问使用matplotlib/python的平方根比例

EN

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()

Nx = 100
x = np.linspace(0,50,Nx)
y = np.sqrt(x)

fig, ax = plt.subplots(1, 1)

plt.plot(np.sqrt(x), y)
ax.set_xticks([np.sqrt(x[i]) for i in range(0, Nx, Nx // 10)])
ax.set_xticklabels([str(round(x[i],0))[:-2] for i in range(0, Nx, Nx // 10)])
plt.xlabel('x')
plt.ylabel(r'y = $\sqrt{x}$')
plt.grid()
plt.show()

x = np.arange(2, 15, 2)
y = x * x

fig = plt.figure()
ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)

ax1.plot(x,y)

ax2.plot(x, np.sqrt(y))
ax2.set_yticks([2,4,6,8,10,12,14])
ax2.set_yticklabels(['4','16','36','64','100','144','196'])