Scipyのcurve_fitで最小2乗法近似、決定係数R2も求める。

Scipy_curvefit_parabolic.py

# -*- coding: utf-8 -*-
# AWS cloud9

import matplotlib
matplotlib.use("Agg")
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit  
import numpy as np

x_data = np.linspace(-10, 10, 20)
 
y_data = np.random.rand() * x_data **2
y_data_error_1 = np.random.normal(size=len(x_data))
y_data_1 = y_data + y_data_error_1

def func(x, a):
    f = a*x**2
    return f
    
fig = plt.figure(figsize=(6, 4))
plt.rcParams["font.size"] = 16
ax1 = fig.add_subplot(111)

popt, pcov = curve_fit(func,x_data,y_data_1)
residuals =  y_data_1- func(x_data, popt)
rss = np.sum(residuals**2)#residual sum of squares = rss
tss = np.sum((y_data_1-np.mean(y_data_1))**2)#total sum of squares = tss
r_squared = 1 - (rss / tss)

ax1.plot(x_data,y_data_1,'mo')
ax1.plot(x_data,func(x_data, popt),'g-')
ax1.annotate("$R^2$="+str(r_squared)[0:5], xy=(0.6, 0.6), xycoords='axes fraction')
ax1.annotate("$y$="+str(popt)[1:6]+"$x^2$", xy=(0.6,0.7), xycoords='axes fraction')

fig.savefig("Scipy_curve_fit_parabolic.png", dpi=200,transparent = False, bbox_inches = 'tight')