The MATLAB function magicN constructs an magic square magic

The MATLAB function magic(N) constructs an magic square.

>> magic(3) ans = 8 1 6 3 5 7 4 9 2

The “magical” property of a magic square is that it contains the integers 1 to exactly once each and every row, column, and diagonal has the same sum:

8+1+6=15 3+5+7=15 4+9+2=15 8+3+4=15 1+5+9=15 6+7+2=15 8+5+2=15 6+5+4=15

Now it’s your turn. Write a function (verify_magic.m) that that take as input a square matrix and computes the sum of each row, column, and diagonal of the matrix to determine whether the input is a magic square. If the input is not a square matrix, use the error function to display an error message and abort the function. The output of the function should be a logical value indicating whether or not the input is a magic square: logical true for a magic square, logical false for a muggle square.

Example: >> verify_magic(magic(3)) ans = 1

>> verify_magic([1 2 3 ; 4 5 6 ; 7 8 9]) ans = 0

Solution

function isMagicSquare = verify_magic(squareMatrix)

    if nargin ~= 1
        error(\'Number of input arguments should be exactly one! \');
    elseif size(squareMatrix,1) ~= size(squareMatrix,2)
        error(\'Input is not a square matrix! \')
    else
        % side length
        rows = size(squareMatrix,1);

        % Assume it is a magic square in the beginning
        % Now check the if it contains integers 1 to N^2 exactly once

        % Initialize an empty logical array with N^2 length
        numCheck = false(1,rows ^ 2);

        % Iterate through the matrix (Column array to row array)
        for i = squareMatrix(:)\'
            if i <= 0 || i > rows^2 % Not in range, exit loop
                break;
            elseif numCheck(i) % Already marked true, repeated
                break;
            else
                numCheck(i) = true; % Mark it as true
            end
        end

        % if all is marked true then isMagicSquare remain true for now
        isMagicSquare = all(numCheck);

        % Now check the sum of rows, columns and diagnoals equal
        if isMagicSquare % If already false, then don\'t need the step

            % Sum array of all rows and columns
            sumRows = sum(squareMatrix,1);
            sumCols = sum(squareMatrix,2)\'; % Column vector to row vector

            % Sum of two diagnoals
            sumDiags1 = 0;
            sumDiags2 = 0;
            for i = 1:rows
                sumDiags1 = sumDiags1 + squareMatrix(i,i);
                sumDiags2 = sumDiags2 + squareMatrix(rows-i+1, i);
            end

            % Check, in sequence:
            %   - Two diagnoals have the same sumRows
            %   - The row sums all equal to diagnoal sum
            %   - The column sums all equals to diagnoal sum
            if ~all([sumDiags1 == sumDiags2, sumRows == sumDiags1, sumCols == sumDiags1])
                isMagicSquare = false;
            end

        end
    end
end