A functional dataset where the individual functions are given by: \(y_i(t) = z_{i,1} e^{-(t-1.5)^2/2} + z_{i,2}e^{-(t+1.5)^2/2}\), \(t \in [-3, 3], ~i=1,2,\dots, 21\), where \(z_{i,1}\) and \(z_{i,2}\) are i.i.d. normal with mean one and standard deviation 0.25. Each of these functions is then warped according to: \(\gamma_i(t) = 6({e^{a_i(t+3)/6} -1 \over e^{a_i} - 1}) - 3\) if \(a_i \neq 0\), otherwise \(\gamma_i = \gamma_{id}\) (\(gamma_{id}(t) = t\)) is the identity warping). The variables are as follows: f containing the 21 functions of 101 samples and time which describes the sampling.
simu_datasimu_data
A list with 2 components:
f: A numeric matrix of shape \(101 \times 21\) storing a sample of size
\(N = 21\) of curves evaluated on a grid of size \(M = 101\).
time: A numeric vector of size \(M = 101\) storing the grid on which
the curves f have been evaluated.