What are relational operators and logical values? How to

3-2

What are relational operators and logical values?

How to use the input and disp functions.

Learn to use if, if-else and else-if conditional

statements.

What are logical operators?

Using while to perform loops.

Readings: Matlab by Pratap Chapters 3.2.2, 3.2.3,

4.3.4, 4.3.5

3-3

1. Problem Definition

Write a Matlab function named count_axles to compute the

number of 4 axle vehicles traveling past a specific location on a

road over a fixed time interval.

2. Refine, Generalize, Decompose the problem definition

(i.e., identify sub-problems, I/O, etc.)

The input to count_axles will be a vector containing the number

of axles for each vehicle that passes a specific location. A

second input will be the number of axels for which you want to

obtain a count. In our example this value is 4.

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3. Develop Algorithm (processing steps to solve problem)

We first identify each vehicle with the desired number of axles.

For example if, >> data = [2 3 4 4 2 4 4];

then the vector identifying the 4 axle vehicles is,

match = [0 0 1 1 0 1 1]

Use the relational operator == to find matches >> match = data == 4

match =

[0 0 1 1 0 1 1]

Next, use the sum function to add all the 1’s.

Note that match is a logical valued vector >> whos match

Name Size Bytes Class

match 1x7 7 logical array

3-5

4. Write the “Function" (Code)

function count = count_axles(data, target)

% function count = count_axles(data, target)

match = data == target ;

count = sum( match);

3-6

The relational operators are:

< <= > >= == ~=

Relational operators generate logical values.

>> match = [2 3 4 4 2 4 4] ~= 4

match =

1 1 0 0 1 0 0

3-7

Example: Extract the bad data from the data vector.

Suppose negative values are bad data.

>> data = [2 -5 3 4 -1 4 2 4 4 -9];

>> match = data > 0

match =

1 0 1 1 0 1 1 1 1 0

>> data = data(match)

data =

2 3 4 4 2 4 4

3-8

Problems subscripting with logicals.

Rather than using a relational operator to generate a logical

array we can use the logical function.

>> data = [2 -5 3 4 -1 4 2 4 4 -9];

>> match = logical([1 0 1 1 0 1 1 1 1 0]);


data =

2 3 4 4 2 4 4

Note that the following does NOT work!

>> match = [1 0 1 1 0 1 1 1 1 0];


??? Subscript indices must either be real positive integers or logicals.

3-9


Write a Matlab function named “guess” that plays a guessing

game with the user. The user will guess an integer number

between 1 and x where x is given by the user as an input

argument to the function.



This function has one input parameter x. Using a loop the

function gets successive inputs from the user and compares to

the correct answer. At each guess the user is told whether the

guess is correct or not.

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To generate a random number between 1 and x that the user

must guess we use the Matlab rand function.

For example (from lab 2) we learned about the use of the ceil

function, so that if you typed, >> x = 10;

>> correct_answer = ceil(rand()*x)

then the correct_answer will have a randomly chosen value

between 1 and x.

We can use the Matlab input function to prompt the user for a

guess and to read the guess from the keyboard.

For example, you can type, >> guess = input(‘Enter your guess: ‘);

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To check whether the user has entered a correct value we can use

the Matlab if-else statement as follows:

if correct_answer == guess

disp(‘Match!!!’);

else

disp(‘No Match!’);

end

3-12


To repeat one or more Matlab statements ( a loop) we can use the

while statement as follows:

while flag == 1

% one or more Matlab statements here

end

where the flag variable keeps track of whether the game is

over (flag == 0) or is still in progress (flag = 1).

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obtain next guess

tstart function

tend function

iflag == 1?

icorrect guess?

generate random number and set flag = 1

display MATCH

set flag = 0

display NO MATCH

TRUE FALSE

TRUE FALSE

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function guess(x)

% x is an integer

%generate random integer between 1 and x

correct_answer = ceil(rand()*x);

flag = 1; % why???

while flag == 1

guess = input(‘Enter your guess: ‘);

if correct_answer == guess


flag = 0;

else

disp(‘No Match!’);

end

end

Loop

3-15


Modify the guessing game function by giving the user feedback

if their guess is higher or lower than the correct answer.



We will use a variation of the if-else statement which we call the

elseif statement.

3-16


To check whether the user has entered a correct value we can use

the Matlab else-if statement as follows:

if correct_answer < guess

disp(‘Answer is too high!’); elseif correct_answer > guess

disp(‘Answer is too low!’);

else


flag = 0;

end

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function guess(x)

% x is an integer



flag = 1;

while flag == 1



disp(‘Answer is too high!’);

elseif correct_answer > guess


else


flag = 0;

end

end

else-if

3-18


Modify the guessing game function by giving the user a fixed

number of guesses.



We will use the logical AND operator in the while loop. We will

add one more input parameter to our function, named

num_tries, which contains the maximum number of guesses

that will be allowed. We assume that the user enters positive

integer values for x and num_tries.

If the user runs out of attempts before guessing the correct

number we will notify the user that the game is over and display

the correct answer.

3-19


To check whether the user should be allowed another attempt at

guessing we can add a simple if statement that uses the AND

operator ( & ) as follows:

if (flag == 1) & (attempts == num_tries)

disp(‘Game Over!’)

disp(‘The correct answer is’)

disp(correct_answer)

flag = 0;

end

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function guess(x, num_tries)

% intitialize the number of attempts

attempts = 0;



flag = 1;

while flag == 1



disp(‘Answer is too high!’);

elseif correct_answer > guess


else


flag = 0;

end

attempts = attempts + 1; % update the number of attempts

if (flag == 1) & (attempts == num_tries)

disp(‘Game Over!’)

disp(‘The correct answer is’)

disp(correct_answer)

flag = 0;

end

end

simple

if

3-21

A B A & B

AND

A | B

OR

TRUE TRUE TRUE TRUE

TRUE FALSE FALSE TRUE

FALSE TRUE FALSE TRUE

FALSE FALSE FALSE FALSE

A ~A

NOT

TRUE FALSE

FALSE TRUE

3-22


Write a function named minmax that given a vector of values,

returns two scalar values, the min and max values of the vector.



If the input value is [-1 -2 3 5 4] then minmax returns two values, -2 and 5.

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Natural-Language Algorithm

If x is the input vector then min(x) is the minimum

value and max(x) is the maximum.


3-24


(instruction sequence to be carried out by the computer)

Use the Matlab editor to create a file minmax.m .

function [smallest,largest] = minmax(x)

% function [smallest,largest] = minmax(x)

% x is a vector.

% Programmer: Tom Gambill

% Date: 2/2/01

% Input: a vector, x

% Output: smallest and largest values of x.

smallest = min(x);

largest = max(x);

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Note the use of [lower, upper] to receive the values that

minmax(x) returns .

3-26

Logical values can be generated by the relational

operators or the logical function.

A while statement can be used to execute a block

of statements until the logical condition is false.

The logical condition can use logical operators. We

can use a flag variable to control when to exit a

loop.

We can control the flow of execution of statements

in a Matlab function by using if, if-else and else-if

conditional statements.

Although input parameters are used when one

function calls another function but we can use the

input and disp functions to receive and display

values from the command terminal.

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What are relational operators and logical values? How to