How to produce an exponentially scaled axis?

Question

Consider the following code:

from numpy import log2
import matplotlib.pyplot as plt

xdata = [log2(x)*(10/log2(10)) for x in range(1,11)]
ydata = range(10)
plt.plot(xdata, ydata)
plt.show()

This produces the following plot: My question is, how can I modify this, so that the plot, with the exact same data as input, appears as a straight line? This basically requires scaling the x-axis appropriately, but I cannot figure how to do this. The reason for doing this is that I am displaying a function that changes very little at the beginning, but starts to fluctuate more towards the end of the valid interval, so I want to have a higher horizontal resolution towards the end. If anyone can propose an alternative solution to my approach, feel free to do so!

Answer 1

Here is how it is done. A good example to follow. You just subclass the ScaleBase class.

Here's your transform. It's not too complicated when you whittle out all the custom formatters and stuff. Just a little verbose.

from numpy import log2
import matplotlib.pyplot as plt

from matplotlib import scale as mscale
from matplotlib import transforms as mtransforms

class CustomScale(mscale.ScaleBase):
    name = 'custom'

    def __init__(self, axis, **kwargs):
        mscale.ScaleBase.__init__(self)
        self.thresh = None #thresh

    def get_transform(self):
        return self.CustomTransform(self.thresh)

    def set_default_locators_and_formatters(self, axis):
        pass

    class CustomTransform(mtransforms.Transform):
        input_dims = 1
        output_dims = 1
        is_separable = True

        def __init__(self, thresh):
            mtransforms.Transform.__init__(self)
            self.thresh = thresh

        def transform_non_affine(self, a):
            return 10**(a/10)

        def inverted(self):
            return CustomScale.InvertedCustomTransform(self.thresh)

    class InvertedCustomTransform(mtransforms.Transform):
        input_dims = 1
        output_dims = 1
        is_separable = True

        def __init__(self, thresh):
            mtransforms.Transform.__init__(self)
            self.thresh = thresh

        def transform_non_affine(self, a):
            return log2(a)*(10/log2(10))

        def inverted(self):
            return CustomScale.CustomTransform(self.thresh)


mscale.register_scale(CustomScale)

xdata = [log2(x)*(10/log2(10)) for x in range(1,11)]
ydata = range(10)
plt.plot(xdata, ydata)

plt.gca().set_xscale('custom')
plt.show()

Answer 2

The easiest way is to use semilogy

from numpy import log2
import matplotlib.pyplot as plt

xdata = log2(range(1,11)) * (10/log2(10))
ydata = range(10)
plt.semilogy(xdata, ydata)
plt.show()