プログラミング問題集解答例（問２６）

import numpy as np
f = lambda x: 1/(1 + np.exp(-x))
g = lambda x: 1.0/(1.0+x**2)
h = lambda x: np.sin(x)

x_observed = np.linspace(-10, 10, 11) # 観測点

def lagurange(x_observed, y_observed):
    def accept_variables(x):
        interpolation = 0
        px = [1] * len(x_observed)
        qx = [1] * len(x_observed)
        for i in range (len(x_observed)):
            for j in range (len(x_observed)):
                if i != j:
                    px[i] = px[i] * (x - x_observed[j])
                    qx[i] = qx[i] * (x_observed[i] - x_observed[j])
            interpolation = interpolation + px[i] * y_observed[i] / qx[i]
        return interpolation
    return accept_variables

fitted_curve = lagurange(x_observed, f(x_observed))
fitted_curve

<function __main__.lagurange.<locals>.accept_variables>

x_latent = np.linspace(-10, 10, 101)
fitted_curve(x_latent)

array([ 0.54402111,  1.87516858,  2.42669307,  2.44151156,  2.11182678,
        1.58666499,  0.97861224,  0.36980792, -0.18274842, -0.64252334,
       -0.98935825, -1.21591199, -1.32459162, -1.32492766, -1.23135279,
       -1.06134513, -0.83389931, -0.56829098, -0.28310231,  0.00452185,
        0.2794155 ,  0.52875707,  0.74228372,  0.91237695,  1.03404053,
        1.10479017,  1.12447229,  1.09502822,  1.02021822,  0.90531846,
        0.7568025 ,  0.58201782,  0.38886626,  0.18549619, -0.01998685,
       -0.2197856 , -0.40664816, -0.57407311, -0.71648025, -0.82934527,
       -0.90929743, -0.95418025, -0.96307581, -0.93629387, -0.8753277 ,
       -0.78277906, -0.66225497, -0.51823979, -0.35594594, -0.18114742,
        0.        ,  0.18114742,  0.35594594,  0.51823979,  0.66225497,
        0.78277906,  0.8753277 ,  0.93629387,  0.96307581,  0.95418025,
        0.90929743,  0.82934527,  0.71648025,  0.57407311,  0.40664816,
        0.2197856 ,  0.01998685, -0.18549619, -0.38886626, -0.58201782,
       -0.7568025 , -0.90531846, -1.02021822, -1.09502822, -1.12447229,
       -1.10479017, -1.03404053, -0.91237695, -0.74228372, -0.52875707,
       -0.2794155 , -0.00452185,  0.28310231,  0.56829098,  0.83389931,
        1.06134513,  1.23135279,  1.32492766,  1.32459162,  1.21591199,
        0.98935825,  0.64252334,  0.18274842, -0.36980792, -0.97861224,
       -1.58666499, -2.11182678, -2.44151156, -2.42669307, -1.87516858,
       -0.54402111])

%matplotlib inline
import matplotlib.pyplot as plt

fitted_curve = lagurange(x_observed, f(x_observed))
plt.scatter(x_observed, f(x_observed), label="observed")
plt.plot(x_latent, f(x_latent), label="latent")
plt.plot(x_latent, fitted_curve(x_latent), label="fitted")
plt.grid()
plt.legend()
plt.show()

%matplotlib inline
import matplotlib.pyplot as plt

for func in [f, g, h]:
    fitted_curve = lagurange(x_observed, func(x_observed))
    plt.scatter(x_observed, func(x_observed), label="observed")
    plt.plot(x_latent, func(x_latent), label="latent")
    plt.plot(x_latent, fitted_curve(x_latent), label="fitted")
    plt.grid()
    plt.legend()
    plt.show()