python自定義函數的參數擬合

example：xdata是輸入，ydata是輸出

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

def func(x, a, b, c):
  return a * np.exp(-b * x) + c

# Define the data to be fit with some noise:
xdata = np.linspace(0, 4, 50)
y = func(xdata, 2.5, 1.3, 0.5)
np.random.seed(1729)
y_noise = 0.2 * np.random.normal(size=xdata.size)
ydata = y + y_noise
plt.plot(xdata, ydata, 'b-', label='data')

# Fit for the parameters a, b, c of the function func:
popt, pcov = curve_fit(func, xdata, ydata)
print(popt)
plt.plot(xdata, func(xdata, *popt), 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

# Constrain the optimization to the region of 0 <= a <= 3, 0 <= b <= 1 and 0 <= c <= 0.5:
popt, pcov = curve_fit(func, xdata, ydata, bounds=(0, [3., 1., 0.5]))
print(popt)
plt.plot(xdata, func(xdata, *popt), 'g--',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

 全參考圖像質量評價中，PSNR的輸出取值範圍是0～100 dB，想要把其輸出範圍映射到0～1區間的話，參考[2]的方法，用下面的式子來擬合，總共有5個參數。

下面的代碼中，xdata表示PSNR的數值，ydata表示對應的0～1範圍數值。

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


def func(x, a, b, c, d, e):
  logist = 0.5 - 1/(1+np.exp(b * (x-c)))
  return a*logist + d*x + e


# Define the data to be fit with some noise:
xdata = np.hstack([np.linspace(0, 18, 20), np.linspace(19, 21, 20), np.linspace(21, 30, 50),np.linspace(31, 40, 20),np.linspace(41, 100, 30)])
ydata = np.hstack([np.linspace(0, 0.05, 20),np.linspace(0.1, 0.15, 20), np.linspace(0.2, 0.8, 50), np.linspace(0.81, 0.9, 20), np.linspace(0.9, 1.0, 30)])

np.random.seed(1729)
y_noise = 0.005 * np.random.normal(size=xdata.size)
ydata = ydata + y_noise


for i in range(ydata.size):
  if ydata[i] < 0:
    ydata[i] = 0
  if ydata[i] > 100:
    ydata[i] = 100

plt.plot(xdata, ydata, 'b-', label='data')

# Fit for the parameters a, b, c of the function func:
popt, pcov = curve_fit(func, xdata, ydata)
print(popt)
plt.plot(xdata, func(xdata, *popt), 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f, d=%5.3f, e = %5.3f' % tuple(popt))


plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

 

[1] python 自定義函數表達式 擬合求係數

[2] H. R. Sheikh, M. F. Sabir, and A. C. Bovik, “A statistical evaluation of recent full reference image quality assessment algorithms,”IEEE Trans. Image Process., vol. 15, no. 11, pp. 3440–3451, Nov. 2006.