I need to make a plot that functions like a density plot for high-density regions on the plot, but below some threshold uses individual points. I couldn't find any existing code that looked similar to what I need in the matplotlib thumbnail gallery or from google searches. I have a working code I wrote myself, but it is somewhat tricky and (more importantly) takes an unacceptably long time when the number of points/bins is large. Here is the code:
import numpy as np
import math
import matplotlib as mpl
import matplotlib.pyplot as plt
import pylab
import numpy.random
#Create the colormap:
halfpurples = {'blue': [(0.0,1.0,1.0),(0.000001, 0.78431373834609985, 0.78431373834609985),
(0.25, 0.729411780834198, 0.729411780834198), (0.5,
0.63921570777893066, 0.63921570777893066), (0.75,
0.56078433990478516, 0.56078433990478516), (1.0, 0.49019607901573181,
0.49019607901573181)],
'green': [(0.0,1.0,1.0),(0.000001,
0.60392159223556519, 0.60392159223556519), (0.25,
0.49019607901573181, 0.49019607901573181), (0.5,
0.31764706969261169, 0.31764706969261169), (0.75,
0.15294118225574493, 0.15294118225574493), (1.0, 0.0, 0.0)],
'red': [(0.0,1.0,1.0),(0.000001,
0.61960786581039429, 0.61960786581039429), (0.25,
0.50196081399917603, 0.50196081399917603), (0.5,
0.41568627953529358, 0.41568627953529358), (0.75,
0.32941177487373352, 0.32941177487373352), (1.0,
0.24705882370471954, 0.24705882370471954)]}
halfpurplecmap = mpl.colors.LinearSegmentedColormap('halfpurples',halfpurples,256)
#Create x,y arrays of normally distributed points
npts = 1000
x = numpy.random.standard_normal(npts)
y = numpy.random.standard_normal(npts)
#Set bin numbers in both axes
nxbins = 25
nybins = 25
#Set the cutoff for resolving the individual points
minperbin = 1
#Make the density histrogram
H, yedges, xedges = np.histogram2d(y,x,bins=(nybins,nxbins))
#Reorient the axes
H = H[::-1]
extent = [xedges[0],xedges[-1],yedges[0],yedges[-1]]
#Compute all bins where the density plot value is below (or equal to) the threshold
lowxleftedges = [[xedges[i] for j in range(len(H[:,i])) if H[j,i] <= minperbin] for i in range(len(H[0,:]))]
lowxrightedges = [[xedges[i+1] for j in range(len(H[:,i])) if H[j,i] <= minperbin] for i in range(len(H[0,:]))]
lowyleftedges = [[yedges[-(j+2)] for j in range(len(H[:,i])) if H[j,i] <= minperbin] for i in range(len(H[0,:]))]
lowyrightedges = [[yedges[-(j+1)] for j in range(len(H[:,i])) if H[j,i] <= minperbin] for i in range(len(H[0,:]))]
#Flatten and convert to numpy array
lowxleftedges = np.asarray([item for sublist in lowxleftedges for item in sublist])
lowxrightedges = np.asarray([item for sublist in lowxrightedges for item in sublist])
lowyleftedges = np.asarray([item for sublist in lowyleftedges for item in sublist])
lowyrightedges = np.asarray([item for sublist in lowyrightedges for item in sublist])
#Find all points that lie in these regions
lowdatax = [[x[i] for j in range(len(lowxleftedges)) if lowxleftedges[j] <= x[i] and x[i] <= lowxrightedges[j] and lowyleftedges[j] <= y[i] and y[i] <= lowyrightedges[j]] for i in range(len(x))]
lowdatay = [[y[i] for j in range(len(lowyleftedges)) if lowxleftedges[j] <= x[i] and x[i] <= lowxrightedges[j] and lowyleftedges[j] <= y[i] and y[i] <= lowyrightedges[j]] for i in range(len(y))]
#Flatten and convert into numpy array
lowdatax = np.asarray([item for sublist in lowdatax for item in sublist])
lowdatay = np.asarray([item for sublist in lowdatay for item in sublist])
#Plot
fig1 = plt.figure()
ax1 = fig1.add_subplot(111)
ax1.plot(lowdatax,lowdatay,linestyle='.',marker='o',mfc='k',mec='k')
cp1 = ax1.imshow(H,interpolation='nearest',extent=extent,cmap=halfpurplecmap,vmin=minperbin)
fig1.colorbar(cp1)
fig1.savefig('contourtest.eps')
This code produces an image that looks like this:
However, when used on larger data sets the program takes several seconds to minutes. Any thoughts on how to speed this up? Thanks!
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