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Visualize your data with gnuplot
Advanced graphs and data-plotting mastery at your disposal
Level: Introductory
Nishanth Sastry ([email protected]), Staff Software Engineer, IBM
22 Jul 2004
Turn your data and functions into professional-looking graphs with Gnuplot 4.0, a freely distributed plotting tool. In this article, get a hands-on guide to gnuplot that emphasizes the idioms you'll need to use this tool effectively.
Gnuplot is a freely distributed plotting tool with ports available for nearly every major platform. It can be operated in one of two modes: when you need to adjust and prettify a graph to "get it just right," you can operate it in interactive mode by issuing commands at the gnuplot prompt. Alternately, gnuplot can read commands from a file and produce graphs in batch mode. Batch-mode capability is especially useful if you are running a series of experiments and need to view graphs of the results after each run, for example; or when you need to return to a graph to modify some aspect long after the graph was originally generated. While it is hard to capture the mouse-clicks that you would use to prettify a graph in a WYSIWIG editor, you can easily save gnuplot commands in a file and load them up to re-execute in an interactive session six months later.
Gnuplot was originally developed in 1986 by Colin Kelley and Thomas Williams. A number of contributors added support for different "terminals," creating variants. In 1989 and 1990, these were merged into gnuplot 2.0. And in April 2004, version 4.0 was announced. This tutorial will apply to version 4.0, but most of the commands introduced here should apply to other versions as well. Where possible, I will mention the major differences. The official Web site for gnuplot is listed in Resources.
In the following, we present a hands-on tutorial for the novice; but even if you have prior experience with gnuplot, you might find new idioms and new commands introduced in version 4.0. We start with a simple sine curve and customize it to look just as we want it to. Then we will study how to plot a set of data points. In this article, we confine ourselves to 2D plots, since they are the most common.
GNG: Gnuplot's Not GNU While its name may imply otherwise, gnuplot is not covered by the GPL. For the legally curious, gnuplot FAQ #1.7 says: "Gnuplot is freeware in the sense that you don't have to pay for it. However, it is not freeware in the sense that you would be allowed to distribute a modified version of your gnuplot freely. Please read and accept the Copyright file in your distribution."
Oftentimes, novice users may have a pretty good idea about how their graphs should look, but it is not apparent what gnuplot command they need to use. So the key to understanding gnuplot is to get a good grasp of its vocabulary, and the rest should be intuitive enough. In this tutorial, I will only be able to provide a feel for some of the common options you will end up using in gnuplot; it is by no means exhaustive. So, for example, I tell you how to set the x-range to limit the range on the x-axis of the graph. Setting the y-range is similar (use yrange instead of xrange in the command), but I don't talk about it.
The basics
Fire up gnuplot by typing gnuplot at the command prompt of your shell. The first thing you will see is the prompt sign >. The prompt is the point of input into gnuplot; Linux users will be used to its behavior. For example, you can use arrow keys to navigate the history of commands you have typed before, then edit and re-execute them; and the
Home and End keys work as expected. gnuplot can be recompiled to use the GNU readline library to move around on the input prompt, but the defaults function similarly.
Gnuplot comes with extensive online help, which you cannot avoid using if you intend to do anything non-trivial. The syntax is uniform: help for any command is obtained by typing help . Go ahead and start up gnuplot, and try the commands help set yrange and help set now (use q to quit the help after each command). Notice that yrange is one of the sub-options available under help set. In general, gnuplot help offers further help for all possible customizations of a command. Glancing at the examples section in the help is usually more than sufficient to understand how to use a command.
Gnuplot also has an extensive set of demos that showcase its capabilities, usually located in the demo subdirectory of the install. To get the tour-de-force, change into this directory at the gnuplot prompt (for example, cd '/opt/gnuplot/demo' -- note that gnuplot requires all file and directory names to be enclosed in single or double quotes) and type in load 'all.dem'. Individual .dem files in this directory demonstrate individual functions, and all.dem loads them all one at a time. You may want to hold off on this exercise until the end of this article, though, so that we can get started without further ado...
For those who want to follow along, you may type each line of code in the code listings individually at the prompt. Alternatively, save the whole listing into a temporary file and run it by typing load 'filename' at the gnuplot prompt (don't forget the quotes).
The command for 2D plots is, predictably, plot. Type in plot sin(x) at the prompt: you should see the familiar sine curve in a pop-up window.
Figure 1. sin(x)
We just created the simplest possible graph. Let us see how we can customize it in different ways. Let us say we want to see just one cycle of the sine wave. We do this by restricting the default x-range of the graph. Ranges are specified using the notation [min:max]. To specify only the min, use [min:] and to specify only the max, use [:max]. Mathematicians know this as the notation for so-called "closed" intervals.
Here we use [-pi:pi] to get one sinusoid cycle:
Listing 1. sin(x) from -pi to +pi set xrange [-pi:pi] replot
From just these three simple examples, you can see that gnuplot understands pi and has a rich and natural vocabulary of mathematical functions. It even knows useful statistical functions governing normal distribution, and esoteric special functions like the lambert, bessel, beta and gamma functions (and more!) that you would ordinarily only expect from a full-fledged math tool like mathematica. A rule of thumb is that the syntax is similar to the syntax in C, which in turn is similar to the syntax used in everyday mathematics. (An important exception is the notation for exponentiation: x raised to the power y is conveniently written as x**y).
Next, let us give titles to the graph ("My First Graph") and the axes (x-axis is "angle, in degrees," and y-axis is "sin(angle)").
Listing 2. Giving titles to the graph and axes set title "My first graph" set xlabel "Angle, \n in degrees" set ylabel "sin(angle)" plot sin(x)
Notice that the \n in the xlabel produces a new line. In general, gnuplot does C-like backslash processing within double quoted strings. Windows users beware: If you tend to use double quoted strings for filenames, you will have to use two backslashes: for example, "c:\developerworks" (or you can use a forward slash: "c:/developerworks").
Now, we notice that the x-axis is not really marked in degrees and does not look good. Let us fix this by adjusting the tic marks on the x-axis to make named (major) marks only at 90 degree increments and minor marks at 45 degree increments. The major tics have a "level" of 0, which is the default; and the minor tics have a level of 1. Each point is separately specified by a 3-tuple: "label" (in quotes), , and .
Listing 3. Altering the tics on the axes and setting a grid set xrange [-pi:pi] # we want only one cycle set xtics ("0" 0, "90" pi/2, "-90" -pi/2, "" pi/4 1, "" -pi/4 1, \
"" 3pi/4 1, "" -3pi/4 1) set grid set xlabel "Angle,\n in degrees" set ylabel "sin(angle)" plot sin(x)
Figure 4. sin(x) with tics, title, grid and labeled axes
Notice the use of empty labels ("") for the minor marks at +45 and -45 degrees. Also observe that we don't need to list the points in any order. Like everything else in gnuplot, the xtics command is enormously versatile and there are convenient options for creating tic marks at regular increments (regular multiples, in logarithmic scale), and special formats for time-related data. Look up the examples in help set xtics for the juicy stuff.
As a side note, observe that we use a backslash to extend the xtics command over more than one line of input. This can make a long or complex command more readable.
We also slapped on a grid with set grid, which lets you eye the graph quantitatively. We have been extensively using the set command until now. Gnuplot has a consistent way to undo sets: in gnuplot 4.0, the command is unset. For example, if you don't like grids, use unset grid. Prior to 4.0, the command would have been set nogrid.
Incidentally, all the examples we give can be run in interactive mode or in batch mode. To run it in interactive mode, type each command at the prompt. To run it in batch mode, type or cat the commands into a text file and either read it in at the gnuplot prompt using load 'filename', or give it as an argument to gnuplot at the shell prompt: $ gnuplot filename With the second method, gnuplot exits after executing all the commands in the input file, so it is especially efficient for batch-mode execution when plotting directly to a file (see next section). If the second method is used when plotting onscreen, the output window will disappear as soon as it is rendered (when gnuplot exits), so you will need to use an explicit "pause -1" command (see help pause) to make the window stick.
Gnuplot command files used in batch-mode operation tend to stick around for a while, so it helps to use comments to improve readability. Anything after a # until the end of line is a comment. So in the example in Listing 3, gnuplot does not process we want only one cycle.
Mouse support also enables a bunch of useful hotkeys: u unzooms the graph if you have zoomed in previously. g toggles the grid, l toggles logscale on both axes; L toggles the logscale on the axis nearest to the pointer, r toggles a ruler, which establishes an arbitrary point of origin. When the ruler is enabled, the bottom of the screen shows the x and y distances of the current mouse pointer from ruler origin, as well as the x-y distances from the actual origin -- which is the same as the coordinates of the point). In 3D, the arrow keys can be used in lieu of the mouse drag to rotate the image. The space bar raises the command window, and q quits the terminal window. To see all the options, type h on a mouse-enabled terminal.
Controlling scale and aspect ratio
By default, gnuplot uses a scaling factor of 1 for both the x and y-axes, but it makes no effort to control the aspect ratio (the ratio of the length of the y-axis to the length of the x-axis) of the figure. The terminal driver uses the default aspect ratio of the terminal. Either the scaling factor or aspect ratio, or both, may be specified with the set size command, for example:
square is synonymous to an aspect ratio of 1;
scale y-axis by 2, retain x-axis size
set size ratio square 1,
The success of gnuplot in drawing a graph with a given aspect ratio may be limited by the capabilities of the terminal. set size is also useful in conjunction with the multiplot command, which is used to produce more than one graph on the same output screen or file.
Plotting more than one curve
As the astute reader may have guessed from the comments above on replot, gnuplot lets you graph multiple lines simultaneously. Let us plot both the sine and the cosine curves. The simple plot command would be plot sin(x), cos(x); the lines being graphed are separated by commas. If you do not specify anything else, gnuplot automatically displays the two graphs so that they are distinguishable from each other -- in terminals like Windows and X11, gnuplot uses different colors. Monochrome terminals display the graphs using different kinds of lines. By looking at the legend (or key), you should be able to tell which line in the graph is which. Alternatively, gnuplot lets you take greater control by specifying the style with which to draw a graph: unset xtics # keep all other things simple plot sin(x) with linespoints pointtype 5, cos(x) w boxes lt 4 Figure 5. Multiple curves
The with clause (see help plot with, and also help plotting styles if using version 4.0) lets you specify in dizzying detail, exactly how you want your lines to look. In this example, we show two useful styles. The first style, linespoints, is generally useful when plotting data. It marks a point at each sample or data point considered, and connects consecutive points using linear interpolation. Here we additionally specify the point type as 5 , which chooses the fifth kind of point that the terminal is capable of. The second style, boxes, is more appropriate when plotting histogram data. Notice how we abbreviate with as w in the cos(x) curve. Similarly, lt is an abbreviation for linetype, and is another terminal-specific setting that chooses the fourth kind of line that the terminal can draw. Needless to say (what, you did not try help plot with yet?), you can use pt instead of the verbose pointtype. If you intend to use the same plotting style across several lines (either on a single plot command or over several plot commands), you can set the plotting style with a set command. In gnuplot 4.0, use set style function linespoints; prior versions use the syntax set function style boxes. To change the style used for plotting data sets as opposed to functions, use set style data linespoints (set data style linespoints in prior versions).
How gnuplot does what it does As an interesting aside, this exercise reveals how gnuplot actually plots functions -- it takes several samples and plots the value at each sample point. Usually, it smoothly interpolates between these points; using the boxes style forces it to use a flat histogram bar instead, and the linespoints style marks each sample with a point. To see this more clearly, explicitly set the sampling rate to 10 (set samples 10 ) and replot. (Then set it back to the default of 100).
The with clause is the first example where we used something other than a set to customize a graph. A few other commonly-used options can also be set directly in the plot command. For example, you can set the xrange also: plot [-pi:pi] sin(x). Use this sort of syntax for a quick-and-dirty one-time change to the default plotting options. To re-use across multiple graphs, or across multiple plot commands, use the set command.
When plotting two or more curves, we need a key or legend to distinguish them. By default, the key is in the top right corner; but if it is interfering with your graph, you can place the key elsewhere -- even outside the graph, if you wish. The snippet below places the key on the top left corner, and sets a box around it. We also control the names given to curves in the legend by giving explicit titles in the plot command. The title can be abbreviated to t , as we do for the
This sets up bounding boxes and may be required on some terminals
set size 1, set origin 0,
Done interactively, this takes gnuplot into multiplot mode
and brings up a new prompt ("multiplot >" instead of "gnuplot >")
set multiplot
plot the first graph so that it takes a quarter of the screen
set size 0.5,0. set origin 0,0. plot sin(x)
plot the second graph so that it takes a quarter of the screen
set size 0.5,0. set origin 0, plot 1/sin(x)
plot the third graph so that it takes a quarter of the screen
set size 0.5,0. set origin 0.5,0. plot cos(x)
plot the fourth graph so that it takes a quarter of the screen
set size 0.5,0. set origin 0.5, plot 1/cos(x)
On some terminals, nothing gets plotted until this command is issued
unset multiplot
remove all customization
reset
Figure 7. Multiplot madness
Plotting data
While most of this tutorial has, for expository purposes, concentrated on plotting the sinusoid, you will most likely be plotting data from experiments or sales data or the like. In this section, we will demonstrate how to plot different graphs using IBM's stock price as the data set (The raw data for this example is included in the Resources section):
Table 1. IBM stock price
Date Open High Low Close 10-Jun-04 90.23 90.75 89.89 90. 9-Jun-04 89.90 90.55 89.81 90. 8-Jun-04 88.64 90.50 88.40 90. 7-Jun-04 88.75 88.99 88.01 88. 4-Jun-04 87.95 88.49 87.50 87. 3-Jun-04 87.85 88.10 87.35 87. 2-Jun-04 88.64 88.64 87.89 87. 1-Jun 04 88.00 88.48 87.30 88.
Most data sets have numerical columns, but this one represents a challenge because the x-axis is time data. The following lines tell gnuplot how to read and format the time data on the x-axis (see help time/data and help set timefmt for more details):
Listing 8. Setting up timeseries data set xdata time # The x axis data is time set timefmt "%d-%b-%y" # The dates in the file look like 10-Jun- set format x "%b %d" # On the x-axis, we want tics like Jun 10
Once that is set up, we can plot the opening price with the following command. We choose to use straight-line interpolation between the different opening prices, and use the linespoints style instead of just points:
plot ["31-May-04":"11-Jun-04"] 'ibm.dat' using 1:2 with linespoints
Figure 8. Charting IBM stock prices
The errorlines style is similar, but it also draws line segments between the y-points plotted. Gnuplot also has a separate style for plotting finance bars, with the high and low values and tics on the left and right for the opening and closing values, respectively. We use set bars to show larger tics for the opening and closing values):
set bars 5 plot ["31-May-04":"11-Jun-04"] 'ibm.dat' using 1:2:3:4:5 with financebars
Figure 10. Plotting finance bars
You should also look up help plotting styles for other relevant styles like candlesticks, boxerrorbars and error plotting styles.
Dealing with real-life data sets
Of course, things can get more complicated in real-life data sets. Having data sets with a non-white space character separating the data points is a very common occurrence. New to gnuplot 4.0, you can specify your own separator using set datafile separator . Similarly, you can also specify a comments character other than # with set datafile commentschar. If you need more control, you can explicitly specify a format string for the using modifier. Gnuplot reads in the data using the C standard library's scanf function, with the given format string (see help using for all the details). I have only mentioned this method for the sake of completeness; most of the data sets that can be read in this way can also be handled using either the set data file separator or by explicitly specifying the column numbers to use in the using modifier. For instance, if you have a string in the first column that you need to ignore, plot using 2:3 instead. For complete flexibility, in Unix-like systems with a popen function, you can pre-process the file with text processing utilities before it is passed into the plot command. For example: plot "< awk --f preprocess.awk data.file". Unfortunately, this does not work across all systems. A last resort would be to explicitly pre-process the input file before using it in gnuplot.
At times, a real-life data set may not have all the points -- there may be an x-value but the corresponding y-value may be missing for the column you are trying to plot. Gnuplot lets you specify a character string to mean a missing data point. For example:
set datafile missing 'NaN' # The IEEE floating point not-a-number
Note that, prior to 4.0, the command was set missing .
Unfortunately, the way a data point with missing data is handled depends on the using specification. See help using if you want to know the gory details of the differences between the usages plot 'file', plot 'file' using 1:2, and plot 'file' using ($1):($2)). But to be safe, always specify the columns to use with an explicit using format, and if you want to completely weed out bad data points, do not use the expression evaluation (the third option evaluates the expressions because of the parentheses) -- instead, pre-process the data file and add explicit columns with the result of the calculated expressions.
set xlabel "jw (radians)" set xrange [1.1 : 90000.0] set x2range [1.1 : 90000.0] set ylabel "magnitude of A(jw)" set y2label "Phase of A(jw) (degrees)" set ytics nomirror set y2tics set tics out set autoscale y set autoscale y plot abs(A(jw)), 180/pi*arg(A(jw)) axes x2y
Figure 11. Amplitude and phase frequency response
Conclusion
In this article, we discussed the intricacies of plotting 2D graphs using the newly-released gnuplot 4.0. Although we touched upon most of the important aspects of using gnuplot, there were a few topics we could not discuss owing to space reasons. Notable omissions range from the very simple plotting of parametric functions (See help parametric), and polar coordinates (help polar), to curve-fitting, which fits a user-defined curve to a given data set. Curve-fitting is an art, and a whole article could easily be devoted to it, but look up help fit and the beginners_guide and tips sub-topics to get a start.
Tips for frequent usage
As we have seen, gnuplot is highly customizable. I will conclude with this final tip that shows how to re-use your customizations across several gnuplot sessions: The main command for customization is the set command. You can save all sets from the current session using save set 'filename'. save var and save func save user-defined variables and functions, respectively. But there is no way to save customizations that were passed to a single plot command (for example, the x-range in plot [-pi:pi] sin(x)). These files can be read
back using load . Gnuplot also looks up a file called .gnuplot on startup. It looks first in the current directory, and then in the home directory of the user (The USERPROFILE directory in Windows). If the initialization file is found, gnuplot executes the commands in it. Some users use this for setting the terminal type and defining frequently-used functions or variables.
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Resources
Visit the official site for gnuplot and download the latest version.
Do please note that gnuplot is not GPL'd, nor in any way related to GNU or the Free Software Foundation. An older GNU bulletin explains: "Curiously, [gnuplot] was neither written nor named for the GNU Project; the name is a coincidence. Various GNU programs use gnuplot."
Indeed: gnuplot works exceptionally well in combination with the GNU plotutils; see also the plotutils documentation.
The official Gnuplot FAQ is very useful, as is the unofficial not so Frequently Asked Questions site (the latter has specific information about using gnuplot in scientific papers).
A Google search on "gnuplot introduction" or "gnuplot tutorial" yields several short gnuplot 3.7.x tutorials that can be useful, even though they reference the previous, and not the most recent, release version.
Download the IBM stock price data (ibm.dat) used for the data plots, and the example TeX file (input.tex), which shows how you can include gnuplot plots in a LaTeX report.
The article " Data visualization using Perl/Tk" ( developerWorks , 2003) discusses plotting with Perl.
For an overview of using ImageMagick from the command line, read "Graphics from the command line" ( developerWorks , July 2003).
"Introduction to Scalable Vector Graphics" ( developerWorks , 2004) shows how to to easily generate graphics (such as graphs and charts) from database information, and how to to add animation and interactivity to graphics.
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