**
GNUPLOT 4.0 - A Brief Manual and Tutorial**

Department of Civil and Environmental Engineering

Edmund T. Pratt School of Engineering

Duke University - Box 90287, Durham, NC 27708-0287

Gnuplot is a free, command-driven, interactive, function and data plotting program. Pre-compiled executeables and source code for Gnuplot 4.0 may be downloaded for OS X, Windows, OS2, DOS, and Linux. The important enhancements provided by version 4.0 are described here.

On Windows, unzip gp400win32.zip into an appropriate directory, (e.g. C:\My Programs\Gnuplot, C:\Gnuplot, C:\Apps\gnuplot, etc.). Make a link from ...\gnuplot\bin\wgnuplot.exe to your desktop or some other convenient location. Click on this link, and the Gnuplot window should open.

Instructions for installing on OS X are at the end of this document.

On Unix, Linux and OS X systems start Gnuplot by simply typing:

gnuplot

For help on any topic type **help** followed by the name of the topic.
Full documentation is provided here.

In general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC may be plotted. The precedence of operators is determined by the specifications of the C programming language.

The supported functions include:

__________________________________________________________ Function Returns ----------- ------------------------------------------ abs(x) absolute value of x, |x| acos(x) arc-cosine of x asin(x) arc-sine of x atan(x) arc-tangent of x cos(x) cosine of x, x is in radians. cosh(x) hyperbolic cosine of x, x is in radians erf(x) error function of x exp(x) exponential function of x, base e inverf(x) inverse error function of x invnorm(x) inverse normal distribution of x log(x) log of x, base e log10(x) log of x, base 10 norm(x) normal Gaussian distribution function rand(x) pseudo-random number generator sgn(x) 1 if x > 0, -1 if x < 0, 0 if x=0 sin(x) sine of x, x is in radians sinh(x) hyperbolic sine of x, x is in radians sqrt(x) the square root of x tan(x) tangent of x, x is in radians tanh(x) hyperbolic tangent of x, x is in radians ___________________________________________________________ Bessel, gamma, ibeta, igamma, and lgamma functions are also supported. Many functions can take complex arguments. Binary and unary operators are also supported.

The supported operators in Gnuplot are the same as the corresponding operators in the C programming language, except that most operators accept integer, real, and complex arguments. The ** operator (exponentiation) is supported as in FORTRAN. Parentheses may be used to change the order of evaluation. The variable names x, y, and z are used as the default independent variables.

**3. THE plot AND splot COMMANDS **

**plot** and **splot** are the primary commands in Gnuplot. They plot
functions and data in many many ways. **plot** is used to plot 2-d
functions and data, while **splot** plots 3-d surfaces and data.

Syntax: plot {[ranges]} {[function] | {"[datafile]" {datafile-modifiers}}} {axes [axes] } { [title-spec] } {with [style] } {, {definitions,} [function] ...}

where either a [function] or the name of a data file enclosed in quotes is supplied. For more complete descriptions, type: help plot help plot with help plot using or help plot smooth .

**3.1 Plotting Functions **

To plot functions simply type: plot [function] at the gnuplot> prompt.

For example, try:

gnuplot> plot sin(x)/x gnuplot> splot sin(x*y/20) gnuplot> plot sin(x) title 'Sine Function', tan(x) title 'Tangent'

**3.2 Plotting Data **

Discrete data contained in a file can be displayed by specifying the name
of the data file (enclosed in quotes) on the
**plot** or **splot**
command line. Data files should have the data arranged in columns of
numbers. Columns should be separated by white space (tabs or spaces)
only, (no commas). Lines beginning with a # character are treated
as comments and are ignored by Gnuplot. A blank line in the data file
results in a break in the line connecting data points.

For example your data file, force.dat , might look like:

# This file is called force.dat # Force-Deflection data for a beam and a bar # Deflection Col-Force Beam-Force 0.000 0 0 0.001 104 51 0.002 202 101 0.003 298 148 0.0031 290 149 0.004 289 201 0.0041 291 209 0.005 310 250 0.010 311 260 0.020 280 240

You can display your data by typing:

gnuplot> plot "force.dat" using 1:2 title 'Column', \ "force.dat" using 1:3 title 'Beam'

Do not type blank space after the line continuation character, "\" .

Your data may be in multiple data files. In this case you may make your plot by using a command like:gnuplot> plot "fileA.dat" using 1:2 title 'data A', \ "fileB.dat" using 1:3 title 'data B'For information on plotting 3-D data, type:

gnuplot> help splot datafile

**4. CUSTOMIZING YOUR PLOT **

Many items may be customized on the plot, such as the ranges of the axes, the labels of the x and y axes, the style of data point, the style of the lines connecting the data points, and the title of the entire plot.

** 4.1 plot command customization **

Customization of the data columns, line titles, and line/point style
are specified when the **plot** command is issued. Customization of the
data columns and line titles were discussed in section 3.

Plots may be displayed in one of eight styles:
lines, points, linespoints, impulses, dots, steps, fsteps, histeps,
errorbars, xerrorbars, yerrorbars, xyerrorbars, boxes, boxerrorbars,
boxxyerrorbars, financebars, candlesticks or vector
To specify the line/point style use the **plot** command as follows:

gnuplot> plot "force.dat" using 1:2 title 'Column' with lines, \ "force.dat" u 1:3 t 'Beam' w linespoints

Note that the words: using , title , and with can be abbreviated as: u , t , and w . Also, each line and point style has an associated number.

** 4.2 set command customization **

Customization of the axis ranges, axis labels, and plot title, as well as many other features, are specified using the set command. Specific examples of the set command follow. (The numerical values used in these examples are arbitrary.) To view your changes type: replot at the gnuplot> prompt at any time.

Create a title: > set title "Force-Deflection Data" Put a label on the x-axis: > set xlabel "Deflection (meters)" Put a label on the y-axis: > set ylabel "Force (kN)" Change the x-axis range: > set xrange [0.001:0.005] Change the y-axis range: > set yrange [20:500] Have Gnuplot determine ranges: > set autoscale Move the key: > set key 0.01,100 Delete the key: > unset key Put a label on the plot: > set label "yield point" at 0.003, 260 Remove all labels: > unset label Plot using log-axes: > set logscale Plot using log-axes on y-axis: > unset logscale; set logscale y Change the tic-marks: > set xtics (0.002,0.004,0.006,0.008) Return to the default tics: > unset xtics; set xtics auto

Other features which may be customized using the set command are:
arrow, border, clip, contour, grid, mapping, polar, surface, time,
view, and many more. The best way to learn is by reading the
on-line help information, trying the command, and reading the
Gnuplot manual.
You may also post questions to the newsgroup *comp.graphics.apps.gnuplot *

The Gnuplot demo page and the gnuplot intro page have many examples like this script for a transfer function producing this postscript plot.

**5. PLOTTING DATA FILES WITH OTHER COMMENT CHARACTERS **

If your data file has a comment character other than # you can tell Gnuplot about it. For example, if your data file has "%" comment characters (for Matlab compatability), typing

gnuplot> set datafile commentschars "#%"indicates that either a "#" or a "%" character starts a comment.

**6. GNUPLOT SCRIPTS **

Sometimes, several commands are typed to create a particular plot, and it is easy to make a typographical error when entering a command. To stream- line your plotting operations, several Gnuplot commands may be combined into a single script file. For example, the following file will create a customized display of the force-deflection data:

# Gnuplot script file for plotting data in file "force.dat" # This file is called force.p set autoscale # scale axes automatically unset log # remove any log-scaling unset label # remove any previous labels set xtic auto # set xtics automatically set ytic auto # set ytics automatically set title "Force Deflection Data for a Beam and a Column" set xlabel "Deflection (meters)" set ylabel "Force (kN)" set key 0.01,100 set label "Yield Point" at 0.003,260 set arrow from 0.0028,250 to 0.003,280 set xr [0.0:0.022] set yr [0:325] plot "force.dat" using 1:2 title 'Column' with linespoints , \ "force.dat" using 1:3 title 'Beam' with points

Then the total plot can be generated with the command: gnuplot> load 'force.p'

**7. CURVE-FITTING WITH GNUPLOT **

To fit the data in force.dat with a function use the commands:

f1(x) = a1*tanh(x/b1) # define the function to be fit a1 = 300; b1 = 0.005; # initial guess for a1 and b1 fit f1(x) 'force.dat' using 1:2 via a1, b1 Final set of parameters Asymptotic Standard Error ======================= ========================== a1 = 308.687 +/- 10.62 (3.442%) b1 = 0.00226668 +/- 0.0002619 (11.55%)

and the commands:

f2(x) = a2 * tanh(x/b2) # define the function to be fit a2 = 300; b2 = 0.005; # initial guess for a and b fit f2(x) 'force.dat' using 1:3 via a2, b2 Final set of parameters Asymptotic Standard Error ======================= ========================== a2 = 259.891 +/- 12.82 (4.933%) b2 = 0.00415497 +/- 0.0004297 (10.34%)

The curve-fit and data may now be plotted with the commands:

set key 0.018,150 title "F(x) = A tanh (x/B)" # title to key! set title "Force Deflection Data \n and curve fit" # note newline! set pointsize 1.5 # larger point! set xlabel 'Deflection, {/Symbol D}_x (m)' # Greek symbols! set ylabel 'Force, {/Times-Italic F}_A, (kN)' # italics! plot "force.dat" using 1:2 title 'Column data' with points 3, \ "force.dat" using 1:3 title 'Beam data' with points 4, \ a1 * tanh( x / b1 ) title 'Column-fit: A=309, B=0.00227', \ a2 * tanh( x / b2 ) title 'Beam-fit: A=260, B=0.00415'

**8. SPREAD-SHEET LIKE CALCULATIONS ON DATA **

Gnuplot can mathematically modify your data column by column:

to plot sin( col.3 + col.1 ) vs. 3 * col.2 type:

plot 'force.dat' using (3*$2):(sin($3+$1))

**9. MULTI-PLOT **

Gnuplot can plot more than one figure in a frame ( like subplot in matlab ) i.e., try:

set multiplot; # get into multiplot mode set size 1,0.5; set origin 0.0,0.5; plot sin(x); set origin 0.0,0.0; plot cos(x) unset multiplot # exit multiplot mode

**10. GNUPLOT DEMO FILES AND THE GNUPLOT FAQ **

Most of Gnuplot's current features are illustrated in one or more of the Gnuplot demonstration files. To run the demo's yourself, download and unzip demo.zip, start Gnuplot from the resulting demo directory, and type

load "all.dem"The Gnuplot feature you are looking for will probably be illustrated in one of the demo files. Gnuplot 4.0 also has an extensive FAQ.

**11. HARD-COPY (PLOTTING ON PAPER) **

You can create a PostScript file of your plot by using the following files and commands. First, download and save the following general-purpose Gnuplot script: save.plt

# File name: save.plt - saves a Gnuplot plot as a PostScript file # to save the current plot as a postscript file issue the commands: # gnuplot> load 'saveplot' # gnuplot> !mv my-plot.ps another-file.ps set size 1.0, 0.6 set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14 set output "my-plot.ps" replot set terminal x11 set size 1,1Then simply type the following commands to create and print the plot

gnuplot> load 'save.plt' gnuplot> !mv my-plot.ps force.ps gnuplot> !lpr force.psThe PostScript files produced by Gnuplot may be read and edited with a text editor. The PostScript file format convention used by Gnuplot is described in this document by Richard Crawford.

**12. ADVANCED COMPUTATION AND VISUALIZATION **

Gnuplot is used for plotting in a free and open Matlab-like programming environment called Octave.

**13. PRINTING TWO FIGURES ON ONE PAGE **

If you would like two figures to be laser-printed on the same page, you may use the following shell script. Create file cat2 , below, and make the file executable by typing: unix% chmod +x cat2

# cat2: Shell script for putting two Gnuplot plots on one page echo %! > g.ps echo gsave >> g.ps echo 0 400 translate >> g.ps # for Gnuplot plots cat $1 | sed -e "s/showpage//" >> g.ps echo grestore >> g.ps echo gsave >> g.ps echo 0 090 translate >> g.ps # for Gnuplot plots cat $2 >> g.ps lpr -Phudsonlp1 g.ps

To combine two PostScript figures (plot1.ps and plot2.ps) on one page:

cat2 plot1.ps plot2.ps

You'll need both AquaTerm and Gnuplot.

* Download and install AquaTerm v1.0.0 (not v1.0.1). Click on "v1.0.0" then click on "AquaTerm1.0.0.dmg" to start the download. Click on the AquaTerm1.0.0.dmg icon in your HardDisk download directory. Click on the AquaTerm.pkg icon and continue with the installation. Type in the administrator password when asked. If you have already installed AquaTerm v1.0.1, you may not be able to instal v1.0.0. In that case: Open the Terminal (Applications > Utilities > Terminal) and ... ...$ cd /usr/local/lib/ ...$ sudo ln -s libaquaterm.1.0.1.dylib libaquaterm.1.0.0.dylib Enter administrator password when asked. * Download and install Gnuplot 4.0.0. Click on the green Download button for gnuplot 4.0.0 Click on "Gnuplot-4.0.0.dmg" and save to disk. Click on the Gnuplot-4.0.0.dmg icon in your HardDisk download directory. Click on the gnuplot.pkg icon and continue with the installation. Enter the administrator password when asked. * Set your PATH Create a file called ".profile" in your home directory containing the line export PATH=".:$PATH:/usr/local/bin" Create a file called ".gnuplot" in your home directory containing the line set term aqua Quit the Terminal application. [APPLE] [Q] * Test that Gnuplot works. Open the Terminal (Applications > Utilities > Terminal) and ... ...$ gnuplot gnuplot> set term aqua gnuplot> plot sin(x)/x gnuplot> quit

© 2000-2007 Henri P. Gavin

updated: 12-18-2002; 10-11-2004; 12-5-2006; 12-8-2006; 3-30-2007