高斯曲線擬合

轉自：https://blog.csdn.net/renjie10/article/details/114933766

1.目的
針對光譜離散數據，尋峰完成后截取near峰值的數據，利用高斯擬合重繪單峰曲線，進而實現分峰功能

2.原理

 

 

 

 

3.代碼

import numpy as np
from math import log, exp
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy import asarray as ar,exp
 
# 將txt文件讀入numpy數組

yOriginal = np.loadtxt('C:\\工作\數據.txt')
#一維數據
#yOriginal = np.array([5.81528E-05, 0.000111682, 0.000271214, 0.000391546, 0.000786933, 0.002034528, 0.002968284, 0.005004177, 0.007329225, 0.011119662, 0.017025547, 0.02488255, 0.04219861, 0.040429801, 0.035320014, 0.05154864, 0.06894745,
     #                 0.105841984, 0.083166325, 0.110311517, 0.055681743, 0.093540639, 0.066621081, 0.056688568, 0.045128754, 0.045911571, 0.028179728, 0.021262112, 0.018781554, 0.008240159, 0.008562607, 0.004372914, 0.002847578, 0.001717186, 0.001081616])
xOriginal = np.arange(len(yOriginal))
print("輸入數據n", yOriginal)
average = sum(yOriginal)/len(yOriginal)
 
#y = yOriginal
#x = xOriginal
 
#print("過濾數據n", y)
 
y = np.log(y)
zMatrix = np.matrix(y)
print("取對數n", y)
 
# 構造 X 矩陣
 
xMatrixT = np.matrix(np.reshape(np.concatenate(
    (np.ones((len(y))), x, x*x)), (3, len(y))))
xMatrix = np.matrix(xMatrixT.T)
print("X 矩陣n", xMatrix)
 
#np.matrix.__mul__ = np.dot  # 重載運算符
print(xMatrixT*xMatrix)
bMatrix = ((xMatrixT*xMatrix).I*xMatrixT)*zMatrix.T#矩陣運算
print("B 矩陣n", bMatrix)
 
b2, b1, b0 = float(bMatrix[2][0]), float(bMatrix[1][0]), float(bMatrix[0][0])
print("b0={}b1={}b2={}".format(b0, b1, b2))

s = -1/b2
xMaxi = s*b1/2
yMaxi = exp(b0+xMaxi**2/s)
print(yMaxi, xMaxi, s)

def gaussian(x,*param):
    return param[0]*np.exp(-np.power(x - param[1], 2.) / (2 * np.power(param[2], 2.)))#高斯公式

popt,pcov = curve_fit(gaussian,xOriginal,yOriginal,p0=[yMaxi,xMaxi,s])     
print(popt)
print(pcov)          
           
plt.plot(xOriginal,yOriginal,'b+:',label='data')
plt.plot(xOriginal,gaussian(xOriginal,*popt),'ro:',label='fit')#繪圖
plt.legend()
plt.show()

其中傳參數時s應改為 np.sqrt(s/2) 

 

 

4.效果

 

 

 

 

 

參考：

最小二乘法： https://www.zhihu.com/question/37031188

高斯曲線擬合公式推導： https://blog.csdn.net/Abaqus3_0/article/details/82011159

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