Speed comparisons for different methods of comparing rectangles

Rectangles.R

#* A broader experiment on this stack overflow question
#* http://stackoverflow.com/questions/33298196/how-to-avoid-a-double-for-loop-when-accessing-all-combinations-of-colums-of-a-ma/33301080?noredirect=1#comment54403634_33301080
#* I really need to find something better to do with my Friday mornings

#* Change n to make a larger experiment
n <- 1000

#* Change reps to run more cycles in 'microbenchmark'
reps <- 10

#* Peer review: is this a fair way to make arbitrary rectangles?
random_rectangle <- function(){
  x <- sort(sample(1:25, 2, replace = TRUE))
  y <- sort(sample(1:25, 2, replace = TRUE))
  c(x, y)
}

D <- do.call("cbind",
             lapply(1:n, 
                    function(i) random_rectangle()))


library(sp)
library(rgeos)
library(microbenchmark)

intersecting_rects <- function(edge1, edge2){
#* index 1 is left edge, index 2 is right edge
#* index 3 is lower edge, index 4 is upper edge
  (edge1[1] < edge2[2] && edge1[2] > edge2[1] &&
    edge1[3] < edge2[4] && edge1[4] > edge2[3])
}

D1 <- t(D)
D1 <- D1[, c(1, 3, 2, 3, 2, 4, 1, 4)]
ID <- paste0('rect', seq_len(nrow(D1)))

# Create SP
#http://stackoverflow.com/a/26620550/1412059
polys <- SpatialPolygons(mapply(function(poly, id) {
  xy <- matrix(poly, ncol=2, byrow=TRUE)
  Polygons(list(Polygon(xy)), ID=id)
}, split(D1, row(D1)), ID))

# Create SPDF
polys.df <- SpatialPolygonsDataFrame(polys, data.frame(id=ID, row.names=ID))


microbenchmark(
  poly = {
    res <-  gOverlaps(polys.df, byid = TRUE) | 
            gContains(polys.df, byid = TRUE) | 
            gWithin(polys.df, byid = TRUE) | 
            gCovers(polys.df, byid = TRUE)
    diag(res) <- 0
  },
  full_loop = {
    E <- mat.or.vec(nr=n, nc=n)
    for (i in 1:n){
      for (j in 1:n){
        E[i, j] <- as.numeric(intersecting_rects(D[, i], D[, j]))
      }
    }
  },
  partial_loop = {
    E <- mat.or.vec(nr=n, nc=n)
    for (i in 1:n){
      for (j in (i:n)[-1]){
        E[i, j] <- as.numeric(intersecting_rects(D[, i], D[, j]))
      }
    }
    E[lower.tri(E)] <- t(E)[lower.tri(E)]
  },
  times = 10
)