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Given the following text description, write Python code to implement the functionality described below step by step
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Description:
 Fitting Models Exercise 2
Imports
Step1:  Fitting a decaying oscillation
For this problem you are given a raw dataset in the file decay_osc.npz. This file contains three arrays
Step2:  Now, using curve_fit to fit this model and determine the estimates and uncertainties for the parameters
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Python Code:
%matplotlib inline
import matplotlib.pyplot as plt
import numpy as np
import scipy.optimize as opt
Explanation: Fitting Models Exercise 2
Imports
End of explanation
# 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)
assert True # leave this to grade the data import and raw data plot
Explanation: 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.
End of explanation
# 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)
assert True # leave this cell for grading the fit; should include a plot and printout of the parameters+errors
Explanation: 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.
End of explanation
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