## ----setup, include=FALSE-----------------------------------------------------
knitr::opts_chunk$set(echo = TRUE, eval = FALSE)

## -----------------------------------------------------------------------------
#  library("fdaPOIFD")
#  library("MASS")
#  library("fdapace")
#  library("FastGP")
#  
#  # auxiliary functions to generate Gaussian processes
#  Cov_exponential <- function(X1, X2, alpha = NULL, beta = NULL){
#    x.aux <- expand.grid(i = X1, j = X2)
#  
#    cov <- alpha*exp(-beta*abs(x.aux$i - x.aux$j))
#  
#    Sigma <- matrix(cov, nrow = length(X1))
#    return(Sigma)
#  }
#  
#  Cov_Periodic <- function(X1, X2, sigma = NULL, p = NULL, l = NULL) {
#    #p = period, l = wiggles, sigma = noise
#    Sigma <- matrix(rep(0, length(X1)*length(X2)), nrow=length(X1))
#    for (i in 1:nrow(Sigma)) {
#      for (j in 1:ncol(Sigma)) {
#        Sigma[i,j] <- sigma*exp(-(2*(sin(pi*abs(X1[i]-X2[j])/(p)))^2)/(l^2))
#      }
#    }
#    return(Sigma)
#  }
#  

## -----------------------------------------------------------------------------
#  n <- 100
#  p <- 200
#  
#  #parameters
#  time_grid <- seq(0, 1, length.out = p)
#  sigmaPeriodic <- Cov_Periodic(time_grid, time_grid, sigma = 3, p = 1 , l = 0.5)
#  sigmaExpo <- Cov_exponential(time_grid, time_grid, alpha = 0.5, beta = 5)
#  
#  # Generate the random mean
#  centerline <- MASS::mvrnorm(1, rep(0, p), sigmaPeriodic)
#  
#  # Generate the random sample
#  dataY <- FastGP::rcpp_rmvnorm(n, sigmaExpo, centerline)
#  data <- t(dataY)
#  colnames(data) <- as.character(c(1:n))
#  rownames(data) <- round(time_grid, digits=5)
#  
#  
#  dataPOFD <- intervalPOFD(data, observability = 0.5, ninterval = 4, pIncomplete = 0.75)

## -----------------------------------------------------------------------------
#  depth_complete <- POIFD(dataPOFD$fd, type = "MBD")

## -----------------------------------------------------------------------------
#  depth_POIFD <- POIFD(dataPOFD$pofd, type = "MBD")

## -----------------------------------------------------------------------------
#  library("refund")
#  
#  Fit.IV <- ccb.fpc(t(dataPOFD$pofd))
#  
#  goldsmith_reconstruction <- t(Fit.IV$Yhat)
#  depth_goldsmith <- POIFD(goldsmith_reconstruction, type = "MBD")