RMfix: Fixed Covariance Matrix
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value Note References See Also Examples

RMfixcov is a user-defined covariance according to the given covariance matrix.

It extends to the space through a Voronoi tessellation.

1	RMfixcov(M, x, y=NULL, z=NULL, T=NULL, grid, var, proj, raw, norm)

`M`	a numerical matrix defining the user-defined covariance for a random field; the matrix should be positive definite, symmetric and its dimension should be equal to the length of observation or simulation vector.
`x,y,z,T,grid`	optional. The usual arguments as in `RFsimulate` to define the locations where the covariates are given.
`var,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.
`raw`	\argRaw
`norm`	\argNorm

The covariances passed are implemented for the given locations. Within any Voronoi cell (around a given location) the correlation is assumed to be one.

In particular, it is used in RFfit to define neighbour or network structure in the data.

RMfixcov returns an object of class RMmodel.

Starting with version 3.0.64, the former argument element is replaced by the general option set in RFoptions.

Ober, U., Ayroles, J.F., Stone, E.A., Richards, S., Zhu, D., Gibbs, R.A., Stricker, C., Gianola, D., Schlather, M., Mackay, T.F.C., Simianer, H. (2012): Using Whole Genome Sequence Data to Predict Quantitative Trait Phenotypes in Drosophila melanogaster. PLoS Genet 8(5): e1002685.

RMcovariate, RMmodel, RFsimulate, RFfit, RMuser.

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


## Example 1 showing that the covariance structure is correctly implemented
n <- 10
C <- matrix(runif(n^2), nc=n)
(C <- C %*% t(C))
RFcovmatrix(RMfixcov(C), 1:n)


## Example 2 showing that the covariance structure is interpolated
RFcovmatrix(RMfixcov(C, 1:n), c(2, 2.1, 2.5, 3))


## Example 3 showing the use in a separable space-time model
model <- RMfixcov(C, 1:n, proj="space") * RMexp(s=40, proj="time")
(z <- RFsimulate(model, x = seq(0,12, 0.5), T=1:100))
plot(z)