2.2. Basic plotting

MATLAB has an excellent set of graphic tools. Plotting a given data set or the results of computation is possible with very few commands. You are highly encouraged to plot mathematical functions and results of analysis as often as possible. Trying to understand mathematical equations with graphics is an enjoyable and very efficient way of learning mathematics. Being able to plot mathematical functions and data freely is the most important step, and this section is written to assist you to do just that.

MATLAB provides powerful tools for creating visual representations of data and mathematical functions. The goal of plotting is to help you visualize complex equations and datasets, making understanding them easier and more engaging. This section aims to empower you with the skills needed to create these plots using simple commands.

Think of plotting like creating a picture from a recipe. Just as each ingredient adds a unique flavor to a dish, each data point adds detail to your plot, helping you to visualize complex flavors of mathematics.

The basic MATLAB graphing procedure, for example in 2D, is to take a vector of x-coordinates, x = (x1,...,xN), and a vector of y-coordinates, y = (y1,...,yN), locate the points (xi,yi), with i = 1,2,...,n and then join them by straight lines. You need to prepare x and y in an identical array form; namely, x and y are both row arrays or column arrays of the same length.

The MATLAB command to plot a graph is plot(x,y). The vectors x = (1,2,3,4,5,6) and y = (3,-1,2,4,5,1) produce the picture shown in Figure 2.1.

x = [1 2 3 4 5 6]; y = [3 -1 2 4 5 1]; plot(x,y)

To create a plot in MATLAB, you first define two sets of coordinates: x-coordinates and y-coordinates. Both these sets should be of the same length and can be either in row or column format. The command 'plot(x,y)' is used to render the graph, which connects the designated points with lines. For example, if you have arrays of x values from 1 to 6 and corresponding y values, plotting them will visualize their relationship on a 2D graph.

Imagine mapping a journey on a map where each point you visit has coordinates (x,y). Connecting these points helps visualize your travel path, just as plotting connects data points to show trends or patterns.

MATLAB enables you to add axis labels and titles. For example, using the graph from the previous example, add an x- and y-axis labels. Now label the axes and add a title. The character \pi creates the symbol π. An example of a 2D plot is shown in Figure 2.2.

xlabel('x = 0:2\pi') ylabel('Sine of x') title('Plot of the Sine function')

After creating a plot, it is essential to enhance it with labels and titles to make it informative. The 'xlabel' function adds a label to the x-axis, 'ylabel' adds a label to the y-axis, and 'title' provides a title for the entire plot. This step ensures that anyone viewing the graph understands its context and content.

Similar to how a well-labeled map enhances understanding of a geographical area, labeling your plot provides clarity. Imagine reading a book with clear headings—this helps quickly grasp the themes and subjects being discussed.

Multiple (x,y) pairs arguments create multiple graphs with a single call to plot. For example, these statements plot three related functions of x: y = 2cos(x), y = cos(x), and y = 0.5cos(x), in the interval 0 ≤ x ≤ 2π.

x = 0:pi/100:2pi; y1 = 2cos(x); y2 = cos(x); y3 = 0.5cos(x); plot(x,y1,'--',x,y2,'-',x,y3,':') xlabel('0 ≤ x ≤ 2π') ylabel('Cosine functions') legend('2cos(x)','cos(x)','0.5cos(x)') title('Typical example of multiple plots') axis([0 2pi -3 3])

You can plot multiple functions on a single graph to compare them directly. By providing multiple (x,y) pairs in the 'plot' function, you can visualize how different functions behave in the same interval. Adding a legend helps differentiate which line belongs to which function, thus making multitasking comparisons clear and efficient.

This is like comparing the prices of three different brands of the same product over a period. If you plot their prices together on the same graph, you can easily observe which brand is cheaper or more expensive at any given time, making decision-making simpler.

It is possible to specify line styles, colors, and markers (e.g., circles, plus signs, ...) using the plot command:

plot(x,y,'style_color_marker')

where style_color_marker is a triplet of values from Table 2.3.

Customizing your plot with different line styles, colors, and markers enhances clarity and presentation. The format for customizing is 'style_color_marker', where you can choose options from a predefined set of styles listed in a table, allowing for varied visual differentiation among data sets.

Just like an artist chooses different colors and brush strokes to bring a painting to life, you can choose various styles and colors in MATLAB to improve the visual appeal and convey different messages with your data plots.

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