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matplotlib: missed errorbars in logarithmic plot

While manipulating some data I came across to, what looked, a strange behavior with the errorbar of matplotlib, when plotting the results from linear to logarithmic scale.

Suppose these data:

import matplotlib.pyplot as plt
import numpy as np

s=[19.0, 20.0, 21.0, 22.0, 24.0]
v=[36.5, 66.814250000000001, 130.17750000000001, 498.57466666666664, 19.41]
verr=[0.28999999999999998, 80.075044597909169, 71.322124839818571, 650.11015891565125, 0.02]
plt.errorbar(s,v,yerr=verr)
plt.show()

and the result looked like this:

where the errorbars are obviously visible, but when I switched to the logarithmic scale, by using:

plt.yscale('log')
plt.show()

then the result was this:

where some errorbars are not visible (although their caps are still visible). So, what is going on?

I couldn’t figure out what was the problem, so I asked at StackOverflow. I got an answer by “Dan”, in which he pointed to the fact that some of the errors were (that large) that led to negative values (not valid for log). That’s why they were not displayed. The solution was to use asymmetric errors, by substituting basically the negative error values with a value close to 0 (actually the plotted value, but slightly over 0).
The piece of code that corrected the display is:

import matplotlib.pyplot as plt
import numpy as np

s=[19.0, 20.0, 21.0, 22.0, 24.0]
v=np.array([36.5, 66.814250000000001, 130.17750000000001, 498.57466666666664, 19.41])
verr=np.array([0.28999999999999998, 80.075044597909169, 71.322124839818571, 650.11015891565125, 0.02])
verr2 = np.array(verr)
verr2[np.where(v-verr<=.0)] = v[np.where(v-verr<=.0)]*.999999 plt.errorbar(s,v,yerr=[verr2,verr]) plt.ylim(1E1,1E4) plt.yscale('log') plt.show()

with the final output (by adjusting also the axes):

Derivatives of non natural logarithms and exponentials

Some useful calculations to keep in mind !!

> changing bases in logarithms: loga x = logb x / logb a
for base 10 and e: log x = ln x / ln 10
(log e = 1 / ln 10)

> derivative of exponential with other base:

d (ax) / dx = ax ln a

in the case of base 10: d (10x) / dx = 10x ln 10

> derivative of logarithm with other base:

d (loga x) / dx = d (ln x / ln a) / dx = 1 / ( x ln a)

so in the case of base 10: d (log x) / dx = 1 / ( x ln 10)

A useful online resource for calculations is Wolfram Alpha ‘s engine.