sim_functional_process {SpatFD}

Simulation of unconditional or conditional functional spatial process.

Description

Given a variogram model, this functions simulates several realizations of a functional spatial process. This simulation can be conditioned to observed data.

Usage

sim_functional_process(nsims,variograms,nbasis,coords,data = NULL,
                      data_coords = NULL,basis = NULL,mu = NULL,L = NULL)

Arguments

nsims

Integer giving the number of curves to simulate.

variograms

gstat::gstatVariogram or list of them giving the variogram model for each score. If only one is provided, it will be recycled.

nbasis

Integer giving the number of basis functions on which the process is going to be projected.

coords

Gridded sp::SpatialPoints or sp::SpatialPixels, or array coordinates of the curves that are going to be simulated.

data

fda::fd object containing the observed curves for conditional simulation. If data is not provided, inconditional simulation is performed.

data_coords

sp::SpatialPoints or array coordinates of the observed data.

basis

Character giving the basis of functions (only for inconditional simulation) (nbasis must be provided).

mu

fda::fd object of the mean function of the process, default is zero. Only used in unconditional simulation.

L

Limits of the symetric interval centered on zero that is the domain of the basis that is going to be created in unconditional simulation case.

Details

When data is passed, conditional simulation is performed. That means that each simulated realization of the process interpolated the observed curves in data. If data is NULL, the realizations of the process are simulated without imterpolation restrictions.

Value

A list of nsims SpatFD objects each one with as much curves as points are in coords.

Author(s)

Samuel Sánchez Gutiérrez [e-mail].

References

Bohorquez, M., Giraldo, R. & Mateu, J. Multivariate functional random fields: prediction and optimal sampling. Stoch Environ Res Risk Assess 31, 53–70 (2017). https://doi.org/10.1007/s00477-016-1266-y

See Also

generate_basis

Examples

library(gstat)
library(fda)
library(sp)

data("CanadianWeather")
canada.CRS <- CRS("+init=epsg:4608")
coords <- SpatialPoints(CanadianWeather$coordinates,
                        proj4string = CRS("+init=epsg:4326"))
coords <- spTransform(coords,canada.CRS)
obs <- CanadianWeather$dailyAv[,,1] # Temperature

Lfd_obj <- int2Lfd(m = 2)
create.bspline.basis(rangeval = c(1,365),
                     nbasis = 40, norder = 4) -> mi.base
mi.fdPar <- fdPar(mi.base, Lfd_obj, lambda = 7.389)
mi.fd <- smooth.basis(argvals = 1:365,
                      y = obs, fdParobj = mi.fdPar)

nbasis <- 5
canada <- mi.fd$fd
canada.pca <- pca.fd(canada,nharm = 10)
base_ort <- canada.pca$harmonics[1:nbasis]
canada_mean <- canada.pca$meanfd

formula2fd <- function(rango, expresion) {
  # Generate grid
  n <- 500  # length of the grid
  x <- seq(rango[1], rango[2], length.out = n)
  
  # evaluate expression on the grid
  y_vals <- eval(parse(text = expresion))
  
  # convert to fd
  basis <- create.bspline.basis(rangeval = rango, nbasis = 30)
  fd_obj <- Data2fd(x, y_vals,basisobj = basis)
  
  return(fd_obj)
}
media <- formula2fd(c(-1,1),"3*sin(x*4)")

# No conditional
vario <- vgm(.25, "Exp", .5, .05)
nbasis <- 6
sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre',mu = media)
class(sims)
length(sims)

class(sims[[1]])
# plot(sims[[3]][[1]]$data_fd)

sims <- sim_functional_process(10,vario,nbasis,coords,basis = 'Legendre')
class(sims)
length(sims)
class(sims[[1]])
# plot(sims[[3]][[1]]$data_fd)

# Conditional
vario <- vgm(100, "Exp", 900, 10)
new_coords <- spsample(coords,100,type = "regular")
gridded(new_coords) <- TRUE
length(new_coords)
a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords)
class(a)
length(a)
class(a[[1]])
#plot(a[[1]][[1]]$data_fd)

vario <- vgm(100, "Wav", 900, 10)
a <- sim_functional_process(10,vario,nbasis,new_coords,canada,coords)
class(a)
length(a)
class(a[[1]])
#plot(a[[1]][[1]]$data_fd)