LKrigSAR {LatticeKrig}

Method that creates the spatial autoregressive (SAR) matrix.

Description

Using the information in LKinfo create the SAR matrix for a given level of the multi-resolution.

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, ...)
   ## S3 method for class 'LKSphere'
LKrigSAR(object, Level, ...)

Arguments

object

An LKinfo object.

Level

The level of the multi-resolution.

...

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.

Author(s)

Doug Nychka

See Also

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)