Say in Matlab I have a matrix like this:
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
I now need to find submatrixes 3×3 around every element (so each element in turn is the center of a 3×3 submatrix). When in the middle, it is no problem to find fx
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
which is the submatrix:
2 3 4
2 3 4
2 3 4
But when in the border of the matrix, that is elements in the first og last row or column, it of course isn’t possible to find a 3×3 submatrix. Instead I need the submatrix that fits. In the corner fx I would get
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
where the submatrix is:
1 2
1 2
and in the middle of the border, I get fx:
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
which gives:
4 5 6
4 5 6
or as another example:
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9
which gives:
6 7 8
6 7 8
I hope you understand my point. I am missing some feature that lets me find the distance from an element to the border.
I can treat every element as a center of a submatrix, and if I can just test, if the distance from the element to the border is below the submatrix’s border (the submatrix dimension will namely change, to fx a 5×5 submatrix), then I can truncate a part of the submatrix while it is being made.
How do I find the distance from an element to the border of the matrix in the most efficient way?
Let’s specify the question a bit further: You have a matrix of the size nxm and you pick an element i,j. You want to know the distance of element i,j from the border? That would be: min(i,j,n-i,m-j)