1. Introduction to MATLAB
Computational Probability and Statistics CIS 2033 Section 003
Djordje Gligorijevic, Temple University, Spring 2015

2. Djordje Gligorijevic, Temple University, Spring 2015
About MATLAB
MATLAB (MATrix LABoratory) is a high level language made for:
Numerical Computation (Technical computing)
Visualization
Application Development
Everything is a matrix – easy to do Linear Algebra and other mathematical fields that use Linear Algebra (Statistics, Fourier Analysis, Optimization, Filtering,…)
Useful tool for mathematical analysis and simulation
Djordje Gligorijevic, Temple University, Spring 2015

3. MATLAB Software Access
All Temple University in-campus computers have student-version MATLAB installed
Temple University also provides a student license for every student, just go to MATLAB Site Licensed Software page:
Djordje Gligorijevic, Temple University, Spring 2015

4. Layouts of versions MATLAB 1.0 to MATLAB 8.2
Matlab Layouts
Layouts of versions MATLAB 1.0 to MATLAB 8.2
Editor
Workspace
Current folder view
Command Window
Command History
Djordje Gligorijevic, Temple University, Spring 2015

5. Matlab Layouts – new movement
Layouts of versions MATLAB 8.3 -
Editor/Variables View
Current Window
Workspace
Command Window
Djordje Gligorijevic, Temple University, Spring 2015

6. Djordje Gligorijevic, Temple University, Spring 2015
MATLAB competition
Due to its cost, MATLAB has a hard time finding a dominance in the industry.
Other languages provide a “bigger bang for the buck” thanks to the active communities that maintain widely used libraries.
An examples of such languages that have became a “hot topic” recently are:
Python (NumPy, SciPy, Matplotlib, SciKit Learn,…) R
However, MATLAB is still completely dominating when it comes to performance.
Djordje Gligorijevic, Temple University, Spring 2015

7. There are a few predefined variables in MATLAB:
MATLAB Variables
There are a few predefined variables in MATLAB:
ans
Variable which has been assigned a value of most recent expression, which hasn’t had assigned a value of its output to a specific variable pi
Number pi =
eps
Smallest difference between two numbers MATALB can see 
inf
Stands for an infinite value
NaN
Undefined value (Not-a-Number), Ex. 0/0 i
Imaginary one
Djordje Gligorijevic, Temple University, Spring 2015

8. Djordje Gligorijevic, Temple University, Spring 2015
Matlab Structures
Numeric Types: Matlab provides wide range of numerical and floating point types such are
double,
int (8,16,32 and 64 bits),
uint ( 8,16,32,64 bits).
Some functions on numeric types:
Djordje Gligorijevic, Temple University, Spring 2015

9. Elementary math functions
sqrt(x)
Square root
sin(x)
Sinus x (in radians)
exp(x)
Exponential function - ex
cos(x)
Cosinus s
abs(x)
Absolute value
tan(x)
Tangens x
log(x)
Natural logarithm - ln(x), loge(x)
cot(x)
Cotangens x
log10(x)
Logarithm with basis 10
round(x)
Round to an integer
factorial(x)
Factoriel x – x!
ceil(x)
Round to higher value
fix(x)
Round to lower value
rem(y,x)
Remainder of x/y division
sign(x)
Signum function
Djordje Gligorijevic, Temple University, Spring 2015

10. Matlab Structures, Contd.
Matrices and Vectors
To enter a matrix:
>> A = [2, 5, 3; 6, 4, 1]
>> B = [1:1.5:6; ]
>> for i=1:4
for j=1:3
C(i,j)=i*j;
end
>> D =[]; D=[D;5]; D=[D;6;7]
>> E = zeros(4, 5)
Djordje Gligorijevic, Temple University, Spring 2015

11. Matlab Structures, Contd.
Matrices and Vectors
As every variable in MATLAB can be a matrix, we can do basic operations on them:
Addition:
>> C = A + B
Subtraction:
>> D = A – B
Multiplication:
>> E = A * B (Matrix multiplication)
>> E = A .* B (Element wise multiplication, A and B same size)
Division:
Left Division and Right Division
>> F = A . / B (Element wise division)
>> F = A / B = A*inv(B) (A * inverse of B)
>> F = A . \ B (Element wise division)
>> F = A \ B=inv(A)*B (inverse of A * B)
Djordje Gligorijevic, Temple University, Spring 2015

12. Elementary matrix functions
max
Maximum of elements +
Matrix addition
min
Minimum of elements -
Matrix substraction
sum
Sum of elements *
Matrix multiplication
prod
Product of elements /
Matrix division
median
Median (Middle value) \
Left matrix division
mean
Mean (Agerage) ^
Power
std
Standard deviation '
Transpose
any
Is there any zero
inv
Inverse of the matrix Never use it!!!!
all
Are all elements zero
sort
Sort columns (or rows)
Djordje Gligorijevic, Temple University, Spring 2015

13. Generating basic matrices
Matrix with ZEROS:
>> A = zeros(m, n)
Matrix with ONES:
>> B = ones(m, n)
IDENTITY Matrix:
>> I = eye(m, n)
RANDOM Matrix:
>> I = rand(m, n)
MAGIC SQUARE Matrix:
>> I = magic(n)
m  Rows
n  Columns
zeros, ones, eye, rand, magic  Matlab functions
Djordje Gligorijevic, Temple University, Spring 2015

14. Random Number Generators
Rand(m,n): matrix with each entry ~ U(0,1)
Randn(m,n): standard normal distribution
Mvnrnd(Mu, Sigma): Multivariate normal random numbers
Djordje Gligorijevic, Temple University, Spring 2015

15. Array indexing, obtaining information
Size(A): return [m n]
Length(A): length of a vector
Length(A) = max(size(A))
B = A(2:4,3:5)
B is the subset of A from row 2 to row 4, column 3 to column 5
C = A(2)
C is a scalar with value of second index in matrix A
Matlab matrix indicies go iteratively top-down, column by column
D = A(:, [1,15,20])
Select all rows but a few columns
A(:, 2)=[]
Delete second column
Djordje Gligorijevic, Temple University, Spring 2015

16. Characters and Strings
A sequence of characters enclosed in single quotes 
assign a string to a variable
A = ‘Alice’
use two single quotes within the definition if  the text includes  a single quote
Concatenaton  
With square brackets  as concatenate numeric arrays
A = [‘Alice’, ’followed’, ’the’, ’rabbit.’]
Convert numeric values to strings
num2str
int2str
Djordje Gligorijevic, Temple University, Spring 2015

17. Djordje Gligorijevic, Temple University, Spring 2015
Save/Load Data
Save fname
Save all workspace data into fname.mat
Save fname x y z
Save(fname): when fname is a variable
Save large files
save('fname.mat','fname','-v7.3');
Load fname
Load fname x y
No error in data
You can run simulation intermittently
Save/load data between runs
Djordje Gligorijevic, Temple University, Spring 2015

18. Programming in MATLAB - Scripts
A file with a .m extension containing
Multiple sequential lines of MATLAB commands
Function calls
To run a script
Save a file in the current folder and type its name at the command line
Run scripts from the Editor by pressing the Run button
Comments
To describe the code
Add comments whenever you write code
For comments add % symbol first
Djordje Gligorijevic, Temple University, Spring 2015

19. Programming in MATLAB - Functions
Equivalent to subroutines or methods in other programming languages
To call a function, enclose its input arguments in parentheses
If there are multiple input arguments, separate them with commas
Return output from a function by assigning it to a variable
When there are multiple output arguments, enclose them in square brackets
To call a function that does not require any inputs and does not return any outputs, type only the function name
Djordje Gligorijevic, Temple University, Spring 2015

20. Programming in MATLAB – Control Flow
MATLAB allows control flow operations:
Conditional statements, loops, branching
Djordje Gligorijevic, Temple University, Spring 2015

21. Plotting in MATLAB – Basic 2-D Figure Plot
Plot(X, Y):
Plots vector Y versus vector X
Hold: next plot action on the same figure
Title(‘title text here’)
Xlabel(‘…’), ylabel(‘…’)
Axis([XMIN XMAX YMIN YMAX])
Or use xlim or ylim
Legend(‘…’)
Grid
Example demo
Djordje Gligorijevic, Temple University, Spring 2015

22. Plotting in MATLAB – Basic 3-D Figure Plot
x=[0:10]; y=[0:10]; z=x’*y;
mesh(x,y,z); figure; surf(x,y,z);
Djordje Gligorijevic, Temple University, Spring 2015

23. Djordje Gligorijevic, Temple University, Spring 2015
MATLAB – Help
The most important thing to remmember about MATLAB – it has great Help and Documentation
Just press Shift + F1 to search for needed function
Or select a function and press F1
Djordje Gligorijevic, Temple University, Spring 2015

24. End of MATLAB introduction
Any Questions?
Djordje Gligorijevic, Temple University, Spring 2015