I have a text file with 3 columns defining 3D points.
I want to paint every point in 3D and an ellipsoid centered in every point. I discard using the
set parametric
way because I need to iterate my text file.
So i think in doing something like this:
gnuplot
reset
set xrange [-5:5]
set yrange [-5:5]
set zrange [-5:5]
Rx = 1
Ry = 1
Rz = 1
fx(u,v) = column(2) + Rx*cos(u)*cos(v)
fy(u,v) = column(1) + Ry*sin(u)*cos(v)
fz(u,v) = column(3) + Rz*sin(v)
iMax = 200
splot "file.txt" using ($2):($1):($3) title "Input " with points ps 2 pt 7,\
for [i=0:iMax] "file.txt" u (fx(2*pi*i/iMax, pi*i/iMax)):(fy(2*pi*i/iMax, pi*i/iMax)):(fz(2*pi*i/iMax, pi*i/iMax)) notitle with points ps 2 pt 7
But the only think I can get is this strange and heavy (I know that they are a lot of iterations per row, but maybe there is another approach) pattern
Any help? Thank you.
There is something wrong for the mathematic point of view? Using something like this Im perfectly able to plot spheres, but without parsing data:
set parametric
R = 1
set urange [-pi/2:pi/2]
set vrange [0:2*pi]
splot R*cos(u)*cos(v),R*cos(u)*sin(v),R*sin(u) w l lc rgb "yellow"
I assume you want to plot the 2D surfaces of 3D ellipsoids. But the plot command has only a loop over i which is only 1D. This can not give a 2D surface. It might be possible to nest another 1D loop to get this approach to work.
I would suggest something else. Before plotting, you can store the center coordinates into a gnuplot array. Then you loop over this array and plot a sphere/ellipsoid using parametric mode.
This might be a starting point:
# This is the file with the center coordinates.
datafile = "ellipses.dat"
# The "stats" command stores the number of rows in the STATS_records variable.
stats datafile nooutput
num_rows = STATS_records
# Generate arrays which will contain the center coordinates of the ellipsoids.
array centers_x[num_rows]
array centers_y[num_rows]
array centers_z[num_rows]
# Read the center coordinates into the prepared arrays.
# I "misuse" the stats command. The "using" expression in parenthesis executes
# the respective commands and returns the value after the last comma: row + 1.
# This return value is not needed anywhere.
row = 1
stats datafile using (centers_x[row]=$1, \
centers_y[row]=$2, \
centers_z[row]=$3, \
row = row + 1) nooutput
# Output into an image file.
set terminal pngcairo
set output "ellipsoids.png"
# Set parameters for ellipsoids.
Rx = 0.1
Ry = 0.1
Rz = 0.7
# Use parametric mode for plotting.
set parametric
set urange [-pi/2:pi/2]
set vrange [0:2*pi]
# Finally plot:
splot datafile using 1:2:3 title "Input " with points ps 2 pt 7, \
for [i=1:num_rows] centers_x[i] + Rx*cos(u)*cos(v), \
centers_y[i] + Ry*cos(u)*sin(v), \
centers_z[i] + Rz*sin(u) notitle
Please doublecheck x, y, and z: I was not that careful. This is the result:
I have used this example data:
1 2 3
2 2 4
2 3 4
3 3 3
3 4 5
Arrays are available starting with gnuplot 5.2. For older versions, please search the internet for workarounds.
Related
I have data files "y.csv" which contains several runs (data sets) of an experiment in columns that I want to simultaneously fit to a single function. It should work like plot for [i=2:*] "y.csv" using 1:i
to automatically accomodate however many columns are in the file. Here is a short example data file:-
,B,C,D,E,F,G,H
01,,,,,,,
02,0.2200,0.2200,0.2080,0.2170,0.1530,,
03,0.2720,0.3230,0.2530,0.2380,0.2620,,
04,0.3900,0.3790,0.3770,0.3760,0.3500,,
05,0.5520,0.5600,0.5450,0.4830,0.4870,,
06,0.6640,0.6300,0.6830,0.6030,0.6520,,
07,0.6440,0.6900,0.6360,0.5960,0.6520,,
08,0.6030,0.6470,0.6190,0.6300,0.6280,,
09,0.5450,0.5890,0.5860,0.6830,0.5540,,
10,0.6370,0.6430,0.5800,0.5270,0.6180,,
11,0.6400,0.5600,0.7190,0.6780,0.7420,,
12,,,,,,,
I can automatically plot each of these columns, overlooking column headers, etc with:-
set datafile separator ","
set datafile columnheaders
set key autotitle columnheader
set key top left
set key title "Run"
set xrange [1:12]
set xlabel "Dilution (Proportional to log([]) )"
set ylabel "Response"
plot for [i=2:*] "y.csv" using 1:i with linespoints
I can set up a function to fit with the following:-
sig(x) = 1 / (1+exp(-x)) ; # Appears stable enough in gnuplot
A = 0.6 ; # Sigmoid Amplitude
B = 0.2 ; # Sigmoid offset
C = 6 ; # Center shift on displayed X axis
K = 1 ; # Shape factor
ssig(x) = B + A*sig(K*(x-C)) ; # Fit to this
And, I can fit to the first data column with:-
fit ssig(x) "y.csv" using 1:2 via A,B,C,K
But I can't work out the syntax of how to automatically do this over all the columns like I can for plotting. I was expecting something like
fit [1:-1:i=2:*] ssig(x) "y.csv" using 1:i via A,B,C,K
would iterate over the columns. I just don't understand the multi-branch syntax, and guess I am missing some simple concept.
Many thanks
Based on your comment you are actually not searching for a multi-branch fit, but you want to merge all columns into one single data set and perform a fit using all data points at the same time. This can be achieved quite easily by reshaping the data file into a datablock first:
set datafile separator ","
set table $FITDATA
plot for [i=2:*] "y.csv" u 1:i
unset table
unset datafile separator
sig(x) = 1 / (1+exp(-x)) ; # Appears stable enough in gnuplot
A = 0.6 ; # Sigmoid Amplitude
B = 0.2 ; # Sigmoid offset
C = 6 ; # Center shift on displayed X axis
K = 1 ; # Shape factor
ssig(x) = B + A*sig(K*(x-C)) ; # Fit to this
set fit errorvariables
fit ssig(x) $FITDATA u 1:2 via A,B,C,K
In the datablock the columns are separated by tabs, not comma, therefore one has to revert the datafile separator to default while fitting, and change it back again for plotting. Maybe someone else has a cleaner solution for this. set fit errorvariables saves the fit errors, so that they can be used for the plot title later.
set datafile separator ","
set datafile columnheaders
set key autotitle columnheader
set key top left
set key title "Run"
set xrange [1:12]
set xlabel "Dilution (Proportional to log([]) )"
set ylabel "Response"
plot for [i=2:*] "y.csv" u 1:i w lp, \
ssig(x) lc black lw 3 t "fit", \
keyentry t sprintf("A = %.3f ± %.3f", A, A_err), \
keyentry t sprintf("B = %.3f ± %.3f", B, B_err), \
keyentry t sprintf("C = %.3f ± %.3f", C, C_err), \
keyentry t sprintf("K = %.3f ± %.3f", K, K_err)
With palette it is easy to create color gradients
set view map
set samp 50,50
set palette defined (0 "blue", 1 "green", 2 "red")
spl "++" us 1:2:1 palette pt 5
Now I would like to apply transparency in vertical direction. The option lc rbg variable supports transparency via the alpha channel (see also here):
spl "++" us 1:2:1:(int(($2+5)/10*255)<<24) lc rgb var pt 5
But how can I translate the palette colors into rgb colors?
A second question: why I get only 10 horizontal rows, albeit I specified 50 in samp?
Easy answer first: When there is 2-dimensional sampling, either automatically from splot or explicitly from plot '++', the number of samples in the first dimension is controlled by set sample and the number of samples in the second dimension is controlled by set isosample.
Now the harder one. In gnuplot versions through the current 5.2.8 you cannot add transparency directly to the palette. You can, however, go through a multi-step process of saving the palette into a file or datablock and then reading it back it as an array of RGB colors. Once you have that array you can add an alpha channel value so that it expresses transparency as well. I will show this process using the datablock created by the command test palette. In older versions of gnuplot you may have to instead use the file created by set print "palette.save"; show palette palette 256;.
# save current palette to a datablock as a list of 256 RGB colors, one per line
set palette defined (0 "blue", 1 "green", 2 "red")
test palette
# print one line to show the format (cbval R G B NTSCval)
print $PALETTE[4]
# Create an array of packed RGB values
array RGB[256]
do for [i=1:256] {
Red = int(255. * word($PALETTE[i],2))
Green = int(255. * word($PALETTE[i],3))
Blue = int(255. * word($PALETTE[i],4))
RGB[i] = Red << 16 | Green << 8 | Blue
}
# Sample from '++' are generated to span ranges on the u and v axes
# I choose 1:256 so that the y coordinates match the range of array indices
set sample 50
set isosample 50
set urange [1:256]
set vrange [1:256]
set xrange [*:*] noextend
set yrange [*:*] noextend
# Now you can use colors stored in the array via colorspec `rgb variable`
# which will also accept an alpha channel in the high bits
plot "++" using 1:2:(RGB[int($2)]) with points pt 5 lc rgb variable
# The final step is to add an alpha channel as a function of y
# Here I go from opaque (Alpha = 0) to 50% transparent (Alpha = 127)
# This works because I know y will run from 1-256
ARGB(y) = RGB[int(y)] + (int(y/2)<<24)
plot "++" using 1:2:(ARGB($2)) with points pt 5 lc rgb variable
Output shown below.
The required command sequence, as you can see, is a mess.
It will be much easier in the next gnuplot release (5.4). The new version will provide a function palette(z) that converts from the current palette directly to a packed RGB value. Note that the palette() function isn't in the -rc1 testing version but will be in -rc2. So in version 5.4 all that palette/array/RGB manipulation can be replaced by
plot '++' using 1:2:(palette($2) + (int($2)<<24)) with points pt 5 lc rgb variable
Check also this: Gnuplot: transparency of data points when using palette
First of all, you can check what your defined palette is doing:
set palette defined (0 "blue", 1 "green", 2 "red")
test palette
You will get this:
Each channel (R,G,B) has a function with an input range [0:1] and an output range [0:1]. In this case it is a linear gradient.
So, you have to define such a function and put the channels together with the transparency (alpha) channel using the bit shift (see help operators binary).
The nice thing about a palette is that gnuplot takes care about the range. Here, you have to know minimum and maximum in advance and scale the color accordingly. You could use stats for this.
Code:
### your own palette with transparency
reset session
r(x) = x < 0.5 ? 0 : 2*x -1
g(x) = x < 0.5 ? 2*x : 2-2*x
b(x) = x < 0.5 ? 1-2*x : 0
a(y) = y
myColor(x,y) = (int(a((y-yMin)/(yMax-yMin))*0xff)<<24) + \
(int(r((x-xMin)/(xMax-xMin))*0xff)<<16) + \
(int(g((x-xMin)/(xMax-xMin))*0xff)<<8) + \
int(b((x-xMin)/(xMax-xMin))*0xff)
set samples 50
set isosamples 50
set size square
xMin=-5; xMax=5
yMin=-5; yMax=5
plot '++' u 1:2::(myColor($1,$2)) w p pt 5 ps 0.5 lc rgb var notitle
### end of code
Result:
I'm making some speedup graphs using histogram clustered. For each instance, I group the speedup reached using 2,4,8,16 and 32 computers. I also use a line to indicate the "linear speedup". However, for each instance/computer, I would like also to place a point on top of it, to indicate a value I'm comparing my speedup to.
I've tried to use the same strategy for plotting the boxes, but using points instead. However, the points are plotted on the same place, they are not obeying the ''clustered'' spacing.
Here is the code I'm using:
set yrange [0:105]
set grid ytics
set style line 1 lc rgb '#0e1111' lt 1 lw 2 pt -1 ps 1.0
set xlabel "Instance" font "sans, 18"
set ylabel "Normalized Speedup (In %)" font "sans, 18"
set style histogram clustered
plot for [COL=2:2] 'data.dat' using COL:xticlabels(1) title columnheade lc rgbcolor "black" lt -1 fs pattern 3,\
for [COL=3:3] 'data.dat' using COL:xticlabels(1) title columnheade lc rgbcolor "black" lt -1 fs pattern 1,\
"linear.t" t "Lin" with linespoints ls 1
Example of data
0 2 4 8 16 32
ta22 65.67 37.98 38.16 30.91 19.24
ta23 73.69 45.59 48.59 44.20 34.19
That's what I got. The points are what I would like to have.
Is it possible to have such a thing? It would also work like an error bar. However, without line and just a ''max''.
Thank you all!
I couldn't run your code. But, based on your image, I understood you problem.
To plot the points with you want, I created a file called points.dat.
0 2 4 8 16 32
ta22 75.67 47.98 48.16 40.91 29.24
ta23 83.69 55.59 58.59 54.20 44.19
This one nothing else is that your data + 10.
The gnuplot code
reset # Restore the default settings
set encoding utf8 # Selects the character encoding
set terminal pngcairo size 800,500 # Generates output in png
set output 'histogram.png' # The filename
set grid ytics ls -1 lc 'gray' # Grid lines ytics only
set yrange [0:100] # Yrange 0 to 100 (% ?)
set style data histograms # Type of data: histograms
set style histogram clustered gap 1 # Type of histogram: clustered with gap 1
set style fill transparent solid 1 border lt -1 # Style: fillstyle and border
stats 'points.dat' skip 1 matrix nooutput # Statistical summary with skip
# for header and without output
numRows = STATS_size_y # Y size of matrix (rows)
numCols = STATS_size_x # X size of matrix (columns)
array Value[numRows*(numCols-1)] # Create an array based on size of data
position = 0 # Count to position on array
# Loop for populate the array
do for [i=1:numRows]{
do for [j=2:numCols]{
# Statistical summary (with skip for header) at each value and without output
stats 'points.dat' skip 1 u j every ::i-1::i-1 nooutput
position = position + 1 # Increase the count of position
Value[position] = STATS_min # Define the array-value as result of statistical analysis
}
}
# Mapping functions:
# i-cluster/rows (x-values),
# j-column (y-values)
# ignore the cluster name ($1)
posX(i, j) = (i - 1) + 1.0*(j - numCols + 3)/numCols # To X-values
posY(i, j) = i == 1 ? Value[j] : Value[numCols - 1 + j] # To Y-values
# The plot itself as newhistogram and nested loops:
# i-loop to bars and title as columnheade
# j-loop to rows (x-values)
# k-loop to columns (y-values)
plot \
newhistogram ,\
for [i=2:numCols]\
'data.dat' u i:xticlabels(1) ls i-1 title columnheade,\
for [j=1:numRows] \
for [k=1:numCols-1] \
'+' u (posX(j, k)):(posY(j, k)) w p pt 5 ps 0.75 lc 'black' notitle
produces
I have x- and y-data points representing a star cluster. I want to visualize the density using Gnuplot and its scatter function with overlapping points.
I used the following commands:
set style fill transparent solid 0.04 noborder
set style circle radius 0.01
plot "data.dat" u 1:2 with circles lc rgb "red"
The result:
However I want something like that
Is that possible in Gnuplot? Any ideas?
(edit: revised and simplified)
Probably a much better way than my previous answer is the following:
For each data point check how many other data points are within a radius of R. You need to play with the value or R to get some reasonable graph.
Indexing the datalines requires gnuplot>=5.2.0 and the data in a datablock (without empty lines). You can either first plot your file into a datablock (check help table) or see here:
gnuplot: load datafile 1:1 into datablock
The time for creating this graph will increase with number of points O(N^2) because you have to check each point against all others. I'm not sure if there is a smarter and faster method. The example below with 1200 datapoints will take about 4 seconds on my laptop. You basically can apply the same principle for 3D.
Script: works with gnuplot>=5.2.0
### 2D density color plot
reset session
t1 = time(0.0)
# create some random rest data
set table $Data
set samples 700
plot '+' u (invnorm(rand(0))):(invnorm(rand(0))) w table
set samples 500
plot '+' u (invnorm(rand(0))+2):(invnorm(rand(0))+2) w table
unset table
print sprintf("Time data creation: %.3f s",(t0=t1,t1=time(0.0),t1-t0))
# for each datapoint: how many other datapoints are within radius R
R = 0.5 # Radius to check
Dist(x0,y0,x1,y1) = sqrt((x1-x0)**2 + (y1-y0)**2)
set print $Density
do for [i=1:|$Data|] {
x0 = real(word($Data[i],1))
y0 = real(word($Data[i],2))
c = 0
stats $Data u (Dist(x0,y0,$1,$2)<=R ? c=c+1 : 0) nooutput
d = c / (pi * R**2) # density: points per unit area
print sprintf("%g %g %d", x0, y0, d)
}
set print
print sprintf("Time density check: %.3f sec",(t0=t1,t1=time(0.0),t1-t0))
set size ratio -1 # same screen units for x and y
set palette rgb 33,13,10
plot $Density u 1:2:3 w p pt 7 lc palette z notitle
### end of script
Result:
Would it be an option to postprocess the image with imagemagick?
# convert into a gray scale image
convert source.png -colorspace gray -sigmoidal-contrast 10,50% gray.png
# build the gradient, the heights have to sum up to 256
convert -size 10x1 gradient:white-white white.png
convert -size 10x85 gradient:red-yellow \
gradient:yellow-lightgreen \
gradient:lightgreen-blue \
-append gradient.png
convert gradient.png white.png -append full-gradient.png
# finally convert the picture
convert gray.png full-gradient.png -clut target.png
I have not tried but I am quite sure that gnuplot can plot the gray scale image directly.
Here is the (rotated) gradient image:
This is the result:
Although this question is rather "old" and the problem might have been solved differently...
It's probably more for curiosity and fun than for practical purposes.
The following code implements a coloring according to the density of points using gnuplot only. On my older computer it takes a few minutes to plot 1000 points. I would be interested if this code can be improved especially in terms of speed (without using external tools).
It's a pity that gnuplot does not offer basic functionality like sorting, look-up tables, merging, transposing or other basic functions (I know... it's gnuPLOT... and not an analysis tool).
The code:
### density color plot 2D
reset session
# create some dummy datablock with some distribution
N = 1000
set table $Data
set samples N
plot '+' u (invnorm(rand(0))):(invnorm(rand(0))) w table
unset table
# end creating dummy data
stats $Data u 1:2 nooutput
XMin = STATS_min_x
XMax = STATS_max_x
YMin = STATS_min_y
YMax = STATS_max_y
XRange = XMax-XMin
YRange = YMax-YMin
XBinCount = 20
YBinCount = 20
BinNo(x,y) = floor((y-YMin)/YRange*YBinCount)*XBinCount + floor((x-XMin)/XRange*XBinCount)
# do the binning
set table $Bins
plot $Data u (BinNo($1,$2)):(1) smooth freq # with table
unset table
# prepare final data: BinNo, Sum, XPos, YPos
set print $FinalData
do for [i=0:N-1] {
set table $Data3
plot $Data u (BinNumber = BinNo($1,$2),$1):(XPos = $1,$1):(YPos = $2,$2) every ::i::i with table
plot [BinNumber:BinNumber+0.1] $Bins u (BinNumber == $1 ? (PointsInBin = $2,$2) : NaN) with table
print sprintf("%g\t%g\t%g\t%g", XPos, YPos, BinNumber, PointsInBin)
unset table
}
set print
# plot data
set multiplot layout 2,1
set rmargin at screen 0.85
plot $Data u 1:2 w p pt 7 lc rgb "#BBFF0000" t "Data"
set xrange restore # use same xrange as previous plot
set yrange restore
set palette rgbformulae 33,13,10
set colorbox
# draw the bin borders
do for [i=0:XBinCount] {
XBinPos = i/real(XBinCount)*XRange+XMin
set arrow from XBinPos,YMin to XBinPos,YMax nohead lc rgb "grey" dt 1
}
do for [i=0:YBinCount] {
YBinPos = i/real(YBinCount)*YRange+YMin
set arrow from XMin,YBinPos to XMax,YBinPos nohead lc rgb "grey" dt 1
}
plot $FinalData u 1:2:4 w p pt 7 ps 0.5 lc palette z t "Density plot"
unset multiplot
### end of code
The result:
i'm having some problems with gnuplot
I have to draw a cdf function and i'm interested in the values of variable x when F(x) is equal to 0.1 and 0.9
How can I tell Gnuplot to show me on the x axis the value corresponding to a given value on the y value (in my example those values are 0.1 and 0.9)
thanks
You're basically asking gnuplot to solve an equation. In your particular case, actually two equations: F(x)=0.1 and F(x)=0.9. As far as I know this cannot be done, but I might be wrong. What you can do if you simply want a graphical solution, is make a conditional plot, and ask that when F(x) is very close to 0.1 0.9, gnuplot plots something other than the function.
For example, assume f(x)=x^2 and you want to know "graphically" for which x f(x)=0.1. Then you can request the value abs(f(x) - 0.1) be small, for example < 0.01. Then tell gnuplot to go to zero (just an example!) if this is the case, otherwise plot f(x)=x^2:
f(x)=x**2
set xrange [-2:2]
set samples 1000
plot abs(f(x)-1) < 0.01 ? 0 : f(x)
Which yields:
The two peaks that go to zero mark graphically on the x axis the solution to the equation f(x)=0.1. Of course, you need gnuplot to sample this point in order to see a peak. Thus you need to play with set samples and set xrange.
From your question it is not clear whether you have a function F(x) as expression or just a x,y-data file. I assume that your function is monotonic increasing in x and y.
Two solutions come to my mind:
via simple linear interpolation
via curve fitting
Let's create some test data. For this, let's assume your function is known (as expression) and something like this (check help norm): F(x) = a*norm(b*x + c)
Let's take a = 1; b = 0.8; c = -4. In the example below, sampling will be only 8, just for illustration purpose.
You can easily set samples 200 and you will get the same results as for the curve fitting method below. From gnuplot 5.0 on, you could write the data into a datablock instead of a file on disk.
Data: SO22276755.dat
0 3.16712e-05
1.42857 0.002137
2.85714 0.043238
4.28571 0.283855
5.71429 0.716145
7.14286 0.956762
8.57143 0.997863
10 0.999968
Script 1: (basically works for gnuplot 4.6.0, March 2012)
### interpolate x-values
reset
FILE = "SO22276755.dat"
yis = '0.10 0.90'
yi(n) = real(word(yis,n))
xis = ''
xi(n) = real(word(xis,n))
Interpolate(yi) = (x1-x0)/(y1-y0)*(yi-y0) + x0
getXis(xis) = xis.(n=words(xis), n<words(yis) ? yi=real(word(yis,n+1)) : 0, \
y0<=yi && y1>=yi ? sprintf(" %g",Interpolate(yi)) : '')
set key left top noautotitle
set grid x,y
plot x1=y1=NaN FILE u (x0=x1,x1=$1):(y0=y1,y1=$2,xis=getXis(xis),y1) \
w l lc rgb "blue" ti "data", \
'+' u (xi=xi(int($0+1))):(yi=yi(int($0+1))):\
(sprintf("(%.4g|%.4g)",xi,yi)) every ::0::1 \
w labels point pt 7 lc rgb "red" right offset -1,0 ti "interpolated"
### end of script
Result:
Script 2: (basically works for gnuplot>=4.6.0, March 2012)
With this approach you are fitting your known function F(x) to constant lines, i.e. your desired values 0.1 and 0.9. For this, a file will be created (could be a datablock for gnuplot>=5.0) and it will basically look like this SO22276755.fit:
0 0.1
1 0.1
0 0.9
1 0.9
### interpolate x-values
reset
F(x) = a*norm(b*x+c) # function
a = 1
b = 0.8
c = -4
yis = '0.10 0.90'
yi(n) = real(word(yis,n))
xis = ''
xi(n) = real(word(xis,n))
set key left top noautotitle
set grid x,y
# create fit levels file
LEVELS = "SO22276755.fit"
set table LEVELS
set samples 2
plot for [i=1:words(yis)] '+' u (yi(i))
unset table
xmin = 0
xmax = 10
set xrange[xmin:xmax]
set samples 100
xis = ''
do for [i=1:words(yis)] {
xi = (xmin+xmax)*0.5 # set start value
fit F(xi) LEVELS u 1:2 index i-1 via xi
xis = xis.sprintf(" %g",xi)
}
plot F(x) w l lc rgb "web-green" ti "F(x)", \
'+' u (xi=xi(int($0+1))):(yi=yi(int($0+1))):(sprintf("(%.4g|%.4g)",xi,yi)) \
every ::0::1 w labels point pt 7 lc rgb "red" righ offset -1,0 ti "fitted"
### end of script
Result: