如何将用户输入的字符串转换为方程式，以找到最适合某些数据的方程式

Question

I have some x and y data which I plot in a graph window. I would like a user to define an equation and then use something like SciPy to find the best values for that equation.

As an example equation user input => y = ((m^2 / c^4) * 2)^0.5

How can I put this string into curve_fitting or something similar and find the missing values please? I thought I could use an anonymous function but that seems to not be working for me.

Answer 1

You might find lmfit ( http://lmfit.github.io/lmfit-py/ ) useful for this purpose. As part of its high-level approach to curve-fitting, it has an ExpressionModel class that supports user-defined model functions taken from Python expressions. More details can be found at http://lmfit.github.io/lmfit-py/builtin_models.html#user-defined-models . As a simple example (taken from the example folder in the github repo):

import numpy as np
import matplotlib.pyplot as plt
from lmfit.models import ExpressionModel

x = np.linspace(-10, 10, 201)

amp, cen, wid =  3.4, 1.8, 0.5

y = amp * np.exp(-(x-cen)**2 / (2*wid**2)) / (np.sqrt(2*np.pi)*wid)  
y = y + np.random.normal(size=len(x), scale=0.01)

gmod = ExpressionModel('amp * exp(-(x-cen)**2 /(2*wid**2))/(sqrt(2*pi)*wid)')

result = gmod.fit(y, x=x, amp=5, cen=5, wid=1)

print(result.fit_report())
plt.plot(x, y, 'bo')
plt.plot(x, result.init_fit, 'k--')
plt.plot(x, result.best_fit, 'r-')
plt.show()

will print out the results of

[[Model]]
    Model(_eval)
[[Fit Statistics]]
    # function evals   = 54
    # data points      = 201
    # variables        = 3
    chi-square         = 0.019
    reduced chi-square = 0.000
    Akaike info crit   = -1856.580
    Bayesian info crit = -1846.670
[[Variables]]
    amp:   3.40478705 +/- 0.005053 (0.15%) (init= 5)
    cen:   1.79930413 +/- 0.000858 (0.05%) (init= 5)
    wid:   0.50051059 +/- 0.000858 (0.17%) (init= 1)
[[Correlations]] (unreported correlations are <  0.100)
    C(amp, wid)                  =  0.577 

and produce a plot of

Just to be clear: this uses the asteval module ( https://newville.github.io/asteval/ ) to parse and evaluate the user input in a way that tries to be as safe as possible from malicious user input that would be exposed using a plain eval .