% Plot the Langrage basis polynomials l_0(x), ..., l_5(x) 
% for [a,b] = [0,1] with x_j = j/5.

 figure(1), clf

 xx = linspace(0,1,300)';          % fine grid for plotting
 N = 5;                            % number of grid points

 x = linspace(0,1,N+1)';           % grid points, x(j+1) = j/N = x_j                                         
 for j=0:N
    lj = ones(size(xx));           % construct l_j on the fine grid, xx
    for k=0:N                   
       if k~=j, lj = lj.*(xx-x(k+1))/(x(j+1)-x(k+1)); end
    end
    plot(xx, lj, 'k-','linewidth',2), hold on
    plot(x,zeros(size(x)), 'k.','markersize',20)
    axis([0 1 -2 2])
    set(gca,'fontsize',16)
    xlabel('x'), ylabel('l_j(x)'), title('Lagrange basis polynomials')
    input(' press <return> ')
 end