| hypersim {FieldSim} | R Documentation |
The function hypersim yields discretization of sample path of a
Gaussian hyperboloïd indexed field following the procedure described in
Brouste et al. (2009).
hypersim(R,Ne=100,Nr=100,Ng=100,nbNeighbor=4)
R |
a covariance function (defined on the hyperboloïd) of a Random hyperboloïd indexed field to simulate. |
Ne |
a positive integer. Ne is the number
of simulation points associated with the uniform distributed discretization
of the hyperboloïd 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 hyperboloïd 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 hypersim yields discretization of sample path
of a Gaussian hyperboloïd indexed field associated with the covariance function given
by R.
A list with the following components:
X |
the vector of length at more Ne+Nr+Nr^2
containing the discretization of the x axis. |
Y |
the vector of length at more Ne+Nr+Nr^2
containing the discretization of the y axis. |
Z |
the vector of length at more Ne+Nr+Nr^2
containing the discretization of the z axis. |
W |
the vector of length at more Ne+Nr+Nr^2
containing the value of the simulated field at point
(X[n],Y[n],Z[n]) |
W1 |
the matrice of size Ng^2
that give values of the simulated hyperboloïd indexed 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.
hypersimgrid,fieldsim,spheresim.
# Load FieldSim library
library(FieldSim)
d<-function(x){ #Distance on the hyperboloïd
u <- -x[1]*x[4]-x[2]*x[5]+x[3]*x[6]
if (u<1){u<-1}
acosh(u)
}
#Example 1: Hyperboloïd indexed Brownian fractional Field with RH1 covariance function
RH1<-function(x){
H<-0.45 # H can vary from 0 to 0.5
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})
}
resh1<- hypersim(RH1,Ne=100,Nr=1000,Ng=50,nbNeighbor=4)
library(rgl)
library(RColorBrewer)
printhyper(resh1)
#Example 2: Hyperboloïd indexed Brownian Field with RH4 covariance function
RH4<-function(x){
H<-0.45
1/(1+d(x)^{2*H})
}
resh4<- hypersim(RH4,Ne=100,Nr=1000,Ng=50,nbNeighbor=4)
printhyper(resh4)