% csdriver.m
% This is a driver that specifies:
% 1. x = Nodes
% 2. y = Function values at those nodes 
%    (Currently f(x) = x + 2/x)
% 3. dx0 and dxn = Derivative values at the left endpoint,
%    f'(x_0), and at the right endpoint, f'(x_n), resp.
%    for a cubic clamped spline.
%
% The driver then calls csfit.m to compute the
% cubic spline function which is stored in a matrix S.
% clear workspace
clear 
% --------------------------- %
% specify nodes
x = [0.5 1.0 1.5 2.0];
% specify function values
y = x+2./x;
% specify clamped conditions
dx0 = 1 - 2./x(1)^2;
dxn = 1 - 2./x(4)^2;
% --------------------------- %
%
% Construct Spline
S = csfit(x,y,dx0,dxn)
%
% --------------------------------------------------- %
% Evaluate the spline on a very fine grid of points
% on each of the three intervals
t1 = [x(1):0.01:x(2)]; y1 = polyval(S(1,:),t1-x(1));
t2 = [x(2):0.01:x(3)]; y2 = polyval(S(2,:),t2-x(2));
t3 = [x(3):0.01:x(4)]; y3 = polyval(S(3,:),t3-x(3));
% --------------------------------------------------- %
%
% --------------------------- %
% Evaluate the true function 
% on a fine grid.
trux = [x(1):0.01:x(4)];
truy = trux +2./trux;
% --------------------------- %
%
% Plots
plot(t1,y1,'b--',t2,y2,'g--',t3,y3,'m--',x,y,'k*',trux,truy,'r-');
xlabel('x');
ylabel('S(x) and f(x)');
title('f(x)=x+2/x');
legend('Spline 1','Spline 2','Spline3','Ordinates','f(x)');