Smoothing of dense one-dimensional functional data

Examples of smoothing of univariate and dense functional data.

# Author: Steven Golovkine <steven_golovkine@icloud.com>
# License: MIT

# Load packages
import matplotlib.pyplot as plt
import numpy as np

from FDApy.simulation import KarhunenLoeve
from FDApy.representation import DenseArgvals
from FDApy.visualization import plot

# Set general parameters
rng = 42
n_obs = 4

# Parameters of the basis
name = "bsplines"
n_functions = 5


kl = KarhunenLoeve(basis_name=name, n_functions=n_functions, random_state=rng)
kl.new(n_obs=n_obs)

# Add some noise to the simulation.
kl.add_noise(0.05)

# Smooth the data
points = DenseArgvals({"input_dim_0": np.linspace(0, 1, 101)})
kernel_name = "epanechnikov"
bandwidth = 0.1
degree = 1

fdata_smooth = kl.noisy_data.smooth(
    points=points,
    method="LP",
    kernel_name=kernel_name,
    bandwidth=bandwidth,
    degree=degree,
)


fig, axes = plt.subplots(2, 2, figsize=(10, 8))
for idx, ax in enumerate(axes.flat):
    plot(kl.noisy_data[idx], colors="k", alpha=0.2, ax=ax)
    plot(kl.data[idx], colors="r", ax=ax)
    plot(fdata_smooth[idx], colors="b", ax=ax)
    ax.set_title(f"Observation {idx + 1}")

# Show the plot
plt.show()