01 intro matlab-basics

8/8/2019 01 Intro Matlab-Basics

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Introduction to Matlab

[email protected]

http://www.telecom.tuc.gr


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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


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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


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Matrices

a vector x = [1 2 5 1]

x =1 2 5 1

a matrix x = [1 2 3; 5 1 4; 3 2 -1]

x =1 2 35 1 4

3 2 -1

transpose y = x. y =1251


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Matrices

x(i,j) subscription

whole row

whole column

y=x(2,3)

y =

4

y=x(3,:)

y =

3 2 -1

y=x(:,2)

y =

2

1

2


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Operators (arithmetic)

+ addition- subtraction* multiplication

/ division^ power complex conjugate

transpose

.* element-by-element mult

./ element-by-element div

.^ element-by-element power

. transpose


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Operators (relational, logical)

== equal~= not equal

< less than greater than>= greater than or equal

& AND| OR~ NOT

1pi 3.14159265

j imaginary unit,

i same as j


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Generating Vectors from functions

zeros(M,N) MxN matrix of zeros

ones(M,N) MxN matrix of ones

rand(M,N) MxN matrix of uniformlydistributed random numberson (0,1)

x = zeros(1,3)

x =

0 0 0

x = ones(1,3)x =

1 1 1

x = rand(1,3)

x =0.9501 0.2311 0.6068


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Operators

[ ] concatenation

( ) subscription

x = [ zeros(1,3) ones(1,2) ]

x =

0 0 0 1 1

x = [ 1 3 5 7 9]

x =

1 3 5 7 9

y = x(2)y =

3

y = x(2:4)

y =

3 5 7


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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 theSine Function')


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Multiple Graphs

t = 0:pi/100:2*pi;

y1=sin(t);

y2=sin(t+pi/2);

plot(t,y1,t,y2)

grid on


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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)


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Graph Functions (summary)

plot linear plot stemdiscrete 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


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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


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Functions

function f=myfunction(x,y)

f=x+y;

save it in myfunction.m call it with y=myfunction(x,y)


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Flow Control

if A > B

'greater'

elseif A < B

'less'

else'equal'

end

for x = 1:10r(x) = x;

end

if statement switch statement

for loops while loops

continue statement

break statement


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Miscellaneous

Loading data from a file load myfile.dat

Suppressing Output x = [1 2 5 1];


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Getting Help

Using the Help Browser (.html, .pdf) View getstart.pdf, graphg.pdf, using_ml.pdf

Type help

help function , e.g. help plot

Running demos type demos type help demos


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Random Numbers

x=rand(100,1);

stem(x);

hist(x,100)


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Coin Tosses

Simulate the outcomes of 100 fair coin tossesx=rand(100,1);p=sum(x


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Coin Tosses

Simulate the outcomes of 1000 biased coin tosses withp[Head]=0.4

x=rand(1000,1);

p=sum(x


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Sum of Two Dies

Simulate 10000 observations of the sum of two fair dies

.

..

.

.

. . . . .

.

. . . .. .

... .

.

. ..

.

...

.. .. .. .

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(3,2) (4,2) (5,2) (6,2)

(3,3) (4,3) (5,3) (6,3)

(2,2)(1,2)

(2,3)(1,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(3,5) (4,5) (5,5) (6,5)(2,5)(1,5)

(3,6) (4,6) (5,6) (6,6)(2,6)(1,6)

1 2 3 4 5 6

1

2

3

4

5

6


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Sum of Two Dies

Simulate 10000 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 = 0.0275 p[2]=0.0278sum(y==3)/10000 ans = 0.0554 p[3]=0.0556sum(y==4)/10000 ans = 0.0841 p[4]=0.0833sum(y==5)/10000 ans = 0.1082 p[5]=0.1111sum(y==6)/10000 ans = 0.1397 p[6]=0.1389sum(y==7)/10000 ans = 0.1705 p[7]=0.1667sum(y==8)/10000 ans = 0.1407 p[8]=0.1389sum(y==9)/10000 ans = 0.1095 p[9]=0.1111sum(y==10)/10000 ans = 0.0794 p[10]=0.0833sum(y==11)/10000 ans = 0.0585 p[11]=0.0556sum(y==12)/10000 ans = 0.0265 p[12]=0.0278


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Sum of Two Dies

for i=2:12

z(i)=sum(y==i)/10000

end

bar(z)


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Bernoulli Trials-Binomial Distribution

k=0:20;

y=binopdf(k,20,0.5);

stem(k,y)

( ) (1 ) , 0,1,...,k n k n p k p p k nk

-

= - =

Bernoulli 1720

k=0:20;

y=binopdf(k,20,0.2);

stem(k,y)

20 0.5n p= = 20 0.1n p= =


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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)

!n

!

( )!n

k

n P

n k =

-

!

!( )!

n nk k n k

=

-

n n

k n k

=

-

!1

0 0! !

n n n

n n

= = =

!

1 1 1!( 1)!

n n nn

n n

= = =

- -

01 intro matlab-basics

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