| spheresim {FieldSim} | R Documentation |
The function spheresim yields discretization of sample path of a
Gaussian spherical field following the
procedure described in Brouste et al. (2009).
spheresim(R,Ne=100,Nr=100,Ng=100,nbNeighbor=4)
R |
a covariance function (defined on the sphere) of a Random spherical field to simulate. |
Ne |
a positive integer. 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) |
Nr |
a positive integer. 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). |
Ng |
a positive integer. Nr is the number of simulation points
associated with the visual grid discretization
of the sphere for the third step of the algorithm
(Visual 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. |
The function spheresim yields discretization of sample path of a
Gaussian spherical field associated with the covariance function given by R.
A list with the following components:
X |
the vector of length at more Ne+Nr+6Nr^2
containing the discretization of the x axis. |
Y |
the vector of length at more Ne+Nr+6Nr^2
containing the discretization of the y axis. |
Z |
the vector of length at more Ne+Nr+6Nr^2
containing the discretization of the z axis. |
W |
the vector of length at more Ne+Nr+6Nr^2
containing the value of the simulated field at point
(X[n],Y[n],Z[n]) |
W1,...,W6 |
the matrices of of size Ng^2
that give values of the simulated spherical field at the points
of the visual grid |
time |
the CPU time |
Alexandre Brouste (http://subaru.univ-lemans.fr/sciences/statist/pages_persos/Brouste/) and Sophie Lambert-Lacroix (http://ljk.imag.fr/membres/Sophie.Lambert).
A. Brouste, J. Istas and S. Lambert-Lacroix (2009). On simulation of manifold indexed fractional Gaussian fields.
spheresimgrid,fieldsim,hypersim.
# load FieldSim library
library(FieldSim)
d<-function(x){ #Distance on the sphere
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)
}
# Example 1 : Fractional spherical field with RS1 covariance function
RS1<-function(x){
H<-0.45 # H can vary from 0 to 0.5
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})
}
res1<- spheresim(RS1,Ne=100,Nr=1000,Ng=25,nbNeighbor=4)
library(rgl)
library(RColorBrewer)
printsphere(res1)
# Example 2 : Fractional spherical field with RS2 covariance function
RS2<-function(x){
H<-0.45 # H can vary from 0 to 0.5
exp(-d(x)^{2*H})
}
res2<- spheresim(RS2,Ne=100,Nr=1000,Ng=25,nbNeighbor=4)
printsphere(res2)