bin 3d points into 3d bins in python

Question

How can I bin 3d points into 3d bins? Is there a multi dimensional version for np.digitize? I can use np.digitize separately for each dimension, like here. Is there a better solution? Thanks!

Answer 1

You can do this with numpy.histogramdd(sample), where the number of bins in each direction and the physical range can be adjusted as with a 1D histogram. More info on the reference page. For more general statistics, like the mean of another variable per point in a bin, you can use the scipy scipy.stats.binned_statistic_dd function, see docs. For your case with an array of three dimensional points, you would use this in the following way,

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from scipy import stats


#Setup some dummy data
points = np.random.randn(1000,3)
hist, binedges = np.histogramdd(points, normed=False)

#Setup a 3D figure and plot points as well as a series of slices
fig = plt.figure()
ax1 = fig.add_subplot(111, projection='3d')
ax1.plot(points[:,0],points[:,1],points[:,2],'k.',alpha=0.3)

#Use one less than bin edges to give rough bin location
X, Y = np.meshgrid(binedges[0][:-1],binedges[1][:-1])

#Loop over range of slice locations (default histogram uses 10 bins)
for ct in [0,2,5,7,9]: 
    cs = ax1.contourf(X,Y,hist[:,:,ct], 
                      zdir='z', 
                      offset=binedges[2][ct], 
                      level=100, 
                      cmap=plt.cm.RdYlBu_r, 
                      alpha=0.5)

ax1.set_xlim(-3, 3)
ax1.set_ylim(-3, 3)
ax1.set_zlim(-3, 3)
plt.colorbar(cs)
plt.show()

which gives a series of histogram slices of occupancy at each location,