Introduction to Matlab Οικονομίδης Δημήτρης doikon@telecom.tuc.gr http://www.telecom.tuc.gr

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

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

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

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

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

Operators (relational, logical) == equal ~= not equal < less than <= less than or equal > greater than >= greater than or equal & AND | OR ~ NOT pi 3.14159265… j imaginary unit, i same as j

Generating Vectors from functions x = zeros(1,3) x = 0 0 0 x = ones(1,3) 1 1 1 x = rand(1,3) 0.9501 0.2311 0.6068 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)

Operators [ ] concatenation ( ) subscription x = [ zeros(1,3) ones(1,2) ] x = 0 0 0 1 1 x = [ 1 3 5 7 9] 1 3 5 7 9 y = x(2) y = 3 y = x(2:4) 3 5 7

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')

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

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)

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

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

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)

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

Miscellaneous Loading data from a file Suppressing Output load myfile.dat Suppressing Output x = [1 2 5 1];

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

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

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

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

Sum of Two Dies Simulate 10000 observations of the sum of two fair dies

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

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

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)

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)