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# Langrange polynomial interpolation

a guest May 15th, 2014 1,776 Never
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1. #!/usr/bin/env python
2.
3. import numpy as np
4. from matplotlib import pyplot as plt
5.
6. data_fname = 'knot_points.csv'
7. # x1,y1
8. # x2,y2
9. # ...
10.
12.     X = []
13.     Y = []
14.     with open(fname, 'r') as f:
15.         for line in f:
16.             (x, y) = line.split(',')
17.             X.append(float(x))
18.             Y.append(float(y))
19.     return (X, Y)
20.
21. def langrange_polynomial(X, Y):
22.     def L(i):
23.         return lambda x: np.prod([(x-X[j])/(X[i]-X[j]) for j in range(len(X)) if i != j]) * Y[i]
24.     Sx = [L(i) for i in range(len(X))]  # summands
25.     return lambda x: np.sum([s(x) for s in Sx])
26.
29. F = langrange_polynomial(X, Y)
30.
31. x_range = np.linspace(X[0], X[-1], 100)
32. plt.plot(X, Y, 'ro')
33. plt.plot(x_range, map(F, x_range))
34. plt.xlabel(r'\$x\$')
35. plt.ylabel(r'\$F(x)\$')
36. plt.title('Lagrange polynomial interpolation')
37. plt.grid(True)
38. plt.show()
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