% m8_leastsquares.m - a little least-squares

    t = 2*pi*(1:30)'/30                                
    A = [ cos(0*t) sin(t) cos(t) sin(2*t) cos(2*t) ]  
    A'*A                                             
    plot(A)
    plot(t,A)

    b = [ linspace(0,3,8) linspace(3,2,7) ...
          linspace(2,6,10) linspace(5,0,5) ]'       
    plot(t,b,'ok'), grid on
    x = A\b                     
    hold on, plot(t,A*x,'r')
  
    b = b + randn(30,1)                            
    hold off, plot(t,b,'ok'), grid on
    x = A\b
    hold on, plot(t,A*x,'r')

%   (and just for fun, after clicking on the red curve...)
    set(gco,'linewidth',20)