Please explain in detail 2D Histogram in Python

Question

I am trying to understand what are the values of a 2D histogram.

I have 2 numpy arrays of the same length X and Y (float numbers in each one).

For example the first 10 values of X: [ 88, 193, 60, 98, 78, 100, 75, 76, 130]

and Y: [ 18. , 9. , 36.1, 18.5, 34.3, 32.9, 32.2, 22. , 15. ]

When I use:

import matplotlib.pyplot as plt

plt.hist2d(X,Y, bins=(10,20)) 

I get a 2D histogram.

But what does it mean?

1D histogram simply shows me how much of each item I have.

Please explain me what does it mean in 2D.

Thanks in advance!

Solution

Suppose you have a 1D array, you plot the position of its values on the x axis, they are so dense that you can't tell the spatial distribution, you use a 1D histogram to show the distribution by count of boxes along the x axis. Problem solved.

Then you have two 1D arrays, a list of 2D dots in (x, y) axes. You plot their positions on the x-y plane, again they are so dense and overlap with each other. You want to view the distribution better by count of boxes in the plane, so you try a 2D diagram. Problem solved.

Here is an example

import numpy as np
import matplotlib.pyplot as plt

%matplotlib inline

# prepare 2D random dots centered at (0, 0)
n = 100000
x = np.random.randn(n)
y = x + np.random.randn(n)

# plot data
fig1 = plt.figure()
plt.plot(x,y,'.r')
plt.xlabel('x')
plt.ylabel('y')

gives

# plot 2D histogram using pcolor
fig2 = plt.figure()
plt.hist2d(x, y, bins=100)
plt.xlabel('x')
plt.ylabel('y')
cbar = plt.colorbar()
cbar.ax.set_ylabel('Counts')

gives