Working with Variables

Last updated on 2024-11-06 | Edit this page

Estimated time: 12 minutes

Overview

Questions

  • How can I fetch data out of a variable?
  • How can I change the values of parts of variables?
  • What are operations?

Objectives

  • Access MATLAB variables and change them
  • Use variables to execute mathematical operations and in functions

Introduction

So far we have learnt how to create variables of various sizes with different methods. This episode will now focus on how ways we can use variables.

Now is a good time to clear and clc your workspace and command window!

Extracting Variables

First lets start by making a dummy variable that we can use as our stand-in dataset.

MATLAB 

data = 100*rand(6,4);

Subsets

Subsets of values or single values can be extracted from a variable with round brackets ()

For example to take the value on the third row and second column:

MATLAB 

data(3,2)

We can use colon notation to extract multiple values as well:

MATLAB 

% Extract columns 1, 2, and 3 on row 3
data(3,1:3)

A single colon with no numbers will select all

MATLAB 

% Select all rows in the second column
data(:,2)

Some more examples bringing together the tools we’ve seen so far:

MATLAB 

% Extract the first 4 rows and all columns and save it in the variable subset1
subset1 = data(1:4,:) 

% Select every other column in the first row, save in subset2
subset2 = data(1,1:2:end)

% Select the first, third and forth rows for all columns, save in subset3
subset3 = data([1 3 4], :)

end

When extracting the subset of a matrix, or slicing it, when specifying the range you can use the keyword end to represent the last value in a vector (or row or column of a matrix, etc.).

Altering Variables

As we have seen so far, the object on the left hand side of the equal sign ‘=’ is set to what is on the right hand side. So to change the value of a variable we simply put it on the left:

MATLAB 

% Set the value on the 3rd row and 2nd column to equal 10
data(3,2) = 10

If you look at data in your workspace now you will see that value has been changed!

One use case of altering data may be when you find an erroneous value. For example, if you were looking at a table of reviews out of 5, you may wish to change a rating that was somehow set to above 5 to NAN, to show it was invalid.

MATLAB 

data(3,2) = NaN

Transpose

One useful tool in manipulating matrices (plural of matrix) in MATLAB is the transpose. This will effectively pivot the matrix so each row becomes a column and each column becomes a row. This is done in MATLAB by adding an apostrophe ' after a variable:

MATLAB 

% Transpose data and save it as data_t
data_t = data'

You should see that data_t has a flipped size compared to data

Concatenation

Concatenation is a common operation in data handling. Concatenating means to link or put together, it allows to to take two matricies or variables and add them into a single variable. This is useful for if example your dataset is saved across multiple files.

First let’s clear our workspace again, create a new data variable and some subsets of the data to work with.

MATLAB 


clear
data = 100*rand(6,4);

subset1 = data(:,1);
subset2 = data(:,2);

Both our subsets are column vectors, if we wanted to concatenate them together into a larger column vector there are three ways

MATLAB 

new_data = [subset1; subset2]

new_data = cat(1, subset1, subset2)

new_data = vertcat(subset1, subset2)

All [;], cat, and vertcat are all different ways to do the same vertical concatenation.

Callout

Don’t forget if you find a function you aren’t familiar with you can use help or doc to learn more!

This is a good point to use help cat and explain how they can learn that the parameters to it are and why you need a 1 at the front. Getting them used to looking up functions and not getting stuck is important!

If we wanted to concatenate the subsets into 1 variable as separate columns we could do

MATLAB 


new_data2 = [subset1 subset2]

new_data2 = cat(2,subset1,subset2)

new_data2 = horzcat(subset1,subset2)

One advantage of using cat is that it can work for arrays of larger dimensions, whereas the square bracket shortcut, vertcat, and horzcat only works for the first two dimensions of the data.

Challenge 1

  1. Extract every other row from Data assign it to the varibale name subset_a

  2. Extract the first four rows from the 2nd column of Data and call it subset_b

  3. Transpose subset_b, call this variable subset_t

  4. Concatenate subset_a and subset_t along the first dimension

MATLAB 

% Extract every other row from Data assign it to the varibale name subset_a
subset_a = data(1:2:6,:)

% Extract the first four rows from the 2nd column of Data and call it subset_b
subset_b = data(1:4,2)

% Transpose subset_b, call this varibale subset_t 
subset_t = subset_b'

% Concatenate subset_a and subset_t along the first dimension
subset_concatenated = cat(1, subset_a, subset_t)

subset_concatenated should be of size 4x4

Operations

We’re now going to look at some mathematical operations we can perform on our variables.

Before continuing this is a good point to clear your workspace again and make a new dummy data variable. This time we will round each data point to the nearest whole number with the function round

MATLAB 

clear
data = 100 * rand(10,10)

% Round to nearest whole number and overwrite data variable
data = round(data)

You may be familiar with the syntax (syntax is a word typically used in programming to mean format) of the most basic operators from other computer programs.

MATLAB 


data_add = data + 10;
data_subtract = data - 10;
data_divide = data / 10;
data_multiply = data * 10;

One common mistake made by users of MATLAB is with the multiply operator. When multiplying pay attention to make sure you are getting the result you expect!

Challenge 2

  1. Make a row vector called row with values 1, 2 & 3
  2. Make a column vector called column with values 4, 5 & 6
  3. Before trying to multiply them, guess the size of the result of row * column
  4. Multiply row and column and see if the result is as you expect

MATLAB 


row = [1 2 3];
column = [4; 5; 6];
row * column

OUTPUT 


ans =
    32

The resulting variable is a scalar! If you are familiar with matrix multiplication this may make sense to you, don’t worry if you are not however.

As seen in the challenge above, by default MATLAB will attempt to perform something called matrix multiplcation, you don’t need to know about matrix multiplication but it is worth knowing it is the default behaviour.

What you may expect to have been doing is something called dot multiplication.

MATLAB 


row2 = [4 5 6];
row.*row2

OUTPUT 

ans =

     4    10    18

As the example above shows, dot multiplication multiplies each element of both variables with each other 1 to 1. This is why it is also sometimes called element-wise multiplication.

Functions

Next we will look at some key functions that you may want to use in data analysis and processing

MATLAB 


% Find the size of a matrix
matrix_size = size(data)

% Add together the rows in each column
column_totals = sum(data, 1)

% Take the mean of the rows in each row
row_means = mean(data, 2)

% Find the maximum value in each column
data_max = max(data)

% Find the minimum value in each row
data_min = min(data, [], 2)

% Find the maximum value of the entire matrix
data_max_all = max(data, [], "all")

It is worth exploring why the square brackets exist here, demoing using the help or doc command to find why that exists and use it as a learning example.

Indian Rainfall Example

In this example we will combine the tools we have learnt so far to compare rainfall data between Sheffield and India

Each dataset comprises of monthly rainfall averages per year from 1901-2014.

Sheffield (https://www.metoffice.gov.uk/pub/data/weather/uk/climate/stationdata/sheffielddata.txt) Peninsular India (https://www.tropmet.res.in/DataArchival-51-Page)

MATLAB 

% Import rainfall data. 
sheffield_data = load('Sheffield_Rain.csv');
india_data = load('SouthIndia_Rainfall.csv');

Challenge

Investigate the data, open it up in the workspace and think about what is in each column

Each dataset contains 13 columns, the first column is the year and the other 12 are for each month of the year

Challenge

  1. Create a subset of sheffield_data and india_data that contains only the rain data, call these subsets sheffield_rain and india_rain

  2. The Indian rainfall series is in tenths of a millimeter. Convert to millimeters by dividing each point by 10

  3. The columns contain monthly rainfall, find the average monthly rainfall over the 114 years. Call these new variables india_monthly and sheffield_monthly

MATLAB 

% Select all data except the first column
sheffield_rain = sheffield_data(:,2:end);
india_rain = india_data(:,2:end); 

% Convert india_rain to millimeters
india_rain = india_rain/10;

% Take the mean of each column to find the average monthly rainfall
sheffield_monthly = mean(sheffield_rain, 1);
india_mothly = mean(india_rain, 1);

If your sheffield_monthly and india_monthly variables are correctly made, you should be able to run the following code to generate a bar chart comparing the two average rainfalls.

MATLAB 

bar([1:12],cat(1, india_mothly, sheffield_monthly),'grouped')
legend('South India', 'Sheffield')
ylabel('Rainfall (mm)')

Key Points

  • Use functions to create, edit and operate on variables
  • Operations are used to perform simple mathematical functions
  • help and docs are valuable tools for understanding functions