varcov.spatial {geoR} | R Documentation

## Computes Covariance Matrix and Related Results

### Description

This function builds the covariance matrix for a set of spatial locations, given the covariance parameters. According to the input options other results related to the covariance matrix (such as decompositions, determinants, inverse. etc) can also be returned.

### Usage

    varcov.spatial(coords = NULL, dists.lowertri = NULL,
                   cov.model = "matern", kappa = 0.5, nugget = 0,
                   cov.pars = stop("no cov.pars argument"),
                   inv = FALSE, det = FALSE,
                   func.inv = c("cholesky", "eigen", "svd", "solve"),
                   scaled = FALSE,  only.decomposition = FALSE,
                   sqrt.inv = FALSE, try.another.decomposition = TRUE,
                   only.inv.lower.diag = FALSE)

### Arguments

`coords` | an n x 2 matrix with the coordinates of the data locations. If not provided the argument `dists.lowertri` should be provided instead.
`dists.lowertri` | a vector with the lower triangle of the matrix of distances between pairs of data points. If not provided the argument `coords` should be provided instead.
`cov.model` | a string indicating the type of the correlation function. More details in the documentation for `cov.spatial`. Defaults are equivalent to the exponential model.
`kappa` | values of the additional smoothness parameter, only required by the following correlation functions: `"matern"`, `"powered.exponential"`, `"cauchy"` and `"gneiting.matern"`.
`nugget` | the value of the nugget parameter tau^2.
`cov.pars` | a vector with 2 elements or an ns times 2 matrix with the covariance parameters. The first element (if a vector) or first column (if a matrix) corresponds to the variance parameter sigma^2. second element or column corresponds to the correlation function parameter phi. If a matrix is provided each row corresponds to the parameters of one spatial structure. Models with several structures are also called nested models in the geostatistical literature.
`inv` | if `TRUE` the inverse of covariance matrix is returned. Defaults to `FALSE`.
`det` | if `TRUE` the logarithmic of the square root of the determinant of the covariance matrix is returned. Defaults to `FALSE`.
`func.inv` | algorithm used for the decomposition and inversion of the covariance matrix. Options are `"chol"` for Cholesky decomposition, `"svd"` for singular value decomposition and `"eigen"` for eigenvalues/eigenvectors decomposition. Defaults to `"chol"`.
`scaled` | logical indicating whether the covariance matrix should be scaled. If `TRUE` the partial sill parameter sigma^2 is set to 1. Defaults to `FALSE`.
`only.decomposition` | logical. If `TRUE` only the square root of the covariance matrix is returned. Defaults to `FALSE`.
`sqrt.inv` | if `TRUE` the square root of the inverse of covariance matrix is returned. Defaults to `FALSE`.
`try.another.decomposition` | logical. If `TRUE` and the argument `func.inv` is one of `"cholesky"`, `"svd"` or `"solve"`, the matrix decomposition or inversion is tested and, if it fails, the argument `func.inv` is re-set to `"eigen"`.
`only.inv.lower.diag` | logical. If `TRUE` only the lower triangle and the diagonal of the inverse of the covariance matrix are returned. Defaults to `FALSE`.

### Details

The elements of the covariance matrix are computed by the function `cov.spatial`. Typically this is an auxiliary function called by other functions in the geoR package.

### Value

The result is always list. The components will vary according to the input options. The possible components are:

`varcov` | the covariance matrix.
`sqrt.varcov` | a square root of the covariance matrix.
`lower.inverse` | the lower triangle of the inverse of covariance matrix.
`diag.inverse` | the diagonal of the inverse of covariance matrix.
`inverse` | the inverse of covariance matrix.
`sqrt.inverse` | a square root of the inverse of covariance matrix.
`log.det.to.half` | the logarithmic of the square root of the determinant of the covariance matrix.

### Author(s)

Paulo J. Ribeiro Jr. Paulo.Ribeiro@est.ufpr.br,
Peter J. Diggle p.diggle@lancaster.ac.uk.

### References

Further information on the package geoR can be found at:
http://www.est.ufpr.br/geoR.

### See Also

`cov.spatial` for more information on the correlation functions; `chol`, `solve`, `svd` and `eigen` for matrix inversion and/or decomposition.

[Package geoR version 1.5-7 Index]