gmfd_simulate {gmfd} | R Documentation |
Simulation of a functional sample
Description
Simulate a univariate functional sample using a Karhunen Loeve expansion.
Usage
gmfd_simulate(size, mean, covariance = NULL, rho = NULL, theta = NULL)
Arguments
size |
a positive integer indicating the size of the functional sample to simulate. |
mean |
a vector representing the mean of the sample. |
covariance |
a matrix from which the eigenvalues and eigenfunctions must be extracted. |
rho |
a vector of the eigenvalues in descending order to be used for the simulation. |
theta |
a matrix containing the eigenfunctions in its columns to be used for the simulation. |
Value
The function returns a functional data object of type funData
.
Examples
# Define parameters
n <- 50
P <- 100
K <- 150
# Grid of the functional dataset
t <- seq( 0, 1, length.out = P )
# Define the means and the parameters to use in the simulation
# with the Karhunen - Loève expansion
m1 <- t^2 * ( 1 - t )
rho <- rep( 0, K )
theta <- matrix( 0, K, P )
for ( k in 1:K ) {
rho[k] <- 1 / ( k + 1 )^2
if ( k%%2 == 0 )
theta[k, ] <- sqrt( 2 ) * sin( k * pi * t )
else if ( k%%2 != 0 && k != 1 )
theta[k, ] <- sqrt( 2 ) * cos( ( k - 1 ) * pi * t )
else
theta[k, ] <- rep( 1, P )
}
# Simulate the functional data
x <- gmfd_simulate( n, m1, rho = rho, theta = theta )
[Package gmfd version 1.0.1 Index]