magic squars

gistfile1.txt

function iain_magic(n::Int)
    if n % 2 == 1
        # Odd-order magic square
        # http://en.wikipedia.org/wiki/Magic_square#Method_for_constructing_a_magic_square_of_odd_order
        M = zeros(Int, n, n)
        for I = 1:n, J = 1:n  # row, column
            @inbounds M[I,J] = n*((I+J-1+div(n,2))%n) + ((I+2J-2)%n) + 1
        end
        return M
    elseif n % 4 == 0
        # Doubly-even order magic square
        # http://en.wikipedia.org/wiki/Magic_square#A_method_of_constructing_a_magic_square_of_doubly_even_order
        # http://hal.archives-ouvertes.fr/docs/00/94/51/29/PDF/magicsquarev2.pdf
        M = [(i-1)*n+j for i = 1:n, j = 1:n]
        for outer_col = 1:4:n, outer_row = 1:4:n
            # Sides
            for i in (1,2), j in (0,3)
                @inbounds M[outer_row+i,outer_col+j] = n^2 - M[outer_row+i,outer_col+j]
            end
            # Top and bottom
            for i in (0,3), j in (1,2)
                @inbounds M[outer_row+i,outer_col+j] = n^2 - M[outer_row+i,outer_col+j]
            end
        end
        return M
    end
end