Python 曲线拟合，高斯

Question

我正在尝试使用 scipy 和曲线拟合对我的数据进行高斯拟合，这是我的代码:

import csv
import numpy as np
import matplotlib.pyplot as plt

from scipy.optimize import curve_fit

A=[]
T=[]
seuil=1000
range_gauss=4
a=0

pos_peaks=[]
amp_peaks=[]

A_gauss=[]
T_gauss=[]

new_A=[]
new_T=[]

def gauss(x,a,x0,sigma):
  return a*np.exp(-(x-x0)**2/(2*sigma**2))

with open("classeur_test.csv",'r') as csvfile:
  reader=csv.reader(csvfile, delimiter=',')
for row in reader :
  A.append(float(row[0]))
  T.append(float(row[1]))

npA=np.array(A)
npT=np.array(T)

for i in range(1,len(T)):
  #PEAK DETECTION
  if (A[i]>A[i-1] and A[i]>A[i+1]) and A[i]>seuil:
    pos_peaks.append(i)
    amp_peaks.append(A[i])
    #GAUSSIAN RANGE
    for j in range(-range_gauss,range_gauss):
        #ATTENTION AUX LIMITES
        if(i+j>0 and i+j<len(T)-1):
            A_gauss.append(A[i+j])
            T_gauss.append(T[i+j])

npA_gauss = np.array(A_gauss)
npT_gauss = np.array(T_gauss)

for i in range (0,7):
  new_A.append(npA_gauss[i])
  new_T.append(npT_gauss[i])

new_npA=np.array(new_A)
new_npT=np.array(new_T)

n = 2*range_gauss
mean = sum(new_npT*new_npA)/n
sigma = sum(new_npA*(new_npT-mean)**2)/n

popt,pcov = curve_fit(gauss,new_npT,new_npA,p0=[1,mean,sigma])
plt.plot(T,A,'b+:',label='data')
plt.plot(new_npT,gauss(new_npT,*popt),'ro:',label='Fit')

print ("new_npA : ",new_npA)
print ("new_npT : ",new_npT)

plt.legend()
plt.title('Fit')
plt.xlabel('X')
plt.ylabel('Y')
plt.show()

我的数组 new_npT 和 new_npA 是这样的 numpy 数组:

new_npA : [ 264. 478. 733. 1402. 1337. 698. 320.]

new_npT:[229.609344 231.619385 233.62944 235.639496 237.649536 239.659592 241.669647]

这是结果

我不明白为什么我不能成功绘制高斯曲线...
有什么解释吗？

Answer 1

我现在可以在我的数据上拟合高斯曲线

我仍然不明白 Jannick 是如何找到曲线拟合的 p0 的，但它确实有效。

我创建了一个包含峰值位置和振幅的 3 维数组，并为 rang_gauss 使用了一个 while 循环。我对我的 3D 阵列正确使用了 scipy curve_fit，并用系数 f 校正了振幅。

import csv
import numpy as np
import matplotlib.pyplot as plt

from scipy.optimize import curve_fit
seuil=1000 # calculer en fonction du bruit etc ................................
range_gauss=4

A=[]
T=[]

pos_peaks=[]
amp_peaks=[]
indices_peaks=[]

tab_popt=[]
l=[] 
gauss_result=[]

tab_w=[]

def gauss1(x,a,x0,sigma):
    return a*np.exp(-(x-x0)**2/(2*sigma**2))

def gauss2(x,a,x0,sigma):
    return (a/sigma*np.sqrt(2*np.pi))*np.exp(-0.5*((x-x0)/sigma)**2)

#LECTURE DU FICHIER ET INITIALISATION DE TABLEAUX CONTENANT TOUTES LES VALEURS
with open("classeur_test.csv",'r') as csvfile:
    reader=csv.reader(csvfile, delimiter=',')
    for row in reader :
        A.append(float(row[0]))
        T.append(float(row[1]))

#PEAK DETECTION
for i in range(1,len(T)):
    if (A[i]>A[i-1] and A[i]>A[i+1]) and A[i]>seuil:
        pos_peaks.append(T[i])
        amp_peaks.append(A[i])
        indices_peaks.append(i)

#TABLEAU 3D AVEC LES AMPLITUDES ET TEMPS DE CHAQUE PIC
Tableau=np.zeros((len(pos_peaks),2,2*range_gauss+1))

#POUR CHAQUE PIC
m=0
j=-range_gauss
for i in range(0,len(pos_peaks)):
    while(j<range_gauss+1):
        #PEAK DETECTION & LIMITS CONSIDERATION
        if(pos_peaks[i]+j>=0 and pos_peaks[i]+j<=T[len(T)-1] and m<=2*range_gauss+1 and indices_peaks[i]+j>=0):  
            Tableau[i,0,m]=(A[indices_peaks[i]+j])
            Tableau[i,1,m]=(T[indices_peaks[i]+j]) 
            m=m+1
            j=j+1
        else :
            j=j+1
            print("else")
            print("1 : ",pos_peaks[i]+j,", m : ",m," , indices_peaks[i]+j : ",indices_peaks[i]+j)
    m=0
    j=-range_gauss

    popt,pcov = curve_fit(gauss2,Tableau[i,1,:],Tableau[i,0,:],p0=[[1400,240,10]])
    tab_popt.append(popt)
    l.append(np.linspace(T[indices_peaks[i]-range_gauss],T[indices_peaks[i]+range_gauss],50))

    gauss_result.append(gauss2(l[i],1,tab_popt[i][1],tab_popt[i][2])*(1))
    f= amp_peaks[i]/max(gauss_result[i])
    gauss_result[i]=gauss_result[i]*f

    #LARGEUR MI HAUTEUR
    w=2*np.sqrt(2*np.log(2))*tab_popt[i][2]
    tab_w.append(w)

    ####################################PLOTS
    plt.subplot(2,1,1)
    plt.plot(T,A,label='data')
    plt.axis([T[0]-5,T[len(T)-1]-10,0,max(A)+200])
    #plt.plot(Tableau[i,1,:],gauss2(Tableau[i,1,:],*popt),'ro:',label='fit')
    plt.subplot(2,1,2)
    plt.plot(l[i],gauss_result[i])
    plt.axis([T[0]-5,T[len(T)-1]-10,0,max(A)+200])

'''TEST POINTS INFLEXIONS
    for j in range(0,len(A)-1):
        inflex_points.append((np.diff(np.diff(A[j],n=2),n=2)))
        print(inflex_points[j])

        for k in range(0,len(inflex_points[j])-1):
            if (inflex_points[j][k] < 1 and inflex_points[j][k] > -1):
                print("j : ",j)'''

'''TEST INTERNET GRADIENT ???
plt.plot(np.gradient(gauss_result[0]), '+')
spl = UnivariateSpline(np.arange(len(gauss_result[0])), np.gradient(gauss_result[0]), k=5)
spl.set_smoothing_factor(1000)
plt.plot(spl(np.arange(len(gauss_result[0]))), label='Smooth Fct 1e3')
spl.set_smoothing_factor(10000)
plt.plot(spl(np.arange(len(gauss_result[0]))), label='Smooth Fct 1e4')
plt.legend(loc='lower left')
max_idx = np.argmax(spl(np.arange(len(gauss_result[0]))))
plt.vlines(max_idx, -5, 9, linewidth=5, alpha=0.3)
'''

plt.show()