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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]).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:
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f = np.load("trajectory.npz")
t = f['t']
x = f['x']
y = f['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.
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X = interp1d(t, x, kind='cubic')
Y = interp1d(t, y, kind='cubic')
newt = np.linspace(min(t), max(t), 200)
newx = X(newt)
newy = Y(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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plt.figure(figsize=(12,5))
plt.plot(t, x, 'b', linestyle='', marker='o', label="Original Point for x(t)")
plt.plot(t, y, 'r', linestyle = '', marker='o', label="Original Point for y(t)")
plt.plot(newt, newx, 'c-', label="Interpoled x(t)")
plt.plot(newt, newy, 'm-', label="Interpoled y(t)")
plt.grid(False)
ax = plt.gca()
ax.set_axis_bgcolor("white")
plt.xlabel("Time", fontsize=14)
plt.title("X and Y Trajectory", fontsize = 14)
plt.ylabel("Position", fontsize = 14)
plt.legend()
plt.show()
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assert True # leave this to grade the trajectory plot
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