Gnuplot Quick Start

Gnuplot is a quick and easy plotting program. You can plot functions (like x+6) or data from files.

Start gnuplot from a shell by typing:

gnuplot

You should then get a gnuplot prompt (gnuplot>) where you type gnuplot commands.

To plot a function, type something like

plot x

You can also try the following:

plot 3*x+6
plot x**2
plot log(x)

This plots the functions 3x+6, x² (note the use of ** to denote exponentiation), and ln(x) respectively. For base 10 logs, use log10(x). For logs of other bases, you can exploit the fact that log_a b = log_c b / log_c a.

For gaining intuition about big-Theta, it is useful to change the range of x values shown in the plot. Try:

set xrange [0:10]
replot

The first command sets the range of x values to be 0 to 10, and the second repeats the last plot command. (The display won't update until you issue a replot or plot command.)

To test if you've gotten a function into the right big-Theta class, you can first plot the lower bound, your function, and the upper bounds. For example, to test if 3n+6 = Theta(n), I might choose n as the lower bound and 4n as the upper bound. Then plot:

plot x, 3*x+6, 4*x

(Note that n is replaced by x.)

Now, set the xrange to something smallish:

set xrange [0:10]
replot

Observe that 3x+6 does eventually end up between the two bounds. But let's try a larger range:

set xrange [0:100]
replot

Now 3x+6 seems to be pretty solidly between the bounds. Try increasing the range a few more times, though:

set xrange [0:1000]
replot
set xrange [0:10000]
replot

Observe that the shape of the plot changes less and less with each increase, and that 3x+6 stays solidly between the lines. Looks like our big-Theta is correct!

Useful tip: use the up arrow to retrieve previously-typed commands. (You can also edit them before pressing enter.)

Now pick a big-Theta that grows too fast, say n². Plot x², 3x+6, and 4x² (to use the same constant multipliers as we picked before) starting with a small x range and then repeatedly increasing the x range. What happens?

Now pick a big-Theta that grows too slowly, say 1. Plot 1, 3x+6, and 4 (to use the same constant multipliers as we picked before) starting with a small x range and then repeatedly increasing the x range. What happens?

Typing

help

takes you into gnuplot's help system, which will tell you quite a bit about what it can do. Press enter when asked for a help topic to get back to the gnuplot prompt.

Quit gnuplot by typing

quit