GNUPLOT : Plot sum of distributions given by parameters in text file - gnuplot

Question

Suppose I have a text file with an arbitrary number of rows where each row gives some set of parameters that define a function (say the (x,y) location and sigmas (possibility unequal) of a 2D Gaussian). For example, in that case, the text file might contain:
100 112 3 4
97 38 8 9
88 79 3 9
...
...
102 152 9 5
I would like to plot (using pm3d) the SUM of all the distributions defined by the text file. How can that be done?

Answer 1

I would like to plot (using pm3d) the SUM of all the distributions defined by the text file. How can that be done?
I think that cannot be done in native gnuplot, at least not in any sane way that I know. That kind of number crunching is not really what gnuplot is designed to do.
Python, however, makes it pretty doable...
#!/usr/bin/env python2
import math
import numpy
import os
class Gaussian(object):
'''A 2D gaussian function (normalized), defined by
mx: x mean position
my: y mean position
sx: sigma in x
sy: sigma in y'''
def __init__(self, mx, my, sx, sy):
self.mx = float(mx)
self.my = float(my)
self.sx = float(sx)
self.sy = float(sy)
def value(self,x,y):
'''Evaluates the value of a Gaussian at a certain point (x,y)'''
prefactor = (1.0/(self.sx*self.sy*2*math.pi))
ypart = math.exp(-(x - self.mx)**2/(2*self.sx**2))
xpart = math.exp(-(y - self.my)**2/(2*self.sy**2))
return prefactor*ypart*xpart
def getLimits(self, devs):
'''Finds the upper and lower x and y limits for the distribution,
defined as points a certain number of deviations from the mean.'''
xmin = self.mx - devs*self.sx
xmax = self.mx + devs*self.sx
ymin = self.my - devs*self.sy
ymax = self.my + devs*self.sy
return (xmin, xmax, ymin, ymax)
def readGaussians(filename):
'''reads in gaussian parameters from an input file in the format
mx my sx sy
This makes some assumptions about how perfect the input file will be'''
gaussians = []
with open(filename, 'r') as f:
for line in f.readlines():
(mx, my, sx, sy) = line.split()
gaussians.append(Gaussian(mx, my, sx, sy))
return gaussians
def getPlotLimits(gaussians, devs):
'''finds the x and y limits of the field of gaussian distributions.
Sets the boundary a set number of deviations from the mean'''
# get the limits from the first gaussian and work from there
(xminlim, xmaxlim, yminlim, ymaxlim) = gaussians[0].getLimits(devs)
for i in range(1, len(gaussians)):
(xmin, xmax, ymin, ymax) = gaussians[i].getLimits(devs)
if (xmin < xminlim):
xminlim = xmin
if (xmax > xmaxlim):
xmaxlim = xmax
if (ymin < yminlim):
yminlim = ymin
if (ymax > ymaxlim):
ymaxlim = ymax
return (xminlim, xmaxlim, yminlim, ymaxlim)
def makeDataFile(gaussians, limits, res, outputFile):
'''makes a data file of x,y coordinates to be plotted'''
xres = res[0]
yres = res[1]
# make arrays of x and y values
x = numpy.linspace(limits[0], limits[1], xres)
y = numpy.linspace(limits[2], limits[3], yres)
# initialize grid of z values
z = numpy.zeros((xres, yres))
# compute z value at each x, y point
for i in range(len(x)):
for j in range(len(y)):
for gaussian in gaussians:
z[i][j] += gaussian.value(x[i], y[j])
# write out the matrix
with open(outputFile, 'w') as f:
for i in range(len(x)):
for j in range(len(y)):
f.write('%f %f %f\n' % (x[i], y[j], z[i][j]))
f.write('\n')
def makePlotFile(limits, outputFile):
'''makes a plot file for gnuplot'''
with open('plot.plt', 'w') as f:
f.write("#!/usr/bin/env gnuplot\n")
f.write("set terminal png font 'Courier'\n")
f.write("set output 'gaussians.png'\n")
f.write("set xr [%f:%f]\n" % (limits[0], limits[1]))
f.write("set yr [%f:%f]\n" % (limits[2], limits[3]))
f.write("set pm3d map\n")
f.write("plot '%s' with image\n" % outputFile)
# make plot file executable
os.system('chmod 755 plot.plt')
# plot
os.system('./plot.plt')
# name of input file
inputFile = 'data.dat'
# name of output (processed data)
outputFile = 'gaussians.dat'
# number of x and y points in plot
res = (100, 100)
# deviations from the mean by which to define Gaussian limits
devs = 3
# read in the gaussians from the data file
print 'reading in data...'
gaussians = readGaussians(inputFile)
# find the plot limits
limits = getPlotLimits(gaussians, devs)
# make the gaussian data file
print 'computing data for plotting...'
makeDataFile(gaussians, limits, res, outputFile)
# make the plot file
print 'plotting...'
makePlotFile(limits, outputFile)
This script produces the following output when run on your example data.