851-0585-04L – Modeling and Simulating
Social Systems with MATLAB
Lecture 9 – Simulation Speed & Parallelization
Karsten Donnay and Stefano Balietti
Chair of Sociology, in particular of
Modeling and Simulation
© ETH Zürich |
2011-11-21
Schedule of the course
Introduction to
MATLAB
26.09.
03.10.
10.10.
17.10.
24.10.
31.10.
Working on
projects
(seminar
thesis)
07.11.
14.11.
Introduction to
social-science
modeling and
simulations
21.11.
28.11.
05.12.
12.12.
19.12.
2011-11-21
Handing in seminar thesis
and giving a presentation
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2
Goals of Lecture 9: students will
1. Refresh knowledge on continuous simulations acquired in
lecture 8, through brief repetition of the main points.
2. Get an overview of potential issues that might affect
computational performance/speed in MATLAB and learn
strategies to avoid performance loss.
3. This lecture emphasizes both the importance of efficient
program design and strategies to avoid MATLABspecific performance issues.
4. Understand the basics of MATLAB’s parallel computing
toolbox.
5. Put some of the above concepts into practice with code
examples.
2011-11-21
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Repetition

Transition from discrete spatial models to continuous
spatial models where computational agents are treated
analogous to particles in Physics

Random walk introduced as one generic microscopic
agent dynamic that microscopically leads to diffusion of
the whole ensemble of agents (micro-macro link)

Concept of random walk is not limited to spatial dynamics;
successfully used for example also in modeling of financial
markets

Continuous models vs. discrete models (CA, lattice):
depending on context one or the other can be more
suitable, both approaches are used in the literature!
2011-11-21
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4
How To Optimize Your Program
General Remarks
 Plan your program/ work flow before
implementing the program
 Only perform the minimal number of
computational steps necessary to obtain results
 Store intermediate results and re-use them
 Use global variables with caution
 Do not visualize in real time if not necessary
2011-11-21
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How To Optimize Your Program
Strategy
 The design and structure of your program is
the place to most easily gain performance
 Use functions to run your program, they are
best performance-optimized in MATLAB!
 Subroutines both improve performance and
readability of your code
 In a second step optimize each routine for
individual speed & test its performance
2011-11-21
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6
How To Optimize Your Program
Possible Program Structure
 Define and initialize all variables in a script file
that serves as the main of your program
 Execute the actual program as function with the
above variables as inputs
 Automated analysis, visualization etc. of the
simulation output may then be implemented in
the main file using the outputs of the function
that runs the actual program
2011-11-21
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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), cell(n,m)
2011-11-21
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MATLAB-specific Performance Issues
Limit the Complexity of The Program
 MATLAB has a limit on the complexity of program code it can
interpret!
 Subdivide your program in routines of which each is
independently implemented as a function
 Avoid excessive use of if… else… statements, in particular
multiply nested expressions
 “Minimalistic” programming will not only improve performance
but also greatly improve readability!
2011-11-21
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MATLAB-specific Performance Issues
Variable Casting
 Do not recast your data structures during program execution
 In particular, avoid storing the “wrong” data type in a data
structure (for example a complex number or a string in an
array of type double)
MATLAB is otherwise forced to recast the data structure!
 The MATLAB default number format is double; if you explicitly
need another number format, use for example zeros(10,
‘int32’) to initialize the array
2011-11-21
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MATLAB-specific Performance Issues
Short-circuit Operators
 In logical operations make use of the short-circuit operators
that MATLAB provides, i.e. use && and || instead of & and |
 Advantage:
in a complicated logical statement MATLAB only evaluates
the first expression if this already returns false, e.g. in
(x >= 3) && (y > 4) it stops after the first argument if x < 3
 Evaluating as few Boolean expressions as possible is a direct
performance boost
2011-11-21
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MATLAB-specific Performance Issues
Overloading Build-in Functions
 MATLAB is optimized for performance of its built-in functions
 Other than for example in C++, overloading a built-in function
can lead to performance losses since you might interfere
with particular optimizations in the built-in function
 MATLAB is a closed source software, you usually do not know
what you are tempering with
 our advice:
stay away from overloading built-in functions!
2011-11-21
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MATLAB-specific Performance Issues
MATLAB Specifics
 MATLAB is best optimized for the execution of functions, use
them over scripts whenever possible
 If you need to store data structures outside your program, use
the MATLAB ‘save’ and ‘load’ commands
they are superior to routines like ‘fread’ or ‘fwrite’
(faster and less memory fragmentation)
 Avoid running CPU and/or memory intensive programs at the
same time as MATLAB OR prioritize MATLAB
2011-11-21
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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=1:10
x(i)=i^2
end
2011-11-21
indices=1:10
x=indices.^2
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MATLAB-specific Performance Issues
Vectorizing
 There are a number of functions specifically used in the
context of vectorized computations, examples are meshgrid or
reshape
 There is an exhaustive documentation of vectorizing
techniques available on the Internet
 A quick overview and a list of useful functions in MATLAB
when vectorizing computations may be found here, a more
detailed introduction here
2011-11-21
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A word of caution…
 The fact that MATLAB is optimized for matrix
operations does not in every case mean that
such a routine is faster!!


vectorizing a computation can be quite costly and
greatly affect the performance
MATLAB uses an just-in-time (JIT) compiler that
recognizes high level commands and replaces them
with native machine instructions
This can for example greatly accelerate loops!
 In the end you have to test your code to see
what is faster!!
2011-11-21
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16
Measuring performance
 MATLAB has a profiler that tracks the performance of your
code at the resolution of lines
 It may be called with profile on, the command profile viewer
stops the profiler and displays the results
 Using the profiler make sure to first optimize the slowest
sections of your code as the performance gain is the largest
 It is important to test the code for the full load of the program,
it might perform differently for small/ large data structures!
 The MATLAB documentation of the profiler may be found here
2011-11-21
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Measuring performance
 Alternatively use the tic and toc commands to test a
particular routine
 tic starts the time counter and toc stops the timer &
displays the elapsed time
 It is often convenient to store the timer results in a variable,
the MATLAB default is elapsedTime = toc
 You can also test several routines simultaneously using the
ticID and the the specific timing command toc(ticID)
 Documentation may be found here
2011-11-21
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Parallelization in MATLAB
When Is It Useful?
 When performing large number of independent operations
MATLAB’s parallel computing features are useful
 E.g when the same simulation has to be run for multiple
parameter combinations parallelization boosts performance
 Note that the data structures and program routines have to be
parallelizable
 You also require multiple cores on your computer or access
to a computational cluster
2011-11-21
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19
Parallelization in MATLAB
The Toolbox
 The toolbox comes with a number of high level
programming constructs such as the parfor loop
 A number of built-in routines automatically parallelize their
work stream if possible with your hardware
 Built-in distributed computing interface supports various
schedulers like Platform LSF®, Microsoft® Windows® Compute
Cluster Server & HPC Server 2008 or Altair PBS Pro®
 Newest MATLAB version also supports GPU computing
2011-11-21
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20
How to use parallel for loops: Parfor
matlabpool open N
clear A
parfor i = 1:8
A(i) = i;
end
A
matlabpool close
2011-11-21
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How to use parallel for loops: Parfor
How many parallel workers
matlabpool open N
clear A
parfor i = 1:8
A(i) = i;
end
A
The real number you can
use depends on the number
of cores of your CPU
matlabpool close
2011-11-21
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Batch
 Because we still need our laptop while running MATLAB…
j = batch(‘myScript’);
wait(j);
load(j);
% Wait for the job to finish
% Load the job results
destroy(j);
2011-11-21
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23
The Multi-Agent Simulator Revisited
 Programming an agent-based simulator often
goes in five steps

Initialization
Initialization
- Initial state; parameters; environment

Time loop
Time loop
Agents loop
- Processing each time steps

Agents loop
Update state
- Processing each agents

Update
end
end
- Updating agent i at time t

Save data
Save data
- For further analysis
2011-11-21
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The Multi-Agent Simulator Revisited
Main Program
1. Initialization
2. Simulation
3. Saving Results
 Keep 1., 2., 3. (as much as possible) separated
 Create interfaces between the components
 Make input and output more re-usable with objects
 Separate data generation and data analysis
2011-11-21
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25
The Multi-Agent Simulator Revisited
Main Program
1. Initialization
2. Simulation
3. Saving Results
Data Analysis
 Keep 1., 2., 3. (as much as possible) separated
 Create interfaces between the components
 Make input and output more re-usable with objects
 Separate data generation and data analysis
2011-11-21
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26
The Multi-Agent Simulator Revisited
Object definition:
 Objects can be used to store both input and output
 A simple way to define objects is using struct
myObj = struct( ‘property_A’, 1, …
‘property_B’, 2);
myObj.property_A = 1
2011-11-21
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27
The Multi-Agent Simulator Revisited
The main program:
1. Loads the configuration file: load(‘conf_file’);
2. Generates all the combinations of parameter sets
specified in the configuration file
3. Launch N simulations per parameter set
4. Save the results
2011-11-21
K. Donnay & S. Balietti / [email protected] [email protected]
28
The Multi-Agent Simulator Revisited
The main program:
1. Loads the configuration file: load(‘conf_file;);
2. Generates all the combinations of parameter sets
specified in the configuration file
3. Launch N simulations per parameter set
4. Save the results
2011-11-21
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29
The Multi-Agent Simulator Revisited
Initialization:
 Should be placed in a separate file containing:
 Model variables:
 One (or more) combination of model parameters
 N. simulations per parameter set (single combination)
 ‘Global’ settings:
 Relevant directories (log, dump…), dummies, etc.
 Other info: name, description, version, date…
2011-11-21
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Initialization file example
% GLOBAL Conf
simName = 'MyCoolSym’;
dumpDir = 'dump/';
RUNS = 10;
globals = struct('dumpDir', dumpDir, 'RUNS', RUNS);
% MODEL Conf
dts = [0.01];
steps = [2];
n_agents = [10:10:100];
% time_step
% number of simulation steps
% number of agents
model = struct('dts', dts, 'steps', steps, 'n_agents', n_agents);
% Put all together
init = struct('name', simName,'globals', globals,'model', model);
save(simName); % Creates a loadable file
2011-11-21
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31
Initialization file example
% GLOBAL Conf
simName = 'MyCoolSym’;
dumpDir = 'dump/';
RUNS = 10;
globals = struct('dumpDir', dumpDir, 'RUNS', RUNS,);
% MODEL Conf
dts = [0.01];
steps = [2];
n_agents = [10:10:100];
Notice: we are using
% time_step
vectors here!
% number of simulation steps
% number of agents
model = struct('dts', dts, 'steps', steps, 'n_agents', n_agents);
% Put all together
init = struct('name', simName,'globals', globals,'model', model);
save(simName); % Creates a loadable file
2011-11-21
K. Donnay & S. Balietti / [email protected] [email protected]
32
The Multi-Agent Simulator Revisited
The main program:
1. Loads the configuration file: load(‘conf_file’);
2. Generates all the combinations of parameter sets
specified in the configuration file
3. Launch N simulations per parameter set
4. Save the results
Parameter Sweeping
2011-11-21
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33
The Multi-Agent Simulator Revisited
 The combinatorial exploration of the parameter space is
also called ‘Parameter Sweeping’.
 Its purpose is to determine the behavior of the system in
different parameter ranges.
 It is normally executed by “exploding” the input vectors of
parameters into multiple independent parameter sets.
 Nested for loops are a solution.
2011-11-21
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34
Example of vectorization of parameter sets
for i1=1:size(param_As,2)
param_A = param_As(i1);
for i2=1:size(param_Bs,2)
param_B = param_Bs(i2);
% Repeat the same simulation nRUNS times
for rCount=1:nRUNS
simulation(param_A, param_B);
end
end
end
2011-11-21
K. Donnay & S. Balietti / [email protected] [email protected]
35
The Multi-Agent Simulator Revisited
The main program:
1. Loads the configuration file: load(‘conf_file;);
2. Generates all the combinations of parameter sets
specified in the configuration file
3. Launch N simulations per parameter set
4. Save the results
2011-11-21
K. Donnay & S. Balietti / [email protected] [email protected]
36
The Multi-Agent Simulator Revisited
 Saving the results:
save(fileName,’results’)
 It is good practice to save the output of the simulation together
the input object which was used to run it.
 Save save each parameter set into a separate folder:
mkdir(‘foldername’)
 Saved results may already include the average or leave the
computation to the data analysis part.
2011-11-21
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37
Projects
 There are no exercises today, please work on
your projects!
 We would like to remind you that the oral project
presentations will start in the week of the 19th of
December. All projects are due for midnight
Friday 16th of December.
2011-11-21
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38
References
 MATLAB documentation on performance
 Manual on writing fast MATLAB code
 MATLAB Technical Note on code vectorization
 MATLAB Parallel Computing Toolbox
 Short-circuit operators in MATLAB
 https://github.com/msssm/lectures_files/optimiza
tion/
2011-11-21
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39