R/data-toy_curves.R

In fda.vi: Functional Data Analysis using Variational Inference

#' Toy Simulated Functional Dataset
#'
#' @description
#' A small simulated dataset of three functional curves used in package
#' examples. Curves are generated from a known cubic B-spline expansion with
#' correlated errors, making it suitable for demonstrating basis selection and
#' recovery of true coefficients.
#'
#' @details
#' Each curve is generated as:
#' \deqn{y_i(t) = \sum_{k=1}^{8} \xi_{ki} B_k(t) + \varepsilon_i(t)}
#' where \eqn{(\boldsymbol{\xi}_i) = (1.5, 0, -1, 0.8, 0, -0.5, 1.2, -0.9)}
#' for all \eqn{i}, and \eqn{\varepsilon_i \sim \text{GP}(0, \sigma^2 \Psi(w))} with
#' \eqn{\sigma = 0.1} and \eqn{w = 6} (correlation function of an
#' Ornstein-Uhlenbeck (OU) process).
#' Basis functions 2 and 5 have zero coefficients, providing a ground truth
#' for evaluating basis selection.
#'
#' @format A list with the following elements:
#' \describe{
#'   \item{\code{y}}{Named list of 3 numeric vectors of length 50, one per curve.}
#'   \item{\code{Xt}}{Numeric vector of 50 equally spaced time points on \eqn{[0,1]}.}
#'   \item{\code{true_coef}}{Numeric vector of length 8. True basis coefficients:
#'     \code{c(1.5, 0, -1, 0.8, 0, -0.5, 1.2, -0.9)}.}
#'   \item{\code{K}}{Integer. Number of basis functions used (\code{8}).}
#'   \item{\code{m}}{Integer. Number of curves (\code{3}).}
#'   \item{\code{sigma}}{Numeric. True noise standard deviation (\code{0.1}).}
#'   \item{\code{w}}{Numeric. True correlation decay parameter (\code{6}).}
#' }
#'
#' @source Generated via \code{data-raw/generate_toy_curves.R}.
#'
#' @examples
#' data(toy_curves)
#' str(toy_curves)
#'
#' # Plot the three raw curves
#' plot(toy_curves$Xt, toy_curves$y[[1]], type = "l",
#'      ylab = "y", xlab = "t", main = "Toy curves")
#' lines(toy_curves$Xt, toy_curves$y[[2]], col = "blue")
#' lines(toy_curves$Xt, toy_curves$y[[3]], col = "red")
"toy_curves"