## Gnuplot Manual and Tutorial

General:Main page Image Manipulation Graphics

Applications:CorelDraw Photoshop Photo Editor

On Linux:Gnuplot

1. GNUPLOT - version 3.7.1Gnuplot is a free, command-driven, interactive, function and data plotting program. Gnuplot can be run under DOS, Windows, Macintosh OS, BeOS, OS2, VMS, Linux, and many others. On Unix/Linux systems start Gnuplot by simply typing:

gnuplotFor help on any topic type

helpfollowed by the name of the topic.

2. FUNCTIONSIn general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC is valid. 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. x, y, and z are the default independent variables.

3. THE plot AND splot COMMANDS

plotandsplotare the primary commands in Gnuplot. They plot functions and data in many many ways.plotis used to plot 2-d functions and data, whilesplotplots 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 FunctionsTo plot functions simply type: plot [function] at the gnuplot> prompt.

For example, try:

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

3.2 Plotting DataDiscrete data contained in a file can be displayed by specifying the name of the data file (enclosed in quotes) on the

plotorsplotcommand 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 240You 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 using

4. CUSTOMIZING YOUR PLOTMany 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 customizationCustomization of the data columns, line titles, and line/point style are specified when the

plotcommand 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

plotcommand as follows:gnuplot> plot "force.dat" using 1:2 title 'Column' with lines, \ "force.dat" u 1:3 t 'Beam' w linespointsNote 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 customizationCustomization 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: > set nokey Put a label on the plot: > set label "yield point" at 0.003, 260 Remove all labels: > set nolabel Plot using log-axes: > set logscale Plot using log-axes on y-axis: > set nologscale; set logscale y Change the tic-marks: > set xtics (0.002,0.004,0.006,0.008) Return to the default tics: > set noxtics; set xticsOther 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.gnuplotThe 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 CHARACTERSIf your data file has a comment character other than # you can pass your data file through the tr filter as you plot it. For example, if your data file has % comment characters (for Matlab compatability) typing

gnuplot> plot "< tr '%' '#' < datafile"will replace all % characters with # characters prior to plotting.

6. GNUPLOT SCRIPTSSometimes, 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 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 pointsThen the total plot can be generated with the command: gnuplot> load 'force.p'

7. CURVE-FITTING WITH GNUPLOTTo 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 DATAGnuplot 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-PLOTGnuplot can plot more than one figure in a frame ( like subplot in matlab ) i.e., try:

set multiplot; set size 1,0.5; set origin 0.0,0.5; plot sin(x); set origin 0.0,0.0; plot cos(x) set nomultiplot

10. HARD-COPY (PLOTTING ON PAPER)You can create a Post-Script file of your plot by using the following files and commands. First, create a general-purpose script file:

# File name: saveplot - saves a plot as a Post-Script file set size 1.0, 0.5 set terminal postscript portrait enhanced "Helvetica" 14 replot set size 1,1 # return to normal size set terminal x11 replotThen you can simply type the following commands to create and laser-print the hard-copy.gnuplot> set out "force.ps" gnuplot> load 'saveplot' gnuplot> !lpr -Pteerlp1 force.ps

11. PRINTING TWO FIGURES ON ONE PAGEIf 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.psTo combine two Post-Script figures (plot1.ps and plot2.ps) on one page:

cat2 plot1.ps plot2.psNote: This page is modified from GNUPLOT - Manual and Tutorial.