% spline_demo

%  load the splines package (needed for octave only)
  pkg load splines

%  delete all existing figures
  all_figs = findobj(0, 'type', 'figure');
  delete(all_figs);
%  close all

  x = [0 1 2];
  y = [-1 -1 7];
  z = linspace(0, 2, 300);
  
  figure(1)
%  natural spline 
  [s, ds, dds] = dcubicspline(x, y, z);
  plot(z, s, z, ds, z, dds, x, y, '*')
  title('natural spline - 2nd derivative = 0 at endpoints')
  
  type = 0;
  der = [0 0];
  
  figure(2)
%  spline with first derivative at endpoints = der
  [s, ds, dds] = dcubicspline(x, y, z,type,der);
  plot(z, s, z, ds, z, dds, x, y, '*')
  title('complete spline - 1st derivative = 0 at endpoints')
  
  figure(3)
%  spline and 1st derivative
  plot(z, s, z, ds, x, y, '*')
  title('complete spline - spline + 1st derivative')

  figure(4)
%  lagrange interpolating polynomial and 1st derivative
  c = polyfit(x,y,2);
  d = polyder(c); % coefficients in derivative
  p = polyval(c,z);
  dp = polyval(d,z);
  plot(z,p,z,dp,x,y,'*')
  title('quadratic lagrange interpolating polynomial + 1st derivative')