LKrigSetupAwght: Method to create a.wght component from the 'LKinfo' object.

In LatticeKrig: Multi-Resolution Kriging Based on Markov Random Fields

Description

This method takes a vector or more complicated object and based on the geometry creates a list with the a.wght information.

Usage

LKrigSetupAwght(object, ...)
## Default S3 method:
LKrigSetupAwght(object, ...)

## S3 method for class 'LKRectangle'
LKrigSetupAwght(object, ...)

LKrigSetupAwghtObject(object)

Arguments

object	The partial or complete LKinfo object created within LKrigSetup.
...	Any additional arguments to this method.

Details

The simplest function of this method is to convert the a.wght value into a list that has the length of the number of levels. If only a scalar a.wght value is supplied then the default method just repeats this for each level.

The function LKrigSetupAwghtObject uses the a.wghtObject component in the LKinfo object to fill in a.wght parameters for the different levels. This is convenient because the lattice locations are different at each level. The parameters are filled in at level, Level according to

 	 latticeLocations<- make.surface.grid( 
 	                          object$latticeInfo$grid[[Level]])
 	 a.wght<- predict( object$a.wghtObject, latticeLocations )
 	

here the predict function is whatever is supplied according to the class for a.wghtObject. Note that since the returned set of parameters will be in the format used internally a.wght here will be a list with each component being a matrix. Number of rows are each to the number of lattice points (or basis functions) at that level. This is easier implement that it may seem and see the examples in nonstationaryModels.

The attribute fastNormalize (either TRUE or FALSE) is attached to this list to indicate how the marginal variance of the process should be found.

 	 	
  LKinfo<- LKrigSetup( x,LKGeometry="LKInterval", alpha=c( 1,.2,.01),
                   nlevel=3, a.wght=4.5, NC= 3)
  LKrigSetupAwght( LKinfo)
  
[[1]]
[1] 4.5

[[2]]
[1] 4.5

[[3]]
[1] 4.5

attr(,"fastNormalize")
[1] FALSE

Currently the only geometry with fastNormalization being TRUE is for a rectangular domain.

For the LKRectangle geometry, however, more complicated anisotropic and non-stationary a.wght specifications are possible. See LKrig for details. Also in the case that the fastNormalization is TRUE for rectangles several more attributes are added to the a.wght list that precompute some matrices of the SAR.

Value

A list with nlevel components. The attribute fastNormalize is added to this list. In the case that the geometry is LKRectangle several more attributes are added indicating the type of covariance model and possibly an eigen decomposition of the SAR matrix exploiting Kronecker products.

Author(s)

Doug Nychka

See Also

LKrigSetup, LKrigSetupAlpha, LKrigSAR, LKrig

Examples

  x<- cbind( c(0,1))
  LKinfo<- LKrigSetup( x,LKGeometry="LKInterval", alpha=c( 1,.2,.01),
                   nlevel=3, a.wght=4.5, NC= 3)
  a.wghtList<- LKrigSetupAwght( LKinfo)
  
  x<- cbind( c(0,1), c(0,1))
  LKinfo<- LKrigSetup( x, alpha=c( 1,.2,.01),
                   nlevel=3, a.wght=4.5, NC= 3)
  a.wghtList<- LKrigSetupAwght( LKinfo)
# see   
  names(attributes( a.wghtList))
 
  

LatticeKrig documentation built on Nov. 9, 2019, 5:07 p.m.