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

Question

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

Answer 1

This should do it:

import matplotlib.pyplot as plt, numpy as np, numpy.random, scipy

#histogram definition
xyrange = [[-5,5],[-5,5]] # data range
bins = [100,100] # number of bins
thresh = 3  #density threshold

#data definition
N = 1e5;
xdat, ydat = np.random.normal(size=N), np.random.normal(1, 0.6, size=N)

# histogram the data
hh, locx, locy = scipy.histogram2d(xdat, ydat, range=xyrange, bins=bins)
posx = np.digitize(xdat, locx)
posy = np.digitize(ydat, locy)

#select points within the histogram
ind = (posx > 0) & (posx <= bins[0]) & (posy > 0) & (posy <= bins[1])
hhsub = hh[posx[ind] - 1, posy[ind] - 1] # values of the histogram where the points are
xdat1 = xdat[ind][hhsub < thresh] # low density points
ydat1 = ydat[ind][hhsub < thresh]
hh[hh < thresh] = np.nan # fill the areas with low density by NaNs

plt.imshow(np.flipud(hh.T),cmap='jet',extent=np.array(xyrange).flatten(), interpolation='none', origin='upper')
plt.colorbar()   
plt.plot(xdat1, ydat1, '.',color='darkblue')
plt.show()