%title:- to find a funcational value of a discrete function at any
%arbitrary pont using lagrange's interpolation
%develope by:binod dhami
%date:2080/03/28
%____________________three critical statement______________
    close all;
    clear variables;
    clc;
%__________________user I/P section_________________________
x=input('enter the value for x[]=');
y=input('enter the value for y[]=');
while(length(x)~=length(y))
    clc;
    disp('x and y must be equal length');
    x=input('enter the value for x[]=');
    y=input('enter the value for y[]=');
end;
out=[x,y];
disp(out);
X=input('enter the value of x at which y is to be found x=');
%_____________________Calculation Section______________
Y=0;
n=length(x);
for i=1:n
    temp=1;
    for j=1:n
        if i~=j
            temp=temp*(X-x(j))/(x(i)-x(j));
        end;
        
    end 
    Y=Y+temp*y(i);
end 
%__________________Ouput section__________________
result=strcat('the value of y at X=',num2str(X),'is Y=',num2str(Y));
disp('__________________________');
disp(result);