1. 851-0585-04L – Modeling and Simulating Social Systems with MATLAB
L – Modeling and Simulating Social Systems with MATLAB
Lecture 1 – Introduction to MATLAB
Karsten Donnay and Stefano Balietti
Chair of Sociology, in particular of Modeling and Simulation
© ETH Zürich |

2.
MATLAB
Why MATLAB? Language is 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

3.
MATLAB environment
LIVE DEMO here!!

4. 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
Allows for object oriented programming (but has poor performance then...)

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

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

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

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

9. 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

10. 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 ‘;’ cancels the validation display
>> B=5;
>> C=10*B
C = 50

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

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

13. 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 =

14. 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 =

15. 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.

16. 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 =

17. 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 =
Important: the first element of a vector has index 1

18. 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 =

19. 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]

20. 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

21. 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 =

22. 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

23. 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’

24. 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

25. 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
Each element of the new matrix is given by the sum of th

26. 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

27. 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

28. 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

29. 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
Attention!
/ (slash) and \ (back slash)
produce different results

30.
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

31. Matrices Dimensions size() returns info about a matrix’s dimensions.
Matrices Dimensions
size() returns info about a matrix’s dimensions.
>> A = zeros(3,4);
>> size(A)
ans =
>> size(A,1) 3
>> size(A,2) 4

32.
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

33.
The for loop
MATLAB waits for the keyword end before computing the result.
>> for i=1:3
i^2
end
i = 1 4 9

34.
The for loop
MATLAB waits for the keyword end before computing the result.
>> for i=1:3
y(i)=i^2;
end
>> y
y =

35. 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

36. 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)

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

38. 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

39. 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

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

41. 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

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

43. 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)

44. 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

45. 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

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

47.
Exercise 2
Solve for x:

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

49. References http://www.mathworks.ch/products/matlab/index. html