R: Methods relying on square roots of the covariance matrix

Square roots {RandomFields} | R Documentation

## Methods relying on square roots of the covariance matrix

### Description

Methods relying on square roots of the covariance matrix

### Usage

    RPdirect(phi, boxcox)

    RPsequential(phi, boxcox, back_steps, initial)

### Arguments

`phi` | object of class `RMmodel`; specifies the covariance model to be simulated.
`boxcox` | the one or two parameters of the box cox transformation. If not given, the globally defined parameters are used. see `RFboxcox` for Details.
`back_steps` | Number of previous instances on which the algorithm should condition. If less than one then the number of previous instances equals `max` / (number of spatial points). Default: `10` .
`initial` | First, N=(number of spatial points) * `back_steps` number of points are simulated. Then, sequentially, all spatial points for the next time instance are simulated at once, based on the previous `back_steps` instances. The distribution of the first N points is the correct distribution, but differs, in general, from the distribution of the sequentially simulated variables. We prefer here to have the same distribution all over (although only approximatively the correct one), hence do some initial sequential steps first. If `initial` is non-negative, then `initial` first steps are performed. If `initial` is negative, then `back_steps` - `initial` initial steps are performed. The latter ensures that none of the very first N variables are returned. Default: `-10` .

### Details

`RPdirect` is based on the well-known method for simulating any multivariate Gaussian distribution, using the square root of the covariance matrix. The method is pretty slow and limited to about 8000 points, i.e. a 20x20x20 grid in three dimensions. This implementation can use the Cholesky decomposition and the singular value decomposition. It allows for arbitrary points and arbitrary grids.

`RPsequential` is programmed for spatio-temporal models where the field is modelled sequentially in the time direction conditioned on the previous k instances. For k=5 the method has its limits for about 1000 spatial points. It is an approximative method. The larger k the better. It also works for certain grids where the last dimension should contain the highest number of grid points.

### Value

`RPsequential` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### References

- Schlather, M. (1999) An introduction to positive definite functions and to unconditional simulation of random fields. Technical report ST 99-10, Dept. of Maths and Statistics, Lancaster University.

### See Also

Gaussian, RP,

### Examples

    RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
    ##                   RFoptions(seed=NA) to make them all random again
    model <- RMgauss(var=10, s=10) + RMnugget(var=0.01)
    plot(model, xlim=c(-25, 25))

    z <- RFsimulate(model=RPdirect(model), 0:10, 0:10, n=4)
    plot(z)

[Package RandomFields version 3.1.50 Index]