Functional basis set

In this example, we present a subset of implemented functional basis set.

import numpy as np
import matplotlib.pyplot as plt

import VolterraBasis.basis as bf

from scipy.interpolate import splrep

x_range = np.linspace(-2, 2, 30).reshape(-1, 1)

t, c, k = splrep(x_range, x_range ** 4 - 2 * x_range ** 2 + 0.5 * x_range)

basis_set = {"Linear": bf.LinearFeatures(), "Polynom": bf.PolynomialFeatures(3), "Hermite Polynom": bf.PolynomialFeatures(3, np.polynomial.Hermite), "Fourier": bf.FourierFeatures(order=2, freq=1.0), "B Splines": bf.BSplineFeatures(6, k=3), "Splines Fct": bf.SplineFctFeatures(t, c, k)}
for key, basis in basis_set.items():
    basis.fit(x_range)

fig_kernel, axs = plt.subplots(2, 3)
m = 0
for key, basis in basis_set.items():
    axs[m // 3][m % 3].set_title(key)
    axs[m // 3][m % 3].set_xlabel("$x$")
    axs[m // 3][m % 3].set_ylabel("$h_k(x)$")
    axs[m // 3][m % 3].grid()
    y = basis.basis(x_range)

    for n in range(y.shape[1]):
        axs[m // 3][m % 3].plot(x_range[:, 0], y[:, n])
    m += 1
plt.show()