RMprod {RandomFields}

R Documentation

Plain scalar product

Description

RMprod is a non-stationary covariance model given by

C(x,y) = \langle \phi(x), \phi(y)\rangle

Usage

RMprod(phi, var, scale, Aniso, proj)

Arguments

phi	any function of class RMmodel
var, scale, Aniso, proj	optional arguments; same meaning for any RMmodel. If not passed, the above covariance function remains unmodified.

Details

In general, this model defines a positive definite kernel and hence a covariance model for all functions \phi with values in an arbitrary Hilbert space. However, as already mentioned above, \phi should stem from a covariance or variogram model, here.

Value

RMprod returns an object of class RMmodel.

Note

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.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

References

Wendland, H. Scattered Data Approximation (2005) Cambridge: Cambridge University Press.

See Also

RMid, RMid, RMsum, RMmodel, RMmult.

Examples

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)

---