Compute mean value per pixel using weighted 2d histogram

Question

I am using pyplot.hist2d to plot a 2D histogram (x vs.y) weighted by a third variable, z. Instead of summing z values in a given pixel [x_i,y_i] as done by hist2d, I'd like to obtain the average z of all data points falling in that pixel.

Is there a python script doing that ?

Thanks.

Answer 1

Numpy's histogram2d() can calculate both the counts (a standard histogram) as the sums (via the weights parameter). Dividing both gives the mean value.

The example below shows the 3 histograms together with a colorbar. The number of samples is chosen relatively small to demonstrate what would happen for cells with a count of zero (the division gives NaN, so the cell is left blank).

import numpy as np
import matplotlib.pyplot as plt

N = 1000
x = np.random.uniform(0, 10, N)
y = np.random.uniform(0, 10, N)
z = np.cos(x) * np.sin(y)

counts, xbins, ybins = np.histogram2d(x, y, bins=(30, 20))
sums, _, _ = np.histogram2d(x, y, weights=z, bins=(xbins, ybins))

fig, (ax1, ax2, ax3) = plt.subplots(ncols=3, figsize=(15, 4))
m1 = ax1.pcolormesh(ybins, xbins, counts, cmap='coolwarm')
plt.colorbar(m1, ax=ax1)
ax1.set_title('counts')
m2 = ax2.pcolormesh(ybins, xbins, sums, cmap='coolwarm')
plt.colorbar(m2, ax=ax2)
ax2.set_title('sums')
with np.errstate(divide='ignore', invalid='ignore'):  # suppress possible divide-by-zero warnings
    m3 = ax3.pcolormesh(ybins, xbins, sums / counts, cmap='coolwarm')
plt.colorbar(m3, ax=ax3)
ax3.set_title('mean values')
plt.tight_layout()
plt.show()