Introduction to MATLAB Michael Fink fink@cs.huji.ac.il

1. Introduction to MATLABMichael Fink fink@cs.huji.ac.il • Login and press the Matlab icon • Part 1: Using vectors and matrices • Part 2: Performing calculations • Part 3: Programming basics • Part 4: Visualization (graphs) • Part 5: Functions & function handles

2. Introduction to matlab • A technical computing environment for high performance numeric computation and visualization • No. 1 software development environment in the academia and in industry research • Quick coding (not efficient in running time) • A lot of existing code is available in the matlab core, toolboxes and internet

3. Getting started with Matlab • Press on the Matlab icon (and wait…) • Matlab is a functional language the Matlab prompt is >> Write: >> 100+1 ans = 101

4. Getting started with Matlab Define variables (use meaningful names): >> income = 3000 income = 3000 >> car = 1000; >> rent = 2000; >> x = income - car - rent x = 0

5. Language elements: Data types • Matrices arrays of similar elements >> a = rand(3) % a double matrix >> b = (a>0.9) % a logical matrix • Strings >> myName = 'Michael Fink' >> myName(4:5) % returns 'ha' • Cells arrays of different types of elements >> c{1,1} = 'Michael Fink' >> c{1,2} = 3000 • Structs variables with different fields >> me.myName = 'Michael Fink' >> me.income = 3000 >> you = me Notice: no pointers 

6. Scripts, functions and the matlab path • Three places to write code • Prompt: write and press enter • Script file: file name / F5 / mark code and F9 >> edit myscript.m • Function file: file name and parameters • (details later) • Notice: prompt and script variables share the same scope (unlike function variables)

7. Scripts, functions and the matlab path • When using files be sure they're on the matlab path: >> editpath% selecting the appropriate directory Or >> cd C:\work\ Or Select path at the top of the Matlab prompt window

8. Help! >> help sum

9. Vectors, matrices and indices Matlab basic variable is matrices (vectors are 1-D matrices) >> h0 = zeros(1,3) h0 = 0 0 0 >> v0 = zeros(3,1) v0 = 0 0 0 >> vec1 = [3:8] vec1 = 3 4 5 6 7 8 >> mySkip = [3:2:8] mySkip = 3 5 7

10. Vectors, matrices and indices When defining a vector: , or space for insertion in same row ; for insertion in same column • >> row = [1 7 13 2] • >> col = [1;7;13;2]

11. Concatenating matrices >> hCat = [h0 mySkip] hCat = 0 0 0 3 5 7 >> vCat = [h0; mySkip] vCat = 0 0 0 3 5 7 >> skip3 = repmat(mySkip,3,1) skip3 = 3 5 7 3 5 7 3 5 7

12. Running example: Year = [2 0 0 6] MonthDay = [0 0 0 0] Basic = [MonthDay Year ] November = repmat( Basic, 30, 1)

13. Concatenating matrices >> x = ones(2) x = 1 1 1 1 >> y = eye(2) y = 1 0 0 1 >> x(1,:) = [3 5] x = 3 5 1 1 >> y(:,2) = [3;5] y = 1 3 0 5

14. Indices >> Rand3=rand(3) Rand3 = 0.9501 0.4860 0.4565 0.2311 0.8913 0.0185 0.6068 0.7621 0.8214 >> Rand3(2:3,2) = 0 Rand3 = 0.9501 0.4860 0.4565 0.2311 0 0.0185 0.6068 0 0.8214 >> Rand3(5:6) = 0 Rand3 = 0.9501 0.4860 0.4565 0.2311 0 0.0185 0.6068 0 0.8214

15. Running example: Year = [2 0 0 6] MonthDay = [0 0 0 0] Basic = [MonthDay Year ] November = repmat(Basic,30,1) November(:,3:4) = ones(30,2) November(10:19,1) = 1 November(20:29,1) = 2 November(30,1) = 3 November(1:9, 2) = [1:9]' November(:,2) = repmat(November(1:10, 2),3,1)

16. Common operations • Mathematical operations: + - * / ^ >> 3+(4/6)*8-12^0 >> a = rand(3) - 0.5 >> eye(3)*a • Logical operations: ~1 is 0 >> a<=0 % or a<=zeros(3) will return 3x3 logical matrices ~= <= >= == & | isequal (not ==) tests whether matrices are identical

17. Common operations • Element functions: • mod (e.g. mod([3:5],4) is [3, 0, 1]) • ceil, round, sqrt, sign, .*, .^ , ' (transpose) >> sqrt([4 9]) >> ones(3,1).*zeros(1,3)' • Column-wise functions: sum, max, mean >> sum(a) % similar to ones(1,3)*a • traits of the variables: length, size >> size(a)

18. Running example: students = ['yitzhak ';'Shimon ';'Benjamin '] Leadership = [94; 90; 77] Economics = [78; 84; 94] (Leadership + Economics) / 2 Leadership > 85 bonus = [1.05 1.05 1.00] floor(Leadership.*bonus) % generates an error floor(Leadership.*bonus') mean(Leadership) sum(Leadership/3) var(Economics)

19. Some vector operations • find >> find(x==max(x)) • sort >> [Y I] = sort(x) Running example: students(find(Economics==max(Economics)),:) [vector index] = sort(Economics,'descend') students(index,:) setdiff(Economics,Leadership)

20. Saving and loading variables in current matlab path >> save myVars x >> x = randn(5,3); >> load myVars

21. Language elements: if conditions inChar='67/0'; i=3; val1 = str2num(inChar(1:i-1)); val2 = str2num(inChar(i+1:end)); if val2==0 okInput = false else exVal= val1 / val2 end

22. Language elements: switch conditions inChar = '65*20'; i = 3; val1 = str2num(inChar(1:i-1)); val2 = str2num(inChar(i+1:end)); switch inChar(i) case '*', exVal= val1 * val2 case '/', if val2==0 okInput=0; else exVal= val1 / val2 end otherwise i=i+1; end

23. Language elements: Loops • for loops for i=1:10, for j=1:10, m(i,j)=i*j; end end m % for loops are often unnecessary in Matlab m=[1:10]'*[1:10] • while loops total = 0; while total<1000 itemPrice = input(' enter product price: '); if itemPrice==0, break; end total = total + itemPrice; end total

24. Copy paste into myscript.m and press F5 inChar = input('enter formula: ','s'); okInput = true; i=1; while okInput == true switch inChar(i) case '*', finalVal=str2num(inChar(1:i-1))*str2num(inChar(i+1:end)); break case '/', if str2num(inChar(i+1:end))==0 okInput = false; else finalVal=str2num(inChar(1:i-1))/str2num(inChar(i+1:end)); break end otherwise i=i+1; end end if okInput, disp(['is ' num2str(finalVal)]); else 'div by 0!' end

25. Visualization: plots figure(1); x = -5:0.1:5; y = cos(x); plot(x,y) hold on; y2 = sin(x); plot(x, y, 'm', x, y2, 'g.'); axis([-2*pi 2*pi -1 1]); axis tight;

26. Visualization: images % display noisy matrix clf; imagesc(randn(10)); title('noisy x'); axis square;

27. Language elements: functions • Functions are called externally with some input, use their own variables and return an output • Several functions could be defined in a single file but only the heading function (with the same name as the file) will be available externally >> edit myfunc.m function [x2, x3, x4] = myfunc(x) x2 = x.^2; x3 = x.^3; x4 = x.^4; Copy paste into myfunc.m

28. Function handles functions as variables: efficient when different functions need to be used in the same way a=0; b=pi/2; dt=0.001; for i=1:3 switch i case 1, f1=@sin; case 2, f1=@sqrt; case 3, f1=@myfunc; end ff = f1([a:dt:b]); ['integral = ' num2str(sum(ff*dt))] end

29. Matlab is endless • Linear algebra • det (matrix determinant) • eig (eigenvalues and get eigenvectors) • Optimization toolbox • Linear / quadratic programming • Statistics toolbox • Neural Network Toolbox • Symbolic toolbox • Image processing toolbox • …