Friday, 8 May 2009

Gnuplot tricks


Many say that it is impossible to produce a publication quality plot with gnuplot. I strongly
believe that this assertion is simply wrong, and once you know what and how to do, gnuplot is
just as good as it gets. Of course, one shouldn't forget that gnuplot is a plotting utility, and
one won't have the conveniencies of FFT and the like, but this would be off the point.

In the following pages, I explain a couple of tricks that will help you produce high-quality
plots with gnuplot. While I understand the advantages of using a point-and-click type plotting
utility (e.g. Origin under Windows, Kst, Grace, Labplot under Linux), there are certain things
that are just much easier with gnuplot, once you get the hang of it.

Including unconventional symbols in a graph



So, you want to make a decent-looking, publication quality plot, with a couple of fancy
symbols here and there. There are several ways to go.



Enhanced EPS



If all you need is a couple of greek symbols and the like, then the easiest route is to use
the postscript terminal with the enhanced option, and simply enter the code for that particular
letter. (postscript is not the only terminal that has an enhanced option, however, the
degree to which those terminals are properly implemented is varying. Postscript works perfectly,
while others don't.) So, you would write

set terminal postscript eps enhanced solid "Helvetica" 14

and then, if you want to have a label with an α in it, you write

set label 1 at graph 0.1, 0.1 "{/Symbol a}^2 = 12"

which, once you set the output and replot your graph, will place
α2=12 at position (0.1,0.1) on your figure. You can find all available
characters and their corresponding code in Dick Crawford's
postscript guide

While setting the characters is quite easy, the problem with this method is that the character set is somewhat limited (though, almost always enough), and that the relative placement of the characters must be done manually, through trial and error. E.g., you would have a hard time, if you tried to write an overhead vector on some symbol. If this is the case, then you should use the epslatex terminal of gnuplot. We cover this subject in the next paragraph.


Using the epslatex terminal



As always, first we have to set our terminal as

set terminal epslatex

At this point, we can set labels with any LaTeX symbols, the generated output will contain it properly. For the sake of example, we will plot the error function, and write its definition on the figure as follows:

set terminal epslatex
set xrange [-3:3]
set yrange [-1:1]
set label 1 at -2, 0.5 "$erf(x) = \\frac{2}{\\sqrt{\\pi}}\\int_0^x\\, dt e^{-t^2}$" centre
plot erf(x)

Note that we have crammed a lot of LaTeX commands in the label, enclosed by the two $ signs, to indicate that we are dealing with mathematical expressions. You might have to escape the instructions twice, so you will have \\frac{}{} etc.

Now, if you set your output

set output 'errorf.tex'

and replot your graph, you will get two files. (At this point, I would also recommend re-setting the terminal, otherwise, there is no guarantee that gnuplot has closed both your output files, and this could create some trouble later on.) errorf.eps will contain the "visual" part of the graph, i.e., the axes, tics, points, lines, arrows and the like, while errorf.tex holds all the typographic elements. We then have got to combine these two by invoking LaTeX or pdflatex, depending on the exact route you would like to follow. The destination is the same in both cases.

So, let us suppose for the moment that you want to work with postscript, and not with pdf. You should create a LaTeX file, which includes nothing but the file that we have just produced, errorf.tex.

\documentclass{article}
\usepackage{graphics}
\usepackage{nopageno}
\usepackage{txfonts}
\usepackage[usenames]{color}

\begin{document}
\begin{center}
\input{errorf.tex}
\end{center}
\end{document}

You can read everything about epslatex in the gnuplot documentation. If you
want to compile with pdflatex, first you have to convert the postscript file to pdf. In principle, one could use the pdf terminal of gnuplot, but I have had problems with that, and the end result is far from the expected. I would recommend using the eps terminal, and then converting the file by

ps2pdf -dEPSCrop error.eps error.pdf


Of course, this assumes that you have ghostview installe on your computer. By passing the -dEPSCrop argument to ps2pdf, we can retain the bounding box in the eps file, so the pdf graph won't be bigger. By this time, you should have something like this figure:






Plotting on top of a map



Sometimes you might want to have overlapping plots. The first thing that comes to my mind
is a map, on which you would like to show a function that you have fitted to the peaks. An
example is shown in the figure below. It works only with gnuplot 4.3 or later, though.

We will have to use multiplot. The standard way is to tell gnuplot what, where and in what
size we want to plot, as in


set multiplot
set size 0.5, 1
set origin 0,0
plot sin(x)

set origin 0.5, 0
plot cos(x)
unset multiplot

The problem here is that when gnuplot determines how big the actual plot is going to be, it
counts the borders, axis label, tics and so on in the size. So, in the example above, the
width of 0.5 is the full with of one plot, and not the size of the plotting are, where the
curve is shown. Thus, when putting two plots on top of each other, strange things might happen.
The difficulty is that the second plot shouldn't contain axis labels, tics and so on. However,
when one takes those off, there is no telling as to what the final size of that graph is going
to be, and when they are on top of each other, there is a fair chance that they will be
misaligned.


In order to alleviate the situation, we have to force gnuplot to allocate a certain amount of
space for the curves, regardless the surroundings. We can do this with the command

set lmargin at screen 0.10
set rmargin at screen 0.85
set bmargin at screen 0.15
set tmargin at screen 0.95

where the four margins determine the white space on the left, right, bottom, and top,
respectively. This won't work on gnuplot 4.2 or earlier. Once we have specified the margins,
the rest is plain sailing. We plot both figures, and they will be aligned and top of each other.





The gnuplot commands that produced this figure are

reset
set terminal postscript enhanced eps solid colour "Helvetica" 22
unset key
set multiplot
set lmargin at screen 0.10
set rmargin at screen 0.85
set bmargin at screen 0.15
set tmargin at screen 0.95
set pm3d map
set palette rgbformulae 33,13,10
set xrange [0:1279]
set yrange [0:255]
set cbrange [4e4:2e5]
set cbtics ("4" 4e4, "8" 8e4, "12" 12e4, "16" 16e4, "20" 20e4)
set xlabel 'Pixel'
set ylabel 'Grey value'
splot 'shiftimage.dat' mat
unset xtics
unset ytics
unset xlabel
unset ylabel
p 'peak1.dat' using 2:0 with lines lt 3, 'peak2.dat' using 2:0 with lines lt 3
unset multiplot

(Obviously, you should replace the file names with some appropriate ones.)

Incidentally, the same method can be used to plot things that are not on top of each other,
but should still be aligned, as in the example below, where on the bottom, a horizontal, while
on the left hand side, a vertical cut through the centre are shown.




And here is the code producing this graph

reset
set out 'multi.svg'
set term svg size 600,400 dynamic enhanced fname 'arial' fsize 11 butt solid
set multiplot
set lmargin screen 0.20
set rmargin screen 0.85
set bmargin screen 0.25
set tmargin screen 0.90

set pm3d map
set palette rgbformulae 33,13,10
set samples 50, 50
set isosamples 50, 50
set xrange [ -15.00 : 15.00 ]
set yrange [ -15.00 : 15.00 ]
set cbrange [ -0.250 : 1.000 ]
set cbtics -0.25,0.25,1

unset xtics
unset ytics
unset key

splot sin(sqrt(x**2+y**2))/sqrt(x**2+y**2)
unset pm3d
set lmargin screen 0.10
set rmargin screen 0.20
set ytics

set parametric
set dummy u,v
set view map

f(h) = sin(sqrt(h**2))/sqrt(h**2)

set urange [ -15.00 : 15.00 ]
set vrange [ -15.00 : 15.00 ]
set xrange [*:*]
set surface

splot f(u), u, 0 with lines lc rgb "green"

unset parametric
set lmargin screen 0.20
set rmargin screen 0.85
set bmargin screen 0.10
set tmargin screen 0.25
set xrange [ -15.00 : 15.00 ]
set yrange [ * : * ]
set xtics
unset ytics

plot sin(sqrt(x**2))/sqrt(x**2)
unset multiplot


Broken axes in gnuplot



A broken axis definitely comes handy, if part of a curve doesn't contain too much relevant
information. Unfortunately, there is no easy way to do this in gnuplot. On the other hand, there is a work-around that can be applied in most situations. However, this method requires version 4.3
or later, so, if you don't have it, you should check it out on the development page.

For the sake of example, we will learn how to plot the cosine function in the [0:6π]
interval with a break point at 2.5π and 4.5π.

First, we have to determine what is the ratio of the two parts of the figure. Since the first
half is 2.5π long, while the second is 1.5π, we have to split the figure in a 2.5:1.5
ratio. I will choose 0.8 for the length of the whole figure (without the gap), so the first
half will be 0.5 long, while the second 0.3. We then insert the first half in a multiplot,
while keeping in mind that this part will have only three boundaries: left, bottom, and top.
The border is defined as the sum of bottom (1), left (2), top (4), and right (8).



set multiplot
unset key
unset xlabel
set border 1+2+4
set lmargin at screen 0.10
set rmargin at screen 0.6
set bmargin at screen 0.15
set tmargin at screen 0.95

Then, we specify the range and the tic marks

set ytics -1,0.5,1 nomirror
set xrange [0:2.5*pi]
set xtics ("0" 0, "{/Symbol p}" pi, "2{/Symbol p}" 2*pi)

and we also add the two slanted tics that denote the broken axis. These will just be two
arrows with no heads.

set arrow 1 from 2.5*pi-tiny, -1-tiny to 2.5*pi+tiny, -1+tiny nohead
set arrow 2 from 2.5*pi-tiny, 1-tiny to 2.5*pi+tiny, 1+tiny nohead

Now, that we are done with the outline of the first half, we plot the function, cosine in this
case.

plot cos(x)


The second half is very similar, with some small differences: First, this graph will still have
three boundaries, but on the bottom, right, and top. We also have to take off the vertical tics,
and keep an eye on the position of the graph. Therefore, we have


unset ytics
set border 1+4+8
set key right
set lmargin at screen 0.63
set rmargin at screen 0.93
set bmargin at screen 0.15
set tmargin at screen 0.95
set label 1 'cos(x)' at screen 0.5, 0.05 centre
set xrange [4.5*pi:6*pi]
set xtics ("5{/Symbol p}" 5*pi, "6{/Symbol p}" 6*pi)
set arrow 1 from 4.5*pi-tiny, -1-tiny to 4.5*pi+tiny, -1+tiny nohead
set arrow 2 from 4.5*pi-tiny, 1-tiny to 4q.5*pi+tiny, 1+tiny nohead
plot cos(x)
unset multiplot

At the end of the plot, we closed the multiplot, and also added an xlabel, which is located
at the centre of the whole graph. After setting the appropriate terminal, we get a figure
that looks like this:





It's quite re-assuring that the cosine function has the same value at 2.5π and 4.5π.
You would have never guessed, would you?


Plotting a histogram



From version 4.3, there is an option to plot data in a histogram, but this hasn't always been
the case. However, there is a way to rectify the situation, using the smooth option.
First, we have to define our bins, and then we have got to count the number of data points
falling into each of the bins. The frequency specifier of the smooth option takes care
of this, and we only have to determine into which bin a particular data point falls. The
bin(x, width) function will do this; its working should be obvious. As an example, we take
10000 numbers normally distributed between 0 and 6, and plot their frequency. At the same
time, we can also plot the cumulative frequency, which is another specifier of the smooth
option.

unset key
set ylabel 'Frequency'
set y2label 'Cumulative frequency'
set y2tics 0,2e3,1e4
set ytics nomirror
set boxwidth 0.7 relative
set style fill solid 0.5
f(x) = a*exp(-(x-b)*(x-b)/c/c)
a=560.0
b=3.0
c = 1.0
bw = 0.1
bin(x,width)=width*floor(x/width)
plot 'gauss.dat' using (bin($1,bw)):(1.0) smooth frequency with boxes,\
'' using (bin($1,bw)):(1.0) smooth cumulative axis x1y2 w l lt 2 lw 2, \
f(x) w l lt 3 lw 2






Coloured axes



Sometimes you might need a left and a right vertical axis with different colours, to signify
the scale that belongs to two curves shown on the graph. We will discuss an easy way to achieve
this effect. Since we cannot set the colour of the axes one by one, we will do this in two
steps. Let us suppose that the two axes should be red and blue.


First, we draw the border that is meant to be red. The command

set border 1+2 lt 1

sets the left and the bottom axis red, which is linetype 1. The top and the right axes are not
drawn at this moment. We will plot sin(x) on the left axis.
Then we draw two blue arrows without heads where the right and the top axes are
supposed to be, as in

set arrow 1 from 10, -1 to 10, 1 nohead lt 3
set arrow 2 from -10, 1 to 10, 1 nohead lt 3

The function on the right axis will be exp(x)|sin(x)|, although it doesn't really matter. The
rest of the code sets up the tics, label colours and the like. There is only one small thing
worth looking at: when we specify the format of y2tics, we give it as format "10^{%T}", where
%T is a format specifier, and it tells gnuplot to substitute the exponent of the 10-base
value of the y2tics. Using specifiers like this, very nice results can be obtained. I will cover
this subject in a later post.


reset
unset key
set border 1+2 lt 1
set y2tics 1e-5, 1e2, 1e5 textcolor rgb "blue" format "10^{%T}"
set ytics nomirror format "%.1f"
set xtics nomirror
set xlabel 'x' textcolor rgb "red"
set ylabel 'sin(x)' textcolor rgb "red"
set y2label 'exp(x)|sin(x)|' textcolor rgb "blue"
set log y2
set arrow 1 from 10, -1 to 10, 1 nohead lt 3
set arrow 2 from -10, 1 to 10, 1 nohead lt 3
set sample 1000
plot sin(x) with lines lt 1, exp(x)*abs(sin(x)) with lines lt 3 axis x1y2

After plotting the two functions, we would get a graph like this:




If the colour of the tics on y2 still bothers you, you can change it by tampering with the
eps file.

19 comments:

  1. This comment has been removed by the author.

    ReplyDelete
  2. Can you please post the gauss.dat file you have used to generate the histgogram. Your result is very decent looking and I wanted to use it but without the gauss.dat file, it is difficult to recreate.

    Thanks
    -Jeb

    ReplyDelete
  3. Sure, you can download it
    from here
    Thanks for visiting!
    Cheers,
    gnuplotter

    ReplyDelete
  4. Absolutely wonderful post!
    Thank you for the broken axis example! Unfortunately it is really difficult to be realized.

    ReplyDelete
  5. You can also check out a later post, on the 26th of June, where I gave an easier solution.
    http://gnuplot-tricks.blogspot.com/2009/06/broken-axis-revisited.html
    Cheers,
    Zoltán

    ReplyDelete
  6. I'm interested in the 2D sinc function example, where you have generated the 1D cross-sections through x=0 and y=0. Currently, I'm trying to do something similar, but with a datafile.

    The data in the file is formatted nicely, with each datablock containing points with the same x value.

    I tried using the every command, for example
    plot 'file' using 1:3 every ::0::0
    to attempt to extract the xz data from just the first line in each block (so points along a line of constant y)

    This works fine until I try to draw it as a line, when it fails with no error. Outputting data to a file using 'set table', I see that it is putting an unplottable point between each of the real data points. I was hoping you would be able to propose a different way to do it, or explain this behaviour...

    Many thanks

    ReplyDelete
  7. Hello Nick,

    Could you post one chunk of your data file? I mean, not the whole data file, just a couple of lines of it (e.g., a 5 x 5 segment should probably be enough). Is your original data file a matrix which you converted into a table?
    Cheers,
    Zoltán

    ReplyDelete
  8. QUOTE: Outputting data to a file using 'set table', I see that it is putting an unplottable point between each of the real data points. I was hoping you would be able to propose a different way to do it, or explain this behaviour...

    I sort of overlooked this sentence here. I have tried this, and I also get one extra line everywhere. Since I don't know where actually it comes from, I can only suggest a workaround: once you plotted to a file, plot that file as
    plot 'foo' using 1:2 ev 2

    so that you don't read the invalid lines. This worked for me.
    I hope this helps!
    Cheers,
    Zoltán

    ReplyDelete
  9. Thanks, I shall use that solution for the present. Although I'm quite new to gnuplot, I can't see any reason for the unplottable points to be there... Do you think this is a bug that ought to be reported?

    Nick

    ReplyDelete
  10. I have a question that I haven't yet been able to answer searching online and in the gnuplot help: When using postscript, specifically "set terminal postscript color eps enhanced", how does one label the x-axis with fractions of pi (vertical fractions or upright fractions)? I imagine there's a special command to enter a TeX mode so one can write \frac{3{/Symbol-Oblique p}}{2}. Is this correct? The dollar signs $ don't seem to be cutting it with the postscript terminal.

    ReplyDelete
  11. You should look at the postscript guide to which I have a link in this post: the first page of that discusses tricks about creating fractions and the like in the postscript terminal.
    Cheers,
    Zoltán

    ReplyDelete
  12. Hi. Thanks for the article.

    Do you know how to fit the best width for the data set if we want to plot a histogram?

    Thanks,

    Atenágoras Souza Silva.

    ReplyDelete
  13. Hi,
    thanks for your articles, you really save me ;).
    I have a question...How I can change the Y starting point of the impulses?? Ok I'm a mineralogist and I need a trick to put two different groups of impulses: one from y=-200 to y=-400 and also the second one is normal from y=0 to y=-200.
    Thank you,
    Fede

    ReplyDelete
  14. Hey,

    I m really thankful for your heatmaps, they saved me from a ton of work! Nevertheless, I got a question:

    I got into trouble when I tried to plot something like that
    plot 'C:/test/test.dat' \
    using 63:($65+$64+$58+$59) with filledcurve y1=0 ls 2 lw 2 title 'title1', '' \
    using 63:($64+$58+$59) with filledcurve y1=0 ls 1 lw 2 title 'title2', '' \
    using 57:($58+$59) with filledcurve y1=0 ls 2 fs solid title 'title3', '' \
    using 57:($58) with filledcurve y1=0 ls 1 fs solid title 'title4'

    It should be a plot where the lines are y-cumulative (no smooth cumulative!), meaning every line is over the other with different colours and filled; it looks quite nice at the first look but in fact (I ve got some missing data in my .dat file) the title1 line has no points where title2 has no points (concretely: if there is a missing point in $64, but not in $65, I don t get a line at all!)

    I googled all those sites but didn t get a soluation for it. I also tried "set missing data" ... no soluation as well... any hints? I would be really thankful!

    Best,
    stefan

    ReplyDelete
  15. Hey, thank a lot for the post.

    Is there any way of changing the tic colors as well?
    I mean if you see, your y2tics are still colored red, while the y2axis is blue in the "colored text" section.

    --V

    ReplyDelete
  16. I have following error while pdflatex the output file.
    \put(0,0){\includegraphics{test1}}

    How can I fix it ?
    Thank you.

    ReplyDelete
  17. ! LaTeX Error: File `test1' not found.

    ReplyDelete
  18. Plz email your datafiles - 'shiftimage.dat', 'peak1.dat', 'peak2.dat' to suza.rri@gmail.com, thank you very much.

    ReplyDelete
  19. Hi,your article is very helpful.
    But , i am having a problem with ploting single points. I have googled a lot and not found any answer.
    I am having a 2D graph.and i want to draw y-axis parallel lines at specific points on x-axis, which are read from a file.

    Looking forward for your reply.
    Thank you.

    Amit

    ReplyDelete