Function to make a magic square matrix is taking too long?

function [magicMatrix] = magicSquare(n)
%Function that iterates through a matrix of dimension n x n
%   to create a magic square, where n must be an odd number 
%   that is greater than or equal to 3

if mod(n,2) ~= 0 && n >= 3 %Checks to make sure the number is odd and greater or equal to 3
    magicMatrix = zeros(n); %Creates a variable that holds a matrix of size n x n filled with zeros
    x = (n - 1)/2 + 1; %Initializes the x position to the middle index of the matrix
    y = 1; %Initializes the y position to be the first row of the matrix
    iterator = 1; %Sets the initial number to start inputing into the matrix
    matrixSize = n*n; %Gives the size of the matrix and the highest number included in the matrix
    moveDown = true; %Boolean to see if we need to continue to move down

      for i = 1:n %Loop to iterate through the entire matrix

          magicMatrix(x,y) = iterator; %Sets the number in the position of the matirx

          x = x - 1; %Decrement x to move up one
          if x < 1 %Checks if x is on the boarder of the matrix
              x = n;
          end

          y = y + 1; %Increment y to move to the right one
          if y > n %Checks if y is on the boarder of the matrix
              y = 1;
          end

          if magicMatrix(x,y) == 0 %Checks if the matix holds a zero at the position x,y
              iterator = iterator + 1; %Increment the iterator
              magicMatrix(x,y) = iterator; %Inserts the iterator number into the matrix at position x,y
          else
              x = x + 1; %Increment x to move down one
              if x > n %Checks if x is on the boarder of the matrix
                  x = 1;
              end

              y = y - 1; %Decrement y to move left one
              if y < 1 %Checks if y is on the boarder of the matrix
                  y = n;
              end

              while moveDown %Loop to see if we need to continue to loop down
                  x = x + 1; %Increment x to move down one
                  if x > n %Checks if x is on the boarder of the matrix
                      x = 1;
                  end

                  if magicMatrix(x,y) == 0 %Checks if matrix holds a 0 at position x,y
                      iterator = iterator + 1; %Increment the iterator
                      magicMatrix(x,y) = iterator;
                      moveDown = false;
                  end

                  if magicMatrix(x,y) ~= 0 %If matrix does not hold a zero at position x,y
                      moveDown = true;
                  end
              end
          end
          iterator = iterator + 1; %Increments the iterator
      end
  else %Prints an error statement if the number entered is not odd or greater than or equal to 3
      fprintf('Error: Must enter an odd number greater or equal to 3 \n'); 
  end
  end

[Stephen23]

When I call

magicSquare(3)

when i=3 and iterator=7 the while loop goes into an infinite loop, cycling forever over the values x=1,2,3,4, but nothing else changes (in particular the while condition). This means that your algorithm has a bug. You need to learn how to debug code, and fix your algorithm:

https://www.mathworks.com/help/matlab/debugging-code.html

Answer 1

[Image Analyst]

Try this:

function magicMatrix = magicSquare(n)
magicMatrix = magic(n)

Otherwise step through your code with the debugger and figure out where it's spending so much time.

[Sabrina Edelmann]

Unfortunately I cannot use the built in function, but thanks

[Image Analyst]

Why not?

And, in your function, you have decalred the function recursively.

After this line:

moveDown = true; %Boolean to see if we need to continue to move down

You have this line:

function [magicMatrix] = magicSquare(n)

That is probably causing problems. Why are you defining a function with the same name within a function???

[Sabrina Edelmann]

The class I am taking wants us to make the function on our own. And that is an error that is on this page that it would not let me fix

[Image Analyst]

I'll tag it as "homework" for you. And I never heard of an error that the editor will not let you fix. Can you explain more about that?

[Sabrina Edelmann]

It is nothing to worry about, this webpage accidentally posted it twice, but I have fixed it now

[Image Analyst]

I can't even get your code to run so I can't even time it. Why don't you look at the links to the right, where Cleve's blog goes over what looks like much simpler algorithms than yours?