align2D: Function to align points from ordination with known locations
In jhmaindonald/DAAG: Data Analysis and Graphics Data and Functions

Description Usage Arguments Details Value Note Author(s) Examples

Find the linear transformation which, applied to one set of points in the ($x$, $y$) plane, gives the best match in a least squares sense to a second set of points.

1	align2D(lat, long, x1, x2, wts=NULL)

`lat`	Latitude or other co-ordinate of point to align to
`long`	Longitude or other co-ordinate of point to align to
`x1`	First coordinate of point to align
`x2`	First coordinate of point to align
`wts`	If non-NULL, specifies weights for the points.

Achieves the best match, in a least squares sense, between an ordination and known locations in two-dimensionaL space.

`fitlat`	Fitted values of `lat`
`fitlong`	Fitted values of `long`
`lat`	Input values of `lat`
`long`	Input values of `long`

An ordination that is designed to reproduce distances between points is specified only to within an arbitrary rotation about the centroid. What linear transformation of the points ($x1$, $x2$) given by the ordination gives the best match to the known co-ordinates?

John H Maindonald

if(require(DAAG)&require(oz)){
aupts <- cmdscale(audists)
xy <- align2D(lat = aulatlong$latitude, long = aulatlong$longitude,
              x1 = aupts[, 1], x2 = aupts[, 2], wts = NULL)
oz()
fitcoords <- align2D(lat=aulatlong$latitude,
                      long=aulatlong$longitude,
                      x1=aupts[,1], x2 = aupts[,2],
                      wts=NULL)
x <-with(fitcoords,
         as.vector(rbind(lat, fitlat, rep(NA,length(lat)))))
y <-with(fitcoords,
         as.vector(rbind(long, fitlong, rep(NA,length(long)))))
points(aulatlong, col="red", pch=16, cex=1.5)
lines(x, y, col="gray40", lwd=3)
}

## The function is currently defined as
function(lat, long, x1, x2, wts=NULL){
    ## Get best fit in space of (latitude, longitude)
    if(is.null(wts))wts <- rep(1,length(x1))
    fitlat <- predict(lm(lat ~ x1+x2, weights=wts))
    fitlong <- predict(lm(long ~ x1+x2, weights=wts))
    list(fitlat = fitlat, fitlong=fitlong, lat=lat, long=long)
}