Logic

Last updated on 2025-04-28 | Edit this page

Estimated time: 12 minutes

Overview

Questions

  • How can I make my code do different things when variables change?
  • How can I compare values in an array to other values?
  • How can I select subsets of my data depending on a comparison?

Objectives

  • Learn to use relational operators to compare values
  • Understand if and else statements to create conditional code
  • Learn some new tools and functions relating to logic

Relational Operators

Relational operators are used to compare the values in 2 arrays and returns a logical array.

Here are the most common logical operators in MATLAB:

MATLAB 

data == 50 % Are any data points equal to 50?
data ~= 50 % Are any data points not equal to 50?
data > 50 % Are any data points greater than 50?
data < 50 % Are any data points less than 50?
data >= 50 % Are any data points greater than or equal to 50?
data <= 50 % Are any data points less than or equal to 50?

Here is an example of comparing two arrays:

MATLAB 


a = [1 1 1 1];
b = [1 2 1 2];

a == b

OUTPUT 

ans =

  1×4 logical array

   1   0   1   0

MATLAB Logic

MATLAB represents logical true and false statements with 1 and 0, where 1 is true and 0 is false

The returned logical array tells us that the first values were equal, the second not equal, etc.

If Statements

If statements allow us to execute different lines of code depending on a logical value.

MATLAB 

c = 10

if c > 0
  disp('c is positive')
end

OUTPUT 

c is positive

In this example, c > 0 is called the condition, disp('c is positive') is the code which will be executed if the condition is true, and every if statement in MATLAB should be terminated with an end

We can use some inbuilt functions such as any or all to test a condition across an entire array.

For example, we have a data set representing student marks called data, where each value is a mark out of 100, each row a student and each column a subject:

MATLAB 

student_marks = round(100*rand(4,6));

We could test if any there any marks below or equal to 10 with the following code

MATLAB 



if any(student_marks < 10)
  disp('Severe failing mark in dataset')
end

Challenge

Using the student_marks data above, display a sentence if any student achieves a first (70 or more) in the 3rd subject

MATLAB 


if any(student_marks(:,3) >= 70)
  disp('At least 1 student has achieved a first in subject 3')
end

if else elseif

Conditions can be chained together using the else and elseif terms. This allows for multiple different code blocks to be used depending on multiple conditions.

MATLAB 

if all(student_marks(:,2) >= 70)
  disp('All students have a first in subject 2')
elseif any(student_marks(:,2) >= 70)
  disp('At least 1 student has a first in subject 2')
else
  disp('No students have a first in subject 2')
end

Logical Indexing

In the working with variables chapter, we looked at how we can index a variable with row and column numbers.

MATLAB 

data = [1 3 5 7; 2 4 6 8];
data(2,4)

OUTPUT 

8

Here we will look at indexing using logic arrays, which going back are the result of relational operators.

MATLAB 

big_data = data >= 4 

data(big_data)

OUTPUT 

ans =

     4
     5
     6
     7
     8

First we create a logical array called big_data, which is the result of us looking for numbers in our data greater than or equal to 4.

We can then use this to index data, like slicing by index number, the result being only the part of data that is bigger than 4.

These two lines can be combined as well, avoiding the need to save the logical array as it’s own variable

MATLAB 

data(data >= 4)

OUTPUT 

ans =

     4
     5
     6
     7
     8

logical not

A useful tool when handling logical arrays is the logical not, represented with the ~ symbol.

This operation inverts a logical array, which can be used to find values that don’t meet a condition.

MATLAB 


big_data = data >= 4;
disp(big_data)
disp(~big_data)

OUTPUT 

   0   0   1   1
   0   1   1   1

   1   1   0   0
   1   0   0   0

isnan

The final thing we will look at in this episode is the isnan function. This function returns a logical array containing true (1) where there is a NaN in the array. This could be used to replace the NaN values with a default value like 0, or combined with the logical not to only select non-nan data:

MATLAB 

data = [2 4 NaN 8; 1 NaN 5 7];

data = data(~isnan(data))

OUTPUT 

data =

     2
     1
     4
     5
     8
     7

Key Points

  • The result of a relational operator is a logical array
  • if, elseif and else can be used to create powerful conditions
  • Logical arrays can be used to index variables