How to fit data logarithmic in python?

Question

I've been trying to fit some data I have gained from some simulations. From the curve, I guess a logarithmic fit would be ideal. However, the curve comes looking out quite funky. I've also tried higher order polynomials and np.polyfit, but I couldn't get either to work. Any help would be appreciated!

from scipy.optimize import curve_fit
import numpy as np
import matplotlib.pyplot as plt


xdata=[9.24104360013e-06, 4.72619458107e-06, 4.03957328857e-06, 9.78301182748e-06, 1.36994566431e-05, 1.16294573409e-05, 7.70899546232e-06, 2.72587766232e-06, 2.19089955631e-06, 5.34851640035e-06, 7.84434545123e-06, 7.6524185787e-06, 1.00592536363e-05, 6.08711035578e-07, 4.08259572135e-07, 5.74424798328e-07, 6.20036326494e-07, 4.34755225756e-06, 4.72832211908e-06, 1.25156011417e-06, 1.44996714816e-05, 3.79992166335e-06, 4.45935911838e-06, 6.6307841155e-06, 2.38540191336e-06, 9.4649801666e-07, 9.11518608157e-06, 3.1944675219e-06, 5.32674287313e-06, 1.48463901861e-05, 3.41127723277e-06, 3.40027150288e-06, 3.33064781566e-06, 2.12828505238e-06, 7.22565690506e-06, 7.86527964811e-06, 2.25791582571e-06, 1.94875869207e-05, 1.54712884424e-05, 5.82300791075e-06, 9.5783833758e-06, 1.89519143607e-05, 1.03731970283e-05, 2.53090894753e-05, 9.26047056658e-06, 1.05428610146e-05, 2.89162870493e-05, 4.78624726782e-05, 1.00005855557e-05, 6.88617910928e-05]

ydata=[0.00281616449359, 0.00257023004939, 0.00250030932407, 0.00284317789756, 0.00300158447316, 0.00291690879783, 0.00274898865728, 0.0023625485679, 0.0023018015629, 0.00259860025555, 0.00269155777824, 0.00265941197135, 0.0028073724168, 0.00192920496041, 0.00182900945464, 0.00191452746379, 0.00193227563253, 0.00253266811688, 0.00255961306471, 0.00212426145702, 0.00285906942634, 0.00247877245272, 0.0025348504727, 0.00269881922057, 0.00232270371493, 0.00204672286703, 0.00281306442303, 0.00241938445736, 0.00261083321385, 0.00287440363274, 0.00244324770882, 0.00244364989768, 0.00244593671433, 0.00228714406931, 0.00263301289418, 0.00269385915315, 0.0022968948347, 0.00313898537645, 0.00305650121575, 0.00265291893623, 0.00278748794063, 0.00312801724905, 0.00289450806538, 0.00313176225397, 0.00284010926578, 0.0028957865422, 0.00335438183977, 0.00360421739757, 0.00270734995952, 0.00377301191882]


plt.plot(xdata,ydata,'o')

x = np.array(xdata, dtype=float) #transform your data in a numpy array of floats 
y = np.array(ydata, dtype=float) #so the curve_fit can work

#def func(x,a,b,c):
#    return a*x**2+ b*x +c

def func(x,a,b):
    return a*np.log(x)+ b


popt, pcov = curve_fit(func, x, y)
plt.plot(x, func(x, *popt), label="Fitted Curve")
plt.show()

Plot

Possible duplicate of scipy.curve_fit() returns multiple lines — DavidG
– DavidG, Commented Apr 29, 2019 at 13:46
If the data is logarithmic, you can compute the exponential and try a linear/polynomial fit. — javidcf
– javidcf, Commented Apr 29, 2019 at 13:51
You just need to sort your data while plotting the line. Use plt.plot(sorted(x), func(sorted(x), *popt), label="Fitted Curve"); plt.legend(). — Sheldore
– Sheldore, Commented Apr 29, 2019 at 13:55

Adarsh Chavakula · Accepted Answer · 2019-04-29 13:58:56Z

2

Sort x before plotting

x_sorted = np.sort(x)
plt.plot(x_sorted, func(x_sorted, *popt), label="Fitted Curve")
plt.show()

answered Apr 29, 2019 at 13:58

Adarsh Chavakula

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3 Comments

Sheldore Over a year ago

You can also just use plt.plot(sorted(x), func(sorted(x), *popt), label="Fitted Curve")

Jan Christoph Terasa Over a year ago

@Sheldore sorted is a python standard function, and thus is one order of magntitude slower than np.sort (at least on my machine). In addition, it returns a list, which you'd need to convert back to an ndarray again, if you process it further (does not matter just for plotting). Finally, you are calling the sorting algorithm twice, which is less efficient (does not matter in this case, either). Generally, when working with ndarrays, one should try to stick to pure numpy functions as much as possible.

Sheldore Over a year ago

Right, at least for such small list doesn’t make a difference though

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