拟合实验数据并获得2个参数

Question

I am trying to fit a messy expression to some experimental data. The formula has 2 free parameters (in the code denoted by "a" and "b") and I need to find the values for a and b. I tried using the scipy module but I keep getting an error when compiling the curve_fit procedure. I tried to find something regarding the error but I couldn't find anything that solved the issue.

Screenshot with the error:

here

Please keep in mind that my experience with python is not that great (basically I just started to learn it for this fitting procedure). Segment of the code is here if it would make it easier:

def fun1(x,a,b):
    result=tsd1(x,17,6.5,a,b)
    return result
params, extras = curve_fit(fun1,mydata.spin,mydata.energy)
print(params)

tsd1 is another function which depends on some parameter (the full expression for the tsd1 function can be seen here ) and mydata are 2 arrays with the spin and energy, represented by the first and second column in the data file. Full input data here

I would like to know what is wrong with my fitting procedure and how I can solve this issue.

Answer 1

The problem you experience is that you use the functions of the math module (they work on scalars) instead of the numpy functions that are designed to work on arrays. A simplified version of your problem (I am too lazy to go through all the functions you declared) would be:

from math import cos
import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit
import pandas as pd

#works perfectly fine with the numpy arrays from the pandas data frame
def fun1(x, a, b, c, d):
    return a * np.cos(b * x / 1000 + c) + d

#this version doesn't work because math works only on scalars
#def fun1(x, a, b, c, d):
#    return a * cos(b * x / 1000 + c) + d

#read data from file you provided
mydata = pd.read_csv("test.txt", names = ["spin", "energy"])

#curve fit
params, extras = curve_fit(fun1,mydata.spin,mydata.energy)
print(params)

#generation of the fitting curve
x_fit = np.linspace(np.min(mydata.spin), np.max(mydata.spin), 1000)
y_fit = fun1(x_fit, *params)

#plotting of raw data and fit function
plt.plot(mydata.spin, mydata.energy, "ro", label = "data")
plt.plot(x_fit, y_fit, "b", label = "fit")
plt.legend()
plt.show()

So, the solution is to find all math functions in your script like sin , cos , sqrt and substitute them with their numpy equivalents. Luckily, they are usually simply np.sin etc.