Matplotlib: add twin y axis without using its values in the plots

Question

This is to clarify the question title. Say you have four lists of integers, with which you want to produce a scatter plot:

a=[3,7,2,8,12,17]
b=[9,4,11,7,6,3]
c=[9,3,17,13,10,5]
d=[5,1,1,14,5,8]

You also have a function, for simplicity f(x)=1/x, that applies to all lists, so that:

from __future__ import division
a1=[1/i for i in a]
b1=[1/i for i in b]
c1=[1/i for i in c]
d1=[1/i for i in d]

My question: how to add a second y axis, knowing that the values returned by the function range from 0.06 to 1.0, without using any of the a1, b1, c1, d1 lists in the scatter plots?

What I am saying is: if you produce the following scatter plots in the traditional way, how can you then add the second y axis based on the values of a1, b1, c1, d1, without having any series using them in the plot itself?

import matplotlib.pyplot as plt
plt.scatter(a,b,c='red',label='reds')
plt.scatter(c,d,c='blue',label='blues')
plt.legend(loc='best')

This is the scatter without the second y axis:

And this is a made up version of the same one, including the second y axis discussed so far:

NB: This question is different from this, in that I am not trying to plot with different scales. I only want to add a second axis with the relevant values.

Possible duplicate of [Adding a second y-axis related to the first y-axis](http://stackoverflow.com/questions/43149703/adding-a-second-y-axis-related-to-the-first-y-axis) — ImportanceOfBeingErnest, Apr 19 '17 at 10:48
The scale on the right side you show in the picture doesn't make sense if the function to use would be 1/x, which can be seen by plotting the values b1 and d1 to that axes. — ImportanceOfBeingErnest, Apr 19 '17 at 11:07
But I don't want to plot any of the a1, b1 and such series. That scale was only put there to show the meaning. Also, the function is just a simple example. — FaCoffee, Apr 19 '17 at 11:09
There is no meaning in that function because you cannot share a linear and a non-linear axes. If you have a linear relationship between the two axes, the duplicate question shows you what to do, if you have a non-linear relation, you need to provide more details in the question. — ImportanceOfBeingErnest, Apr 19 '17 at 11:15
I believe the question is more about changing the tick labels than the ticks themselves, hence my proposed answer. I had a similar problem when wanting to show wavenumber and wavelength values on the same graph. — berna1111, Apr 19 '17 at 11:27

score 3 · Accepted Answer · answered Apr 19 '17 at 11:20

To make sure the numbers on the new axis are in the corresponding position to their inverses:

import matplotlib.pylab as plt

a=[3,7,2,8,12,17]
b=[9,4,11,7,6,3]
c=[9,3,17,13,10,5]
d=[5,1,1,14,5,8]

fig = plt.figure()
ax = fig.add_subplot(111)

ax.scatter(a,b,c='red',label='reds')
ax.scatter(c,d,c='blue',label='blues')
ax.legend(loc='best')
ax.set_ylabel('Y')
# make shared y axis
axi = ax.twinx()
# set limits for shared axis
axi.set_ylim(ax.get_ylim())
# set ticks for shared axis
inverse_ticks = []
label_format = '%.3f'
for tick in ax.get_yticks():
    if tick != 0:
        tick = 1/tick
    inverse_ticks.append(label_format % (tick,))
axi.set_yticklabels(inverse_ticks)
axi.set_ylabel('1/Y')
fig.tight_layout()
fig.show()

And you can also do it for the X axis:

# make shared x axis
xaxi = ax.twiny()
# set limits for shared axis
xaxi.set_xlim(ax.get_xlim())
# set ticks for shared axis
inverse_ticks = []
label_format = '%.3f'
for tick in ax.get_xticks():
    if tick != 0:
        tick = 1/tick
    inverse_ticks.append(label_format % (tick,))
xaxi.set_xticklabels(inverse_ticks)
xaxi.set_xlabel('1/X')

You can also take advantage of the fact that you are already looking out for the `0` value and changing only the string value of the tick labels to label it with `"inf"` or whatever you feel like. — berna1111, Apr 19 '17 at 11:23

score 1 · Answer 2 · answered Apr 19 '17 at 10:40

Just make shared y axis and set desired limits and ticks for new axis like here:

import matplotlib.pylab as plt
import numpy as np

a=[3,7,2,8,12,17]
b=[9,4,11,7,6,3]
c=[9,3,17,13,10,5]
d=[5,1,1,14,5,8]

plt.scatter(a,b,c='red',label='reds')
plt.scatter(c,d,c='blue',label='blues')
plt.legend(loc='best')
ax = plt.gca()
# make shared y axis
ax2 = ax.twinx()
# set limits for shared axis
ax2.set_ylim([0,1])
# set ticks for shared axis
plt.yticks(np.arange(0.06, 1, 0.14))
plt.show()

This solution is pretty obviously not correct. Try plotting the inverted lists; the points will not overlap! — ImportanceOfBeingErnest, Apr 19 '17 at 11:02

Matplotlib: add twin y axis without using its values in the plots

2 Answers2

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