Interpolation Exercise 1



In [13]:

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



In [14]:

    
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]:

    
traj = np.load('trajectory.npz')
x = traj['x']
y = traj['y']
t = traj['t']



In [27]:

    
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 [43]:

    
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)



In [44]:

    
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 [55]:

    
plt.plot(newt, newx)
plt.plot(newt, newy)
plt.plot(t, x, marker='o', linestyle='')
plt.plot(t, y, marker='o', linestyle='')









    Out[55]:





[<matplotlib.lines.Line2D at 0x7fb2603605f8>]



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assert True # leave this to grade the trajectory plot