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Computational Approach to

Materials Science and Engineering

Prita Pant and M. P. Gururajan

January, 2012

Copyright c 2012, Prita Pant and M P Gururajan. Permissionis granted to copy, distribute and/or modify this document underthe terms of the GNU Free Documentation License, Version 1.3or any later version published by the Free Software Foundation;with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the sectionentitled GNU Free Documentation License.

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Module: gnuplot the plotting freeware

gnuplot is a freeware, primarily used for visualization of data, that is, plot-ting. Typically, the data used for plotting could be experimental, or gener-ated on a computer using a programming language; gnuplot itself can alsogenerate simple data for plotting.

In this chapter, we give a tutorial introductions to working with gnuplot.For further information, we recommend the reader to peruse some of thelinks listed in the references below.

A note: In these notes, sometimes, when the information on the gnuplot

terminal is too long to be shown verbatim, we have used two backslashes(\\) to identify the line break introduced by us.

1 Working with gnuplot

1.1 Invoking gnuplot

Open a terminal. Type gnuplot and Enter. You will get the following mes-sage and prompt.

G N U P L O T

Version 4.2 patchlevel 6

last modified Sep 2009

System: Linux 2.6.38-11-generic

Copyright (C) 1986 - 1993, 1998, 2004, 2007 - 2009

Thomas Williams, Colin Kelley and many others

Type help to access the on-line reference manual.The gnuplot FAQ is available from http://www.gnuplot.info/faq/

Send bug reports and suggestions to \\

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Terminal type set to wxtgnuplot>

1.2 Getting help

Type help in the gnuplot prompt and Enter. You get the following informa-tion.

gnuplot> help

gnuplot is a command-driven interactive function and data plotting \\program.

Any command-line arguments are assumed to be names of files containing

gnuplot commands, with the exception of standard X11 arguments, which \\

are

processed first. Each file is loaded with the load command, in the \\

order

specified. gnuplot exits after the last file is processed. The \\

special

filename "-" is used to denote standard input. When no load files \\

are named,gnuplot enters into an interactive mode. See help for \\

batch/interactive

for more details.

gnuplot is case sensitive (commands and function names written \\

in lowercase

are not the same as those written in CAPS). All command names \\

may be

abbreviated as long as the abbreviation is not ambiguous. Any \\

number ofcommands may appear on a line (with the exception that \\

load or call must

be the final command), separated by semicolons (;). \\

Strings are indicated

with quotes. They may be either single or double quotation \\

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marks, e.g.,

load "filename"

cd dir

although there are some subtle differences \\

(see syntax for more details).

Press return for more:

You can continue with reading more information on gnuplot using the Enter

keystroke. After all the information is shown, you get the gnuplot> promptback. This help page also lists all the topics on which help is available.For example, if you need help on colornames, typing help colornames fol-lowed by the Enter keystroke on the gnuplot prompt gets you the relevantinformation.

gnuplot> help colornames

Gnuplot knows a limited number of color names. You can use these to define

the color range spanned by a pm3d palette, or to assign a terminal-independent

color to a particular linetype or linestyle. To see the list of known color

names, use the command show palette colornames.See set palette, linestyle.

gnuplot>

1.3 Testing

Typing test on the gnuplot prompt gets a gnuplot test window as shownbelow.

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Figure 1: The test window that pops up on typing test at the gnuplot prompt.

1.4 Modes of working

One can work with gnuplot in two modes. The first is the interactive mode;in this mode, we can keep giving commands to gnuplot and it executes themimmediately. On the other hand, it is also possible to run it the script mode;in this mode, all the commands are kept in a file and the processing startswith the load command:

load "./test.plt"

As noted above, the typical script file is given an extension of .plt.

1.4.1 Plotting sin(x) in interactive mode

Plotting a function in interactive mode is very easy. All you need to do is totype plot sin(x) at the gnuplot prompt. The plot generated is shown inthe Figure. 2.

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Figure 2: The plot of sin(x).

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gnuplot also allows the use of abbreviations; for example, p sin(x), plsin(x), and plo sin(x) are all equivalent to plot sin(x) and producethe same result; as long as the abbreviation is unambiguous (that is, theabbreviation can uniquely identify a single gnuplot command) it would work.

1.4.2 Plotting sin(x) using a script file

If we write all the gnuplot commands in a file (say, filename.plt), we canuse the command load "filename.plt" at the gnuplot command prompt

and obtain the same effect.

Here is the file for plotting sin(x); note that gnuplot identifies comments bythe use of the # symbol. In data files too, we can use # to write informationabout data for a human reader; gnuplot would disregard these lines whileplotting.

# This is a comment! Plotting sin(x) with gnuplot

plot sin(x)

1.5 Plotting more than one curve in the same figure

The following script, for example, plots sin(x) and cos(x) in the samefigure, with lines and points; the sin(x) is plotted with filled circles whilecos(x) is plotted with filled squares. In addition, the script also shows howto do the following:

Make the plot square;

Set the x-range (from 0 to 2, in this case);

Set the y-range (from -1.1 to 1.1, in this case);

Label the x- and y-axes; and,

Give a title to the plot.

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# Grain size data at heating rate of 10 K/s

# The first column is the peak temperature (K)# The second column is the Mean Volumetric Grain Size (in microns)

# The Third column is the standard deviation

# The fourth column is the number of grains

# The data is from Kumkum Banerjee, Matthias Millitzer,

# Michel Perez, and Xiang Wang, Nonisothermal austenite

# grain growth kinetics in a microalloyed X80 linepipe

# steel, Metallurgical and Materials Transactions A,

# Vol. 41, No. 12, pp. 3161-3172, December 2010.

1223 6.0 0.52 14971423 15.0 0.60 670

1623 61.0 0.53 763

grainsize100KperS.dat

# Grain size data at heating rate of 100 K/s

# The first column is the peak temperature (K)

# The second column is the Mean Volumetric Grain Size (in microns)

# The Third column is the standard deviation

# The fourth column is the number of grains# The data is from Kumkum Banerjee, Matthias Millitzer,

# Michel Perez, and Xiang Wang, Nonisothermal austenite

# grain growth kinetics in a microalloyed X80 linepipe

# steel, Metallurgical and Materials Transactions A,

# Vol. 41, No. 12, pp. 3161-3172, December 2010.

1223 4.4 0.47 1700

1423 11.0 0.54 839

1623 33.0 0.52 514

grainsize1000KperS.dat

# Grain size data at heating rate of 1000 K/s

# The first column is the peak temperature (K)

# The second column is the Mean Volumetric Grain Size (in microns)

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The first thing to notice is that gnuplot ignores lines that start with the (#)

symbol; hence, it is easy to incorporate all the relevant information aboutthe data for a human reader but make gnuplot ignore the same. The secondaspect is that simple plot tells gnuplot to plot the first two columns of thedata with the first column being the x-axis and the second being the y-axis.

We can get a plot with labeled axes and appropriate title by executing thefollowing script. We also draw a line through the data points as a guide tothe eye. The resultant plot is shown in Figure. 6.

set xlabel "Temperature (in K)"

set ylabel "Grain size (in microns)"

plot "grainsize10KperS.dat" with linespoints title "Heating rate: 10 K/s"

Figure 6: The plot of grain size versus temperature, with labeled axes and aline drawn as a guide to the eye.

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Figure 13: The 3D plot of exp((x2 + y2))

Figure 14: The 3D plot of exp((x2 + y2)) with denser isolines

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set pm3d

set contourset xrange[-2:2]

set yrange[-2:2]

set isosamples 41,41

f(x,y) = exp(-x*x-y*y)

splot f(x,y)

Figure 16: The 3D plot of exp((x2 + y2)) with contours

2 References and further reading gnuplot manual

See http://www.gnuplot.info for FAQ, documentation and other rel-evant links.

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