Interpolation Exercise 1



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%matplotlib inline
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np



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from scipy.interpolate import interp1d

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:



In [26]:

    
# YOUR CODE HERE
data = np.load("trajectory.npz")
t = data["t"]
x = data["x"]
y = data["y"]



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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

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.



In [37]:

    
# YOUR CODE HERE
#She turned me into a
newt = np.linspace(min(t), max(t), 200)

x_approx = interp1d(t, x, kind="cubic")
y_approx = interp1d(t, y, kind="cubic")
newx = x_approx(newt)
newy = y_approx(newt)



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assert newt[0]==t.min()
assert newt[-1]==t.max()
assert len(newt)==200
assert len(newx)==200
assert len(newy)==200

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.



In [47]:

    
# YOUR CODE HERE
plt.plot(newx, newy, marker="o", color="burlywood", label="Interpolated")
plt.plot(x, y, marker="o", color="red", linestyle="", label="Original")
plt.legend(bbox_to_anchor=(1,1), loc=2)









    Out[47]:





<matplotlib.legend.Legend at 0x7f24d4e54390>



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assert True # leave this to grade the trajectory plot