155
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Appendix B:
Graphing with Gnuplot
GRAPHING FUNCTIONS
The usual way to create graphs in Gnuplot is with the plot command:
plot <range> <comma-separated list of functions>
For a function y = f ( x), <range> is the range of x values (and optionally the range of y values) over which to plot. To specify an x range, use an expression of the form [ a : b], for
some numbers a < b. This will cause the graph to be plotted for a ≤ x ≤ b.
To specify an x range and a y range, use an expression of the form [ a : b][ c : d], for some numbers a < b and c < d. This will cause the graph to be plotted for a ≤ x ≤ b and c ≤ y ≤ d.
Function definitions use the x variable in combination with mathematical operators, listed
below:
Appendix B:
Graphing with Gnuplot
157
Symbol
Operation
Example
Result
+
Addition
2 + 3
5
−
Subtraction
3 − 2
1
*
Multiplication
2*3
6
/
Division
4/2
2
**
Power
2**3
23 = 8
exp( x)
ex
exp(2)
e 2
log( x)
ln x
log(2)
ln 2
sin( x)
sin x
sin(pi/2)
1
cos( x)
cos x
cos(pi)
−1
tan( x)
tan x
tan(pi/4)
1
Note that we use the special keyword “pi” to denote the value of π.
Example B.1. To graph the function y = sin x from x = 0 to x = 2 π, type this at the gnuplot> prompt:
plot [0:2*pi] sin(x)
The result is shown below:
1
sin( x)
0.8
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
0
1
2
3
4
5
6
Notice that the x-axis is labeled with integers. To get the x-axis labels with fractions of π,
you need to modify the terminal setting. In Windows, you would do this:
set terminal windows enhanced
158
Appendix B:
Graphing with Gnuplot
In Linux you would do this:
set terminal wxt enhanced
You can then (provided the Symbol font is installed, which it usually is) set the x-axis to
have multiples of π/2 from 0 to 2 π as labels with this command (all on one line):
set xtics (’0’ 0,’{/Symbol p}/2’ pi/2,’{/Symbol p}’ pi,’3{/Symbol p}/2’ 3*pi/2,
’2{/Symbol p}’ 2*pi)
In the above example, to also plot the function y = cos 2 x + sin 3 x on the same graph, put a
comma after the first function then append the new function:
plot [0:2*pi] sin(x), cos(2*x) + sin(3*x)
By default, the x-axis is not shown in the graph. To display it, use this command before the
plot command:
set zeroaxis
Also, to label the axes, use these commands:
set xlabel "x"
set ylabel "y"
The default sample size for plots is 100 units, which can result in jagged edges if the curve
is complicated. To get a smoother curve, increase the sample size (to, say, 1000) like this:
set samples 1000
Putting all this together, we get the following graph:
Appendix B:
Graphing with Gnuplot
159
2
sin( x)
cos(2 ∗ x) + sin(3 ∗ x)
1.5
1
0.5
y
0
-0.5
-1
-1.5
-2
0
π/2
π
3 π/2
2 π
x
PRINTING AND SAVING
In Windows, if you are using the windows enhanced terminal then to print a graph from
Gnuplot click on the printer icon in the menubar of the graph’s window. If you are using the
default wxt terminal then select Print near the top of the main Gnuplot window and enter
png in the Terminal type? textfield, then hit OK to get the Print Setup dialog.
In Windows, to save a graph, say, as a PNG file, go to the File menu on the main Gnu-
plot menubar, select “Output Device ...”, and enter png in the Terminal type? textfield, hit
OK. Then, in the File menu again, select the “Output ...” option and enter a filename (say,
graph.png) in the Output filename? textfield, hit OK. Now run your plot command again and
the file will be saved in the current directory, usually in your My Documents folder (it can also
be found by selecting the “show Current Directory” option in the File menu).
In Linux, to save the graph as a file called graph.png run the following commands:
set terminal png
set output ’graph.png’
and then run your plot command. There are many terminal types (which determine the
output format). Run the command set terminal to see all the possible types. In Linux,
the postscript terminal type is popular, since the print quality is high and there are many
PostScript viewers available.
To quit Gnuplot, type quit at the gnuplot> command prompt.
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