1d:T746,# Dissimilarity matrix function This function computes the dissimilarity matrix containing the distances between the curves of the functional dataset ```r gmfd_diss(FD, metric, p = NULL, k_trunc = NULL) ``` ## Arguments - `FD`: a functional data object of type `funData` - `metric`: the chosen distance to be used. Choose `"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. - `k_trunc`: a positive numeric value representing the number of components at which the truncated mahalanobis distance must be truncated ## Returns The function returns a matrix of numeric values containing the distances between the curves. ## Examples ```r # 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 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 ) FD <- funData( t, x ) D <- gmfd_diss( FD, metric = "L2" ) ``` ## References 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. **Statistics & Probability Letters**, 131:102--107.

gmfd_diss function