Traverse matrix (grid of points) in blocks of 4 - r

Question

This question is for a project and nothing to do with homeworks/acads. I am a working statistician.
So my question is, how would you write a R function, given a matrix with 400 rows and two columns where every 20 rows starting from the first, form a first row of coordinates in a grid of points like below where I would like the function to return the four corners of each individual square/rectangle within the grid:
Hence the output would have four columns and each row would indicate a rectangle. I am only looking at adjacent rectangles of the same size as in for example if the numbers below denote the row indices of the example matrix (which has two columns):
Example of row indices:
1 2 3
4 5 6
7 8 9
Would have to be traversed in the following order:
[1,2,4,5],[2,3,5,6],[4,5,7,8],[5,6,8,9] and
return the corresponding 2d points from the example input data set
which would have 9 rows and 2 points. But just that, here the grid is specified to be 3 by 3 while in my example the grid is 20 by 20 and my input dataset is 400 rows by 2 columns. If you look at the traversed result there is a pattern wherethe row indices in each 4 point block are incremented by 1. i just want to generalize this to a 400 by 2 or any setting where there is a 2 column matrix of points and there is a mention of the grid dimension.

Answer 1

Here is a solution if I have understood you correctly. It was a very interesting problem to be honest. :D
The idea is to make a box of a given edge length and then move this box around the grid and record it's vertices. Please see the following:
# Assuming the grid is always a square grid.
grid.size <- 20
# The matrix of row indices.
rindex.grid <- matrix(1:(grid.size * grid.size),
nrow=grid.size, ncol=grid.size, byrow=TRUE)
# We can traverse the grid by moving any given square either right or down in any
# single move. We choose to go right.
move.square.right <- function (this.square, steps=1) {
new.square <- this.square + steps
}
# Going right, capture co-ordinates of all squares in this row.
collect.sq.of.edge.length.in.row.number <- function (grid.size, elength,
rownum=1) {
first.square.in.row <- (rownum - 1) * grid.size + c(1, elength)
first.square.in.row <- c(first.square.in.row,
first.square.in.row + grid.size * (elength - 1))
squares.in.row <- t(sapply(X=seq_len(grid.size - (elength - 1)) - 1,
FUN=move.square.right,
this.square=first.square.in.row))
squares.in.row
}
# Now we start going down the columns and using the function above to collect
# squares in each row. The we will rbind the list of squares in each row into a
# dataframe. So what we get is a (grid.size - (elength - 1) ^ 2) x 4 matrix where
# each row is the co-ordinates of a square of edge length elength.
collect.sq.of.edge.length.in.grid <- function (grid.size, elength) {
all.squares=lapply(X=seq_len(grid.size - (elength - 1)),
FUN=collect.sq.of.edge.length.in.row.number,
grid.size=grid.size, elength=elength)
all.squares <- do.call(rbind, all.squares)
all.squares
}
This seems to show that we are getting the right number of boxes for all edge lengths:
tmp <- sapply(1:20, collect.sq.of.edge.length.in.grid, grid.size=grid.size)
sapply(tt, nrow)
[1] 400 361 324 289 256 225 196 169 144 121 100 81 64 49 36 25 16 9 4 1
Plus, it works well in your 3x3 example:
collect.sq.of.edge.length.in.grid(grid.size=3, elength=2)
[,1] [,2] [,3] [,4]
[1,] 1 2 4 5
[2,] 2 3 5 6
[3,] 4 5 7 8
[4,] 5 6 8 9

Answer 2

If you want to create a movable 20 x 20 "window" that can scroll down and/or across a 400x400 space, then use:
mcorners <- function(xidx, yidx) mat[xidx:(xidx+19),
yidx:(yidx+19])
mcorners(1,1) # should return mat[1:20, mat1:20]
Then supply mcorners() with arguments to fit your somewhat vaguely described needs. The traversal down the first column might involve:
sapply(1:381, function(ix) yourfunc( mcorners(ix, 1) ) )