1. 851-0585-04L – Modelling and Simulating Social Systems with MATLAB
L – Modelling and Simulating Social Systems with MATLAB
Lesson Anders Johansson and Wenjian Yu
© ETH Zürich |

2. Lesson 1 - Contents Introduction MATLAB environment What is MATLAB?
Lesson 1 - Contents
Introduction
MATLAB environment
What is MATLAB?
MATLAB basics:
Variables and operators
Data structures
Loops and conditional statements
Scripts and functions
Exercises

3. Modelling and Simulating Social Systems with MATLAB
Modelling and Simulating Social Systems with MATLAB
Weekly lecture with computer exercises. The two hours will be split into 30 minutes lecture and 60 minutes exercises. We will put the lecture slides and other material on the web page:

4. Aims of the course Learning the basics of MATLAB.
Aims of the course
Learning the basics of MATLAB.
Learning how to implement models of various social processes and systems.
In the end of the course, all students (in pairs) should hand in a Seminar Thesis describing the implementation of a social-science model. The thesis should be about 20 pages long (including figures and source code) and be accompanied by a 10-minutes presentation.

5. Seminar thesis Studying a scientific paper
Seminar thesis
Studying a scientific paper
Reproducing results in MATLAB
Writing a report and giving a talk

6. Projects from previous semesters
Projects from previous semesters
Sugarscape
Civil violence
Group dynamics
Trust
Facebook social networks
Space syntax
Pedestrian dynamics
Cycling strategies
Tumour growth
Segregation
Cancer
Traffic dynamics
Swarms
Sailing strategies
Migration
Flocks
Cockroaches
Size of wars
Civil war
Queuing models
Synchronized clapping
Game theory tournament
Game theory
Language formation

7.
Contents of the course
The two first lectures will be spent on introducing the basic functionality of MATLAB: matrix operations, data structures, conditional statements, statistics, plotting, etc.
In the later lectures, we will introduce various modeling approaches from the social sciences: dynamical systems, cellular automata, game theory, networks, multi-agent systems, …

8. Contents of the course Introduction to MATLAB
Contents of the course
Introduction to MATLAB
22.02.
01.03.
08.03.
15.03.
22.03.
29.03.
12.04.
26.04.
03.05.
10.05.
17.05.
31.05.
Introduction to social-science modeling and simulation
Working on projects (seminar theses)
Handing in seminar thesis and giving a presentation

9.
MATLAB
Why MATLAB? Quick to learn, easy to use, rich in functionality, good plotting abilities.
MATLAB is commercial software from The MathWorks, but there are free MATLAB clones with limited functionality (octave and Scilab).
MATLAB can be downloaded from ides.ethz.ch

10. MATLAB environment Command window Where the user enters commands.
MATLAB environment
Command window
Where the user enters commands.
Where MATLAB displays its results.

11. MATLAB environment Command History Store the typed commands.
MATLAB environment
Command History
Store the typed commands.
A double click on a line execute it on the Command window.

12. MATLAB environment Directory and workspace window
MATLAB environment
Directory and workspace window
Current directory shows local hard drive.
Workspace displays current variables and their value.

13. What is MATLAB? MATLAB derives its name from matrix laboratory
What is MATLAB?
MATLAB derives its name from matrix laboratory
Interpreted language
No compilation like in C++ or Java
The results of the commands are immediately displayed

14. Overview - What is MATLAB?
Overview - What is MATLAB?
MATLAB derives its name from matrix laboratory
Matrices
Vectors
Scalars
x11
x12
x13
x21
x22
x23

15. Overview - What is MATLAB?
Overview - What is MATLAB?
MATLAB derives its name from matrix laboratory
Matrices
Vectors
Scalars
x11
x12
x13
x11
x12
x13

16. Overview - What is MATLAB?
Overview - What is MATLAB?
MATLAB derives its name from matrix laboratory
Matrices
Vectors
Scalars
x11

17. Overview - What is MATLAB?
Overview - What is MATLAB?
MATLAB derives its name from matrix laboratory
Matrices
Vectors
Scalars
Multi-dimensional
x111
x121
x131
x211
x221
x231

18. Pocket calculator MATLAB can be used as a pocket calculator:
Pocket calculator
MATLAB can be used as a pocket calculator:
>> 1+2+3
ans= 6
>> (1+2)/3 1

19. Variables and operators
Variables and operators
Variable assignment is made with ‘=’
Variable names are case sensitive:
Num, num, NUM are all different to MATLAB
>> num=10
num = 10
The semicolon ‘;’ cancel the validation display
>> B=5;
>> C=10*B
C = 50

20. Variables and operators
Variables and operators
Basic operators:
+ - * / : addition subtraction multiplication division
^ : Exponentiation
sqrt() : Square root
>> a=2;
>> b=5;
>> c=9;
>> R=a*(sqrt(c) + b^2);
>> R
R = 56

21. Data structures: Vectors
Data structures: Vectors
Vectors are used to store a set of scalars
Vectors are defined by using square bracket [ ]
>> x=[ ]
x =

22. Data structures: Defining vectors
Data structures: Defining vectors
Vectors can be used to generate a regular list of scalars by means of colon ‘:’
n1:k:n2 generate a vector of values going from n1 to n2 with step k
>> x=0:2:6
x =
The default value of k is 1
>> x=2:5
x =

23. Data structures: Accessing vectors
Data structures: Accessing vectors
Access to the values contained in a vector
x(i) return the ith element of vector x
>> x=1:0.5:3;
>> x(2)
ans =
1.5
x(i) is a scalar and can be assigned a new value
>> x=1:5;
>> x(3)=10;
>> x
x =

24. Data structures: Size of vectors
Data structures: Size of vectors
Vectors operations
The command length(x) return the size of the vector x
>> x=1:0.5:3;
>> s=length(x)
s = 5
x(i) return an error if i>length(x)
>> x=1:0.5:3;
>> x(6)
??? Index exceeds matrix dimensions.

25. Data structures: Increase size of vectors
Data structures: Increase size of vectors
Vectors operations
Vector sizes can be dynamically increased by assigning a new value, outside the vector:
>> x=1:5;
>> x(6)=10;
>> x
x =

26. Data structures: Sub-vectors
Data structures: Sub-vectors
Vectors operations
Subvectors can be addressed by using a colon
x(i:j) return the sub vector of x starting from the ith element to the jth one
>> x=1:0.2:2;
>> y=x(2:4);
>> y
y =

27. Data structures: Matrices
Data structures: Matrices
Matrices are two dimensional vectors
Can be defined by using semicolon into square brackets [ ]
>> x=[0 2 4 ; ; 8 8 8]
x =
0 2 4
1 3 5
8 8 8
>> x=[1:4 ; 5:8 ; 1:2:7]

28. Data structures: Matrices
Data structures: Matrices
Accessing the elements of a matrix
x(i,j) return the value located at ith line and jth column
i and j can be replaced by a colon ‘:’ to access the entire line or column
>> x=[0 2 4 ; ; 8 8 8]
x =
0 2 4
1 3 5
8 8 8
>> y=x(2,3)
y = 5

29. Data structures: Matrices
Data structures: Matrices
Access to the values contained in a matrix
x(i,j) return the value located at ith line and jth column
i and j can be replaced by a colon ‘:’ to access the entire line or column
>> x=[0 2 4 ; ; 8 8 8]
x =
0 2 4
1 3 5
8 8 8
>> y=x(2,:)
y =

30. Data structures: Matrices
Data structures: Matrices
Access to the values contained in a matrix
x(i,j) return the value located at ith line and jth column
i and j can be replaced by a colon ‘:’ to access the entire line or column
>> x=[0 2 4 ; ; 8 8 8]
x =
0 2 4
1 3 5
8 8 8
>> y=x(:,3)
y = 4 5 8

31. Matrices operations: Transpose
Matrices operations: Transpose
Transpose matrix
Switches lines and columns
transpose(x) or simply x’
>> x=[1:3 ; 4:6]
x =
1 2 3
4 5 6
>> transpose(x)
1 4
2 5
3 6
>> x’

32. Matrices operations Inter-matrices operations
Matrices operations
Inter-matrices operations
C=A+B : returns C with C(i,j) = A(i,j)+B(i,j)
C=A-B : returns C with C(i,j) = A(i,j)-B(i,j)
A and B must have the same size, unless one of them is a scalar
>> A=[1 2;3 4] ; B=[2 2;1 1];
>> C=A+B
C =
3 4
4 5
>> C=A-B
-1 0
2 3

33. Matrices operations: Multiplication
Matrices operations: Multiplication
Inter-matrices operations
C=A*B is a matrix product. Returns C with
C(i,j) = ∑ (k=1 to N) A(i,k)*B(k,j)
N is the number of columns of A which must equal the number of rows of B

34. Element-wise multiplication
Element-wise multiplication
Inter-matrices operations
C=A.*B returns C with C(i,j) = A(i,j)*B(i,j)
A and B must have the same size, unless one of them is a scalar
>> A=[2 2 2;4 4 4];
>> B=[2 2 2;1 1 1];
>> C=A.*B
C =
4 4 4

35. Element-wise division
Element-wise division
Inter-matrices operations
C=A./B returns C with C(i,j) = A(i,j)/B(i,j)
A and B must have the same size, unless one of them is a scalar
>> A=[2 2 2;4 4 4];
>> B=[2 2 2;1 1 1];
>> C=A./B
C =
1 1 1
4 4 4

36. Matrices operations: Division
Inter-matrices operations
x=A\b returns the solution of the linear equation A*x=b
A is a n-by-n matrix and b is a column vector of size n
>> A=[3 2 -1; ; ];
>> b=[1;-2;0];
>> x=A\b
x = 1 -2

37.
Matrices: Creating
Matrices can also created by these commands: rand(n, m) a matrix of size n x m, containing random numbers [0,1] zeros(n, m), ones(n, m) a matrix containing 0 or 1 for all elements

38.
The for loop
Vectors are often processed with loops in order to access and process each value, one after the other:
Syntax :
for i=x ….
end
With
i the name of the running variable
x a vector containing the sequence of values assigned to i

39.
The for loop
MATLAB waits for the keyword end before computing the result.
>> for i=1:3
i^2
end
i = 1 4 9

40.
The for loop
MATLAB waits for the keyword end before computing the result.
>> for i=1:3
y(i)=i^2;
end
>> y
y =

41. Conditional statements: if
Conditional statements: if
The keyword if is used to test a condition
Syntax :
if (condition)
..sequence of commands..
end
The condition is a Boolean operation
The sequence of commands is executed if the tested condition is true

42. Logical operators Logical operators
Logical operators
Logical operators
< , > : less than, greater than
== : equal to
&& : and
|| : or
~ : not ( ~true is false)
(1 stands for true, 0 stands for false)

43. Conditional statements: Example
Conditional statements: Example
An example:
>> threshold=5;
>> x=4.5;
>> if (x<threshold)
diff = threshold - x;
end
>> diff
diff =
0.5

44. Conditional statements: else
Conditional statements: else
The keyword else is optional
Syntax :
if (condition)
..sequence of commands n°1..
else
..sequence of commands n°2..
end
>> if (x<threshold)
diff = threshold - x ;
else
diff = x – threshold;
end

45. Scripts and functions
External files used to store and save sequences of commands.
Scripts:
Simple sequence of commands
Global variables
Functions:
Dedicated to a particular task
Inputs and outputs
Local variables

46. Scripts and functions Should be saved as .m files :
From the Directory Window

47. Scripts and functions Scripts : Create .m file, e.g. sumVector.m.
Type commands in the file.
Type the file name, .e.g sumVector, in the command window.
%sum of 4 values in x
x=[ ];
R=x(1)+x(2)+x(3)+x(4); R
sumVector.m
>> sumVector
R = 16

48. Scripts and functions
Make sure that the file is in your working directory!

49. Scripts and functions Functions : Create .m file, e.g. absoluteVal.m
Declare inputs and outputs in the first line of the file,
function [out1, out2, …] = functionName (in1, in2, …)
e.g. function [R] = absoluteVal(x)
Use the function in the command window
functionName(in1, in2, …)
e.g. absoluteVal(x)

50. Scripts and functions >> A=absoluteVal(-5); >> A A = 5
absoluteVal.m
function [R] = absoluteVal(x)
% Compute the absolute value of x
if (x<0)
R = -x ;
else
R = x ;
end
>> A=absoluteVal(-5);
>> A
A = 5

51. Scripts and functions >> A=absoluteVal(-5); >> A A = 5
absoluteVal.m
function [R]= absoluteVal(x)
% Compute the absolute value of x
if (x<0)
R = -x ;
else
R = x ;
end
>> A=absoluteVal(-5);
>> A
A = 5

52. Exercise 1 Compute: a) b) c)
Exercise 1
Compute: a) b) c)
Slides/exercises: (use Firefox!)

53.
Exercise 2
Solve for x:

54. Exercise 3
Fibonacci sequence: write a function which compute the Fibonacci sequence of a given number n and return the result in a vector.
The Fibonacci sequence F(n) is given by :