FieldSim (version 2.1)

hypersimgrid: Random hyperboloid indexed field simulation by the mifieldsim method on the user grid

Description

The function hypersimgrid yields discretization of sample path of a Gaussian hyperbolo�d indexed field on the S grid following the procedure described in Brouste et al. (2009).

Usage

hypersimgrid(R,Ne=100,Nr=100,nbNeighbor=4,S)

Arguments

R

a covariance function (defined on the sphere) of a Random spherical field to simulate.

Ne

a positive integer. $\code{Ne}$ is the number of simulation points associated with the uniform distributed discretization of the hyperbolo�d for the first step of the algorithm (Accurate simulation step)

Nr

a positive integer. $\code{Nr}$ is the number of simulation points associated with the uniform distributed discretization of the hyperbolo�d for the second step of the algorithm (Refined simulation step).

nbNeighbor

a positive integer. nbNeighbor must be between 1 and 32. nbNeighbor is the number of neighbors to use in the second step of the algorithm.

S

a matrix with 3 rows and N columns. (S[1,n],S[2,n],S[3,n]) is the point of the hyperbolo�d where the field must be simulated.

Value

• A list with the following components:
• S
  a matrix with 3 rows and N columns. (S[1,n],S[2,n],S[3,n]) is the point where the field has been simulated.
• Wg
  the vector of length at more N containing the value of the simulated field at point (S[1,n],S[2,n],S[3,n])
• time
  the CPU time

encoding

latin1

Details

The function hypersimgrid yields discretization of sample path of a Gaussian hyperboloid indexed field associated with the covariance function given by R.

References

A. Brouste, J. Istas and S. Lambert-Lacroix (2009). On simulation of manifold indexed fractional Gaussian fields.

See Also

hypersim

Examples

# Load FieldSim library
library(FieldSim)

## Define the grid
Z <- 2
n <- 30 
phi <- Z/n*(0:(n-1))
theta <- 2*pi/n*(0:(n-1))
S <- numeric(0)
for (kk in 1:(n-1)){
S <- cbind(S,rbind(cos(theta[kk])*sinh(phi),sin(theta[kk])*sinh(phi),cosh(phi)))
}

## Define the autocovariance function
d<-function(x){
u <- -x[1]*x[4]-x[2]*x[5]+x[3]*x[6]
if (u<1){u<-1}
acosh(u)
}
R<-function(x){
H<-0.3
1/2*(d(c(0,0,1,x[1:3]))^{2*H}+d(c(0,0,1,x[4:6]))^{2*H}-d(x)^{2*H})
}

Wg <- hypersimgrid(R,Ne=50,Nr=100,nbNeighbor=4,S)$Wg