Hermite.m

clc;
clear;
% Taking the data inputs
x=input("Enter the x-coordinates of the data points as row vector: ");
f=input("Enter the y-coordinates of the data points as row vector: ");
df=input("Enter the derivative of y-coordinates of the function as row vector: ");
N1=length(x);
N2=length(f);
N3=length(df);
p=0;
while (p==0)
    if N1~=N2 || N1~=N3 
        fprintf("Please check the number of data points and re-enter.");
        x=input("Enter the x-coordinates of the data points as row vector : ");
        f=input("Enter the y-coordinates of the data points as row vector : ");
        df=input("Enter the derivative of y-coordinates of the function as row vector : ");
        N1=length(x);
        N2=length(f);
        N3=length(df);
    else 
        N=N1;
        p=1;
        % Displaying the data points 
        fprintf("\n The data is given in a table as: \n\n ");
        D=['       x    ' '       f(x)    ' '      df(x)    '];
        disp(D);
        disp(cell2mat(compose('%14.8f', [x ; f; df]')));
    end
end
z=zeros(1,2*N);
Q=zeros(2*N,2*N);
% constructing the divided difference table
for i=1:N
    z(2*i-1)=x(i);
    z(2*i)=x(i);
    Q(2*i-1,1)=f(i);
    Q(2*i,1)=f(i);
    Q(2*i-1,2)=df(i);
end
for i=1:N-1
    Q(2*i,2)=(Q(2*i+1,1)-Q(2*i,1))/(z(2*i+1)-z(2*i));
end
for j=3:2*N
    for i=1:2*N+1-j
        Q(i,j)=(Q(i+1,j-1)-Q(i,j-1))/(z(i+j-1)-z(i));
    end
end
fprintf("\n Hermite divided difference table is given as: \n\n");
disp(cell2mat(compose('%14.7f', [z' Q])));
fprintf("\n In the above table the entries of the first rows (from 2nd to %dth columns) \n", 2*N+1);
fprintf("are required to contruct the interpolating polynomial.\n");

% Finding values of Hemite polynomial(which approximates the given data) at some point
w=input("\n Enter the point at which we want to find the value of the function : ");
v=Q(1,1);
for k=2:2*N
    m=1;
    for j=1:k-1
        m=m*(w-z(j));
    end
    v=v+Q(1,k)*m;
end
fprintf("\n The value of the Hermite interpolating polynomial (of degree less than or equal to %d  \n", 2*N-1);
fprintf("for the given data) at %2.2f is :%14.7f \n\n", w, v);