1. Introduction to Matlab
Οικονομίδης Δημήτρης

2. Desktop Tools (Matlab v6)
Command Window
type commands
Workspace
view program variables
clear to clear
double click on a variable to see it in the Array Editor
Command History
view past commands
save a whole session using diary
Launch Pad
access tools, demos and documentation

3. Matlab Files (.m) Use predefined functions or write your own functions
Reside on the current directory or the search path
add with File/Set Path
Use the Editor/Debugger to edit, run

4. Matrices a vector x = [1 2 5 1] a matrix x = [1 2 3; 5 1 4; 3 2 -1]
a matrix x = [1 2 3; 5 1 4; ]
transpose y = x.’ y = 1 2 5

5. Matrices x(i,j) subscription whole row whole column y=x(2,3) y = 4
y=x(:,2) 2 1

6. Operators (arithmetic)
+ addition
- subtraction
* multiplication
/ division
^ power
‘ complex conjugate transpose
.* element-by-element mult
./ element-by-element div
.^ element-by-element power
.‘ transpose

7. Operators (relational, logical)
== equal
~= not equal
< less than
<= less than or equal
> greater than
>= greater than or equal
& AND
| OR
~ NOT
pi …
j imaginary unit,
i same as j

8. Generating Vectors from functions
x = zeros(1,3)
x =
x = ones(1,3)
x = rand(1,3)
zeros(M,N) MxN matrix of zeros
ones(M,N) MxN matrix of ones
rand(M,N) MxN matrix of uniformly distributed random numbers on (0,1)

9. Operators [ ] concatenation ( ) subscription
x = [ zeros(1,3) ones(1,2) ]
x =
x = [ ]
y = x(2)
y = 3
y = x(2:4)

10. Matlab Graphics x = 0:pi/100:2*pi; y = sin(x); plot(x,y)
xlabel('x = 0:2\pi')
ylabel('Sine of x')
title('Plot of the Sine Function')

11. Multiple Graphs t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2);
plot(t,y1,t,y2)
grid on

12. Multiple Plots t = 0:pi/100:2*pi; y1=sin(t); y2=sin(t+pi/2);
subplot(2,2,1)
plot(t,y1)
subplot(2,2,2)
plot(t,y2)

13. Graph Functions (summary)
plot linear plot
stem discrete plot
grid add grid lines
xlabel add X-axis label
ylabel add Y-axis label
title add graph title
subplot divide figure window
figure create new figure window
pause wait for user response

14. Math Functions
Elementary functions (sin, cos, sqrt, abs, exp, log10, round)
type help elfun
Advanced functions (bessel, beta, gamma, erf)
type help specfun
type help elmat

15. Functions save it in myfunction.m call it with y=myfunction(x,y)
function f=myfunction(x,y)
f=x+y;
save it in myfunction.m
call it with y=myfunction(x,y)

16. Flow Control if statement switch statement for loops while loops
if A > B
'greater'
elseif A < B
'less'
else
'equal'
end
for x = 1:10
r(x) = x;
if statement
switch statement
for loops
while loops
continue statement
break statement

17. Miscellaneous Loading data from a file Suppressing Output
load myfile.dat
Suppressing Output
x = [ ];

18. Getting Help Using the Help Browser (.html, .pdf) Type Running demos
View getstart.pdf, graphg.pdf, using_ml.pdf
Type
help
help function, e.g. help plot
Running demos
type demos
type help demos

19. Random Numbers
x=rand(100,1);
stem(x);
hist(x,100)

20. Coin Tosses Simulate the outcomes of 100 fair coin tosses
x=rand(100,1);
p=sum(x<0.5)/100
p =
0.5400
Simulate the outcomes of 1000 fair coin tosses
x=rand(1000,1);
p=sum(x<0.5)/1000
0.5110

21. Coin Tosses
Simulate the outcomes of 1000 biased coin tosses with p[Head]=0.4
x=rand(1000,1);
p=sum(x<0.4)/1000
p =
0.4160

22. Sum of Two Dies
Simulate observations of the sum of two fair dies

23. Sum of Two Dies
Simulate observations of the sum of two fair dies
x1=floor(6*rand(10000,1)+1);
x2=floor(6*rand(10000,1)+1);
y=x1+x2;
sum(y==2)/10000 ans = p[2]=0.0278
sum(y==3)/10000 ans = p[3]=0.0556
sum(y==4)/10000 ans = p[4]=0.0833
sum(y==5)/10000 ans = p[5]=0.1111
sum(y==6)/10000 ans = p[6]=0.1389
sum(y==7)/10000 ans = p[7]=0.1667
sum(y==8)/10000 ans = p[8]=0.1389
sum(y==9)/10000 ans = p[9]=0.1111
sum(y==10)/10000 ans = p[10]=0.0833
sum(y==11)/10000 ans = p[11]=0.0556
sum(y==12)/10000 ans = p[12]=0.0278

24. Sum of Two Dies
for i=2:12
z(i)=sum(y==i)/10000
end
bar(z)

25. Bernoulli Trials-Binomial Distribution
k=0:20;
y=binopdf(k,20,0.5);
stem(k,y)
Bernoulli 1720
k=0:20;
y=binopdf(k,20,0.2);
stem(k,y)

26. Combinatorics Permutations: n objects
Permutations: choose k objects from n
(hint: fill 2 spaces on a bookshelf with books chosen from 5 available books)
Combinations: choose k objects from n without
regard to the order
(hint: make a committee of 2 people chosen from a group of 5 people)