# 導入模塊
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

# 導入數據
x = np.linspace(0,1.0,11)
y = np.array([-0.447, 1.978, 3.28, 6.16, 7.08, 7.34, 7.66, 9.56, 9.48, 9.30, 11.2])

# 擬合二次多項式
f = lambda x, a, b, c: a*x**2 + b*x + c
 
# popt為擬合參數，pcov為參數的協方差矩陣
popt, pcov = curve_fit(f, x, y)
print("擬合的參數值a,b,c分別為：", popt)
 
# x=0.25, 0.35的預測值
print("x=0.25, 0.35的預測值為", f(np.array([0.25, 0.35]), *popt))

plt.rc('font', size=15)
plt.plot(x, y, '*')    # 觀測值數據的散點圖
# 擬合數據的折線圖
plt.plot(np.linspace(0.0, 1.0, 50), f(np.linspace(0.0, 1.0, 50), *popt), '-')
plt.show()