How does numpy.histogram() work?

While reading up on numpy, I encountered the function numpy.histogram().

What is it for and how does it work? In the docs they mention bins: What are they?

Some googling led me to the definition of Histograms in general. I get that. But unfortunately I can't link this knowledge to the examples given in the docs.

A bin is range that represents the width of a single bar of the histogram along the X-axis. You could also call this the interval. (Wikipedia defines them more formally as "disjoint categories".)

The Numpy histogram function doesn't draw the histogram, but it computes the occurrences of input data that fall within each bin, which in turns determines the area (not necessarily the height if the bins aren't of equal width) of each bar.

In this example:

 np.histogram([1, 2, 1], bins=[0, 1, 2, 3])

There are 3 bins, for values ranging from 0 to 1 (excl 1.), 1 to 2 (excl. 2) and 2 to 3 (incl. 3), respectively. The way Numpy defines these bins if by giving a list of delimiters ([0, 1, 2, 3]) in this example, although it also returns the bins in the results, since it can choose them automatically from the input, if none are specified. If bins=5, for example, it will use 5 bins of equal width spread between the minimum input value and the maximum input value.

The input values are 1, 2 and 1. Therefore, bin "1 to 2" contains two occurrences (the two 1 values), and bin "2 to 3" contains one occurrence (the 2). These results are in the first item in the returned tuple: array([0, 2, 1]).

Since the bins here are of equal width, you can use the number of occurrences for the height of each bar. When drawn, you would have:

• a bar of height 0 for range/bin [0,1] on the X-axis,
• a bar of height 2 for range/bin [1,2],
• a bar of height 1 for range/bin [2,3].

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You can plot this directly with Matplotlib (its hist function also returns the bins and the values):

>>> import matplotlib.pyplot as plt
>>> plt.hist([1, 2, 1], bins=[0, 1, 2, 3])
(array([0, 2, 1]), array([0, 1, 2, 3]), <a list of 3 Patch objects>)
>>> plt.show()

import numpy as np    
hist, bin_edges = np.histogram([1, 1, 2, 2, 2, 2, 3], bins = range(5))

Below, hist indicates that there are 0 items in bin #0, 2 in bin #1, 4 in bin #3, 1 in bin #4.

print(hist)
# array([0, 2, 4, 1])   

bin_edges indicates that bin #0 is the interval [0,1), bin #1 is [1,2), ..., bin #3 is [3,4).

print (bin_edges)
# array([0, 1, 2, 3, 4]))  

Play with the above code, change the input to np.histogram and see how it works.

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But a picture is worth a thousand words:

import matplotlib.pyplot as plt
plt.bar(bin_edges[:-1], hist, width = 1)
plt.xlim(min(bin_edges), max(bin_edges))
plt.show()   

Another useful thing to do with numpy.histogram is to plot the output as the x and y coordinates on a linegraph. For example:

arr = np.random.randint(1, 51, 500)
y, x = np.histogram(arr, bins=np.arange(51))
fig, ax = plt.subplots()
ax.plot(x[:-1], y)
fig.show()

This can be a useful way to visualize histograms where you would like a higher level of granularity without bars everywhere. Very useful in image histograms for identifying extreme pixel values.