COMP 116: Introduction to Scientific Programming

1. COMP 116: Introduction to Scientific Programming Lecture 36: Final Review I

2. Final Exam Details • The final will be • Comprehensive • Roughly like the midterms, but will have more stuff • Short programs (5-10 lines of code) • No linear programming, image manipulation, audio filtering

3. Course objectives • To teach you how to write code • We’ve mainly used MATLAB as a vehicle for this int my_function() { int data[ ] = {6, 3, 3, 8, 43, 2, 19, 7, 5, 88}; int num_elements = 10; int res = data[0]; for (int i = 1; i < num_elements; ++i) { if (data[i] < res) { res = data[i]; } } return res; } What does this function do?

4. Course objectives • To teach you how to write code • We’ve mainly used MATLAB as a vehicle for this • …but the concepts you’ve learnt in this class carry over to almost every other programming language

5. Course objectives • What I hope you’ve learnt: If you have some data • Read it into MATLAB • Process it in some way • Display/plot it in some way • Write out the results • Keep going! • Many other great courses in Comp. Science • In today’s world, programming is a fantastic skill to have

6. Matlab as a Calculator Important points: • Operator precedence • When in doubt use parentheses • Semicolon suppresses output • 5+3; % does not create output • 5+3 % creates output

7. Operators / Full Precedencedoc ops Super-important: Distinguish between element by element operators and matrix operators.

8. Special Characters

9. Special Characters

10. Array & Vector Operations

11. Working with Vectors / Matrices Colon Operator ‘:’ v = <start>:<stop> v = <start>:<step>:<stop> >> A = [1.1:1.1:4.4; 5.5:1.1:8.8; ... 9.9:1.1:13.2]; Linspace command: >> linspace(0,2*pi,100); Indexing Operator () A(7) % a(n) = 1D Indexing A(3,2) % a(r,c) = 2D Indexing

12. Important Matrix Functions

13. Important Matrix Functions

14. Concatenation • Vectors and matrices can only be concatenated if the number of rows/columns line up [1 2 3; 4 5 6] % works [1 2 3; 4 5] % does not work

15. Matrix Operators element-by-element operations Compatibility Rules: C4x5 = A4x5 .* B4x5 A, B must be same size and shape solves a linear equation system of the form Ax = b Matrix Multiplication Rules: C4x7 = A4x3 * B3x7 A.nCols == B.nRows Inner dimensions agree, outer dimensions become new size & shape

16. An example Note: Not necessary to compute actual values. Simply determine size of the individual factors. rand(3,4)*[1 2; 3 4; 5 6; 7 8]*ones(2,3) (3x4) * (4x2) * (2x3) Results in: (3x3)

17. Resulting Matrix Sizes of Matrix-value Expressions Gets trickier if e.g. .* and * are used. Example: rand(3,4)*[1 2; 3 4; 5 6; 7 8].*ones(3,2) (3x4) * (4x2) .* (3x2) (3x2) (3x2) Evaluates from the left to the right!

18. Matrix indexing • A is a preassigned matrix >>B=A(u,v) • B(i,j)=A(u(i),v(j)) • What does A(1:2:end,1:2:end) return? • How do you extract the 3x3 matrix around the (4,5) element of A?

19. Solving Systems of EquationsAx = b % System of equations 5x + 10y – 4z + w = 2 x - 2y + z = 1 2x + 3y + z – 6w = 3 7x + 2z + 3w = 4 % Set up coefficient matrix A = [5 10 -4 1; 1 -2 1 0; ... 2 3 1 -6; 7 0 2 3]; b = [2 1 3 4]; % Setup solution vector x = A \ b'; % Solve for unknowns

20. Plotting & Publishing

21. 2D Plotting Basics Title y axis Legend y label Marker x axis x label

22. Plottingplot( x, y, ‘LineSpec’, ‘PropertyName’, ‘PropertyValue’, … ); • Plot Attributes • line attributes ( ‘-.ro’ ) • Line style, Color, Marker • other properties • Line Width, Marker Colors • Formatting: • xlabel, ylabel, title • legend, text, … • More Commands • axis <min,max>, square, equal • gcf, clf, grid [on|off], … • Multiple plots • Overlaying plots • plot( x, [y1 y2…], … ) • plot( plot1, plot2,… ) • hold on|off • subplot( 3, 2, 3 ) • More Plots • hist, semilogx, loglog • bar, pie, polar, …

23. Conditional Logic:

24. Relational OperatorsTests relationship between two objects or arrays • Result is always a logical data type or array of logical data types

25. Logical OperatorsBoolean operators • Performs binary logic on two logical data type operands (or arrays) to return a logical result.

26. Formulating Logical Expression • Most expressions can be written directly: E.g. Point is within or on the unit circle • Condition: x^2+y^2<=1 • Sometimes differs from standard math notation • (2<x)&(x<3) % is correct (Program Style) • 2<x<3 % is incorrect (Math Style) • When in doubt: use parentheses.

27. if Statements Single Test if <test> commands; % Section 1 end Test between Two Choices if <test> commands; % Choice #1 (test was true) else commands; % Choice #2 (test == false) end

28. if Statements Nested Tests if <Test1> if <Test2> commands1; % T1,T2 both true else commands2; % T1=1, T2=0 end else if <Test3> commands3; % T1=0, T3=1 else commands4; % T1,T3 both false end end Chained Tests if <Test1> commands1; % T1 true elseif <Test2> commands2; % T1 false T2 %true elseif <Test3> commands3; % T1, T2 %false, T3 true else commands4; % T1,T2,T3false end

29. Finding Elements/Indexing

30. Finding Elements/Indexing Two different ways of finding elements • Using the find command ind = find( x>3 ); % returns indices of elements in x satisfying test • If you want to extract the respective elements use • x( ind ) % returns elements at specified indices

31. Finding Elements/Indexing If you want to find the maximum or minimum element in a vector or matrix you can get both the value and indices through min or max. • [minVal, minIndex] = min( x ) • [maxVal, maxIndex] = max( x )

32. Functions

33. Writing Simple function function [o1, o2]=funcName( i1, i2 ) % Function Comments … % Body (implementation) end %optional • Can have multiple inputs (i1) and multiple outputs (o2) • function [] = funcName() • function o1 = funcName() • function o1 = funcName( i1 ) • function o1 = funcName( i1, i2 ) • function [o1, o2] = funcName( i1, i2, i3)

34. WorkspaceGlobal vs. Local Storage • Global Workspace • Shared by Command Window and script commands • Local Workspace • Created locally on entry to each function • Disappears on exit from function call. % This is a script radius = 10; area = pi .* radius .^2; function [area] = circ_area(radius) area = pi .* radius .^ 2; % Call function in workspace my_area = circ_area( 10 );

35. Looping

36. Loops: for loop statementthe counted loop solution for <varindex> = <start>:<stop> <Body: do some work> end for <idx> = <start>:<step>:<stop> <Body: do some work> end

37. Loops: while loop statementthe conditional loop solution while <test> <Body: do some work> <Update:make progress towards exiting loop> end • While loops are great if we don’t know how many times we need to loop, but if we can write a test for when we’re done • For this to work properly, the test needs to evaluate to a logical value • The while loop will run as long as test evaluates to true • The while loop does not have a built-in counter like the for-loop (if you want to count something, you need to implement the counter yourself)

38. Common Idioms: Looping over a matrix • Use a nested for loop: • function ret = findMaxElement( A ) • sz = size(A); • ret = A(1,1); • for i=1:sz(1) • for j=1:sz(2) • if ( A(i,j)>ret ) • ret = A(i,j); • end • end • end