Simple Plot in R
This section will begin a very gentle introduction to plotting in R. The goal is to show how one can draw the plot of a function using R and annotate the resulting plot. The tutorial is easy to follow and it gives you a nice overview of the plotting capabilities of R.
R as a Calculator
Start R on your system. This will open R's interactive shell. Let's start by performing a basic calculation in the shell. Enter the expression 2+2, then press the Enter key. The result follows.
> 2+2 [1] 4
Sweet! R can add two and two! Let's try something a bit harder, such as sin π /2.
> sin(pi/2) [1] 1
Good start! Let's produce a list of numbers, storing the result in the vector x.
> x=0:5
We can see what's stored in the variable x by typing its name and hitting the Enter key.
> x [1] 0 1 2 3 4 5
Let's add 3 to each entry in x.
> x+3 [1] 3 4 5 6 7 8
Let's square each entry in x.
> x^2 [1] 0 1 4 9 16 25
These calculations are pretty typical of the way in which R deals with lists of numbers. Whatever you do to the list is applied to each element in the list.
Let's do something a bit more substantial. First, let's create a list of numbers using R's seq command.
> x=seq(0,2*pi,by=pi/2) > x [1] 0.000000 1.570796 3.141593 4.712389 6.283185
Note the syntax, seq(a,b,by=increment) produces a list of numbers that starts at a, increments by increment, and finishes at b. Hence the command x=seq(0,2*pi,by=pi/2) produces a list of numbers that starts at zero, increments by π /2, and stops at 2 π. Now, let's take the sine of each number in the list stored in x.
> sin(x) [1] 0.000000e+00 1.000000e+00 1.224647e-16 -1.000000e+00 -2.449294e-16
A little strange, but note the scientific notation. This result is approximately 0, 1, 0, -1, 0, which is correct. The small errors are due to round-off error.
Let's apply what we've learned to sketch the graph of a sinusoid.
Plotting a Sinusoid
In this first activity, let's try to draw the graph of a sinusoid with the following equation.
y = 2 sin (2π x - π /2)
In a trigonometry class, the first step would be to identify the amplitude, period, and phase shift. To that effort, we factor out a 2π.
y = 2 sin 2π (x - 1/4)
Comparing this equation with the more general form, y = A sin B (x - φ), we see that A = 2, B = 2π, and φ = 1/4. Thus, we have the following facts:
- The amplitude of the sinusoid is |A| = |2| = 2.
- The phase shift of the sinusoid is φ = 1/4.
- The period of the sinusoid is T = 2π /B = 2π /2π = 1.
Thus, when we draw the graph of the sinusoid, we should see it complete one full cycle every 1 second, it should bounce up and down between 2 and -2, and it should be shifted 1/4 units to the right. With these thoughts in mind, let's sketch 2 periods of the sinusoid, which means that we should sketch the graph of the sinusoid over the domain [0, 2].
Coding
We begin. We first create a list of domain values and store them in x. The following command starts at 0, increments by 0.01, and stops at 2, giving us a large number of points in the domain [0,2].
> x=seq(0,2,by=0.01)
We now need to evaluate the sinusoid y = 2 sin 2π (x - 1/4) at each point of the vector x. This is a simple matter in R.
>> y=2*sin(2*pi*(x-1/4))
The above command evaluates the sinusoid at each point in the vector x and stores the result in the vector y. All that remains is to plot the points in the vector y versus the points in the vector x.
> plot(x,y)
The result of this last command on our system is shown in Figure 1. Results may differ on different systems depending on the windowing system used by your version of R.
Figure 1. A plot of y = 2 sin 2π (x - 1/4) on the interval [0, 2].
Note that R's default behavior is to plot the individual points. We can change the "type" of the plot as follows.
> plot(x,y,type='l')
The result is shown in Figure 2. Note that the points are no longer marked and we have a "smooth curve" instead. Actually, what's going on behind the scenes is each consecutive pair of points is being joined with a small line segment. Because we've plotted a "lot of points," the result has the appearance of a "smooth curve."
Figure 2. Changing the type, giving the appearance of a "smooth curve."
You can add axis labels and a title with the commands that follow below. After typing the first line, namely plot(x,y,type='l', (that's a lower case "L") press the Enter key. The plus sign (+) on the next line is R's "line continuation" character and is automatically supplied by R's interactive shell. Without the "line continuation" character, lines would be too long to include in this document.
> plot(x,y,type='l', + xlab='x-axis', + ylab='y-axis', + main='A plot of a sinusoid.')
It's somewhat difficult to type a number of consecutive lines correctly, so if you make a mistake you will need to start over. However, you can use the "up-arrow" on your keyboard to replay lines you've already typed. Pressing the "up-arrow" a number of times take you back through the "history" of lines you've entered in R's interactive shell. When you get the line you want, press Enter, or edit the line and then press Enter.
The result of this code is shown in Figure 3. Note the addition of axis labels and a "main" title.
Figure 3. Adding axis labels and a title to the figure..
Enjoy
We hope you've enjoyed this small introduction to plotting in R. To find out more about R's plot command, type the following command in R's interactive shell.
> ?plot
This will open a help file on the plot where you can read more about this powerful command.