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.

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 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
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The “old fashioned” way programmers used to work
 More flexibility (and sometimes clarity) in formulating solutions

4-51 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.

Flowchart of a for
Loop .
Figure 4.5–1
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Note the following rules when using for loops with the loop variable expression k = m:s:n:
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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.
4-53

 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)

a) for k = 1:10 y(k)= k*10; end b) for k = 1:11 y(k)= 11 – k; end c) for k = 1:5 y(k)= k*10-100; end d) for k = 1:11 y(k)= (k-1)*0.2; end

 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)

 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

max=0; // make a variable to hold max num=input(‘enter a number’);
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Compare num with max… if num>max max=num; end
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max=0; index=0; for i=1:5 num=input(‘enter a number’); if num > max max = num; end end max
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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);
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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

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
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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.
More? See pages 221-223.

Flowchart of the while loop.
Figure 4.5–3
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4-60
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.

 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

 Hand tracing is a great way to debug a loop
 Make a table of all the variables
 Update table as program changes variables

n = 1; y=20; sum = 0; while (n <= y) sum = sum + n*y; end n = n + 2; y = y/2;
Sum
0
2
32
57 done
3
5 n
1
7 y
20
10
5
2.5

we need a way to check all possibilities
Problem simplified from text

 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???

 A: Nested For Loops for numTV = 1:300 for numSpkr = 1: ??
p = [ numTV numSpkr] profit = … etc… also, check sufficient inventory for p end end