fieldsim {FieldSim}R Documentation

Random field simulation by the FieldSim method

Description

The function fieldsim yields discretization of sample path of a Gaussian field following the procedure described in Brouste et al. (2007).

Usage

fieldsim(S,Elevel=1,Rlevel=5,nbNeighbor=4)

Arguments

S a covariance function (defined on [0,1]^4) of a Random field to simulate.
Elevel a positive integer. Elevel is the level associated with the regular space discretization for the first step of the algorithm (Accurate simulation step). The regular space discretization is of the following form: [[0:2^{Elevel}]/2^{Elevel}]^2.
Rlevel a positive integer. Elevel+Rlevel is the level associated with the regular space discretization for the second step of the algorithm (Refined simulation step). The regular space discretization is of the following form: [[0:2^{Elevel+Rlevel}]/2^{Elevel+Rlevel}]^2.
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.

Details

The function fieldsim yields discretization of sample path of a Gaussian field associated with the covariance function given by R. The subspace [0,1]x[0,1] is discretized in a regular space discretization of size (2^{Elevel+Rlevel}+1)^2. At each point of the grid, the Gaussian field is simulated using the procedure described in Brouste et al. (2007).

Value

A list with the following components:

Zrow the vector of length 2^{Elevel+Rlevel}+1 containing the discretization of the x axis.
Zcol the vector of length 2^{Elevel+Rlevel}+1 containing the discretization of the y axis.
Z the matrix of size (2^{Elevel+Rlevel}+1)x(2^{Elevel+Rlevel}+1) in such a way Z[i,j] containing the value of the process at point (Zrow[i],Zcol[j])
time the CPU time

Author(s)

Alexandre Brouste (http://ljk.imag.fr/membres/Alexandre.Brouste) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).

References

A. Brouste, J. Istas and S. Lambert-Lacroix (2007). On Gaussian random fields simulations.

See Also

quadvar.

Examples

# load FieldSim library
library(FieldSim)

#Example 1: Fractional Brownian Field
R<-function(x,H=0.9){1/2*((x[1]^2+x[2]^2)^(H)+(x[3]^2+x[4]^2)^(H)-((x[1]-x[3])^2+(x[2]-x[4])^2)^(H))}
res<- fieldsim(R,Elevel=1,Rlevel=5,nbNeighbor=4)

# Plot 
x <- res$Zrow
y <- res$Zcol
z <- res$Z
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")

#Example 1: Multifractional Brownian Field

F<-function(y){0.4*y+0.5}

R<-function(x,Fun=F){
H1<-Fun(x[1])
H2<-Fun(x[3])
alpha<-1/2*(H1+H2)
C2D(alpha)^2/(2*C2D(H1)*C2D(H2))*((x[1]^2+x[2]^2)^(alpha)+(x[3]^2+x[4]^2)^(alpha)-((x[1]-x[3])^2+(x[2]-x[4])^2)^(alpha))
}

res<- fieldsim(R,Elevel=1,Rlevel=5,nbNeighbor=4)
# Plot 
x <- res$Zrow
y <- res$Zcol
z <- res$Z
persp(x, y, z, theta = 30, phi = 30, expand = 0.5, col = "lightblue")

[Package FieldSim version 1.2 Index]