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I want to plot points on the interval x in [0, 4]. My function performs something interesting for very small values, so I would like to create a non-linear scale that would use more space for smaller values of x. Logarithmic scale would be a great solution, but the problem is that my x-axis must include 0, which is not part of logarithmic axis.

So I considered using a power scale. After some googling I came across the following solution.

def stratify(ax, power=2):
    f     = lambda x: (x + 1)**(1 / power)
    f_inv = lambda y: y**power - 1
    ax.set_xscale('function', functions=(f, f_inv))

x = np.linspace(0, 4, 100)
y = np.sqrt(x)

fig, ax = plt.subplots()
ax.plot(x, y)
stratify(ax, 2)

plt.show()

The function stratify changes the x-scale of the plot to the square root function. This looks kind of correct. Below is a minimal example plot corresponding to the above code (not actual data).

Plot produced by the attached code

I would like to have control over the nonlinearity in the x-scale, that is why I have introduced the power parameter. However, when I change the power parameter to value different from 2, the plot does not change at all. This is very surprising for me. I would appreciate if somebody could advise me how I can control the extent of non-linearity in x-axis. If possible, I would like it even more non-linear, making the interval [0, 0.5] take half of the plot.

EDIT While the current solution by @Thomas works as intended, the plotting routine throws a lot of errors when one attempts to do anything with it. For example, I would like to insert extra ticks, as the original only has integer ticks for whatever reason. Inserting extra ticks via ax.set_xticks(ax.get_xticks() + [0.5]) results in an error posx and posy should be finite values. What is this error, and how can it be bypassed?

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  • I adressed that EDIT in the comment to my answer below. Commented Nov 10, 2021 at 7:59

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For me, there's a change when switching from power=2 to power=10. Just be careful to edit it at the right position, i.e. when calling stratify=X.

Here's power=2: enter image description here Here's power=10: enter image description here

However, here's another suggestion that is slightly more aggressive:

import numpy as np
import matplotlib.pyplot as plt


def stratify(ax, scale=1):
    f = lambda x: np.log(x / scale + 1)
    f_inv = lambda y: scale * (np.exp(y) - 1)
    ax.set_xscale('function', functions=(f, f_inv))


x = np.linspace(0, 4, 100)
y = np.sqrt(x)

fig, axs = plt.subplots(1, 3)
for i, scale in enumerate([10,1,0.1]):
    ax = axs[i]
    ax.set_title(f'Scale={scale}')
    ax.plot(x, y)
    stratify(ax, scale=scale)

plt.show()

Resulting in enter image description here

Another option are zoom regions.

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6 Comments

Another option are zoom regions: matplotlib.org/stable/gallery/subplots_axes_and_figures/…
Add that comment / link as an edit to your answer. Comments get deleted.
There is another problem. I would like to add extra ticks. But when I insert ax.set_xticks(ax.get_xticks() + [0.5]), I get an error posx and posy should be finite values
For me this works if I set the ticks after calling stratify.
After some fighting I found the culprit. Matplotlib does not stick to the xrange of [0, 4] when plotting, it attempts to make a slightly wider range, e.g. [-0.05, 4.05] to have nice margins. However, the mapping you provided does not work for negative numbers as the logarithm blows up. I designed a more fancy function that performs y=x for negative numbers and the original function you suggested for positive numbers. Now there are no errors and everything seems to work.
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