Matlab Loops
Motivating Example
Suppose you wanted to create a program to see how often a given number turns up in Craps. If we roll two dice, the smallest number that can arise is 2, and the largest is 12. While there are more clever ways of doing this using probability, we take a brute-force method. Let's choose two random numbers between 1 and 6 and do this over again until we achieve the number we are betting on.
bet = 4; % the number we are looking for (between 2 and 12)
dice = round( rand(2,1)*5+1 ); % two numbers between 1 and 6
if ( sum(dice) != bet )
% now what???
end
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The problem is that we want to keep rolling the dice until we get our number (4 in this case). How do we do this? We use loops. There are two kinds of loops: for loops and while loops.
For Loops
A for loop is executed a set number of times. The basic syntax of a for loop is:
for counter = lo:inc:hi
% do some work
end
| counter | A variable that ranges from lo to hi |
| lo | Indicates the starting point for the counter |
| hi | Indicates the stopping point for the counter |
| inc | Indicates the increment for the counter. You can increment forward, backward, and in any size increment. |
Each time through the loop, the counter variable will increment by inc. The loop exits when the counter exceeds hi. The following table shows several simple examples of a for loop.
| Matlab Code | Details | Output | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
for i=5:8
disp(i);
end
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5 6 7 8 | |||||||||||||||
x = 1:7;
for i=2:2:length(x)
x(i) = 2*x(i);
end
disp(x);
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x = 3:7;
for i=length(x):-2:1
fprintf('x(%1.0f) = %1.0f\n',i,x(i));
end
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x(5) = 7 x(3) = 5 x(1) = 3 |
Let's consider another example: calculate the factorial of a number using a for loop. The factorial is given as
We could implement this using a for loop as shown in the following:
| Matlab Code | Results at the end of each pass through the for loop | ||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
n = 7; % we want to find n!
nfact=1; % starting value.
for i=n:-1:2
nfact = nfact * i;
end
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While Loops
Unlike a for loop (which is executed a set number of times), the while loop continues to execute until some condition is met. The basic syntax of a while loop is:
while condition
% do some work. Note that "condition" must change inside the loop!
end
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Here is an example of how to calculate the factorial of a number using a while loop.
| Matlab Code | Results at the end of each pass through the while loop | |||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
n = 7; % we want to find n!
nfact=1; % starting value.
while n>1
nfact = nfact*n
n = n-1
end
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Here is another example of rolling two dice. We keep rolling the dice until we get them to add up to 7. We print out how many rolls it took.
clear; clc;
luckyNum = 7; % our lucky number.
lucky = 0; % 0 is "false" - we will use this to determine when we hit our lucky number.
nrolls = 0; % keep track of how many times we roll the dice.
while ~lucky
% pick 2 random integers between 1 and 6. The "round" function rounds to the nearest integer.
dice = round( rand(2,1)*5+1 );
nrolls = nrolls+1; % increment the counter for how many rolls we have done.
lucky = sum(dice)==luckyNum; % decide if we rolled a lucky 7 or not...
end
fprintf('Rolled a lucky %1.0f after %1.0f rolls\n',luckyNum,nrolls);
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Here we have used the ~ operator, which is the logical "NOT" operator.
