[Note] Two ways of creating an `fd` object for functional inputs

[ruiqwy]

There are two ways to create functional data for modeling. The first is by specifying the positions and values of each observation point and obtaining it via the smooth_basis function of the BsplineFunc class; the second is by directly using the fd function in fda_func, specifying a known basis and coefficients.

[ruiqwy]

Example 1

import numpy as np
from GENetLib.fda_func import create_bspline_basis
from GENetLib.BsplineFunc import BsplineFunc
np.random.seed(1)
n_obs = 100
nbasis = 15
x = np.array(np.linspace(1e-2, 1, 100))
basis = create_bspline_basis(rangeval=[min(x), max(x)], nbasis=nbasis, norder=4)
bspline = BsplineFunc(basis)
smoothed_functions = []
for i in range(1000):
    y_noisy = np.sin(2 * np.pi * x) + np.random.normal(scale=0.1, size=n_obs)
    smoothed = bspline.smooth_basis(x, y_noisy.reshape(-1, 1))
    smoothed_functions.append(smoothed)

[ruiqwy]

Example 2

import numpy as np
from GENetLib.fda_func import fd, create_bspline_basis
nbasis = 15
x = np.array(np.linspace(1e-2, 1, 100))
basis = create_bspline_basis(rangeval=[min(x), max(x)], nbasis=nbasis, norder=4)
fd_function = fd(coef = np.random.randn(15, 1), basisobj = basis)