Fitting Models Exercise 2

Imports



In [70]:

    
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt

Fitting a decaying oscillation

For this problem you are given a raw dataset in the file decay_osc.npz. This file contains three arrays:

tdata: an array of time values
ydata: an array of y values
dy: the absolute uncertainties (standard deviations) in y

Your job is to fit the following model to this data:

$$ y(t) = A e^{-\lambda t} \cos{\omega t + \delta} $$

First, import the data using NumPy and make an appropriately styled error bar plot of the raw data.



In [72]:

    
data = np.load('decay_osc.npz')
tdata = data['tdata']
ydata = data['ydata']
dy = data['dy']



In [73]:

    
plt.errorbar(tdata, ydata, dy,
             fmt='.k', ecolor='lightgray')









    Out[73]:





<Container object of 3 artists>



In [ ]:

    
assert True # leave this to grade the data import and raw data plot

Now, using curve_fit to fit this model and determine the estimates and uncertainties for the parameters:

Print the parameters estimates and uncertainties.
Plot the raw and best fit model.
You will likely have to pass an initial guess to curve_fit to get a good fit.
Treat the uncertainties in $y$ as absolute errors by passing absolute_sigma=True.



In [101]:

    
def exp_model(t,A,Lambda,Omega,Sigma,):
    y = A*np.exp(Lambda*t)*np.cos(Omega*t)
    return y


popt, popy = opt.curve_fit(exp_model,tdata,ydata,absolute_sigma=True)
print (popt)
print ()
print (popy)









    



[-5.25691994 -0.07403659  1.01219347  1.        ]

[[ inf  inf  inf  inf]
 [ inf  inf  inf  inf]
 [ inf  inf  inf  inf]
 [ inf  inf  inf  inf]]



In [ ]:

    
assert True # leave this cell for grading the fit; should include a plot and printout of the parameters+errors