funDist: Distance function
In martinoandrea92/dpdistance: Inference and Clustering of Functional Data

Description Usage Arguments Value References Examples

This function allows you to compute the distance between two curves with the chosen metric.

1	funDist(grid, x, y, metric, p = NULL, lambda = NULL, phi = NULL)

`grid`	the grid (of length `T`) over which the two curves are defined.
`x`	a vector containing the first curve.
`y`	a vector containing the second curve.
`metric`	the chosen distance to be used: `"L2"` for the classical L2-distance, `"trunc"` for the truncated Mahalanobis semi-distance, `"mahalanobis"` for the generalized Mahalanobis distance.
`p`	a positive numeric value containing the parameter of the regularizing function for the generalized Mahalanobis distance.
`lambda`	a vector containing the eigenvalues of the functional data from which `"x"` and `"y"` are extracted.
`phi`	a matrix containing the eigenfunctions of the functional data from which `"x"` and `"y"` are extracted.

The function returns a numeric value indicating the distance between the two curves.

Ghiglietti A., Ieva F., Paganoni A. M. (2017). Statistical inference for stochastic processes: Two-sample hypothesis tests, Journal of Statistical Planning and Inference, 180:49-68.

Ghiglietti A., Paganoni A. M. (2017). Exact tests for the means of gaussian stochastic processes. Statics & Probability Letters, 131:102–107.

# 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 - LoÃ¨ve expansion
m1 <- t^2 * ( 1 - t )

lambda <- rep( 0, K )
theta <- matrix( 0, K, P )
for ( k in 1:K ) {
  lambda[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
z <- simulate_KL( t, n, m1, rho = lambda, theta = theta )

# Extract two rows of the functional data
x <- z$data[[1]][1, ]
y <- z$data[[1]][2, ]

d <- funDist( t, x, y, metric = "L2" )