# LKrigSAR: Method that creates the spatial autoregressive (SAR) matrix. In LatticeKrig: Multiresolution Kriging Based on Markov Random Fields

## Description

Using the information in LKinfo create the SAR matrix for a given level of the multiresolution.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```LKrigSAR(object, ...) ## Default S3 method: LKrigSAR(object, ...) ## S3 method for class 'LKInterval' LKrigSAR(object, Level, ...) ## S3 method for class 'LKRectangle' LKrigSAR(object, Level, ...) ## S3 method for class 'LKBox' LKrigSAR(object, Level, ...) ## S3 method for class 'LKRing' LKrigSAR(object, Level, ...) ## S3 method for class 'LKCylinder' LKrigSAR(object, Level, ...) ## S3 method for class 'LKSphere' LKrigSAR(object, Level, ...) ```

## Arguments

 `object` An LKinfo object. `Level` The level of the multiresolution. `...` Any additional arguments to pass to this method.

## Details

The model for the Gaussian Markov Random field, c, at a given level is

B c = e,

where B is the SAR matrix computed by this method, and e are uncorrelated N(0,1). The precision matrix for this level is

Q= t(B)%*% B

and so the covariance matrix for c is the inverse of Q:

solve( Q)= solve(B)%*% t( solve(B))

## Value

A matrix in the sparse matrix format, `spind`, with dimensions given by the number of lattice points at `Level`. Because this construction is geometry dependent the default version of this method just returns an error message.

Doug Nychka

## See Also

`LKrig.precision` `spind2full`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` x<- cbind( c(0,1)) LKinfo<- LKrigSetup(x,LKGeometry="LKInterval", nlevel=3, NC=3, a.wght=5, alpha=c(1,.5,.2) ) B<- LKrigSAR( LKinfo, Level=2) B<-spind2full(B) image.plot( B) LKinfo<- LKrigSetup(cbind( c(0,360), c(0,1)) ,LKGeometry="LKRing", nlevel=1, NC=3, a.wght=5, alpha=1) B<- LKrigSAR( LKinfo, Level=1) B<-spind2full(B) image.plot( B) ```

LatticeKrig documentation built on May 29, 2017, 7:03 p.m.