# 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

 ```1 2``` ```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.

`RMmodel`, `RFsimulate`, `RFfit`.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50``` ```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) ```