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

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1 Page 1 of 8 2/18/2013 GNUPLOT 42 - A Brief Manual and Tutorial Department of Civil and Environmental Engineering Edmund T Pratt School of Engineering Duke University - Box 90287, Durham, NC INSTALLING AND STARTING GNUPLOT - version 42 Gnuplot is a free, command-driven, interactive, function and data plotting program Pre-compiled executeables and source code for Gnuplot 424 may be downloaded for OS X, Windows, OS2, DOS, and Linux The enhancements provided by version 42 are described here On Windows, unzip gp424win32zip into an appropriate directory, (eg C:\My Programs\Gnuplot, C:\Gnuplot, C:\Apps\gnuplot, etc) Make a link from \gnuplot\bin\wgnuplotexe 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 here On Unix, Linux and OS X systems start Gnuplot by simply opening a terminal and typing: gnuplot For help on any topic type help followed by the name of the topic Full documentation is provided here 2 FUNCTIONS 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

2 Page 2 of 8 2/18/2013 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 31 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' 32 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, forcedat, might look like: # This file is called forcedat # Force-Deflection data for a beam and a bar # Deflection Col-Force Beam-Force

3 Page 3 of 8 2/18/ You can display your data by typing: gnuplot> plot "forcedat" using 1:2 title 'Column', \ "forcedat" 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 "fileadat" using 1:2 title 'data A', \ "filebdat" 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 41 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 "forcedat" using 1:2 title 'Column' with lines, \ "forcedat" 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 42 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

4 Page 4 of 8 2/18/2013 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 [0001:0005] Change the y-axis range: > set yrange [20:500] Have Gnuplot determine ranges: > set autoscale Move the key: > set key 001,100 Delete the key: > unset key Put a label on the plot: > set label "yield point" at 0003, 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 (0002,0004,0006,0008) 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 compgraphicsappsgnuplot 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 "forcedat" # This file is called forcep 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 001,100 set label "Yield Point" at 0003,260 set arrow from 00028,250 to 0003,280 set xr [00:0022]

5 Page 5 of 8 2/18/2013 set yr [0:325] plot "forcedat" using 1:2 title 'Column' with linespoints, \ "forcedat" using 1:3 title 'Beam' with points Then the total plot can be generated with the command: gnuplot> load 'forcep' 7 CURVE-FITTING WITH GNUPLOT To fit the data in forcedat with a function use the commands: f1(x) = a1*tanh(x/b1) # define the function to be fit a1 = 300; b1 = 0005; # initial guess for a1 and b1 fit f1(x) 'forcedat' using 1:2 via a1, b1 Final set of parameters Asymptotic Standard Error ======================= ========================== a1 = / (3442%) b1 = / (1155%) and the commands: f2(x) = a2 * tanh(x/b2) # define the function to be fit a2 = 300; b2 = 0005; # initial guess for a and b fit f2(x) 'forcedat' using 1:3 via a2, b2 Final set of parameters Asymptotic Standard Error ======================= ========================== a2 = / (4933%) b2 = / (1034%) The curve-fit and data may now be plotted with the commands: set key 0018,150 title "F(x) = A tanh (x/b)" # title to key!

6 Page 6 of 8 2/18/2013 set title "Force Deflection Data \n and curve fit" # note newline! set pointsize 15 # larger point! set xlabel 'Deflection, {/Symbol D}_x (m)' # Greek symbols! set ylabel 'Force, {/Times-Italic F}_A, (kn)' # italics! plot "forcedat" using 1:2 title 'Column data' with points 3, \ "forcedat" using 1:3 title 'Beam data' with points 4, \ a1 * tanh( x / b1 ) title 'Column-fit: A=309, B=000227', \ a2 * tanh( x / b2 ) title 'Beam-fit: A=260, B=000415' 8 SPREAD-SHEET LIKE CALCULATIONS ON DATA Gnuplot can mathematically modify your data column by column: to plot sin( col3 + col1 ) vs 3 * col2 type: plot 'forcedat' using (3*$2):(sin($3+$1)) 9 MULTI-PLOT Gnuplot can plot more than one figure in a frame ( like subplot in matlab ) ie, try: set multiplot; set size 1,05; set origin 00,05; set origin 00,00; unset multiplot plot sin(x); plot cos(x) # get into multiplot mode # exit multiplot mode

7 Page 7 of 8 2/18/ 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 demozip, start Gnuplot from the resulting demo directory, and type load "alldem" The Gnuplot feature you are looking for will probably be illustrated in one of the demo files Gnuplot 42 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: saveplt # File name: saveplt - 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-plotps another-fileps set size 10, 06 set terminal postscript portrait enhanced mono dashed lw 1 "Helvetica" 14 set output "my-plotps" replot set terminal x11 set size 1,1 Then simply type the following commands to create and print the plot gnuplot> load 'saveplt' gnuplot>!mv my-plotps forceps gnuplot>!lpr forceps The 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 %! > gps echo gsave >> gps

8 Page 8 of 8 echo translate >> gps # for Gnuplot plots cat $1 sed -e "s/showpage//" >> gps echo grestore >> gps echo gsave >> gps echo translate >> gps # for Gnuplot plots cat $2 >> gps lpr -Phudsonlp1 gps To combine two PostScript figures (plot1ps and plot2ps) on one page: cat2 plot1ps plot2ps

9 Gnuplot: Simple Plotting Gnuplot is a freeware program available on the unix as well as MS Windows system which can be used for plotting To use it in a Unix-based operating system, it is invoked by typing gnuplot in a shell window This will give you a prompt something like: gnuplot> To use it you can now type additional commands For example there is an extensive help facility, just type help To exit type quit You may also wish to consult tutorials available on the internet- just search for gnuplot tutorial in google The following is one such guide In your work suppose you generate data in a le called results with the first column giving x values, the second giving y values and the third column giving y 1 values A simple plot of x versus y 1 is generated with plot results u 1:3 w li with the 1:3 representing the column numbers, 1 for xvalues and 3 for y 1 values Once you are satised with your plot, you can save the output in many formats For postscript output to a le say myploteps use set terminal postscript eps set output myploteps plot results u 1:2 w li Finally, you can also write scripts and load these up I have put an example script on my website with example results To load the script at the command type: load gnucom Note that the statements beginning with a # denote comments 1

10 Gnuplot: Contour Plotting To plot contours in gnuplot the data must be stored in columns, with the following format: x 0 y 0 f(x 0,y 0 ) x 1 y 0 f(x 1,y 0 ) x 2 y 0 f(x 2,y 0 ) x n y 0 f(x n,y 0 ) x 0 y 1 f(x 0,y 1 ) x n y 1 f(x n,y 1 ) x 0 y m f(x 0,y m ) x n y m f(x n,y m ) Notice that there is a single white line space inbetween changing for a new value in the y coordinate If we want to plot different sets of data in a single file we may use a double white space Different sets of data can then be accessed using the index command, where data sets in a file are indexed from 0 To plot a surface from this data, we can use splot resultsdat using 1:2:3 with line Another way to plot different sets of data would be to put it in a different column In order to plot contours from a file of this format, the quickest way to view contours is to issue the following commands: set parametric set contour base set view 0,0,1 unset surface set cntrparam levels 5 splot resultsdat using 1:2:3 with line If you wish to produce better quality graphs you must convert the contours into a data file and them print them using the plot command To do this, we issue the following commands before those listed above: set terminal table set output resultstab The file resultstab will now contain the data needed to plot just the contours You can now set up linestyles manually for each of the contours using the index command to access each one For example the command to plot the tab file may look something like: set terminal postscript eps color solid enhanced set output figureeps set style line 1 lt 1 lw 3 p resultstab i 0 w l ls 1,\ resultstab i 1 w l,\ resultstab i 2 w l,\ resultstab i 3 w l,\ resultstab i 4 w l 2

11 Working with functions Gnuplot Examples Sheet 1 Run the command gnuplot from a terminal Once the program is loaded the command line should now look like: 2 Enter the following: gnuplot> plot sin(x) w l you should see a graph for y = sin(x) appear on screen 3 Similarly, try to generate plots for the following function: (a) y = e x (b) y = e x sin(x) x (c) y = e x2 and y = cosh(x) Multiple plots are separated by a comma 4 Add labels, change the ranges on view and move the key to a different area using the set commands After each command, you need to replot for the changes to take effect Examples may be: set xrange [0:6] set key top left 5 Change the title of your plot using set title, and also the title of the plot within the key 3D Plots 1 Issue the command reset to reset all previous commands 2 Plot the function y = e sin(x)sin(y) xy using the command: splot exp( -sin(x)*sin(y)/x/y ) w l 1

12 3 Use your mouse to spin the plot around to look at it from different angles 4 Now plot contours using the following commands: set contour base set cntrparam levels 15 5 Change the contours from the base to the surface, replot 6 Change the number of samples in the graph using the commands: set samples 51 set isosample 51 7 Try adding more fancy graphics using the commands or set pm3d set hidden WARNING!! these commands may take up a lot of processing (time) to generate plots Output to file In gnuplot, the terminal denotes the output direction for your plots This could be any number of different formats ranging from the default screen option (X11) to encapsulated postscript (eps) or portable network graphics (png) We change terminal (output direction) using the set command 1 Changing to eps, the most workable format with L A TEX2εis executed with the command: set terminal postscript eps This sets the output type/direction, but NOT the destination To set the file which you wish to send the information to we use the command set output So to create a picture of the plot as the file mygrapheps, we could use the command: set output mygrapheps 2

13 2 Then every timeyou issue aplot commandtheinformationissent tothefile (previous information is not overwritten, so multiple figures can be stored in one file) So to create a figure in the file choose a previous plot command to issue, for example: splot exp( -sin(x)*sin(y)/x/y ) w l 3 Can you find where the graph is on your hard drive? Try to view it and see if it looks as you would expect 4 By issuing a set output command again the cache is cleared and a new figure file is created Plot files, Scripting and Variables One of the most powerful aspects of gnuplot is the ability to create script files to generate multiple plots from different files into a standard format You may be able to generate all figures for your thesis with a single command, meaning that changing the look of each and every one of the figures can be done simultaneously 1 First create a empty file called myplotfileplt IN THE SAME DIRECTORY AS WHICH YOU ARE WORKING WITH GNUPLOT! Check which directory gnuplot is working in with the command pwd, and move to a different directory with cd pathtodirectory 2 Open the file with a text editor (try using kate if you like) and type some gnuplot command into the file An example of what the file might look like is: reset set xlabel x set ylabel y p sin(x) title y=f(x) w l Then load the file by issuing the following command at the command line: load myplotfileplt You should see the graph of y = sin(x) appear on screen 3 Edit your plot file so that it generates an eps file using the terminal and output commands 4 Now let us introduce some variables to the plot file: 3

14 reset a = 2 xmin = 0 xmax = 4*atan(1) set xlabel x set ylabel y set xrange[xmin:xmax] p sin(x/a) title y=f(x) w l Notice that we can assign variable values, expressions, and use them inside commands such as the range command 5 Try out using variables for yourself 4