In gnuplot, you can create a histogram like
binwidth=#whatever#
set boxwidth binwidth
bin(x,width)=width*floor(x/width)+binwidth/2.0
plot "gaussian.data" u (bin($1,binwidth)):(1.0/10000) smooth freq w boxes
Currently, my bins seem to be centered on the right-edge. That is, the bin corresponding to x=0 has its right edge above zero. I would like to have the bins center-oriented. That is, I would like to have the center of each bin above the corresponding x values. I have tried messing with the arguments of bin(x,width) but haven't been successful. Any suggestions?
bin(x,width) = width*round(x/width)
should do the trick. You can simply visualize how the binning works:
binwidth = 0.5
round(x) = floor(x+0.5)
bin(x,width) = width*round(x/width)
set xrange [-2:2]
set xlabel "x"
set ylabel "bin position"
set grid
plot bin(x,binwidth)
gives
Note that values in [-0.25,0.25] are mapped to the bin at position 0, values in [0.25, 0.75] are mapped to the bin at position 0.5, and so forth.
Related
I am trying to plot a simple linear surface of the equation x + y + 2z = 0. This is my file:
set xrange [-4:4]
set yrange [-4:4]
set zrange [-4:4]
set xlabel 'x'
set ylabel 'y'
set zlabel 'z'
set xyplane at -4.0
unset xzeroaxis
unset yzeroaxis
unset zzeroaxis
set border 1023-128
set xtics out nomirror
set ytics out nomirror
set ztics out
set xtics add ('' -4)
set label 1 "{/:Italic x} + {/:Italic y} + 2{/:Italic z} = 0" at 4,4.2,-2 font 'Times New Roman, 11'
set arrow 1 from 0,0,-4 to 0,0,4 filled
set arrow 2 from 0,-4,0 to 0,4,0 filled
set arrow 3 from -4,0,0 to 4,0,0 filled
set arrow 4 from 3.9,4.1,-2.1 to 3.6,3.6,-2.5
unset key
set pm3d lighting primary 0.5 specular 0.6
set style fill transparent solid 1 noborder
set palette defined (0 "cyan", 1 "green")
unset colorbox
set pm3d depthorder
splot -x/2-y/2 with pm3d
The result
I'm using arrows to show the axis, since they seem to be stuck to the xy plane, and moving it causes further issues with the tics and border. But now the problem is that they are completely occluded by the surface. Is there a setting which allows to appear in front when they "pierce" the surface? I'd like to make the surface semitransparent, but the problem is clearer with these settings.
I guess your original idea, i.e. "piercing" a 3D surface with an arrow or line does not work right away in gnuplot, because gnuplot will not calculate the piercing points automatically. Please correct me if I am wrong and let me know in case there might be a simple solution to this.
As you did in your simple case, you can just split the arrow at the origin, because you already know the piercing point. However, what do you do if the surface is irregular or has several piercing points?
Solution: take the effort to create a segmented 3D arrow and let gnuplot automatically show and hide the surfaces as needed. This is probably getting close to what you had in mind. However, this solution will show surprises when you want to change the color of the arrows. So, there is still room for improvement.
Code: (simple version with arrows just along x,y,z axes)
### arrows "piercing" a 3D surface
reset session
set view equal xyz
set xyplane relative 0.0
set xrange [-4:4]
set yrange [-4:4]
set zrange [-4:4]
# create 3D arrow
r = 0.01 # radius of arrow
rHead = 0.1 # radius of arrrowhead
n = 6 # corners of arrow
set print $myArrow
do for [h=-100:90] {
do for [a=360/n:360:360/n] {
print sprintf("%g %g %g",r*cos(a),r*sin(a), h/100.)
}
print ""
}
do for [h=90:100] {
do for [a=360/n:360:360/n] {
print sprintf("%g %g %g",rHead*(100-h)/10.*cos(a), \
rHead*(100-h)/10.*sin(a), h/100.)
}
print ""
}
set print
unset key
unset colorbox
set pm3d depthorder
set samples 100
set isosamples 100
set view 65,46,1.3
# function to demonstrate "piercing"
f(x,y) = (sin(x*3)/x + sin(y*3)/y - 3)/2
splot \
f(x,y) w pm3d, \
$myArrow u 1:2:($3*4):(0) w pm3d lc rgb var, \
$myArrow u 2:($3*4):1:(0) w pm3d lc rgb var, \
$myArrow u ($3*4):1:2:(0) w pm3d lc rgb var
### end of code
Result:
gnuplot> help layer
A gnuplot plot is built up by drawing its various components in a fixed order.
This order can be modified by assigning some components to a specific layer
using the keywords `behind`, `back`, or `front`. For example, to replace the
background color of the plot area you could define a colored rectangle with the
attribute `behind`.
set object 1 rectangle from graph 0,0 to graph 1,1 fc rgb "gray" behind
The order of drawing is
behind
back
the plot itself
the plot legend (`key`)
front
Within each layer elements are drawn in the order
grid, axis, and border elements
pixmaps in numerical order
So basically you need to add the "front" attribute to the objects you want to appear in front of the plot.
I am simulating points in a sphere volume with radius 1. I generated 1.000.000 monte-carlo based points in this volume. To make a gnuplot histogram i calculated the length of each vector (every vector length is between 0 and 1). With 100 bins the histogram looks like:
gnuplot data histogram.
If someone is wondering why there no points greater than 0.91 are generated, i also dont know, but this is not the question here.
This is my gnuplot Code:
n=100 #number of intervals
max=1.0 #max value
min=0.0 #min value
width=(max-min)/n #interval width
#function used to map a value to the intervals
hist(x,width)=width*floor(x/width)+width/2.0
#settings
set xlabel "Radius"
set ylabel "Primarys/Intervall"
set xrange [-0.1:1.1]
set yrange [0:32000]
set boxwidth width*0.8
set style fill solid 0.5 #fillstyle
set tics out nomirror
#plot
plot "primaryPosition(1).csv" u (hist($1,width)):(1.0) smooth freq w boxes lc rgb"green"
In general: A Volume grows by r^3 to Radius r.
In my histrogram every spherical shell is one bin and the bin number is 100. So, as the bin number increases, the volume of each sperical shell grows cubically (with r^3). From this point of view, the histogram looks good.
But what i want to do is to plot the density of points per volume: points/shellvolume.
This should be a linear distribution from the center of the sphere to its border.
How can i tell gnuplot to divide each bin by its corresponding volume, which depends on the outer and the inner radius of each spherical shell?
The formula is: (4/3)pi(R^3-r^3) with R outer and r inner radius a shell.
The following example creates some random test data (should be 20'000 equally distributed random points).
One possibility would be that you first you create your histogram data via binning into a table and then you divide it by the volume of the shell.
By the way, the volume of a sphere shell is (4./3)*pi*(R**3-r**3), not the formula you've given. And why are you setting max < min? Maybe you want to fine tune the binning to your exact needs.
Code:
### histogram normalized by sphere shell volume
reset session
set view equal xyz
# create some test data
set print $Data
do for [i=1:20000] {
x = rand(0)*2-1
y = rand(0)*2-1
z = rand(0)*2-1
r = sqrt(x**2 + y**2 + z**2)
if (r <= 1) { print sprintf("%g %g %g %g",x,y,z,r) }
}
set print
n = 100 # number of intervals
min = 0.0 # max value
max = 1.0 # min value
myWidth=(max-min)/n # interval width
bin(x)=myWidth*floor(x/myWidth)
ShellVolume(r) = (4./3)*pi*((r+myWidth)**3-r**3)
set boxwidth myWidth absolute
set table $Histo
plot $Data u (bin($4)):(1) smooth freq
unset table
set multiplot layout 2,1
plot $Histo u 1:2 w boxes ti "Occurrences"
plot $Histo u 1:($2/ShellVolume($1)) w boxes ti "Density"
unset multiplot
### end of code
Result:
Is it possible in Gnuplot to emulate the drawing style of an analogue oscilloscope, meaning thinner+dimmisher lines on larger amplitudes, like this:?
The effect you see in the oscilloscope trace is not due to amplitude, it is due to the rate of change as the trace is drawn. If you know that rate of change and can feed it to gnuplot as a third column of values, then you could use it to modulate the line color as it is drawn:
plot 'data' using 1:2:3 with lines linecolor palette z
I don't know what color palette would work best for your purpose, but here is an approximation using a function with an obvious, known, derivative.
set palette gray
set samples 1000
plot '+' using ($1):(sin($1)):(abs(cos($1))) with lines linecolor palette
For thickness variations, you could shift the curve slightly up and down, and fill the area between them.
f(x) = sin(2*x) * sin(30*x)
dy = 0.02
plot '+' u 1:(f(x)+dy):(f(x)-dy) w filledcurves ls 1 notitle
This does not allow variable colour, but the visual effect is similar.
Another approach:
As #Ethan already stated, the intensity is somehow proportional to the speed of movement, i.e. the derivative. If you have sin(x) as waveform, the derivative is cos(x). But what if you have given data? Then you have to calculate the derivative numerically.
Furthermore, depending on the background the line should fade from white (minimal derivative) to fully transparent (maximum derivative), i.e. you should change the transparency with the derivative.
Code:
### oscilloscope "imitation"
reset session
set term wxt size 500,400 butt # option butt, otherwise you will get overlap points
set size ratio 4./5
set samples 1000
set xrange[-5:5]
# create some test data
f(x) = 1.5*sin(15*x)*(cos(1.4*x)+1.5)
set table $Data
plot '+' u 1:(f($1)) w table
unset table
set xtics axis 1 format ""
set mxtics 5
set grid xtics ls -1
set yrange[-4:4]
set ytics axis 1 format ""
set mytics 5
set grid ytics ls -1
ColorScreen = 0x28a7e0
set obj 1 rect from screen 0,0 to screen 1,1 behind
set obj 1 fill solid 1.0 fc rgb ColorScreen
x0=y0=NaN
Derivative(x,y) = (dx=x-x0,x0=x,x-dx/2,dy=y-y0,y0=y,dy/dx) # approx. derivative
# get min/max derivative
set table $Dummy
plot n=0 $Data u (d=abs(Derivative($1,$2)),n=n+1,n<=2? (dmin=dmax=d) : \
(dmin>d ? dmin=d:dmin), (dmax<d?dmax=d:dmax)) w table
unset table
myColor(x,y) = (int((abs(Derivative(column(x),column(y)))-dmin)/(dmax-dmin)*0xff)<<24) +0xffffff
plot $Data u 1:2:(myColor(1,2)) w l lw 1.5 lc rgb var not
### end of code
Result:
I have (x,y,z) points with coordinates like the following figure,
I would like to color the points based on their concentration.
The idea is to make a heatmap of points but in a 3D figure.
I would appreciate very much any help possible.
Regards.
Use data values in a 4th column to index a smooth color palette
splot DATA using 1:2:3:4 with points lc palette
The gnuplot development version now supports calculation of a point density function that can in turn be used to color individual points. This depends on a new set of commands that operate on a 3D grid of voxels. Sample script and output:
set title "Gaussian 3D cloud of 3000 random samples\ncolored by local point density"
rlow = -4.0; rhigh = 4.0
set xrange [rlow:rhigh]; set yrange [rlow:rhigh]; set zrange [rlow:rhigh]
set xtics axis nomirror; set ytics axis nomirror; set ztics axis nomirror;
set xyplane at 0
set xzeroaxis lt -1; set yzeroaxis lt -1; set zzeroaxis lt -1;
set log cb; set cblabel "point density"
# define 100 x 100 x 100 voxel grid
set vgrid $vdensity size 100
vclear $vdensity
# datablock $random has previously been loaded with 3000 points
# in a spherical Gaussian distribution about the origin
# The vfill command adds 1 to each voxel in a spherical region with radius 0.33
# around each point in $random
vfill $random using 1:2:3:(0.33):(1.0)
# plot the same points colored by local point density
splot $random using 1:2:3:(voxel($1,$2,$3)) with points pt 7 ps 0.5 lc palette
Full demo here: voxel demo in gnuplot online collection
I'm trying to fit data (histogram) in gnuplot. I tried various functions, and by looking at my histogram, I suppose the best fit is lognormal or gamma distribution, but I am not able to do this fit in gnuplot (Im rather new user of gnuplot).
Here is picture of histogram with gaussian distribution:
Also here is code in gnuplot:
reset
n=100 #number of intervals
max=15. #max value
min=0. #min value
width=(max-min)/n #interval width
#function used to map a value to the intervals
hist(x,width)=width*floor(x/width)
set term png #output terminal and file
set output "histogram.png"
set xrange [min:max]
set yrange [0:]
#to put an empty boundary around the
#data inside an autoscaled graph.
set offset graph 0.05,0.05,0.05,0.0
set xtics min,(max-min)/5,max
set boxwidth width*0.9
set style fill solid 0.5 #fillstyle
set tics out nomirror
set xlabel "Diameter"
set ylabel "Frequency"
#count and plot
#fac(x) = (int(x)==0) ? 1.0 : int(x) * fac(int(x)-1.0)
gauss(x)=a/(sqrt(2*pi)*sigma)*exp(-(x-mean)**2/(2*sigma**2))
fit gauss(x) 'hist.temp' u 1:2 via a, sigma, mean
plot 'data.list' u (hist($8, width)):(1.0) smooth freq w boxes lc rgb "green" notitle, \
gauss(x) w lines ls 2 lw 2
In file hist.temp is tabular output ( see this link )