optimize each routine for individual speed & test its performance Modeling and Simulating Social Systems with MATLAB 4

5 MATLAB-specific Performance Issues Vectorizing: A large performance gain can achieved by vectorizing for or while loops Instead of iteratively calculating the results, the loops are expressed as matrix operations for which MATLAB is optimized e.g. instead of: simply use: for i=1:n indices=1:n x(i)=i^2 x=indices.^2 end For large N, differences in speed can be quite large Modeling and Simulating Social Systems with MATLAB 5

6 MATLAB-specific Performance Issues Vectorizing: There are a number of functions specifically used in the context of vectorized computations, examples are meshgrid or reshape - Meshgrid is useful if you are representing functions in many dimensions: will create a mesh for each dimension (vectors to matrix) and you can use these to matrify your operations - Reshape can be used to represent matrices as vectors (also useful in certain circumstances) There is an exhaustive documentation of vectorizing techniques available on the web Modeling and Simulating Social Systems with MATLAB 6

7 MATLAB-specific Performance Issues Memory Preallocation: Data structures (arrays, cell arrays) in MATLAB have a default memory allocated when created without specified size Resizing data structures is both bad for performance and memory efficiency Whenever possible initialize a data structure such that it does not have to be resized while the program is running Use commands zeros(n,m) and cell(n,m) - Speedup is significant (orders of magnitude) Modeling and Simulating Social Systems with MATLAB 7

8 MATLAB-specific Performance Issues Reusing Variables: If you need to store data structures outside your program, use the MATLAB save and load commands (superior to routines like fread or fwrite ) - Generally easiest to store data in.mat types. There are limits to amount of memory Matlab can use (this can be changed), in case this becomes an issue write variables to files. Can assign name dynamically: filename=[ iteration_ int2str(iteratorvar).mat ] save(filename, variabletosave ) %saves in iteration_iterator.mat file - This is also useful in case (for some reason) your program crashes in a next iteration- will not have lost all previous results. - Use clear varname to free up memory Modeling and Simulating Social Systems with MATLAB 8

9 Measuring Performance MATLAB has a profiler that tracks the performance of your code at the resolution of lines Start profiler with profile on, then you can see the results by calling profile viewer will give an overview of the time different functions take within your code It is often helpful to decide whether the number of times the code calls a particular function is reasonable. Because programs often have several layers, your code might not explicitly call the most time-consuming functions It is important to test the code for the full load of the program; performance might be very different for large data structures, and full number of iterations then for small testing iterations Especially true for parallelization where it may take time to set up the pool, and speed-ups may only be noticed in full model Modeling and Simulating Social Systems with MATLAB 9

10 Measuring Performance Alternatively use the tic and toc commands to test a particular routine tic starts the time counter toc stops the timer and displays the elapsed time Store the timer result in a variable: elapsedtime = toc You can also test several routines simultaneously using the ticid and the specific timing command toc(ticid) Can manually check which computation are taking the most time, and see if you can improve speed Modeling and Simulating Social Systems with MATLAB 10

11 Parallelization in MATLAB Normal Parallel Running in parallel means exactly what is sounds like: several iterations are run at the same time Of course if iterations take long time we can save a lot of time by running them parallely Matlab offers no built-in synchronization, but very easy to parallelize things Modeling and Simulating Social Systems with MATLAB 11

12 Parallelization in MATLAB Parallelization Toolbox: Note that there is always a computational overhead that needs paying when you go parallel and if your problem is too trivial then this overhead costs more than the calculation itself. - Split iterations, call parallel scheduler, put outputs together again. MATLAB's parallelization toolbox comes with a number of functions such as the parfor loop (only one we look at) A number of Matlab functions automatically parallelize their work stream if used in a pool - Look at: for a list of functions that suppot built-in parallelization Modeling and Simulating Social Systems with MATLAB 12

13 Parallelization in MATLAB When can I parallelize a loop? When performing large number of independent operations (no synch) - Generally things are parallelizable if the order the computations are done in does not matter: clearly this is the case for checking different parameter combinations and running a (stochastic) simulation several times. If you plan on parallelizing parameter sweeps, make sure you dont use global variables in your loop - Clearly cannot work. In general Matlab will let you know if the loop is parallelizable once you use a parallel function. Very useful for checking parameter combinations, may be able to check all combinations at once Modeling and Simulating Social Systems with MATLAB 13

14 Setting up Configurations Manager : Go to parallel -> ManageConfigurations If running things on your local computer, go to your local configuration manager, and use the right click to get to `properties` Change the number of workers available to the number you want (default is two) Modeling and Simulating Social Systems with MATLAB 14

15 How to use parallel for loops: Parfor Can use parfor loops in exactly the same way as regular for loops: matlabpool open N clear A parfor (i = 1:8, M) A(i) = i; end A matlabpool close Once matlabpool open is called, functions with built-in parallelization will also use their parallel versions Can also tell parfor how many cores to run on using M. Can use this to run nested parfor loops Note that you cannot break a parfor loop Modeling and Simulating Social Systems with MATLAB 15

16 How to use parallel for loops: Parfor matlabpool open N clear A parfor i = 1:8 A(i) = i; end A matlabpool close How many parallel workers? You can use up to 12 workers (more even in ver. 2014). Note that you are not limited to using at most the same number of workers as you have processors (or threads) on your comp. You can use more. How to choose number of cores? Test different pool sizes, and compare computation times. Mainly depends on how often you have to access memory in your loop: If often better fewer workers, if rarely can use many. For example adding two matrices, need to access values in matrix often. But only need to access memory once to initialize a simulation - can use many workers Modeling and Simulating Social Systems with MATLAB 16

17 The Multi-Agent Simulator Revisited Typical steps of an agent-based simulator: Initialization: - Initial state; parameters; environment Time loop: - Processing each time step Agents loop: - Processing each agent Update: - Updating agent i at time t Save data for further analysis Initialization Time loop Agents loop Update state end end Save data Modeling and Simulating Social Systems with MATLAB 17

18 The Multi-Agent Simulator Revisited Main Program 1. Initialization 2. Simulation 3. Saving Results Data Analysis Keep 1, 2, and 3 separated (as much as possible) Use structs for bundling different variable types Separate data generation and data analysis Modeling and Simulating Social Systems with MATLAB 18

19 The Multi-Agent Simulator Revisited Structs: Structs (structured arrays) can contain different kinds of data and can be used for input and output of functions: data = struct( property_a, 1, property_b, 'foo'); %create a struct data.property_a %call value stored in propery_a data.property_a=2 %set the value of propery_a to Modeling and Simulating Social Systems with MATLAB 19

20 Example of vectorization of parameter sets % set up parameter loops matlabpool open N % open cluster parfor i1=1:length(param_as) param_a = param_as(i1); for i2=1:length(param_bs) % set up loop for second parameter (could also parallelize this loop) param_b = param_bs(i2); % Repeat the same simulation nruns times for rcount=1:nruns simulation(param_a, param_b); end end end Modeling and Simulating Social Systems with MATLAB 20

21 The Multi-Agent Simulator Revisited Saving the results: Like shown before can save outputs and specify name dynamically, based on parameter or iteration (this way you are sure to know for what parameter you got the secific output). Can also set up directories to save outputs for different simulations dirname=['foldername_param' num2str(parametervalue)] %specify directory name %using the parameter, for example mkdir(dirname) %make the directory... filename=[ iteration int2str(iteratorvar).mat ] fullpath=[dirname '/' filename] %specify full path where to save output (for windows) save(fullpath, vartosave') %save the output Modeling and Simulating Social Systems with MATLAB 21

22 Overview Vectorize as many operations as possible Preallocate memory Reuse variables Make code modular Parallelize if possible Use profiler and tic/toc to improve performance Modeling and Simulating Social Systems with MATLAB 22

23 Debugging Debugging can be very useful to figure out where problems are arising in your code. Useful, especially for long codes Basic debugging involves printing out values and double checking if these match values computed independently Matlab offers good debugging features to go through code and find sources of errors Modeling and Simulating Social Systems with MATLAB 23

24 Setting a Break Point Setting a break point will let you navigate through your code, and check values of variables The code is paused at the location of the break point, so typically you place a breakpoint right before the lines where you think you might have an error From there one can move down the code and test values of variables without having to print them all out Clearly cant debug parallel codes Modeling and Simulating Social Systems with MATLAB 24

25 Add a break point to the code where you want your simulation to halt by simply clicking next to the line # Then run the function in the Command Window as usual Use toolbar to move around in code Green arrow shows you where you are in code Modeling and Simulating Social Systems with MATLAB 25

26 Test the values assigned by simply calling the variable name(s) in Command Window and stepping through the code Here ran the function in debug mode 27 shows line at which break point was placed. Here checked value of the variable param. Can set several break points Modeling and Simulating Social Systems with MATLAB 26

27 References MATLAB Parallel Computing Toolbox section optimization Modeling and Simulating Social Systems with MATLAB 27