PowerPoint to accompany
Introduction to MATLAB 7
for Engineers
William J. Palm III
Chapter 4B
Programming LOOPS
with MATLAB
Copyright © 2005. The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Agenda
 For
Loops and Common Tasks
 Finding the max using a For loop
 Nested For Loops
 While Loops
Why Loops?

In Chapter 4 you learned a number of powerful
MATLAB features for processing arrays




x(x>5) shows all x cells that are larger than 5
How does this work? A built in loop visits each cell
These are great time-saving features
Some problems are more complex and require
explicitly writing our own loops to solve them


The “old fashioned” way programmers used to work
More flexibility (and sometimes clarity) in formulating
solutions
for Loops
A simple example of a for loop is
for k = 5:10:35
x = k^2
end
The loop variable k is initially assigned the value 5, and
x is calculated from x = k^2. Each successive pass
through the loop increments k by 10 and calculates x
until k exceeds 35. Thus k takes on the values 5, 15, 25,
and 35, and x takes on the values 25, 225, 625, and
1225. The program then continues to execute any
statements following the end statement.
4-51
Flowchart of a for
Loop.
Figure 4.5–1
4-52
Note the following rules when using for loops with the loop
variable expression k = m:s:n:






4-53
The step value s may be negative.
Example: k = 10:-2:4 produces k = 10, 8, 6, 4.
If s is omitted, the step value defaults to 1.
If s is positive, the loop will not be executed if m is
greater than n.
If s is negative, the loop will not be executed if m is less
than n.
If m equals n, the loop will be executed only once.
If the step value s is not an integer, round-off errors can
cause the loop to execute a different number of passes
than intended.
Common Tasks:
Making an Array

Loops can create arrays for you:
for k = 1:10
x(k) = k;
 cell #1 gets 1, #2 gets 2 ...
y(k)= k^2;
 k is a scalar so no '.' needed
end
plot(x,y);

Same as:
x=[1:10]; y=x.^2; plot(x,y)
Q: What values are in y?
a) for k = 1:10
y(k)= k*10;
end
c) for k = 1:5
y(k)= k*10-100;
end
b) for k = 1:11
y(k)= 11 – k;
end
d) for k = 1:11
y(k)= (k-1)*0.2;
end
Common Tasks:
Accessing an Array

Loops can also sample data from the cells of a
pre-existing array. Suppose:
hours=[40, 65, 48, 30, 20];
totalOvertime = 0;
for k = 1:length(hours)
if hours(k) > 40
totalOvertime=totalOvertime + hours(k) - 40;
end
end
totalOvertime
(result is 33)
Common Task:
Finding the Maximum

The easy way:
[max, n] = max(hours)

The hard(er) way:
We can also do this using a loop
 With or without a vector
 Again, we get more flexibility for certain
calculations

Finding the max…core idea
max=0; // make a variable to hold max
num=input(‘enter a number’);

Core idea
 Compare
num with max…
if num>max
max=num;
end
11
Finding the max…put in a
loop
max=0; index=0;
for i=1:5
num=input(‘enter a number’);
if num > max
max = num;
end
end
max
12
Finding the max…of a
vector
max=0;
hours=[40, 65, 48, 30, 20];
for i=1:length(hours)
if hours(i) > max
max = hour(i);
max_cell = i;
 capture cell number
end
end
disp('max = '); disp(max);
disp(' at cell # '); disp(index);
13
1) Finding the min…application
1) create a for loop with t going 0:0.01:4
2) calculate scalar x and y for each t
3) calculate distance, check for min, and
save index of min inside loop
4) then show minT and minD
while Loops
The while loop is used when the looping process
terminates because a specified condition is satisfied, and
thus the number of passes is not known in advance. A
simple example of a while loop is
x = 5;
while x < 25
disp(x)
x = 2*x - 1;
end
The results displayed by the disp statement are 5, 9, and
17.
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The typical structure of a while loop follows.
while logical expression
statements
end
For the while loop to function properly, the following two
conditions must occur:
1. The loop variable must have a value before the while
statement is executed.
2. The loop variable must be changed somehow by the
statements.
4-58
More? See pages 221-223.
Flowchart of the
while loop.
Figure 4.5–3
4-59
A simple example of a while loop is
x = 5;k = 0;
while
x < 25
k = k + 1;
y(k) = 3*x;
x = 2*x-1;
end
The loop variable x is initially assigned the value 5, and it
keeps this value until the statement x = 2*x - 1 is
encountered the first time. Its value then changes to 9.
Before each pass through the loop, x is checked to see if
its value is less than 25. If so, the pass is made. If not, the
loop is skipped.
4-60
Homework #2 Ulam Sequence

The Ulam Sequence
A mathematician named Ulam proposed generating a sequence
of numbers from any positive integer n (n > 0) as follows:
If n is 1, stop.
If n is even, the next number is n/2.
If n is odd, the next number is 3*n + 1.
Continue with this process until reaching 1.
Here are some examples for the first few integers.
2 -> 1
3 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1
4 -> 2 -> 1
5 -> 16 -> 8 -> 4 -> 2 -> 1
Tracing a Loop



Hand tracing is a great way to debug a loop
Make a table of all the variables
Update table as program changes variables
Tracing a Loop (example)
n = 1; y=20;
sum = 0;
while (n <= y)
sum = sum + n*y;
n = n + 2;
y = y/2;
end
Sum
n
y
0
1
20
2
3
10
32
5
5
57
7
2.5
done
Using Nested Loops
3) An optimization problem
we need a way to check all possibilities
Problem
simplified
from text
Hints for # 3

The range of possible TVs: 0 to 300
(why? – check inventory)
Range of possible speakers?

Lots of permutations!

If we have a vector p = [ numTV numSpkr];
 And a vector unit_cost=[ 80 40];
 Then profit = unit_cost*p';


Q: How do we cover all permutations???
Hints for #3, continued

A: Nested For Loops
for numTV = 1:300
for numSpkr = 1: ??
p = [ numTV numSpkr]
profit = … etc…
also, check sufficient inventory for p
end
end