Fitting Models Exercise 2

Imports



In [3]:

    
%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 [83]:

    
# YOUR CODE HERE
data = np.load('decay_osc.npz')
time=data['tdata']
y=data['ydata']
dy=data['dy']

plt.errorbar(time, y, dy,
             fmt='.k', ecolor='lightgray')
plt.xlabel('x')
plt.ylabel('y');
plt.plot(time,y)









    Out[83]:





[<matplotlib.lines.Line2D at 0x7fddaa7dcd68>]



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 [147]:

    
# YOUR CODE HERE
def ymodel(A,lamda,w,sigma,time):
    return A*np.exp(-lamda*time)*np.cos(w*time)+sigma

z,w=opt.curve_fit(ymodel,time,y,p0=[.1,7,-1,.1],sigma=dy,absolute_sigma=True)
plt.plot(z)
plt.plot(time,y)









    



/usr/local/lib/python3.4/dist-packages/IPython/kernel/__main__.py:3: RuntimeWarning: overflow encountered in exp
  app.launch_new_instance()






    Out[147]:





[<matplotlib.lines.Line2D at 0x7fdda8fcd898>]



In [126]:

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



In [ ]: