Plotting the logarithm of a function

Question

I have a function which I am able to plot. Now I would like to plot the logarithm of this function. Python says that log10() is not defined for functions (and I understand that). So the question is: how can I plot the logarithm of a function like f(x,a)=a*(x**2)?

Answer 1

It is misleading to say that matplotlib can plot functions. Matplotlib can only plot values.

So if your function is

f = lambda x,a : a * x**2

you'd first need to create an array of values for x and define a

a=3.1
x = np.linspace(-6,6)

You can then plot the array y = f(x,a) via

ax.plot(x,y)

If you now want to plot the logarithm of f, what you need to really do is plot the logarithm of your array y. So you'd create a new array

y2 = np.log10(y)

and plot it

ax.plot(x,y2)

In some cases, instead of showing the logarithm of a function on a linear scale, it may be better to show the function itself on a logarithmic scale. This can be done by setting the axes in matplotlib to logarithmic and plot the initial array y on that logarithmic scale.

ax.set_yscale("log", nonposy='clip')
ax.plot(x,y)

So here is a showcase example of all three cases:

import matplotlib.pyplot as plt
import numpy as np

#define the function
f = lambda x,a : a * x**2

#set values
a=3.1
x = np.linspace(-6,6)

#calculate the values of the function at the given points
y =  f(x,a)
y2 = np.log10(y)
# y and y2 are now arrays which we can plot

#plot the resulting arrays
fig, ax = plt.subplots(1,3, figsize=(10,3))

ax[0].set_title("plot y = f(x,a)")
ax[0].plot(x,y) # .. "plot f"

ax[1].set_title("plot np.log10(y)")
ax[1].plot(x,y2) # .. "plot logarithm of f"

ax[2].set_title("plot y on log scale")
ax[2].set_yscale("log", nonposy='clip')
ax[2].plot(x,y) # .. "plot f on logarithmic scale"

plt.show()