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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
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]).y 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:
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f=np.load('trajectory.npz')
x=np.array(f['x'])
y=np.array(f['y'])
t=np.array(f['t'])
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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.
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newt=np.linspace(t.min(),t.max(),200)
xt=interp1d(t,x,kind='cubic')
yt=interp1d(t,y,kind='cubic')
newx=xt(newt)
newy=yt(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:
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# referenced http://goo.gl/gixqML for legend formatting
plt.plot(newx,newy,label='interpolated xy-data')
plt.plot(x,y,marker='o',linestyle='',label='original xy-data')
plt.ylim(bottom=-1.0)
plt.xlim(left=-1.0)
plt.xlabel('x-position')
plt.ylabel('y-position')
plt.legend(loc=10, bbox_to_anchor=(1.2,0.5))
plt.title('2D Trajectory');
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assert True # leave this to grade the trajectory plot