COMP 116: Introduction to Scientific Programming

1. COMP 116: Introduction to Scientific Programming Lecture 11: Functions

2. So far • Script files • All code inside one big file • Perhaps structured into cells • Used built-in matlab functions • sin, cos, zeros etc. • How do we structure more complex code? • How do we write our own functions?

3. Calling Functions • How does MATLAB call its own functions? • Matlab loads it’s own function files and runs them through the interpreter • Input variables map onto function inputs • Function outputs get stored in specified variables % MyScript.m x = [4 3 9 2 9 1 2 7 4]; maxX = max(x); ... ... input max.m output

4. Calling Functions • How does MATLAB call its own functions? • In MATLAB, each function should go into a separate m-file % MyScript.m x = [4 3 9 2 9 1 2 7 4]; maxX = max(x); ... ... input max.m output

5. Syntax vs. Semantics • What is syntax? • Grammar • Rules that let you write in the language • Punctuation, etc. • Why do we need syntax rules? • Syntax rules allow compilers and interpreters to correctlyconvert our source code into something the computer understands.

6. Semantics • What are semantics? • Meaning • What does your function actually do? • What problem(s) does it solve?

7. Writing a function: Syntax function [outputs] = funcName( inputs ) % Function Comments … % Body (implementation) end %optional Note: The name of the function and the name of the m-file shouldbe the same

8. Function Syntax • Must start with function keyword • Otherwise, it’s a script

9. Function Syntax • Function name • Again: remember that this must be the same as the name of the m-file

10. Function Syntax • Function return values/output • Potentially multiple values may be returned from the function • [r, c] = size(A)

11. Function Syntax • Function input values/parameters • Potentially multiple arguments may be passed into a function • s = sum(A, 2)

12. Function Syntax • Comment block, just below the first line • Searched by lookfor • Displayed when you type help

13. Function Syntax • Function implementation • Where you do all the ‘work’ • Has comments, expression, function calls…

14. Jargon • Parameters • The variables declared in the function interface • Arguments • The actual values supplied when the function is called. These are function parameters When calling the function: c = DiceToss(num_throws, desired_value); These are function arguments

15. A summary of function rules • Most important: function name and its corresponding .m file name should match. • Functions can have several inputs • common in most languages • Functions can also have severaloutputs • This is different from most other languages. • Input and output are optional • Comments are optional • But a good programming practice

16. More rules … • One function per file • Exception: helper functions • Meant to only be used internally by the main function function [avg, med] = newstats(u) % NEWSTATS Find meanw/ subfuctions. n= length(u); avg= helper_mean(u, n); All in a single m file function a = helper_mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

17. More rules … • Function Names are case sensitive • DiceToss is different from dicetoss is different from diceToss…

18. More rules … function [avg, med] = newstats(u) % NEWSTATS Find meanw/ subfuctions. n= length(u); avg= helper_mean(u, n); function a = helper_mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

19. More rules … function [avg, med] = newstats(u) % NEWSTATS Find meanw/ subfuctions. n= length(u); avg= mean(u, n); • Gotcha: you can accidently hide system functions, constants, and workspace variables by creating your own function with the exact same name. function a = mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

20. More rules … • Be careful with parentheses: [] vs () • [r, c] = size(A) • (r, c) = size(A) • [r, c] = size[A] • Think: • Difference between • myfunc([1, 2, 3]) and myfunc(1, 2, 3) Incorrect

21. Function examples Multiple inputs Multiple outputs No outputs No inputs

22. Exercise 1 • Write an absolute value function • Assume the input is just a scalar • Convert your guess-the-number script to a function • What is the input? • What is the output?

23. Scope • Functions run in their own ‘workspaces’ MATLAB sq.m foo =4 bar =16 x2 =5 x =4 x2 =16

24. Scope: Global Variables (Workspace) • Global MATLAB workspace • Variables belonging to script files and command window • Workspace Variables • come into existence after they are created by assignment. • exist until MATLAB quits or clear command is used on variables to remove them. • Accessible from command window and scripts • NOT accessible from inside functions

25. Scope: Local Variables (Functions) • Function workspaces • Local scope • Variables • Parameter variables live from function entry • Local variables live from assignment • Until function finishes (or clear) • Local workspace is cleared at end of function • Output copied/assigned to variables in calling workspace

26. Scripts vs. Functions

27. Why use Functions? • Top-down design • Encapsulation • More flexible, resuable code • Testing strategy

28. Top-down design • Break a complex problem into simpler manageable problems • Solve simpler problems • Connect simple solutions to solve original problem Functions give your code structure

29. Encapsulation • A function is isolated from the rest of the system, and interacts only through its input and output arguments. • A function can't mess up the variables in your workspace • Likewise, you can't mess up a function by changing values • Much more powerful, and fewer ‘side-effects’ than scripts

30. Flexible, reusable code • A script only solves one instance of a problem • A function can solve all instances • You can call hypotenuse with any values of a and b • Since functions are encapsulated, this means you only need to know its interface (what it does), not its implementation (how it does it) • Share your solution to a problem with others. • Collaboration • Team, organization, world

31. Easier testing • If you write your program as a 500-line script, and it gives the wrong answer. . . • Good luck with that! • If you write your program as a small function that calls other functions that call other functions. . . • Test the simplest functions first • Check that functions are connected correctly

32. Variable number of inputs • How does a function like min() work? • It can take a variable number of inputs • min(x); • min(x, 1) • min(x, [], 1) • varargin, nargin • varargin is a cell array – we’ll talk about cell arrays later • The variable narginis automatically set in the local workspace of each function, and tells you how many input variables were actually supplied to the function.

33. Variable number of outputs • How does size()work? • Can return variable number of outputs • varargout, nargout • nargout returns the number of output arguments specified for a function.