Last data update: 2014.03.03

R: Method that creates the spatial autoregressive (SAR) matrix.
 LKrigSAR R Documentation

## Method that creates the spatial autoregressive (SAR) matrix.

### Description

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

### Usage

```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, ...)
```

### 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 construct is geometry dependent the default version of this method just returns an error message.

### Author(s)

Doug Nychka

`LKrig.precision` `spind2full`

### Examples

```    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)
```

### Results

```
R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(LatticeKrig)
Spam version 1.3-0 (2015-10-24) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

backsolve, forwardsolve

# maps v3.1: updated 'world': all lakes moved to separate new #
# 'lakes' database. Type '?world' or 'news(package="maps")'.  #

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/LatticeKrig/LKrigSAR.Rd_%03d_medium.png", width=480, height=480)
> ### Name: LKrigSAR
> ### Title: Method that creates the spatial autoregressive (SAR) matrix.
> ### Aliases: LKrigSAR LKrigSAR.LKBox LKrigSAR.LKRectangle
> ###   LKrigSAR.LKInterval LKrigSAR.LKRing LKrigSAR.LKCylinder
> ###   LKrigSAR.default
> ### Keywords: spatial
>
> ### ** Examples
>
>     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)
>
>
>
>
>
> dev.off()
null device
1
>

```