1. Introduction to Matlab & Data Analysis
Tutorial 7: Functions and Program Design
Please change directory to directory E:\Matlab (cd E:\Matlab;)
From the course website
( )
Download:
playTicTacToe.m , isLegalMove.m , isPlayerWon.m, getNextMove.m, myFactorial.m
Weizmann 2010 ©

2. Goals Top down design Introduction Functions M file structure
Functions workspace
Functions Input and output
Top down design
Local functions
Debugger
Recursion
More:
Functions and commands
Functions and the matlab search path

3. Function Is an Independent Piece of Code Which Performs a Task
Function (subroutine, method, procedure, or subprogram) –
is a portion of code within a larger program,
which performs a specific task and
can be relatively independent of the remaining code.
One M-file, One Task, One Workspace

4. Variables - The Data Objects, Functions Are The Actions
Input (Object / Data):
X = 80 90 95
100 98 88 92
Functions:
y = mean(x)
y = sum(x)
y = max(x)
Output: (Data)
91.85
643
100

5. A Function Is a Black Box
Output
Input
function
A function is a black box
It hides the code and its workspace and communicates with the “world” using the input and output variables 5 5

6. Functions M file structure
The file is a Matlab function
The output variables (if there are few use []: [out1 out2] )
Should be same as the name of the file
sumTwoNums.m:
function my_sum = sumTwoNums(a,b)
my_sum = a+b;
The input variables
Assign the output variables
(else - Matlab will give an error)

7. Functions Documentation and Variable Verification
function my_sum = sumTwoNums(a,b)
% SUMTWONUMS sum to scalars
% this function sums two scalar
% and returns the result
% INPUT:
% a - the first scalar
% b - the second scalar %
% OUTPUT:
% my_sum - the sum of a and b; sum = a+b
if (~isscalar(a))
error('First argument is not a scalar');
end
if (~isscalar(b))
error('Second argument is not a scalar');
my_sum = a+b;
First line
help:
Usage
Input
Output
Examples
Testing for proper variables
Calculations and Output assignment

8. Each Instance of A Function Run Has Its Own Workspace
Assume we wrote the function:
function my_sum = sumTwoNums(a,b)
my_sum = a + b;
In the workspace we run:
a = 1;
b = 2;
x = 3;
y = 4;
s = sumTwoNums(x, y)
What is the output?
s = 7
Matlab
Workspace:
a = 1
b = 2
X = 3
y = 4
s = 7
Function Workspace:
a = 3
b = 4
my_sum = 7

9. Matlab Functions Can Be Called With Fewer Input Arguments Than Specified
Consider a function that computes
function y = calSecondOrderPoly(x, a, b, c)
switch nargin
case 4
% do nothing
case 3
c = 0;
case 2
b = 0;
otherwise
error('Incorrect input');
end
y = a*x.^2 + b*x + c;
Switch according to input arguments number
Default value

10. Matlab Functions Can Be Called With Fewer Output Arguments Than Specified
Recall:
[r,c] = find(A) , ind = find(A);
sorted_A= sort(A); [sorted_A, sort_ind] = sort(A);
Now lets improve our function such that if it called with two output arguments, the second argument is the derivative:
[y, y_derivative] = calSecondOrderPoly(x, a, b, c);

11. Matlab Functions Can Be Called With Fewer Output Arguments Than Specified
function [y, y_derivative] = calSecondOrderPoly(x, a, b, c)
y = a*x.^2 + b*x + c;
if nargout == 2
y_derivative = 2*a*x + b;
end
Checks number of output arguments
Can help avoid expensive computations when they are not necessary

12. Example - Write a function subtractTwoNums Add Help to the function
Input: a, b
Output: a-b
Add Help to the function
Try calling the function (Debugger)
*Extra: if the function needs to return two output variables:
Output: [a-b, b-a]

13. Top Down Design A method to solve complex problems Principles:
Start from large problems to small
A function does one task
Think before you code

14. Top Down Design and Debugging – Tic-Tac-Toe Example
Problem specifications:
Build a tic-tac-toe game for two players.

15. Lets break the problem top-down
Play Tic-Tac-Toe
Have some
game matrix
Get Next Move
Check for a winner
Initiate the
game matrix
Get column
Get row
Announce the winner
Update the
game matrix
Check whether
the move is legal
Display the
game matrix

16. Choosing the Data Structures
We will use two game matrices
Warning: We use it here for simplicity, usually it is better to avoid data duplication
“Num_mat” - 3x3 numeric matrix
“display_mat” - 3x9 char matrix 1
NaN 2
‘ X ‘
‘ – ‘
‘ O ‘

17. Writing the functions – “Go with the (control) flow”
Play Tic-Tac-Toe
Initiate game matrix
Initiate “who won flag” variable to 0
Initiate “current player flag” variable to 1
Loop 9 times (for i=1:9):
Get Next Move
Update game matrix
Display game matrix
Check for winner – if found a winner:
Update “who won flag” (1 or 2) and Break
Switch the “current player flag” 1<->2
Announce winner according to the “who won flag” variable A
“Flags” –
A variable which holds information
about the program status
and helps you control the flow
Get row
Get column
Check if it is a legal move

18. Lets look at the code of the main function: edit playTicTacToe
Lets look at the code of the main function: edit playTicTacToe.m; Notice the local functions
Weizmann 2010 ©

19. Debugging Run Time Errors
Our weapons:
Break points –
Red
Gray
Modifying a file
Debug buttons
Debug menu
Stop if errors / warn
There are two bugs
Lets find them . .
To the code!

20. Error Syntax errors – Runtime errors – Lets try to run playTicTacToe
func1;
function func1()
func2()
Syntax errors –
Lets try to run playTicTacToe
Runtime errors –
You can plant in the code disp() massages that will help you debug.
You should use errors when the input of the function is not valid
Debugger …
function func2()
Try
func3();
Catch
disp(‘Caught’);
end
function func3()
func4()
function func4 ()
A = ones(1,1);
B = A(1,2);

21. Recursion – factorial example
I don’t know what is factorial of 3
But I know it is 3 multiply the factorial of 2
function res = myFactorial(x)
% check: x is a non-negative integer
if (x == 0 || x == 1)
res = 1;
else
res = x * myFactorial(x-1);
end
I don’t know what is factorial of 2
But I know it is 2 multiply the factorial of 1
Ah ha!
The factorial of 1 is 1!

22. Summary Top down design Introduction Functions M file structure
Functions workspace
Functions Input and output
Top down design
Local functions
Debugger
Recursion
More:
Functions and commands
Functions and the matlab search path