Fixed Covariance Matrix
RMfixcov is a user-defined covariance according to
the given covariance matrix.
It extends to the space through a Voronoi tessellation.
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 |
var,proj |
optional arguments; same meaning for any
|
raw |
logical. If |
norm |
optional model that gives the norm between locations |
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.
Starting with version 3.0.64, the former argument element
is replaced by the general option set in
RFoptions.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
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.
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)
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