xplodnow - 6 months ago 34

Python Question

this is quite a specific problem I was hoping the community could help me out with. Thanks in advance.

So I have 2 sets of data, one is experimental and the other is based off of an equation. I am trying to fit my data points to this curve and hence obtain the missing variables I am interested in. Namely, a and b in the Ebfit function.

Here is the code:

`%matplotlib notebook`

import numpy as np

import matplotlib.pyplot as plt

import scipy.stats as spys

from scipy.optimize import curve_fit

time = [60,220,520,1840]

Moment = [0.64227262,0.468318916,0.197100772,0.104512508]

Temperature = 25 # Bake temperature in degrees C

Nb = len(Moment) # Number of bake measurements

Baketime_a = time #[s]

N_Device = 10000 # No. of devices considered in the array

T_ambient = 273 + Temperature

kt = 0.0256*(T_ambient/298) # In units of eV

f0 = 1e9 # Attempt frequency

def Ebfit(x,a,b):

Eb_mean = a*(0.0256/kt) # Eb at bake temperature

Eb_sigma = b*Eb_mean

Foursigma = 4*Eb_sigma

Eb_a = np.linspace(Eb_mean-Foursigma,Eb_mean+Foursigma,N_Device)

dEb = Eb_a[1] - Eb_a[0]

pdfEb_a = spys.norm.pdf(Eb_a,Eb_mean,Eb_sigma)

## Retention Time

DMom = np.zeros(len(x),float)

tau = (1/f0)*np.exp(Eb_a)

for bb in range(len(x)):

DMom[bb]= (1 - 2*(sum(pdfEb_a*(1 - np.exp(np.divide(-x[bb],tau))))*dEb))

return DMom

a = 30

b = 0.10

params,extras = curve_fit(Ebfit,time,Moment)

x_new = list(range(0,2000,1))

y_new = Ebfit(x_new,params[0],params[1])

plt.plot(time,Moment, 'o', label = 'data points')

plt.plot(x_new,y_new, label = 'fitted curve')

plt.legend()

The main problem I am having is that the fitting of the data to the function does not work when I use large number of points. In the above code When I use the 4 points (time & moment), this code works fine.

I get the following values for

array([ 29.11832766, 0.13918353])

The expected values for a is (23-50) and b is (0.06 - 0.15). So these values are within the acceptable range. This is the corresponding plot:

However, when I use my actual experimental normalized data with about 500 points.

EDIT: This data:

https://www.dropbox.com/s/64zke4wckxc1r75/Normalized%20Data.csv?dl=0

Raw Data

https://www.dropbox.com/s/ojgse5ibp59r8nw/Data1.csv?dl=0

I get the following values and plot for

array([-13.76687781, -12.90494196])

I know these values are wrong and if I were to do it manually (slowly adjusting values to obtain the proper fit) it would be around

I have tried changing the initial guess values for

.

.

.

.

The model I am trying to fit the data to comes from the following equation:

where Dmom = 1 - 2*Psw

Answer

It looks like you do need to play around with the initial guesses for `a`

and `b`

after all. Perhaps the function you're fitting is not very well behaved, which is why it's so prone to fail for intitial guesses away from the global minumum. That being said, here's a working example of how to fit your data:

```
import pandas as pd
data_df = pd.read_csv('data.csv')
time = data_df['Time since start, Time [s]'].values
moment = data_df['Signal X direction, Moment [emu]'].values
params, extras = curve_fit(Ebfit, time, moment, p0=[40, 0.3])
```

Yields the values of `a`

and `b`

of:

```
In [6]: params
Out[6]: array([ 30.47553689, 0.08839412])
```

Which results in a nicely aligned fit of a function.

```
x_big = np.linspace(1, 1800, 2000)
y_big = Ebfit(x_big, params[0], params[1])
plt.plot(time, moment, 'o', alpha=0.5, label='all points')
plt.plot(x_big, y_big, label = 'fitted curve')
plt.legend()
plt.show()
```