COMP 116: Introduction to Scientific Programming

Lecture 11: Functions

So farScript 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?

Calling FunctionsHow 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.mx = [4 3 9 2 9 1 2 7 4];maxX = max(x);......

max.minput

output

Calling FunctionsHow does MATLAB call its own

functions?

In MATLAB, each function should go into a separate m-file

% MyScript.mx = [4 3 9 2 9 1 2 7 4];maxX = max(x);......

max.minput

output

Syntax vs. SemanticsWhat 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 correctly convert our source code into something the computer understands.

SemanticsWhat are semantics?

◦Meaning◦What does your function actually do?◦What problem(s) does it solve?

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 should be the same

Function Syntax

Must start with function keyword◦Otherwise, it’s a script

Function Syntax

Function name◦ Again: remember that this must be the same as

the name of the m-file

Function Syntax

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

Function Syntax

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

Function SyntaxComment block, just below the first line

◦Searched by lookfor◦Displayed when you type help

Function implementation◦Where you do all the ‘work’◦Has comments, expression, function calls…

Function Syntax

JargonParameters

◦ The variables declared in the function interfaceArguments

◦ 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

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 several outputs◦ This is different from most other languages.

Input and output are optional

Comments are optional◦ But a good programming practice

More rules …One function per file

◦Exception: helper functions Meant to only be used internally by the

main functionfunction [avg, med] = newstats(u)% NEWSTATS Find mean w/ subfuctions. n = length(u); avg = helper_mean(u, n);

function a = helper_mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

All in a single m file

More rules …

Function Names are case sensitive◦DiceToss is different from dicetoss is

different from diceToss…

More rules …function [avg, med] = newstats(u)% NEWSTATS Find mean w/ subfuctions. n = length(u); avg = helper_mean(u, n);

function a = helper_mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

More rules …

Gotcha: you can accidently hide system functions, constants, and workspace variables by creating your own function with the exact same name.

function [avg, med] = newstats(u)% NEWSTATS Find mean w/ subfuctions. n = length(u); avg = mean(u, n);

function a = mean(v, n) % Subfunction: calculate average. a = sum(v)/n;

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

Function examplesMultiple inputs

No inputs

Multiple outputs

No outputs

Exercise 1Write 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?

ScopeFunctions run in their own

‘workspaces’

MATLAB

sq.m x =4 x2 =16

foo =4 x2 =5 bar =16

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

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

Scripts vs. Functions

Why use Functions?

Top-down designEncapsulationMore flexible, resuable codeTesting strategy

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

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

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

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

Variable number of inputsHow 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 nargin is automatically set in the

local workspace of each function, and tells you how many input variables were actually supplied to the function.

Variable number of outputsHow does size() work?

◦Can return variable number of outputs

varargout, nargout◦nargout returns the number of

output arguments specified for a function.