RMuser: User-Defined Function
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value Note See Also Examples

RMuser allows for a user-defined covariance function, variogram model, or arbitrary function.

RMuser is very slow – users should avoid this model whenever possible.

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RMuser(type, domain, isotropy, vdim, beta,
       coordnames = c("x", "y", "z", "T"), fctn, fst, snd, envir,  
       var, scale, Aniso, proj)

`type`	See `RMmodelgenerator` for the range of values of the arguments. Default: `"shape function"`.
`domain`	See `RMmodelgenerator` for the range of values of the arguments. Default: `XONLY`.
`isotropy`	See `RMmodelgenerator` for the range of values of the arguments. Default: `'isotropic'` if `type` equals `'tail correlation function'`, `'positive definite'` or `'negative definite'`; `'cartesian system'` if `type` indicates a process or simulation method or a shape function.
`vdim`	multivariability. Default: `vdim` is identified from `beta` if given; otherwise the default value is `1`.
`beta`	a fixed matrix that is multiplied to the return value of the given function; the dimension must match. Defining a vector valued function and `beta` as a vector, an arbitrary linear model can be defined. Estimation of `beta` is, however, not established yet.
`coordnames`	Just the names of the variables. More variable names might be given here than used in the function. See Details for the interpretation of variables.
`fctn, fst, snd`	a user-defined function and its first, second and third derivative, given as `quote(myfunction(x))` or as `quote(myfunction(x, y))`, see Details and Examples below.
`envir`	the environment where the given function shall be evaluated
`var,scale,Aniso,proj`	optional arguments; same meaning for any `RMmodel`. If not passed, the above covariance function remains unmodified.

Primarily, a function is expected that depends on a vector whose components, x, y, z, T, are given separately as scalar quantities.

Alternatively, the function might depend only on the first argument given by coordnames.

A kernel should depend on the first two arguments given by coordnames.

RMuser returns an object of class RMmodel.

The use of RMuser is completely on the risk of the user. There is no way to check whether the expressions of the user are correct in any sense.
Note that x, y, z and T are reserved argument names that define solely the coordinates. Hence, none of these names might be used for other arguments within these functions.
In user-defined functions, the models of RandomFields are not recognized, so they cannot be included in the function definitions.
RMuser may not be used in connection with obsolete commands of RandomFields.

RMcovariate, RMfixcov, RFfit, RMmodelgenerator, RMmodel, RFsimulate, RC_ISO_NAMES, RC_DOMAIN_NAMES.

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

## Alternatively to 'model <- RMexp()' one may define the following
## (which is, however, much slower and cannot use all features of
## RandomFields)

## user-defined exponential covariance model
model <- RMuser(type="positive definite", domain="single variable",
                iso="isotropic", fctn=exp(-x))
x <- y <- seq(1, 10, len=100)
plot(model)
z <- RFsimulate(model, x=x, y=y)
plot(z)

## the kernel, which is the scalar product (see RMprod)
model <- RMnugget(var=1e-5) +
         RMuser(type="positive definite", domain="kernel",
                iso="symmetric", fctn=sum(x * y))
x <- y <- seq(1, 10, len=35)
z <- RFsimulate(model, x=x, y=y, n=6, svdtol=1e-9) 
plot(z)