Krig.simple.sparse {KriSp} R Documentation

## Kriging surface estimate

### Description

Calculating the BLUP or kriging estimate for large two dimensional spatial datasets.

### Usage

```Krig.simple.sparse(x,Y,
cov.fun = "expo.cov",
cov.fun.args = list(range = 10, eps = eps),
taper.fun = "spher.cov",
taper.fun.args = list(range = 10),
ncov = 10000, approxhmax = taper.fun.args\$range,
miles = TRUE, R = NULL, eps = 1e-5,
save.sigma = TRUE, save.chol = FALSE,
verbose = FALSE, nnzmax = 1e+05, tmpmax = 10000, ...) ```

### Arguments

 `x` a `m` times `2` matrix containing the locations. `Y` the observed values at `x`. `cov.fun` Covariance function in the form of an R function, or its name as a string. `cov.fun.args` A list with the arguments to call the covariance function (in addition to the locations). `taper.fun` Taper function in the form of an R function, or its name as a string. `taper.fun.args` A list with the arguments to call the taper function (in addition to the locations). `ncov` Number of knots to evaluate the approximation `approxhmax` Maximum distance over which the covariance is approximated `miles` logical. If `TRUE` (default) distances are in statute miles if `FALSE` distances in kilometers. `R` the radius to use for the sphere to find spherical distances. If `NULL` the radius is either in miles or kilometers of the earth depending on the values of the miles argument. If `R=1` then distances are in radians. `eps` small value, everything smaller is considered zero. `save.sigma` should the covariance matrix be saved (in `SparseM` format). `save.chol` should the Cholesky factor of the covariance matrix be saved (in `SparseM` format). `verbose` should timing and convergence results be printed. `nnzmax` upper bound of non-zero elements in the covariance matrix. `tmpmax` working array for the Cholesky factorisation `...` supplementary parameters that can be given as arguments to the function `chol`.

### Details

For computational reasons, we do not call simple the `solve` function but use `chol(...)` and `backsolve(...)` form the `SparseM` library. We do not allow missing values. We only consider two-dimensional domains.

### Value

`Krig.simple.sparse` returns an object of `class` `c("sparse","Krig")`. The second is to reuse many handy functions of the library `fields`.
An object of the class `"sparse"` is a list containing at least the following components:

 `call` the matched call. `fitted` fitted values at observed values. `solve` vector used for prediction on other grid points. `sigma` if requested, the covariance matrix. `sigmachol` if requested, the Cholesky factor. `timing` time needed for the main calculations. `nnz` The number of nonzero elements in the covariance matrix and its Cholesky factor.

Additionally, most input arguments are passed to the object.

### Note

For REALLY big datasets, it would be wise to dissect the functions.

The radius of the earth is assumed to be 3963.34 miles or 6378.388 kilometers.

`approxhmax` should be at least as big as the taper range or the domain of the field.

If `nnzmax` is too small, R may produce a `core dumped'.

`Krig.simple.sparse`, `predict.sparse`, `plot.sparse`;

`chol` and `backsolve` from the `SparseM` library.

### Examples

```data(simple)
attach(simple.data)

obj <- Krig.simple.sparse( x, Y)
pre <- predict( obj, x=cbind(-104.5,40.5))

surf <- predict.surface( obj)
image.plot( surf)

```

[Package KriSp version 0.4 Index]