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WELCOMEEF 105

Fall 2006

Week 12

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Topics:

1. Program Flows

More on loops (While)

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MATLAB program Structures

Control Structures

In the last lecture three types of control structures were

described: Straight line control

Conditional control (or branching structures)

Iterative control (or looping structures)

Conditional structures were covered in the last lecture. Thefocus of this lecture will be iterative structures.

Iterative Structures

MATLAB offers two types of iterative structures: for loops primarily used to execute a block of statements aspecified number of times

while loops used to execute a block of instructions while acertain logical test is true

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The forloop

The for loop is used to execute a block ofstatements a specified number of times. It has

the form shown to the right.

for loopVar = loopVector

Command 1

Command 2

Command n

endExample

Evaluate the following summation:

10

1i

3iSum

>> for1

Sum = 3025

>> for2Sum = 3025

>>

% filename: for1.m% Example: Use a for loop to find sum(i^3) for i = 1 to 10.

Sum = 0; %Initialize variable to zero

fori = 1:1:10

Sum = Sum + i^3;

end

fprintf('Sum = %0.0f\n',Sum);

% filename: for2.m

% Example: Use a for loop to find sum(i^3) for i = 1 to 10.

Sum = 0; %Initialize variable to zero

fori = [1,2,3,4,5,6,7,8,9,10]

Sum = Sum + i^3;

end

fprintf('Sum = %0.0f\n',Sum);

Results:

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Example

Write a program to determine the balance after N years on an account that containsan initial deposit D and earns a simple interest of I percent. Prompt the user to

enter values for N, D, and I.

>> Interest

Enter the amount of the initial deposit: $1000

Enter the percent interest rate: 6

Enter the number of years: 10

Final balance = $1790.85

% Sample program to determine the final balance in a savings account where

% D = initial deposit

% I = interest rate (percent)

% N = number of years

% Filename: Interest.m

D = input('Enter the amount of the initial deposit: $');

I = input('Enter the percent interest rate: ');N = input('Enter the number of years: ');

Balance = D; %Initial value in the account

foryears = 1:N

Balance = Balance*(1+I/100);

end

fprintf('Final balance = $%0.2f\n',Balance);

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Nested forloops

For loops can occur within other for loops as shown in the examples below. Note thatwhile indenting loops is not required, it helps to make them more readable.

for loopVar1 = loopVector1

Command 1

for loopVar2 = loopVector2

Command A1

Command A2

Command An

end

Command 2

Command n

end

Sum = 0;for I = 1:10

for J = 1:15

Sum = Sum + 1;

end

End

fprintf(\nSum = %0.0f,Sum);

What value for Sum is printedin the program below?

Example:

The example program on the following slide:

Prompts the user to enter each value of a 2D array

Calculates the maximum value of the array (and the row/column where the maxoccurs)

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% Program to prompt the user to enter values in a matrix

% by row and column number.

% Also find the max value in the matrix.

% Filename: Matrixmax.m

format compactRows = input('Enter the number of rows in the matrix: ');

Columns = input('Enter the number of columns in the matrix: ');

fori = 1:Rows

forj = 1:Columns

fprintf('Enter A(%0.0f,%0.0f):',i,j);

A(i,j) = input(' ');

end

end

A

% find the max value in the matrix

Max = A(1,1); %Set max to first value in array

MaxRow = 1;

MaxCol = 1;

fori = 1:Rows

forj = 1:ColumnsifA(i,j)> Max

Max = A(i,j);

MaxRow = i;

MaxCol = j;

end

end

end

fprintf('Max value in array A is A(%0.0f,%0.0f) = %0.2f\n',MaxRow,MaxCol,Max);

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>> Matrixmax

Enter the number of rows in the matrix:

2

Enter the number of columns in the

matrix: 3

Enter A(1,1): 12

Enter A(1,2): 14Enter A(1,3): 17

Enter A(2,1): 23

Enter A(2,2): 11

Enter A(2,3): -8A =

12 14 17

23 11 -8

Max value in array A is A(2,1) = 23.00

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The whileloop

The while loop is used to execute a

block of statements as long as alogical test is true. It has the formshown to the right.

while LogicalTest

Command 1

Command 2

Command n

end

TRY IT: What is the greatest value of n that can be used in

the sum 12 + 22+ + n2 and get a value of less than 100?>> S = 1; n = 1;

>> while S+ (n+1)^2 < 100; n = n+1; S = S + n^2;

end

>> [n, S]

ans = 6 91

The lines of code between while and end will only be

executed if the condition S+ (n+1)^2 < 100 is true.

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Another While Example

Modify the previous program thatcalculated the balance in an account after

N years so that it will determine the

number of years to reach a desiredbalance.

See next slide.

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% Sample program to determine the number of years required for an initial

% balance to reach a final value

% Deposit = initial deposit

% Desired_Balance = final value to be reached

% I = interest rate (percent)

% N = number of years

% Filename: Interest2.m

Deposit = input('Enter the amount of the initial deposit: $');

Desired_Balance = input('Enter the desired final balance: $');

I = input('Enter the percent interest rate: ');

N = 0; %Initialize the number of years

Balance = Deposit; %Initial value in the accountwhileBalance < Desired_Balance

N = N+1;

Balance = Balance*(1+I/100);

end

fprintf('\nResults:\nFinal balance = $%0.2f\n',Balance);

fprintf('Number of years to reach final balance = %0.0f\n',N);

>> Interest2

Enter the amount of the initial deposit: $1000

Enter the desired final balance: $3000

Enter the percent interest rate: 7

Results:

Final balance = $3158.82

Number of years to reach final balance = 17

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While Example2

Suppose we wish to sum the odd integers

from 1 to 9 using a while loop. Here is the

Matlab code to do that:

sum = 0; num = 1;

while num

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Programming Tips

Use descriptive names.This is true forscript names as well as variable names.The name need not be long, but it should

relate to the intended use. Short namessuch as i,j, kcan be used for temporaryvariables and loop counters. Remembernot to use blanks or dashes in M-file

names.

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Other Programming Tips

Whitespace is essential for makingsource files readable.

Meaningful parts of code are grouped

together by using blank lines asseparators.

Indentation - use tabs/spaces to indicatethe level of nesting. Don't forget that you

can use the Smart Indent (Text->SmartIndent) feature of the Matlab text editor tohandle indentation for you.

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CommentsUse commentsthroughout your scripts to explain why

the code is important, not just re-iterate what eachstatement is doing.

Use several lines of comments at the top of each of yourM-Files to describe the script.

You don't need to comment every statement. Usecomments to:

highlight the major steps of your algorithm

explain long calculations or conditions

clarify convoluted or unusual code

mark locations where you suspect a bug may existmark locations where improvements or enhancementsare planned

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A Well Documented M FileTake a look at the baseball trajectory

program.

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MATLAB Exercise 3

See the Word document for this

exercise and perform at end of

class on your own!!