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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:
 Interpolation Exercise 1
Step1:  2D trajectory interpolation
The file trajectory.npz contains 3 Numpy arrays that describe a 2d trajectory of a particle as a function of time
Step2:  Use these arrays to create interpolated functions $x(t)$ and $y(t)$. Then use those functions to create the following arrays
Step3:  Make a parametric plot of ${x(t),y(t)}$ that shows the interpolated values and the original points
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Python Code:
%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
from scipy.interpolate import interp1d
Explanation: Interpolation Exercise 1
End of explanation
traj = np.load('trajectory.npz')
x = traj['x']
y = traj['y']
t = traj['t']
assert isinstance(x, np.ndarray) and len(x)==40
assert isinstance(y, np.ndarray) and len(y)==40
assert isinstance(t, np.ndarray) and len(t)==40
Explanation: 2D trajectory interpolation
The file trajectory.npz contains 3 Numpy arrays that describe a 2d trajectory of a particle as a function of time:
t which has discrete values of time t[i].
x which has values of the x position at those times: x[i] = x(t[i]).
x which has values of the y position at those times: y[i] = y(t[i]).
Load those arrays into this notebook and save them as variables x, y and t:
End of explanation
newt = np.linspace(t[0],t[len(t) - 1],200)
cont_x = interp1d(t, x, kind='cubic')
cont_y = interp1d(t, y, kind='cubic')
newx = cont_x(newt)
newy = cont_y(newt)
assert newt[0]==t.min()
assert newt[-1]==t.max()
assert len(newt)==200
assert len(newx)==200
assert len(newy)==200
Explanation: Use these arrays to create interpolated functions $x(t)$ and $y(t)$. Then use those functions to create the following arrays:
newt which has 200 points between ${t_{min},t_{max}}$.
newx which has the interpolated values of $x(t)$ at those times.
newy which has the interpolated values of $y(t)$ at those times.
End of explanation
plt.plot(newt, newx)
plt.plot(newt, newy)
plt.plot(t, x, marker='o', linestyle='')
plt.plot(t, y, marker='o', linestyle='')
assert True # leave this to grade the trajectory plot
Explanation: Make a parametric plot of ${x(t),y(t)}$ that shows the interpolated values and the original points:
For the interpolated points, use a solid line.
For the original points, use circles of a different color and no line.
Customize you plot to make it effective and beautiful.
End of explanation
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