RMmatrix: Matrix operator

In RandomFields: Simulation and Analysis of Random Fields

Description

RMmatrix is a multivariate covariance model depending on one multivariate covariance model, or one or several univariate covariance models C0,…. The corresponding covariance function is given by

C(h) = M phi(h) M^t

if a multivariate case is given. Otherwise it returns a matrix whose diagonal elements are filled with the univarate model(s) C0, C1, etc, and the offdiagonals are all zero.

Usage

RMmatrix(C0, C1,  C2, C3, C4, C5, C6, C7, C8, C9, M, vdim,
         var, scale, Aniso, proj)

Arguments

C0	a k-variate covariance RMmodel or a univariate model or a list of models joined by c
C1,C2,C3,C4,C5,C6,C7,C8,C9	optional univariate models
M	a k times k matrix, which is multiplied from left and right to the given model; M may depend on the location, hence it is then a matrix-valued function and C will be non-stationary with C(x, y) = M(x) phi(x, y) M(y)^t
vdim	positive integer. This argument should be given if and only if a multivariate model is created from a single univariate model and M is not given. (In fact, if M is given, vdim must equal the number of columns of M)
var,scale,Aniso,proj	optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Value

RMmatrix returns an object of class RMmodel.

Note

• RMmatrix also allows variogram models are arguments.

See Also

RMmodel, RFsimulate, RFfit.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again


## Not run: 
## first example: bivariate Linear Model of Coregionalisation
x <- y <- seq(0, 10, 0.2)

model1 <- RMmatrix(M = c(0.9, 0.43), RMwhittle(nu = 0.3)) + 
  RMmatrix(M = c(0.6, 0.8), RMwhittle(nu = 2))
plot(model1)
simu1 <- RFsimulate(RPdirect(model1), x, y)
plot(simu1)


## second, equivalent way of defining the above model
model2 <- RMmatrix(M = matrix(ncol=2, c(0.9, 0.43, 0.6, 0.8)),
                  c(RMwhittle(nu = 0.3), RMwhittle(nu = 2)))
simu2 <- RFsimulate(RPdirect(model2), x, y)
stopifnot(all.equal(as.array(simu1), as.array(simu2)))


## third, equivalent way of defining the above model
model3 <- RMmatrix(M = matrix(ncol=2, c(0.9, 0.43, 0.6, 0.8)),
                   RMwhittle(nu = 0.3), RMwhittle(nu = 2))
simu3 <- RFsimulate(RPdirect(model3), x, y)
stopifnot(all(as.array(simu3) == as.array(simu2)))

## End(Not run)


## second example: bivariate, independent fractional Brownian motion
## on the real axis
x <- seq(0, 10, 0.1) 
modelB <- RMmatrix(c(RMfbm(alpha=0.5), RMfbm(alpha=1.5))) ## see the Note above
print(modelB)
simuB <- RFsimulate(modelB, x)
plot(simuB)


## third example: bivariate non-stationary field with exponential correlation
## function. The variance of the two components is given by the
## variogram of fractional Brownian motions.
## Note that the two components have correlation 1.
x <- seq(0, 10, 0.1)
modelC <- RMmatrix(RMexp(), M=c(RMfbm(alpha=0.5), RMfbm(alpha=1.5))) 
print(modelC)
simuC <- RFsimulate(modelC, x, x, print=1)
#print(as.vector(simuC))
plot(simuC)

RandomFields documentation built on Jan. 19, 2022, 1:06 a.m.