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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 | ||
11 | def read_data(fname): | |
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 | ||
27 | # F = langrange_polynomial(*read_data(data_fname)) | |
28 | (X, Y) = read_data(data_fname) | |
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() |