R: Evaluate Covariance and Variogram Functions

RFcov {RandomFields} | R Documentation

## Evaluate Covariance and Variogram Functions

### Description

`RFcov` returns the values of a covariance function; `RFvariogram` returns the values of a variogram; `RFpseudovariogram` returns the values of a pseudovariogram; `RFcovmatrix` returns the covariance matrix for a set of points `RFfctn` returns the values of a shape function;

### Usage

    RFcov(model, x, y = NULL, z = NULL, T = NULL, grid, distances, dim,

           ...)

    RFvariogram(model, x, y = NULL, z = NULL, T = NULL, grid, distances, dim, ...)

    RFpseudovariogram(model, x, y = NULL, z = NULL, T = NULL, grid, distances, dim, ...)

    RFcovmatrix(model, x, y = NULL, z = NULL, T = NULL, grid, distances, dim,...)

    RFfctn(model, x, y = NULL, z = NULL, T = NULL, grid, distances, dim,...)

### Arguments

`model` | object of class `RMmodel`; the covariance or variogram model, which is to be evaluated
`x` | vector or (n x \code{dim})-matrix, where n is the number of points at which the covariance function is to be evaluated; in particular, if the model is isotropic or `dim=1` then `x` is a vector. `x`
`y` | second vector or matrix for non-stationary covariance functions
`z` | z-component of point if xyzT-specification of points is used
`T` | T-component of point if xyzT-specification of points is used
`grid` | boolean; whether xyzT specify a grid
`distances` | vector; only if the function `RFcovmatrix` is used; the lower triangular part of the distance matrix column-wise; equivalently the upper triangular part of the distance matrix row-wise; either `x` or `distances` must be missing
`dim` | dimension of the coordinate space in which the model is applied

`...` | arguments passed to `RFcov` (`RFcovmatrix`) and arguments passed to `RFoptions`

### Details

`RFcovmatrix` returns a covariance matrix. Here a matrix of of coordinates (`x`) or a vector or a matrix of `distances` is expected. `RFcovmatrix` allows also for variogram models. Then the negative of the variogram matrix is returned.

### Value

`RFcov` returns a vector of values of the covariance function.

`RFvariogram` returns a vector of values of the variogram model.

`RFpseudovariogram` returns a vector of values of the variogram model.

`RFcovmatrix` returns a covariance matrix.

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de http://ms.math.uni-mannheim.de/de/publications/software

### See Also

`RMmodel`, `RFsimulate`, `RFfit`. `RFcalc`.

### Examples

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

    # locations:
    x <- matrix(runif(15), ncol=3)
     # coordinate matrix of 5 arbitrary points
     # p1, p2, p3, p4, p5 in 3-dimensional space
    y <- matrix(runif(15),ncol=3)
     # coordinate matrix of 5 arbitrary points
     # q1, q2, q3, q4, q5 in 3-dimensional space

    #####################################################
    # get available models
    RFgetModelNames(type=c("tail correlation", "positive definite",
                   "variogram", "shape function", "trend"))

    #####################################################
    # Example 1: a stationary covariance model

    model <- RMexp()

    # covariance only depends on differences
    # of locations hi=pi-qi in 3-dimensional space
    # therefore, the following 2 commands yield the same

    RFcov(model=model, x=x, y=y)
    RFcov(model=model, x=x-y)
     # yields 5 values C(hi)=C(pi,qi) for i=1,2,3,4,5

    ##################################################
    # Example 2: get covariance matrix C(x_i,x_j)
    # at given locations x_i, i=1,...,n
    #
    # here for an isotropic stationary covariance model
    # yields a 4 times 4 covariance matrix of the form
    # C(0)   C(5)   C(3)   C(2.5)
    # C(5)   C(0)   C(4)   C(2.5)
    # C(3)   C(4)   C(0)   C(2.5)
    # C(2.5) C(2.5) C(2.5) C(0)

    model <- RMexp() # the covariance function C(x,y)=C(r) of this model
    #                  depends only on the distance r between x and y
    RFcovmatrix(model=model, distances=c(5,3,2.5,4,2.5,2.5), dim=4)

    ######################################################
    # Example 3: distinguish the different uses of x and y

    x <- c(1,2,1)
    y <- c(4,5,6)

    # coordinate space 1-dimensional, evaluated at 3 points:
    RFcov(model=model, x=as.matrix(x), y=as.matrix(y))
    # coordinate space is 3-dimensional, evaluated at a pair of points
    RFcov(model=model, x=t(x), y=t(y))

[Package RandomFields version 3.1.50 Index]