I have a bunch of points that lie around y=x (see the examples below), and I hope to calculate the orthogonal distance of each point to this y=x. Suppose that a point has coordinates (a,b), then it's easy to see the projected point on the y=x has coordinates ((a+b)/2, (a+b)/2). I use the following native codes for the calculation, but I think I need a faster one without the for loops. Thank you very much!
set.seed(999)
n=50
typ.ord = seq(-2,3, length=n) # x-axis
#
good.ord = sort(c(rnorm(n/2, typ.ord[1:n/2]+1,0.1),rnorm(n/2,typ.ord[(n/2+1):n]-0.5,0.1)))
y.min = min(good.ord)
y.max = max(good.ord)
#
plot(typ.ord, good.ord, col="green", ylim=c(y.min, y.max))
abline(0,1, col="blue")
#
# a = typ.ord
# b = good.ord
cal.orth.dist = function(n, typ.ord, good.ord){
good.mid.pts = (typ.ord + good.ord)/2
orth.dist = numeric(n)
for (i in 1:n){
num.mat = rbind(rep(good.mid.pts[i],2), c(typ.ord[i], good.ord[i]))
orth.dist[i] = dist(num.mat)
}
return(orth.dist)
}
good.dist = cal.orth.dist(50, typ.ord, good.ord)
sum(good.dist)
As easy as
good.dist <- sqrt((good.ord - typ.ord)^2 / 2)
It all boils down to compute the distance between a point and a line. In the 2D case of y = x, this becomes particularly easy (try it yourself).