function [grad_l, grad_r] = eno2x(m,n,i,j,phi,dx)

% phi(m+1,n+1), the level set function, m,n>=3.

    dxdx = dx*dx;

    if i > 1
      phx_l = (phi(i,j) - phi(i-1,j) )/dx;
    else
      phi_l = 3*phi(i,j) - 3*phi(i+1,j) + phi(i+2,j);
      phx_l = (phi(i,j) - phi_l )/dx;
    end

    if i < m+1
      phx_r = (phi(i+1,j) - phi(i,j) )/dx;
    else
      phi_r = 3*phi(i,j) - 3*phi(i-1,j) + phi(i-2,j);      
      phx_r = (phi_r - phi(i,j) )/dx;
    end

    if i > 1
      if i==2
        phi_l = 3*phi(i-1,j) - 3*phi(i,j) + phi(i+1,j);
	phxx_l = (phi(i,j) - 2*phi(i-1,j) + phi_l )/dxdx;
      else
        phxx_l = (phi(i,j) - 2*phi(i-1,j) + phi(i-2,j) )/dxdx;
      end
    else
      phi_l = 3*phi(i,j) - 3*phi(i+1,j) + phi(i+2,j);
      phi_ll = 6*phi(i,j) -8*phi(i+1,j) + 3*phi(i+2,j);
      phxx_l = (phi(i,j) - 2*phi_l + phi_ll )/dxdx;
    end

    if i < m + 1
      if i==m
	phi_r = 3*phi(i+1,j) - 3*phi(i,j) + phi(i-1,j);
        phxx_r = (phi_r - 2*phi(i+1,j) + phi(i,j) )/dxdx;
      else
        phxx_r = (phi(i+2,j) - 2*phi(i+1,j) + phi(i,j) )/dxdx;
      end
    else
      phi_r = 3*phi(i,j) - 3*phi(i-1,j) + phi(i-2,j);
      phi_rr = 6*phi(i,j) -8*phi(i-1,j) + 3*phi(i-2,j);
      phxx_r = (phi_rr - 2*phi_r + phi(i,j) )/dxdx;
    end

    if i==1
      phi_l = 3*phi(i,j) - 3*phi(i+1,j) + phi(i+2,j);
      phxx_o = (phi(i+1,j) - 2*phi(i,j) + phi_l )/dxdx;
      elseif i==m+1
        phi_r = 3*phi(i,j) - 3*phi(i-1,j) + phi(i-2,j);
        phxx_o = (phi_r - 2*phi(i,j) + phi(i-1,j) )/dxdx;;
      else
	phxx_o = (phi(i+1,j) - 2*phi(i,j) + phi(i-1,j) )/dxdx;
    end

    grad_l = phx_l + dx*0.5*absmin(phxx_l, phxx_o);
    grad_r = phx_r - dx*0.5*absmin(phxx_r, phxx_o);