Plain scalar product
RMprod is a non-stationary covariance model given by
C(x,y) = \langle φ(x), φ(y)\rangle.
RMprod(phi, var, scale, Aniso, proj)
In general, this model defines a positive definite kernel and hence a covariance model for all functions φ with values in an arbitrary Hilbert space. However, as already mentioned above, φ should stem from a covariance or variogram model, here.
Do not mix up this model with RMmult.
See also RMS for a simple, alternative method to set
an arbitrary, i.e. location dependent, univariate variance.
Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/
Wendland, H. Scattered Data Approximation (2005) Cambridge: Cambridge University Press.
RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set ## RFoptions(seed=NA) to make them all random again RFcov(RMprod(RMid()), as.matrix(1:10), as.matrix(1:10), grid=FALSE) ## C(x,y) = exp(-||x|| + ||y||) RFcov(RMprod(RMexp()), as.matrix(1:10), as.matrix(1:10), grid=FALSE) ## C(x,y) = exp(-||x / 10|| + ||y / 10 ||) model <- RMprod(RMexp(scale=10)) x <- seq(0,10,len=100) z <- RFsimulate(model=model, x=x, y=x) plot(z)
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