Data Fitting in Python for multiple peaks

Question

import numpy as np
from sympy.physics.wigner import wigner_6j
import matplotlib.pyplot as plt
xr=np.arange(0,33)
[Jo, Ju, I, Ao, Au]=[4.5, 4.5, 2.5,674.4,929]
Ao=Ao*0.00003335640954804
Au=Au*0.00003335640954804
xr1=100000000/np.array(xr)
positions=xr1
centroid = positions.mean(axis=0)
newo=0.005+100000000/4715.2274
Fo=[]
Fu=[]
new=[]
In=[]
Fomax=Jo+I
Fomin=abs(Jo-I)
Fumax=Ju+I
Fumin=abs(Ju-I)
no=int(2*min(Jo,I)+1)
for i in range(0,no):
    Fo.append(Fomax-i)
nu=int(2*min(Ju,I)+1)
for i in range(0,nu):
    Fu.append(Fumax-i)
for i in range(0,no):
    for j in range(0,nu):
        if abs(Fo[i]-Fu[j])<2:
            new.append(newo+(Ao/2)*(Fo[i]*(Fo[i]+1)-Jo*(Jo+1)-I*(I+1))-(Au/2)*(Fu[j]*(Fu[j]+1)-Ju*(Ju+1)-I*(I+1)))
            In.append((2*Fo[i]+1)*(2*Fu[j]+1)*(wigner_6j(Jo,Fo[i],I,Fu[j],Ju,1))**2/(2*I+1))
            max1=np.max(In)
for i in range(0,len(new)):
    for j in range(0,len(new)):
        if new[i]>new[j]:
            temp=new[j]
            new[j]=new[i]
            new[i]=temp
            temp=In[j]

            In[j]=In[i]
            In[i]=temp
zr=[]
sigma=0.031
x2=[]
y2=[]
y2r=[]
for i in range(0, len(new)):
    mew=new[i]
    for j in range(-100,100):
        c=mew+j/1000
        cc=In[i]*(1/(sigma*(44/7)**0.5))*np.exp(-1*((c-mew)/sigma)**2)
        y2.append(cc)
        x2.append(c)
max2=np.max(y2)
for i in range(0,len(new)):
    In[i]=In[i]/max1
for i in range(0,len(y2)):
    y2[i]=y2[i]/max2
for i in range(0,len(y2)):
    y2r.append(y2[i])
for i   in range(0,15):
    a=5
print(centroid)
fig, ax = plt.subplots()
plt.plot(x2, y2r,label="fitted data")
plt.legend()
plt.show()

I have this code which is making multiple peaks. The image 1 shows the data with multiple peaks overlapped with each other but i m trying to achieve only one curve by using these overlapped peaks as shown in image 2 in 'red' line.

But the issue is that have to fit a line as shown in the last picture

Answer 1

I hope I get the question now. If I see it right the problem is basically that the x values differ. On top of it, everything is merged in a single list. To handle this I changed everything after print(centroid) to

from scipy.interpolate import interp1d

def partition( inList, n ):
    return zip( *[ iter( inList ) ] * n )

xSplit = partition( x2, 200 ) ###manually set to 200 as data is created with range(-100,100)
ySplit = partition( y2r, 200 )
allx = sorted( x2 )
ally = np.zeros( len( allx ), np.float )
funcDict = dict()
for i in range( len( xSplit ) ):
    funcDict[i] = interp1d( xSplit[i], ySplit[i], kind='linear', bounds_error=False, fill_value=0 ) 
for i in range( len( xSplit ) ):
    ally += funcDict[i]( allx )

fig, ax = plt.subplots()
ax.plot( allx, ally, linewidth=2 )
for col1, col2 in zip( xSplit, ySplit ):
    plt.plot( col1, col2, linestyle='--' )
plt.legend()
plt.show()

which gives you

which is the sum, but using interpolation of the data. Was that the idea?

Edit Seems that the OP requires more an envelope rather than a sum. On solution is given by James Phillips. One can even shorten this using numpy changing

ally += funcDict[i]( allx )

to

ally = np.maximum(ally, funcDict[i]( allx ) )

which then gives