Square root scale using matplotlib/python

Question

I want to make a plot with square root scale using Python:

However, I have no idea how to make it. Matplotlib allows to make log scale but in this case I ne

Answer 1

You can make your own ScaleBase class to do this. I have modified the example from here (which made a square-scale, not a square-root-scale) for your purposes. Also, see the documentation here.

Note that to do this properly, you should probably also create your own custom tick locator; I haven't done that here though; I just manually set the major and minor ticks using ax.set_yticks().

import matplotlib.scale as mscale
import matplotlib.pyplot as plt
import matplotlib.transforms as mtransforms
import matplotlib.ticker as ticker
import numpy as np

class SquareRootScale(mscale.ScaleBase):
    """
    ScaleBase class for generating square root scale.
    """
 
    name = 'squareroot'
 
    def __init__(self, axis, **kwargs):
        # note in older versions of matplotlib (<3.1), this worked fine.
        # mscale.ScaleBase.__init__(self)

        # In newer versions (>=3.1), you also need to pass in `axis` as an arg
        mscale.ScaleBase.__init__(self, axis)
 
    def set_default_locators_and_formatters(self, axis):
        axis.set_major_locator(ticker.AutoLocator())
        axis.set_major_formatter(ticker.ScalarFormatter())
        axis.set_minor_locator(ticker.NullLocator())
        axis.set_minor_formatter(ticker.NullFormatter())
 
    def limit_range_for_scale(self, vmin, vmax, minpos):
        return  max(0., vmin), vmax
 
    class SquareRootTransform(mtransforms.Transform):
        input_dims = 1
        output_dims = 1
        is_separable = True
 
        def transform_non_affine(self, a): 
            return np.array(a)**0.5
 
        def inverted(self):
            return SquareRootScale.InvertedSquareRootTransform()
 
    class InvertedSquareRootTransform(mtransforms.Transform):
        input_dims = 1
        output_dims = 1
        is_separable = True
 
        def transform(self, a):
            return np.array(a)**2
 
        def inverted(self):
            return SquareRootScale.SquareRootTransform()
 
    def get_transform(self):
        return self.SquareRootTransform()
 
mscale.register_scale(SquareRootScale)

fig, ax = plt.subplots(1)

ax.plot(np.arange(0, 9)**2, label='$y=x^2$')
ax.legend()

ax.set_yscale('squareroot')
ax.set_yticks(np.arange(0,9,2)**2)
ax.set_yticks(np.arange(0,8.5,0.5)**2, minor=True)

plt.show()