How to Plot a Graph in MATLAB

MATLAB is one of the more complex numerical computing and programming platforms. Getting to know MATLAB involves understanding various mathematical concepts, and learning how to plot a graph in MATLAB is one of those concepts at play.

Whether you’re learning about MATLAB for the first time or want a refresher, here’s a brief tutorial on plotting graphs, as well as adding labels and a title, plotting lines, scaling on the graph, and more.

Let’s get started.

Plot a Function Graph

Here’s a step-by-step guide on how to plot the graph of a function with a script. To create a new script, select the icon in the top left corner to begin.

Screenshot: Create a script in MATLAB 2019a

Step 1: Specify the Range of Values for the x variable for which you’re plotting the function. This will define x.

Specify the range of values as a linearly spaced vector with the “linspace” function. The syntax follows the format below:

x = linspace(x1,x2,n)

The “linspace” function generates “n” number of points between x1 and x2. The distance between the points can be calculated with the equation (x2-x1)/(n-1).

For example, the following code will have a distance of (10-0)/(10-1)=1.1111 between each point and have 10 points between 0 and 10.

x = linspace(0,10,10);

x has the following values in this sample:

Having too few points will result in graphs that are inaccurate. Plotting the function y=sin(x) with the range of values set as linspace(0,10,10) would result in the figure below:

MATLAB Figure: sin(x) with only 10 values plotted

However, if linspace(0,10,100) is used to generate 100 points instead of 10, the figure below is produced.

MATLAB Figure: sin(x) with 100 values plotted

If your graph isn’t a smooth plot, it’s likely that the number of points needs to be increased.

Step 2: Define the function, y = f(x)

Declare the desired function with the “=” operator. Any variable name can be used in place of “y”, however “y” is often the standard. Declare an exponential function using the following expression.

y=exp(x);

Step 3: Use the plot function to generate a figure

Use the function “plot” to create a 2D line plot of the function declared in Step 2. The function has the following syntax, where Y is plotted with the corresponding X values. A new window will open with the figure.

plot(X,Y)

Use the code below to plot y = e^x.

x = linspace(0,10,100); %create a set of X values to pass through the function

disp(x); %display the values to the command window

y=exp(x); %declare the exponential function

plot(x,y) %plot the function

The command window output is below:

The following figure will be generated in a new window.

MATLAB Figure: exp(x) with 100 values plotted

Add a Title, Labels, and Grid Lines

MATLAB lets you add a title, labels along the x and y axes, as well as grid lines to make graphs more detailed.

Here’s how to do all of the above:

Step 1: Use the functions xlabel, ylabel, and title to generate labels along the axes.

The function xlabel, ylabel, and title use the syntax below.

xlabel(txt) - This function labels the x-axis of the currently selected axes or of the standalone visualization.

ylabel(txt) - This function labels the y-axis of the currently selected axes or of the standalone visualization.

title(titletext) - This function adds the designated text to the current axes or to the standalone visualization. A subtitle can also be selected with the syntax subtitle(txt).

Run the following script to create a plot with titles.

x = linspace(0,10,100); %create a set of X values to pass through the function

y=exp(x); %declare the exponential function

plot(x,y) %plot the function

title('Sample 2-D Line Plot');

xlabel('Time (h)');

ylabel('Number of Bacteria');

MATLAB Figure: exp(x) with titles

Step 2. Display grid lines

Use the “grid on” function to turn on major gridlines.

grid on;

MATLAB Figure: exp(x) with major gridlines

Use the function “grid minor” to turn on minor gridlines.

grid minor;

MATLAB Figure: exp(x) with minor gridlines

You can also change where the gridlines appear by using the function “xticks(ticks)” and “yticks(ticks)”. The ticks values are specified as a vector of increasing values.

Vectors can be created with the colon operator in MATLAB using the following syntax, x = j:i:k, where a regularly-spaced vector denoted as “x” is created with increment “i” and an ending value of “k”.

The following yields the figure below:

x = linspace(0,10,100); %create a set of X values to pass through the function

y=exp(x); %declare the exponential function

plot(x,y) %plot the function

title('Sample 2-D Line Plot');

xlabel('Time (h)');

ylabel('Number of Bacteria');

grid on;

xticks(0:2:10); %start at 0, increment by 2, and end at 10

yticks(0:10000:25000); %start at 0, increment by 10000, and end at 25000)

MATLAB Figure: exp(x) with manually selected x and y axes

Set Axis Scales

The axis function lets you set the scales for both axes with minimum and maximum values for each axis. This function uses the syntax axis([xmin xmax ymin ymax]). Run the code below to plot a graph with 50 as the maximum y-axis and 10 as the maximum x-axis. Negative numbers can also be selected.

x = linspace(0,10,100); %create a set of X values to pass through the function

y=exp(x); %declare the exponential function

plot(x,y) %plot the function

axis([0 5 0 50]); %x-axis limit is from 0 to 5, y-axis limit is from 0 to 50

title('Sample 2-D Line Plot');

xlabel('Time (h)');

ylabel('Number of Bacteria');

MATLAB Figure: exp(x) with major gridlines

Draw Multiple Functions

You can even draw more than one graph on the same plot or create subplots to display multiple plots at once.

Use the function “hold on” to retain the current plot. Always add a legend to differentiate between the lines on the graph using the function “legend(label1,...,labelN)”. The following script yields the plot below.

x = -pi:0.1:pi; %set x-axis values to start at -pi, increment by 0.1, and end at pi

y1 = 50*sin(x); %declare the first function

y2 = 50*cos(x); %declare the second function

y3= tan(x); %declare the third function

hold on; %retain plots on the graph

plot(x,y1); %plot the first function

plot(x,y2); %plot the second function

plot(x,y3); %plot the third function

hold off; %stop retaining the figure

title('Multiple Plots on a Singular Graph');

legend('50*sin(x)','50*cos(x)','tan(x)'); %create a legend in the order that the functions were plotted

MATLAB Figure: Multiple plots on the same graph

In addition, you can use the “subplot(m,n,p)” function to display multiple plots on multiple graphs, but in the same figure. In this function, “m” refers to the row of the figure, “n” represents the column, and “p” is the pane.

x = -pi:0.1:pi;

y1 = 50*sin(x);

y2 = 50*cos(x);

y3= tan(x);

ax = axes;

subplot(2,2,1); %there are 2 rows in the subplot and 2 columns, plot in the first pane starting from the top left

plot(x,y1,'red');

title('50*sin(x)');

subplot(2,2,2); %plot in the second pane

plot(x,y2,'blue');

title('50*cos(x)');

subplot(2,1,2); %plot in the first column and fill to the second pane

plot(x,y3,'black');

title('tan(x)');

MATLAB Figure: Multiple plots on the same figure

Set Colors on a Graph

MATLAB offers eight colors that can be chosen by color name or by the shortened name in the table below.

As well, you can designate custom colors by RGB triplet or by hexadecimal color code (with MATLAB version R2019a and above).

RGB triplets are declared using a three-element row vector “[red green blue]” where the elements correspond to the intensity of the red, green, and blue components of the custom color. The intensities are in the range between zero and one. For example, a shade of purple would be [0.5 0 0.5]. Some functions do not support RGB triplets.

x = -pi:0.1:pi;

y1 = 50*sin(x);

y2 = 50*cos(x);

y3= tan(x);

ax = axes;

hold on;

plot(x,y1,'red'); %plot in red

plot(x,y2,'blue'); %plot in blue

plot(x,y3,'k'); %plot in black with the short name

hold off;

legend('50*sin(x)','50*cos(x)','tan(x)');

MATLAB Figure: User designated colors

Conclusion

Starting out with plotting in MATLAB can be overwhelming if you’re not familiar with programming. MATLAB uses its own proprietary programming language but has similarities with C. Check out MATLAB’s documentation for more in-depth and specific functions.

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