1. Introduction to MATLAB Michael Fink fink@cs.huji.ac.ilfink@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' Cellsarrays 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 = 000 >> v0 = zeros(3,1) v0 = 0 >> vec1 = [3:8] vec1 = 345678 >> mySkip = [3:2:8] mySkip = 357

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

11. Concatenating matrices >> hCat = [h0 mySkip] hCat = 000357 >> vCat = [h0; mySkip] vCat = 000 357 >> skip3 = repmat(mySkip,3,1) skip3 = 357

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 =11 >> y = eye(2) y = 10 01 >> x(1,:) = [3 5] x = 351 >> y(:,2) = [3;5] y = 13 05

14. Indices >> 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 >> Rand3=rand(3) Rand3 = 0.9501 0.4860 0.4565 0.2311 0.8913 0.0185 0.6068 0.7621 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 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. 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 if okInput, disp(['is ' num2str(finalVal)]); else 'div by 0!' end Copy paste into myscript.m and press F5

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 …