在对数刻度上使用 matplotlib 拟合曲线

Question

I am plotting simple 2D graph using loglog function in python as follows:

plt.loglog(x,y,label='X vs Y');

X and Y are both lists of floating numbers of n size.

I want to fit a line on the same graph. I tried numpy.polyfit , but I am getting nowhere.

How do you fit a line using polyfit if your graph is already in loglog scale?

Answer 1

Numpy doesn't care what the axes of your matplotlib graph are.

I presume that you think log(y) is some polynomial function of log(x) , and you want to find that polynomial? If that is the case, then run numpy.polyfit on the logarithms of your data set:

import numpy as np
logx = np.log(x)
logy = np.log(y)
coeffs = np.polyfit(logx,logy,deg=3)
poly = np.poly1d(coeffs)

poly is now a polynomial in log(x) that returns log(y) . To get the fit to predict y values, you can define a function that just exponentiates your polynomial:

yfit = lambda x: np.exp(poly(np.log(x)))

You can now plot your fitted line on your matplotlib loglog plot:

plt.loglog(x,yfit(x))

And show it like this

plt.show()

Answer 2

np.log(x) extracts the natural logarythm, so the fitting of the above solution is done on natural logs, while plt.loglog draws on 10-base logs.

Both operations should be run in the same base:

logx = np.log10(x)
logy = np.log10(y)

and

yfit = lambda x: np.power(10, poly(np.log(x)))

or

yfit = lambda x: 10**(poly(np.log(x)))