How to draw diagonal lines in a loglog plot in matplotlib?

Question

I have a scatterplot where both axes are in logarithmic scale. For instance, a plot generated with the following code:

import matplotlib.pyplot as plt
import numpy as np

rng = np.random.RandomState(42)

x = np.logspace(0, 3, 100)
y = np.logspace(0, 3, 100) + rng.randn(100) * 2

ax = plt.gca()
ax.scatter(x, y, marker="x", color="orange")

ax.axline((0, 0), (1, 1), color="black", linestyle=":")

ax.set_xscale("log")
ax.set_yscale("log")

ax.set_aspect("equal")
plt.show()

that produces the following plot Scatter plot with bisector

I would like to draw diagonal lines in correspondence of each power of 10, for instance as in the following plot Scatter plot with bisector and two diagonal lines

I tried to add

ax.axline((1, 0), (10, 1), color="black", linestyle=":")
ax.axline((0, 1), (1, 10), color="black", linestyle=":")

but I get Scatter plot with bisector and two lines which is not what I expected.

Answer 1

Multiply the Y coordinate values by a constant

I am not sure your original idea of (0,0) and (1,1) is ideal. It would be better to avoid 0's in a log-log plot. I have changed it to (1,1) and (10,10), which is the same line.

Then you want your next line to be passing through the same X co-ordinates, but at Y coordinates that are, say, 10 times higher. So multiply both Y coordinates by 10.

Likewise for the line on the other side, divide by 10.

In this code I have made the factor k.

import matplotlib.pyplot as plt
import numpy as np

rng = np.random.RandomState(42)

x = np.logspace(0, 3, 100)
y = np.logspace(0, 3, 100) + rng.randn(100) * 2

ax = plt.gca()
ax.scatter(x, y, marker="x", color="orange")

k = 10
ax.axline((1, 1),  (10, 10  ), color="black", linestyle=":")
ax.axline((1,1*k), (10, 10*k), color="black", linestyle=":")
ax.axline((1,1/k), (10, 10/k), color="black", linestyle=":")

ax.set_xscale("log")
ax.set_yscale("log")

ax.set_aspect("equal")
plt.show()

The result is:

Why do the dotted lines intersect the axis a bit low?

They are actually intersecting in the correct place. They should not intersect the Y axis at 1, 10, 100 etc. The Y axis is not at x=1. It is at some number slightly to the left of 1.

If you trace up a line at x=1, and across from x=1, you will see that the dotted line passes through their crossing point.