Gnuplotting

October 17th, 2012 | No Comments

Some data could be nicely visualized by representing them as arrows. For example, assume that we have done an experiment where we played something to a subject through three loudspeakers and the subject should name the direction where he or she perceived it. In Fig. 1 we show the named direction by the direction of the arrows. The color of the arrow indicates the deviation from the desired direction. A white and not visible arrow means no deviation and a dark red one a deviation of 40° or more.

Fig. 1 Vector field showing localization results. The arrows are pointing towards the direction the subject had named. The color indicates the deviation from the desired direction. (code to produce this figure, set_loudspeakers.gnu, data)

In gnuplot the with vectors command enables the arrows in the plot. It requires four parameters, x, y, dx, dy, where dx and dy controls the endpoint of the arrow as offset values to x,y. In our example the direction is stored as an angle, hence the following functions do the conversion to dx,dy. 0.1 defines the length of the arrows.

xf(phi) = 0.1*cos(phi/180.0*pi+pi/2)
yf(phi) = 0.1*sin(phi/180.0*pi+pi/2)

An optional fifth parameter controls the color of the vector together with the lc palette setting. The arrows start at x-dx,y-dy and point to x+dx,y+dy.

plot 'localization_data.txt' \
    u ($1-xf($3)):($2-yf($3)):(2*xf($3)):(2*yf($3)):4 \
    with vectors head size 0.1,20,60 filled lc palette

Tags: data, head, linecolor, palette, vectors

August 17th, 2012 | 2 Comments

As already mentioned gnuplot 4.6 overs an easier way to include loops in your code.
Here we are using it to create an animation of a set of head related impulse responses, which show differences in amplitude and arrival time at the left and right ear of a listener depending on the position of the source.

Fig. 1 Video animation of head related impulse responses (HRIRs) (code to produce this figure, data)

In comparison to the additional file for the loop in Animation I – gif, now all we need is this small code block.

do for [ii=1:181] {
    set output sprintf('hrir_frame%03.0f.png',ii)
    set multiplot layout 2,1
    [...]
    plot 'ir.txt' u ($1*1000):2*ii-1 w l ls 1
    [...]
    plot 'ir.txt' u ($1*1000):2*ii w l ls 1
    [...]
}

Tags: animation, do, grid

July 16th, 2012 | 10 Comments

Sometimes it can be helpful to visualize a third dimension by the color of the line in the plot. For example in Fig. 1 you see a logarithmic sweep going from 0 Hz to 100 Hz. Here the frequency is decoded by the color of the line.

Fig. 1 A logarithmic sweep ranging from 0 Hz to 100 Hz and decoding the frequency with the line color (code to produce this figure, data)

This can be easily achieved by adding a lc palette to the plot command, which uses the values specified in the third row of the data file.

plot 'logarithmic_sweep.txt' u 1:2:3 w l lc palette

The palette can be defined as shown in the Multiple lines with different colors entry. But it can be set in a more easy way, by only setting the start and end color and calculating the colors in between. Therefore, we are picking the two hue values in GIMP (the H entry in Fig. 2 and Fig. 3) for the starting and ending color.

Fig. 2 Picking the HSV value corresponding to the given color of #09ad00.

Fig. 3 Picking the HSV value corresponding to the given color of #0025ad.

These colors are then used to specify the palette in HSV mode. The S and V values can also directly be seen in GIMP.

# start value for H
h1 = 117/360.0
# end value for H
h2 = 227/360.0
# creating the palette by specifying H,S,V
set palette model HSV functions (1-gray)*(h2-h1)+h1,1,0.68

Tags: HSV, lines, palette

June 10th, 2012 | 4 Comments

In one off the last entries we defined a color palette similar to the default one in Matlab. Now we will use a color palette with only a few discrete colors, as shown in Fig. 1. This can be useful if we want to see all values from a measurement lying above a given threshold.

Fig. 1 Photoluminescence yield plotted with a palette with discrete colors (code to produce this figure, data)

The trick is to set maxcolors to the number of colors you want in your plot. In addition, the colors to use can be specified by the defined command. Note, that the absolute values you specify in the palette definition were automatically scaled to your min and max values (0 and 18 in this case).

set palette maxcolors 3
set palette defined ( 0 '#000fff',\
                      1 '#90ff70',\
                      2 '#ee0000')

Tags: colormap, maxcolors, palette, rgb

May 22nd, 2012 | 3 Comments

In one of the last posts we have looked at how to plot equipotential lines. Here we want to plot the equipotential lines of two sources with different charges, like an electron and a positron.

Fig. 1 Equipotential lines of an electron and a positron (code to produce this figure, electron.gnu, positron.gnu)

In addition the sources should be plotted as well, as can be seen in Fig. 1. There the electron is drawn as a red sphere with some lightning effect and the positron as a red sphere. This effect can be achieved with Gnuplot by plotting a bunch of circles with slightly different color and size on top of each other.

set for [n=0:max-1] object n+object_number circle \
    at posx(x,n,max/1.0),posy(y,n,max/1.0) size size(n,max/1.0)
set for [n=0:max-1] object n+object_number \
    fc rgb blue(n,max/1.0) fillstyle solid noborder lw 0

The size and position are determined by the posx,poxy,size functions. The color is chosen according to the blue function for the electron, which is a little tricky and composed of the three color functions r,g,b. These functions generate a color gradient starting from the blue, which is used as the line color for the equipotential lines, into a slight white.

size(x,n) = s*(1-0.8*x/n)
r(x,n) = floor(240.0*x/n)
g(x,n) = floor(144.0*x/n)+96
b(x,n) = floor(67.0*x/n)+173
blue(x,n) = sprintf("#%02X%02X%02X",r(x,n),g(x,n),b(x,n))
posx(X,x,n) = X + 0.03*x/n
posy(Y,x,n) = Y + 0.03*x/n

The code shown so far is put into external functions (electron.gnu, positron.gnu) and can be used in any script to plot equipotential lines, as the one used to generate Fig. 1.

Fig. 2 Equipotential lines of two sources with different charges (code to produce this figure)

The position and size of the source are the parameters of the functions. Fig. 2 shows the result for a negative particle with twice the absolute charge of the positive charged particle.

# positron
x1 = 2; y1 = 1; q1 = 1
# electron
x2 = 1; y2 = 1; q2 = -2
call 'positron.gnu' x1 y1 '0.1'
call 'electron.gnu' x2 y2 '0.2'

Thanks to Gnuplotter for the original idea.

Tags: circle, cntrparam, contour, table

April 2nd, 2012 | No Comments

Since last month the new Gnuplot version 4.6 is officially available. There are a lot of interesting changes in this new version and we will cover the bigger ones within the next posts. Here we start with, in my opinion, the nicest new feature: block-structured conditions and loops.

Until 4.6 an iteration over different lines of code was only possible with the help of an extra file. This technique was used, for example, for the gif animation entry. There the loop was executed by

t = 0
end_time = 1
load 'bessel.plt'

with the file bessel.plt containing the code to execute within the loop

# bessel.plt
t = t + 0.02
outfile = sprintf('animation/bessel%03.0f.png',50*t)
set output outfile
splot u*sin(v),u*cos(v),bessel(u,t) w pm3d ls 1
if(t<end_time) reread;

This can now be reformulated in a much shorter way by applying the new do command and the block-structure given by the { }

do for [t=0:50] {
    outfile = sprintf('animation/bessel%03.0f.png',t)
    set output outfile
    splot u*sin(v),u*cos(v),bessel(u,t/50.0) w pm3d ls 1
}

Now there is no need for an additional file. The only thing to consider is the change of the index t, because for the for-loop t has to be an integer.

The block-structure can in the same way be applied to the if-statement.

Tags: 4.6, do, for, iteration

March 15th, 2012 | 4 Comments

Suppose you have an image and wanted to add some lines, arrows, a scale or whatever to it. Of course you can do this easily with Gnuplot as you can see in Fig. 1.

Fig. 1 Plotting a jpg image within your graph and adding a scale (code to produce this figure, image data). Image source: © SFTEP.

To plot the jpg image of the longnose hawkfish you have to tell the plot command that you have binary data, the filetype, and choose rgbimage as a plotting style. Also we ensure that the image axes are in the right relation to each other by setting ratio to -1.

set size ratio -1
plot 'fish.jpg' binary filetype=jpg with rgbimage

The scale needs a little more work, because Gnuplot can not plot a axis with tics to both directions of it. Hence we are using a bunch of arrows to achieve the same result. The text is than set by labels to the axis.

set arrow from 31,40 to 495,40 nohead front ls 1
set for [ii=0:11] arrow from 31+ii*40,35 to 31+ii*40,45 nohead \
   front ls 1
# set number and unit as different labels in order
# to get a smaller distance between them
set label '0'  at  25,57 front tc ls 1
set label 'cm' at  37,57 front tc ls 1
set label '5'  at 225,57 front tc ls 1
set label 'cm' at 237,57 front tc ls 1
set label '10' at 420,57 front tc ls 1
set label 'cm' at 442,57 front tc ls 1

Tags: arrow, binary, image, iteration, jpg, label

March 5th, 2012 | 3 Comments

If you want to compare some time series of data with each other it could be a good idea to plot them just onto a grid without anything else. Here we will generate a scale paper like grid and plot two simple functions on it.

Fig. 1 Plotting some time data on scale paper like grid (code to produce this figure)

In Fig. 1, two harmonic tone complexes are shown, plotted within the multiplot environment. But the thing to consider here is the grid below them. In order to get such a grid, we have to remove all borders and tics. This is done by the following code.

set style line 11 lc rgb '#ffffff' lt 1
set border 0 back ls 11
set tics out nomirror scale 0,0.001
set format ''

The second number of scale for the tics corresponds to the minor tics and must be greater than zero, otherwise no minor tics will appear.

In the last step we enable minor tics on both axes, set the style for the grid and define the grid itself.

set mxtics
set mytics
set style line 12 lc rgb '#ddccdd' lt 1 lw 1.5
set style line 13 lc rgb '#ddccdd' lt 1 lw 0.5
set grid xtics mxtics ytics mytics back ls 12, ls 13

Tags: grid, multiplot

February 20th, 2012 | No Comments

Most of you will probably know the problem of visualizing more than two dimensions of data. In the past we have seen some solutions to this problem by using color maps, or pseudo 3D plots. Here is another solution which will just plot a bunch of lines, but varying their individual colors.

Fig. 1 Plot of interaural time differences for different frequency channels, indicated by different colors (code to produce this figure, data)

For this we first define the colors we want to use. Here we create a transition from blue to green by varying the hue in equal steps. The values can be easily calculated with GIMP or any other tool that comes with a color chooser.

set style line 2  lc rgb '#0025ad' lt 1 lw 1.5 # --- blue
set style line 3  lc rgb '#0042ad' lt 1 lw 1.5 #      .
set style line 4  lc rgb '#0060ad' lt 1 lw 1.5 #      .
set style line 5  lc rgb '#007cad' lt 1 lw 1.5 #      .
set style line 6  lc rgb '#0099ad' lt 1 lw 1.5 #      .
set style line 7  lc rgb '#00ada4' lt 1 lw 1.5 #      .
set style line 8  lc rgb '#00ad88' lt 1 lw 1.5 #      .
set style line 9  lc rgb '#00ad6b' lt 1 lw 1.5 #      .
set style line 10 lc rgb '#00ad4e' lt 1 lw 1.5 #      .
set style line 11 lc rgb '#00ad31' lt 1 lw 1.5 #      .
set style line 12 lc rgb '#00ad14' lt 1 lw 1.5 #      .
set style line 13 lc rgb '#09ad00' lt 1 lw 1.5 # --- green

Then we plot our data with these colors and get Figure 1 as a result.

plot for [n=2:13] 'itd.txt' u 1:(column(n)*1000) w lines ls n

There the interaural time difference (ITD) between the right and left ear for different frequency channels ranging from 236 Hz to 1296 Hz is shown. As can be seen the ITD varies depending on the incident angle (azimuth angle) of the given sound.

Another possibility to indicate the frequency channels given by the different colors is to add a colorbox to the graph as shown in Figure 2.

Fig. 2 Plot of interaural time differences for different frequency channels, indicated by different colors as shown in the colorbox (code to produce this figure, data)

To achieve this we have to set the origin and size of the colorbox ourselves. Note, that the notation is not the same as for a rectangle object and uses only the screen coordinates which is a little bit nasty. In addition we have to define our own color palette, as has been discussed already in another colorbox entry. In a last step we add a second phantom plot to our plot command by plotting 1/0 using the image style in order to get the colorbox drawn onto the graph.

set colorbox user horizontal origin 0.32,0.385 size 0.18,0.035 front
set cbrange [236:1296]
set cbtics ('236 Hz' 236,'1296 Hz' 1296) offset 0,0.5 scale 0
set palette defined (\
    1  '#0025ad', \
    2  '#0042ad', \
    3  '#0060ad', \
    4  '#007cad', \
    5  '#0099ad', \
    6  '#00ada4', \
    7  '#00ad88', \
    8  '#00ad6b', \
    9  '#00ad4e', \
    10 '#00ad31', \
    11 '#00ad14', \
    12 '#09ad00' \
    )
plot for [n=2:13] 'itd.txt' u 1:(column(n)*1000) w lines ls n, \
   1/0 w image

Tags: colormap, data, for, label, lines, palette

February 3rd, 2012 | No Comments

In the first post regarding animations we have created a bunch of png files and combined them to a single gif animation. Now we want to generate again a bunch of png files, but combine them to a movie.

Fig. 1 Video animation of Huygens principle (code to produce this figure, loop function)

We create the png files in analogy to the gif example, hence we will discuss only the generation of the movie here. In order to compose a avi file from the png files we are using Mencoder. Gnuplot is able to directly start Mencoder by its system command.

# Create movie with mencoder
ENCODER = system('which mencoder');
if (strlen(ENCODER)==0) print '=== mencoder not found ==='; exit
CMD = 'mencoder mf://animation/*.png -mf fps=25:type=png -ovc lavc -lavcopts vcodec=mpeg4:mbd=2:trell -oac copy -o huygen.avi'
system(CMD)

The first two lines check if Mencoder is available and quit gnuplot if not. The Mencoder command itselfs gets the directory containing the png files mf://animation/*.png, frames per second and input type-mf fps=25:type=png, video -ovc and audio -oac options, and finally of course the output file -o huygen.avi.

In order to generate a webm video file for a web site, ffmpeg can be used to convert the video.

$ ffmpeg -i huygen.avi huygen.webm

Tags: animation, if, load, reread, system

Gnuplotting

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Vector field from data file

Animation III – video revisited

Using a palette as line color

Defining a palette with discrete colors

Electron and positron

Gnuplot 4.6 – do

Images within a graph

Scale paper like grid

Multiple lines with different colors

Animation II – video