%This auxiliary program is used to provide a data set to 
% the Hermite subroutine, obtain the interpolating 
% polynomial, evaluate it a point "p", and make a graph of this 
% Hermite polynomial between the end points of the data set.

clear;

% Input Data. 

 x=[1.3,1.6,1.9];
 y=[0.6200860,0.4554022,0.2818186];
 yp=[-0.5220232,-0.5698959,-0.5811571];
 p=1.5;
 N=3;

 disp('Input Data');
 disp([x',y',yp']);

% Call to Hermite subroutine to obtain 
% the value of the interpolating polynomial at point "p".

[HP,Q]=SHerm(p,N,x,y,yp)

% Polynomial obtained by the Hermite subroutine

fprintf('Interpolating Polynomial obtained by the Hermite subroutine in the interval:(%4.2f,%4.2f)\n\n ',...
      x(1),x(N));
  fprintf('HP(x)=%7.4f + %7.4f(x-%4.2f))+ %7.4f(x-%4.2f)^2)+.... +%7.4f(x-%4.2f)^2...(x-%4.2f) \n\n'...
    , Q(1,1),Q(2,2),x(1),Q(3,3),x(1),Q(2*N,2*N),x(1),x(N));

% Graph of the polynomial obtained by evaluating it at 500 points between x(1) and x(N).

step=(x(N)-x(1))/500;
pp(1)=x(1);
PV(1)=Q(1,1);
for i=2:501
   pp(i)=pp(i-1)+step;
   [PV(i),Q]=SHerm(pp(i),N,x,y,yp);
 end
 plot(pp,PV); 
 hold on;
 plot(x,y,'*');