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POEfficiently create a density plot for high-density regions, points for sparse regions
 

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  1. POEfficiently create a density plot for high-density regions, points for sparse regions
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    <p>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:</p> <pre><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] &lt;= minperbin] for i in range(len(H[0,:]))] lowxrightedges = [[xedges[i+1] for j in range(len(H[:,i])) if H[j,i] &lt;= minperbin] for i in range(len(H[0,:]))] lowyleftedges = [[yedges[-(j+2)] for j in range(len(H[:,i])) if H[j,i] &lt;= minperbin] for i in range(len(H[0,:]))] lowyrightedges = [[yedges[-(j+1)] for j in range(len(H[:,i])) if H[j,i] &lt;= 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] &lt;= x[i] and x[i] &lt;= lowxrightedges[j] and lowyleftedges[j] &lt;= y[i] and y[i] &lt;= lowyrightedges[j]] for i in range(len(x))] lowdatay = [[y[i] for j in range(len(lowyleftedges)) if lowxleftedges[j] &lt;= x[i] and x[i] &lt;= lowxrightedges[j] and lowyleftedges[j] &lt;= y[i] and y[i] &lt;= 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') </code></pre> <p>This code produces an image that looks like this:</p> <p><img src="https://i.stack.imgur.com/CuNg0.jpg" alt="countour test"></p> <p>However, when used on larger data sets the program takes several seconds to minutes. Any thoughts on how to speed this up? Thanks!</p>
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