is this code correct?

Write a MATLAB code that creates Magic Square of user defined odd order(for example, 5x5, 7x7, etc.) using Terrace method

1. Calculates elements of the Magic Square. 2. Displays the Magic Square.

Note : you can use the special fuction magic to test your own fuction only

M=zeros(n,n);
row=1;
column=(n+1)/2;

 for k=1:n^2
     M(row,column)=k;
     row=row-1;
     column=column+1;
     if(row==0 && column<=n)
         row=n;
     elseif(row>0 && column>n)
         column=1;
     elseif((row==0 && column>n) || M(row,column)>0 )
         row=row+2;
         column=column-1;
     end
  end

[Jan]

@redcavalry: Please delete your former thread, which contains a Pascal version of the code.

Answer 1

[the cyclist]

I see that you have calculated the elements of the magic square (which look correct to me), but I do not see that you have displayed the magic square.

Answer 2

[Daniel Shub]

you might want to try

   type magic

TMW do it in 4 lines.

[the cyclist]

Guessing that TMW doesn't use the "terrace method", but have to admit that I don't know for sure.

[Walter Roberson]

TMW needs 11 lines for the "singly even" case, at least in R2008b.

(Singly even is a size which is of the form 4*K+2 for non-negative integers K.)

Answer 3

[Image Analyst]

You can determine if your code is correct by subtracting your M from the correct answer. If everything is zero then you matched the correct magic square.

M  % Display M
result = M - magic(n) % Display difference

Answer 4

[Andrei Bobrov]

testing your code (edited)

all(diff([sum(M),sum(M,2)',sum(diag(M)),sum(diag(M(:,end:-1:1)))])==0) &&...
                                                isequal(sort(M(:)'),1:numel(M))

ADDED

Hi redcavalry! You used siamese method. Terrace method is variant of siamese method. About of Terrace method in russian Wikipedia (see "Метод террас").

Cod: 1 variant (eg,for n = 5)

n = 5;
k = n*2-1;
B = zeros(k);
B(1:2:end) = 1;
a = hankel(1:k,k:-1:1);
B = (min(a,a(:,end:-1:1))>=n&B)+0;
A = zeros(n,k);
A(:,1:2:end) = 1;
A(~~A)=1:n^2;
A = reshape(A,k,[])';
B(~~B)=A(~~A);
i1 = [(n+1)/2:n-1,n+1:n+(n-1)/2];
i2 = [i1(end)+1:k,1:i1(1)-1];
B(:,i1) = B(:,i1) + B(:,i2);
B(i1,:) = B(i1,:) + B(i2,:);
M = B(i1(1):i1(end),i1(1):i1(end))

2 variant with use siamese method

i1 = (n+1)/2;
j1 = i1+1;
M = zeros(n);
for k = 1:n^2
   M(i1,j1) = k;
   i1 = i1 - 1;
   j1 = j1 +1;
   if i1 == 0 && j1 <= n
       i1 = n;
   elseif i1 > 0 && j1 > n
       j1 = 1;
   elseif i1 == 0 && j1 > n || M(i1,j1) > 0
       j1 = rem(j1,n)+1;
       i1 = i1 + 1;
   end
end

[Walter Roberson]

length(unique([sum(M),sum(M,2)',sum(diag(M)),sum(flipud(M))]))==1

[Daniel Shub]

I think to be a magic square the sorted elements have to equal 1:M

[Andrei Bobrov]

Yes, Daniel. Added.