filling matrix with circular patern - r

Question

I want to write a function that fill a matrix m by m where m is odd as follows :
1) it's starts from middle cell of matrix (for example for 5 by 5 A, matrix middle cell are A[2,2] ) , and put number 1 there
2) it's go one cell forward and add 1 to previous cell and put it in second cell
3) it's go down and put 3, left 4, left 5, up 6, up 7,...
for example the resulting matrix could be like this :
> 7 8 9
6 1 2
5 4 3
could somebody help me to implement?

Answer 1

max_x=5
len=max_x^2
middle=ceiling(max_x/2)
A=matrix(NA,max_x,max_x)
increments=Reduce(
f=function(lhs,rhs) c(lhs,(-1)^(rhs/2+1)*rep(1,rhs)),
x=2*(1:(max_x)),
init=0
)[1:len]
idx_x=Reduce(
f=function(lhs,rhs) c(lhs,rep(c(TRUE,FALSE),each=rhs)),
1:max_x,
init=FALSE
)[1:len]
increments_x=increments
increments_y=increments
increments_x[!idx_x]=0
increments_y[idx_x]=0
A[(middle+cumsum(increments_x)-1)*(max_x)+middle+cumsum(increments_y)]=1:(max_x^2)
Gives
#> A
# [,1] [,2] [,3] [,4] [,5]
#[1,] 21 22 23 24 25
#[2,] 20 7 8 9 10
#[3,] 19 6 1 2 11
#[4,] 18 5 4 3 12
#[5,] 17 16 15 14 13
Explanation:
The vector increments denotes the steps along the path of the increasing numbers. It's either 0/+1/-1 for unchanged/increasing/decreasing row and column indices. Important here is that these numbers do not differentiate between steps along columns and rows. This is managed by the vector idx_x - it masks out increments that are either along a row (TRUE) or a column (FALSE).
The last line takes into account R's indexing logic (matrix index increases along columns).
Edit:
As per request of the OP, here some more information about how the increments vector is calculated.
You always go two consecutive straight lines of equal length (row-wise or column-wise). The length, however, increases by 1 after you have walked twice. This corresponds to the x=2*(1:(max_x)) argument together with rep(1,rhs). The first two consecutive walks are in increasing column/row direction. Then follow two in negative direction and so on (alternating). This is accounted for by (-1)^(rhs/2+1).