Interpolation Exercise 1



In [30]:

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



In [31]:

    
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 [32]:

    
with np.load('trajectory.npz') as data:
    x = data['x']
    y = data['y']
    t = data['t']



In [33]:

    
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 [34]:

    
newt = np.linspace(np.min(t),np.max(t),200)
xfunc = interp1d(t, x, kind='cubic')
yfunc = interp1d(t, y, kind='cubic')
newx = xfunc(newt)
newy = yfunc(newt)



In [35]:

    
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 [36]:

    
plt.figure(figsize=(9,9))
plt.plot(x,y, marker='o', linestyle='', label='original data');
plt.plot(newx,newy, label='interpolated');
plt.legend();
plt.grid(False)
plt.box(True)
plt.xlabel('x(t)')
plt.ylabel('y(t)')









    Out[36]:





<matplotlib.text.Text at 0x7fb724b09c18>



In [37]:

    
assert True # leave this to grade the trajectory plot