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Introduction to Matlab Οικονομίδης Δημήτρης doikon@telecom.tuc.gr 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 3 5 1 4 3 2 -1 transpose y = x.’ y = 1 2 5 1

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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 <=less than or equal >greater than >=greater than or equal &AND |OR ~NOT pi3.14159265… jimaginary unit, isame 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 uniformly distributed random numbers on (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 the Sine 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) plotlinear plot stemdiscrete plot gridadd grid lines xlabeladd X-axis label ylabel add Y-axis label titleadd graph title subplotdivide figure window figurecreate new figure window pausewait 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 = 1:10 r(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 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 p = 0.5110

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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

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

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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)/10000ans = 0.0275p[2]=0.0278 sum(y==3)/10000ans = 0.0554p[3]=0.0556 sum(y==4)/10000ans = 0.0841p[4]=0.0833 sum(y==5)/10000ans = 0.1082p[5]=0.1111 sum(y==6)/10000ans = 0.1397p[6]=0.1389 sum(y==7)/10000ans = 0.1705p[7]=0.1667 sum(y==8)/10000ans = 0.1407p[8]=0.1389 sum(y==9)/10000ans = 0.1095p[9]=0.1111 sum(y==10)/10000ans = 0.0794p[10]=0.0833 sum(y==11)/10000ans = 0.0585p[11]=0.0556 sum(y==12)/10000ans = 0.0265p[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) Bernoulli1720 k=0:20; y=binopdf(k,20,0.2); stem(k,y)

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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)

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