Andrea Mignone Physics Department, University of Torino AA 2020-2021 What is Gnuplot ?
• Gnuplot is a free, command-driven, interactive, function and data plotting program, providing a relatively simple environment to make simple 2D plots (e.g. f(x) or f(x,y));
• It is available for all platforms, including Linux, Mac and Windows (http://www.gnuplot.info)
• To start gnuplot from the terminal, simply type > gnuplot
• To produce a simple plot, e.g. f(x) = sin(x) and f(x) = cos(x)^2
gnuplot> plot sin(x) gnuplot> replot (cos(x))**2 # Add another plot
• By default, gnuplot assumes that the independent, or "dummy", variable for the plot command is "x” (or “t” in parametric mode). Mathematical 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.
• Gnuplot supports the same operators of the C programming language, except that most operators accept integer, real, and complex arguments.
• Exponentiation is done through the ** operator (as in FORTRAN) Using set/unset
• The set/unset commands can be used to controls many features, including axis range and type, title, fonts, etc… • Here are some examples:
Command Description set xrange[0:2*pi] Limit the x-axis range from 0 to 2*pi, set ylabel “f(x)” Sets the label on the y-axis (same as “set xlabel”) set title “My Plot” Sets the plot title set log y Set logarithmic scale on the y-axis (same as “set log x”) unset log y Disable log scale on the y-axis set key bottom left Position the legend in the bottom left part of the plot set xlabel font ",18" Change font size for the x-axis label (same as “set ylabel”) set tic font ",18" Change the major (labelled) tics font size on all axes. set samples 2500 Set the number of points used to draw a function.
• Immediate help is available inside gnuplot via the "help" command. Plotting Datafiles
• Gnuplot can also plot ASCII datafile in multicolumn format; file.dat # Comments can be placed here x0 y0 z0 . x1 y1 z1 . xN yN zN …
• To plot a multi-column datafile using the 1st column for the abscissa and the 2nd column as the ordinate, use
gnuplot> plot “file.dat” using 1:2
• Add a second plot using 1st (=x) and 3rd (=z) columns:
gnuplot> replot “file.dat” using 1:3
• If the “using” keyword is not specified, 1st and 2nd columns are assumed:
gnuplot> plot “file.dat”
Example of Plotting Styles
• When plotting datafiles, Gnuplot uses symbols:
gnuplot> plot “file.dat”
• To join symbols with lines, use
gnuplot> plot “file.dat” with lines Datafiles containing multiple datasets
• A single datafile may also include more than one data set, file.dat which must be separated by a pair of empty lines, e.g. x1 y1 th 0 dataset x2 y2 x3 y3 • In this case you can tell gnuplot which dataset should be a1 b1 read using the ‘index’ keyword. For instance, 1st dataset a2 b2 a3 b3 a4 b4 gnuplot> plot “file.dat” using 1:2 index 0 c d will plot the 3 points (x , y ), (x , y ), (x ,y ). 1 1 1 1 2 2 3 3 c2 d2 c d • Likewise 2nd dataset 3 3 c4 d4 c5 d5 gnuplot> plot “file.dat” using 1:2 index 2 c6 d6 .
will plot the 6 points (c1, d1), (c2, d2) . (c6,d6). Creating Scripts for Gnuplot
• A Gnuplot script is a simple text file (with the extension “.gp”) containing a set of instructions to produce the desired plot. • Consider the following file, “myscript.gp”
reset # force all graph-related options to default values fname = “myfile.dat” # file name
set autoscale xfixmin # axis range automatically scaled to include the range set autoscale xfixmax # of data to be plotted
set tics font ",18" set xlabel "x" font ",18" set ylabel "y" font ",18"
set lmargin at screen 0.1 # set size of left margin set rmargin at screen 0.82 # set size of right margin set bmargin at screen 0.12 # set size of bottom margin set tmargin at screen 0.95 # set size of top margin plot fname using 1:3 • Comments are preceded with a “#” symbol.
• From gnuplot, you can now invoke this script using the “load” command:
gnuplot> load “myscript.gp” Producing Datafiles from C++
• There’re basically two ways to produce a multicolumn ASCII datafile from the output of a C++ program: 1. [Simple, not very general] By redirecting the output of a program to file: ./myprogram > myprogram.dat
The ">" sign is used for redirecting the output of a program to something other than stdout (standard output, which is the terminal by default). Similarly, the >> appends to a file or creates the file if it doesn't exist.
2. [Clever, more general] By creating the file using the ofstream (or similar) class in C++
#include . ofstream fdata; // declare Output stream class to operate on files fdata.open(“decay.dat”); // open output file . for (. )< fdata x0 y1 f(0,1) . . . xN y1 f(N,1) ß . . . ß x0 yN f(0,N) . . . xN yN f(N,N) Visualizing 2D Arrays
• Gnuplot can be used to display 2D arrays using the “splot” command instead of “plot”.
• Different visualizations are possible:
Colored maps gnuplot> set surface gnuplot> set hidden3d gnuplot> splot “data.dat” u 1:2:3 w lines
gnuplot> set contour gnuplot> unset surface gnuplot> set view map gnuplot> set cntrparam level 20 gnuplot> splot "elliptic.dat" u 1:2:3 w lines
gnuplot> set pm3d map gnuplot> splot “data.dat” u 1:2:3 More on pm3d map
• Pm3D map is a useful plotting style for function of 2D variables. Some tips: – Exact axis range can be forced using
gnuplot> set autoscale xfixmin gnuplot> set autoscale xfixmax gnuplot> set autoscale yfixmin gnuplot> set autoscale yfixmax gnuplot> splot “file.dat”
– Gray-to-rgb mapping can be set through
gnuplot> set palette defined
– A color gradient can be defined and used to give the rgb values.
gnuplot> set palette defined (0 "blue", 1 "white", 2 "yellow") Slicing Datasets: the “every” keyword
• The keyword “every” specifies which datalines (subsets) within a single data set are to be plotted. It has the following syntax:
plot 'file' every I:J:K:L:M:N
I J K L M N Line Data block First line First data Last line Last data increment increment block block
plot 'file' every 2 # Plot every 2 lines plot 'file' every ::3 # Plot starting from the 3rd line plot 'file' every ::3::15 # Plot lines 3-15
• Note: the increments default is set to unity, the start values to the first point or block, and the end values to the last point or block. Slicing Datasets: taking x- and y- slices
• In a 2D datasets (see “Writing 2D Arrays”), we can use plot with the every keyword to produce 1D cuts along a given direction.
• To take an x-slice (a plot at constant y along the x-direction), you may use
j = 2 # Fix the vertical index j = 2 (= 3rd block) plot fname using 1:3 every . (j)::(j) with linespoint
# This is equivalent to (expliciting writing the increment and starting indices): plot fname using 1:3 every 1:1:0:(j)::(j) with linespoint pt 4
• To take an y-slice (a plot at constant x- along the y-direction), you may use
i = 1 # Fix the horizontal index i = 1 (= 2nd block) plot fname using 2:3 every ::(i)::(i)
# Note: the previous command does not allow data points to be connected by lines. # If you wish to connect data points with lines, you may “cheat” # using the splot command:
set view map splot fname using 2:2:3 every ::(i)::(i) w lp Creating Animations
• Animations can be built using the do for[] in gnuplot (v ≥ 4.6).
• Consider the following example (simple_animation1.gp):
omega = 2.0*pi; ntot = 250 # Number of frames in one period dt = 1.0/ntot # The increment between frames do for [n=0:2*ntot]
• If your gnuplot support .png, .gif or .jpeg terminal, images can be saved to disk:
set term png # From now on, plots will be done on png terminal # and not on screen omega = 2.0*pi; ntot = 250 # Number of frames in one period dt = 1.0/ntot # The increment between frames do for [n=0:2*ntot] < fname = sprintf ("sin_%04d.png",n) # File name set output fname # Redirect output to file t = n*dt # Time plot sin(x - omega*t) >Trajectory: 2D Animation
• The following script demonstrate how a trajectory can be animated:
set xrange [-1:1] # Always a good idea to set yrange [-1:1] # fix the axis range
set pointsize 2 # symbol size set style line 2 lc rgb '#0060ad' pt 7 # circle do for [ii=1:3762]
• An improved version adds the Sun (in green) and a red wake (taken from Animations/kepler*.*): . ntail = 50 # number of points to draw in the tail ninc = 3 # increment between frames
# Add the sun in the center as a green filled circle set object circle at first 0,0 size scr 0.01 \ fillcolor rgb 'green’ fillstyle solid