Module simulation 

Simulation functions for functional data.

This module provides tools for generating synthetic functional data using the Karhunen-Loève expansion and various eigenfunction/eigenvalue configurations.

Overview

Functional data can be simulated using the truncated Karhunen-Loève representation:

f_i(t) = μ(t) + Σ_{k=1}^{M} ξ_{ik} φ_k(t)

where:

• μ(t) is the mean function
• φ_k(t) are orthonormal eigenfunctions
• ξ_{ik} ~ N(0, λ_k) are random scores with variances given by eigenvalues

Eigenfunction Types

• Fourier: sin/cos basis functions, suitable for periodic data
• Legendre: Orthonormal Legendre polynomials on [0,1]
• Wiener: Eigenfunctions of the Wiener process

Enums

EFunType

Eigenfunction type enum for simulation

EValType

Eigenvalue decay type for simulation

Functions

add_error_curve

Add curve-level Gaussian noise to functional data.

add_error_pointwise

Add pointwise Gaussian noise to functional data.

eigenfunctions

Unified eigenfunction computation.

eigenvalues

Unified eigenvalue computation.

eigenvalues_exponential

Generate eigenvalue sequence with exponential decay.

eigenvalues_linear

Generate eigenvalue sequence with linear decay.

eigenvalues_wiener

Generate Wiener process eigenvalues.

fourier_eigenfunctions

Compute Fourier eigenfunctions on [0,1].

legendre_eigenfunctions

Compute Legendre polynomial eigenfunctions on [0,1].

sim_fundata

Simulate functional data with specified eigenfunction and eigenvalue types.

sim_kl

Simulate functional data via Karhunen-Loève expansion.

wiener_eigenfunctions

Compute Wiener process eigenfunctions on [0,1].