LKDist: Find all pairwise distances within a maximum distance.

Description

These are the lower level functions to compute the distances among two sets of locations but being limited to distances less than a maximum threshold (see delta below ). These functions are useful for generating a sparse matrix on distances and evaluating a compactly supported function (such as the Wendland). The location - location method supports the distance metrics: Euclidean, spherical, component-wise and Manhattan. LKDistComponent and LKDistComponentGrid return the coordinate-wise distances and are useful for evaluating a tensor product basis functions.

Usage

LKDist(x1, x2, delta, max.points = NULL, mean.neighbor = 50,
             distance.type = "Euclidean")
LKDistComponents(x1, x2, delta, max.points = NULL, mean.neighbor = 50, 
    distance.type = "Euclidean")
    
LKDistGrid(x1, gridList, delta, max.points = NULL, mean.neighbor = NULL,
distance.type = "Euclidean", periodic)
LKDistGridComponents(
x1, gridList, delta,
  max.points = NULL, mean.neighbor = NULL,
  distance.type = "Euclidean") 
LKGridCheck(distance.type, x1, gridList )
LKGridFindNmax(n1, max.points, mean.neighbor, delta, gridList)

Value

LKDist and LKDistGrid a list representing a sparse matrix in spind format.

LKDistComponent andLKDistGridComponent a list representing a sparse matrix using the spind format except the ra component is now a matrix. The columns of ra being the individual distances for each coordinate.

directionCosine a matrix where rows index the different points and columns index x,y,z.

LKGridFindNmax returns the maximum number of nonzero elements expected in a pairwise distance matrix.

LKGridFindNmax checks that the calling arguments are compatible with the pairwise distance computation.

Arguments

gridList: A list with each component vector that specifies the grid points for an equally spaced grid. Can have class gridList. (See also help on gridlist).
n1: Number of rows of x1.

x1: A matrix with rows indexing locations and columns indexing coordinates.
x2: A matrix with rows indexing locations and columns indexing coordinates.
delta: The maximum distance to find pairwise distances.
max.points: Used for dynamically assigning matrix size this should be larger than the total number of pairwise distances less than delta.
mean.neighbor: Used for dynamically assigning matrix size this is the average number of points that are less that delta in distance to the x1 locations.
periodic: A logical vector with length ncol( x1). If a component is TRUE then that dimension is treated as periodic.
distance.type: A text string either "Euclidean", "GreatCircle", "Chordal", "Manhattan".

Author

Doug Nychka

Examples

Run this code

set.seed( 123)	
x<- matrix( runif(100*2), 100,2)

DMatrix<- LKDist( x,x, delta=.1)
# coerce to spam matrix format
DMatrix2<- spind2spam( DMatrix)

# a grid
gridL<- list( x1= seq(0,1,.2), x2= seq( 0,2,.2) , x3= seq( -1,1,.2))
class(gridL)<- "gridList"	
x1<- cbind( runif( 100), runif(100)*2, 2*(runif( 100) -.5) )
look<- LKDistGrid( x1, gridL, delta=.45)
# check against rdist.
# look2<- rdist( x1, make.surface.grid(gridL))
# look2[ look2 >= .45] <- 0
# max( abs(look- look2)[look>0] )

# test of periodic option
 gridL<- structure(
            list( x1= seq(0,1,.02),
                  x2= seq( 0,1,.02)),
            class="gridList")
 look1<- LKDistGrid( rbind(c(0,0)), gridL, delta=.35,
                     periodic=c(TRUE,FALSE))
 look2<- spind2full(look1)
 image.plot( as.surface( gridL, look2) )
 
 look1<- LKDistGrid( rbind(c(0,0)), gridL, delta=.35,
                      periodic=c(TRUE,TRUE))
 look2<- spind2full(look1)
 image.plot( as.surface( gridL, look2) )