spheresimgrid: Random spherical field simulation by the mifieldsim method on user grid

Description

The function spheresimgrid yields discretization of sample path of a Gaussian spherical field following the procedure described in Brouste et al. (2009).

Usage

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

Arguments

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

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

a positive integer. $\code{Nr}$ is the number of simulation points associated with the uniform distributed discretization of the sphere 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.

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

Value

A list with the following components:
Sa 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.
Wgthe vector of length at more N containing the value of the simulated field at point (S[1,n],S[2,n],S[3,n])
timethe CPU time

encoding

latin1

Details

The function spheresimgrid yields discretization of sample path of a Gaussian spherical field associated with the covariance function given by R and at each point of the grid given by S.

References

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

Examples

Run this code

# load FieldSim library
library(FieldSim)

## Define the grid
n <- 30
phi <- pi/n*(1:(n-1))
theta <- 2*pi/n*(1:(n-1))
S <- numeric(0)
for (kk in 1:(n-1)){
S <- cbind(S,rbind(cos(theta[kk])*sin(phi),sin(theta[kk])*sin(phi),cos(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
if (u>1)
u<-1
acos(u)
}
R<-function(x){
H<-0.1 
1/2*(d(c(1,0,0,x[1:3]))^{2*H}+d(c(1,0,0,x[4:6]))^{2*H}-d(x)^{2*H})
}

##Simulate the path
Wg <- spheresimgrid(R,Ne=50,Nr=50,nbNeighbor=4,S)$Wg

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