function x = ApplySymmetry(x,sym)
    [nely,nelx] = size(x);

    switch sym
    case 'iso'
        sym = 'cubic';
    case 'ort'
        sym = 'normal';
    case 'ant'
        sym = 'orth';
    end
    
    switch sym
        % 4-fold symmetry across diagonals
        case 'diag'
            x = (x+x')/2;
            x = rot90(x);
            x = (x+x')/2;
            x = rot90(x);

        % 4-fold symmetry across normals
        case 'normal'
            for row = 1:nelx
                for col = 1:nelx/2
                    x(row,col) = (x(row,col) + x(row,nelx-col+1))/2;
                    x(row,nelx+1-col) = x(row,col);
                end
            end

            for col = 1:nelx
                for row = 1:nelx/2
                    x(row,col) = (x(row,col) + x(nelx-row+1,col))/2;
                    x(nelx+1-row,col) = x(row,col);
                end
            end

        % 4-fold rotational symmetry
        case 'rota'
            A = x;
            A90 = rot90(A);
            A180 = rot90(A,2);
            A270 = rot90(A,3);
            E = zeros(nelx);
            temp = 0.25*(A(1:nelx/2,1:nelx/2)+A90(1:nelx/2,1:nelx/2)+A180(1:nelx/2,1:nelx/2)+A270(1:nelx/2,1:nelx/2));
            for ii = 1:3
                E(1:nelx/2,1:nelx/2) = temp;
                E = rot90(E);
            end
            E(1:nelx/2,1:nelx/2) = temp;
            x = E;

        % Cubic symmetry
        case 'cubic'
            A = x;
            A90 = rot90(A);
            A180 = rot90(A,2);
            A270 = rot90(A,3);
            E = zeros(nelx);
            temp = 0.25*(A(1:nelx/2,1:nelx/2)+A90(1:nelx/2,1:nelx/2)+A180(1:nelx/2,1:nelx/2)+A270(1:nelx/2,1:nelx/2));
            for ii = 1:3
                E(1:nelx/2,1:nelx/2) = temp;
                E = rot90(E);
            end
            E(1:nelx/2,1:nelx/2) = temp;
            x = E;

            for row = 1:nelx
                for col = 1:nelx/2
                    x(row,col) = (x(row,col) + x(row,nelx-col+1))/2;
                    x(row,nelx+1-col) = x(row,col);
                end
            end

            for col = 1:nelx
                for row = 1:nelx/2
                    x(row,col) = (x(row,col) + x(nelx-row+1,col))/2;
                    x(nelx+1-row,col) = x(row,col);
                end
            end

        case 'orth'
            x1 = x(1:nely/2, 1:nelx/2);
            x3 = x(nely/2+1:end, nelx/2+1:end);
            x1 = (rot90(rot90(x3))+x1)/2;
            x3 = rot90(rot90(x1));
            
            x(1:nely/2, 1:nelx/2) = x1;
            x(nely/2+1:end, nelx/2+1:end) = x3;
            
            x2 = x(1:nely/2, nelx/2+1:end);
            x4 = x(nely/2+1:end, 1:nelx/2);
            x2 = (rot90(rot90(x4))+x2)/2;
            x4 = rot90(rot90(x2));
            
            x(1:nely/2, nelx/2+1:end) = x2;
            x(nely/2+1:end, 1:nelx/2) = x4;
    end
end