halton.indices.vector: Halton indices for an entire vector of coordinates
In semmons1/TEST-SDraw: Spatially Balanced Samples of Spatial Objects

Description Usage Arguments Details Value Author(s) See Also Examples

Computes Halton indices of an entire vector of points by matching them with a vector of the Halton sequence. This function is relatively fast, but can only handle reasonably sized vectors.

1 2	halton.indices.vector(hl.coords, n.boxes, D = 2, b = c(2, 3), delta = c(1, 1), ll.corner = c(0, 0))

`hl.coords`	nXD vector of coordinates for points
`n.boxes`	DX1 vector containing number of Halton boxes in each dimension.
`D`	Number of dimensions
`b`	DX1 vector of bases to use for each dimension
`delta`	DX1 vector of study area extents in each dimension. Study area is `delta[i]` units wide in dimension `i`.
`ll.corner`	DX1 vector containing minimum coordinates in all dimensions.

The Halton sequence maps the non-negative integers (the Halton indices) to D-space. This routine does the inverse. Given a point in D-space and a grid of Halton boxes, the point's Halton index is any integer N which gets mapped to the Halton box containing the point. (i.e., any integer in the set ${x:N = x mod C}$, where $C$ = prod(n.boxes)).

This routine uses the Halton sequence and modular arithmetic to find Halton indices. This means several vectors of size nrow(hl.coords) must be created. Depending on memory, this approach fails for a sufficiently large number of points. When this routine fails, see the slower halton.indices.CRT, which computes indices by solving the Chinese Remainder Theorem.

A nX1 vector of Halton indices corresponding to points in hl.coords.

Trent McDonald

halton.indices.CRT, halton.indices

# Compute Halton box index for one value
pt <- data.frame(x=0.43, y=0.64)
n.boxes <- c(16,9) 
halton.indices.vector(pt, n.boxes) # should equal 70

# The following should also equal 70
pt <- data.frame(x=143, y=164)
halton.indices.vector(pt, n.boxes, delta=c(100,100), ll.corner=c(100,100)) 

# Plot Halton boxes and indices to check
b <- c(2,3)
J <- c(4,2)  # or, J <- log(n.boxes) / log(b) # = (log base 2 of 16, log base 3 of 9)
hl.ind <- halton( prod(n.boxes), 2,0 )
plot(c(0,1),c(0,1),type="n")
for( i in J[1]:1) abline(v=(0:b[1]^i)/b[1]^i, lwd=J[1]+1-i, col=i)
for( i in J[2]:1) abline(h=(0:b[2]^i)/b[2]^i, lwd=J[2]+1-i, col=i)
for( i in 1:prod(n.boxes)){
  box.center <- (floor(n.boxes*hl.ind[i,]+.Machine$double.eps*10) + 1-.5)/n.boxes
  text(box.center[1],box.center[2], i-1, adj=.5)  
}
points(pt$x, pt$y, col=6, pch=16, cex=2)