function yint = lagrangeINT( x, y, xint)
%
%  function yint = lagrangeINT(x, y, xint)
%
%  Use Lagrange interpolation to interpolate a set of points
%  Compare with discussion on pages 104-107 of Burden and Faires
%
%  Input parameters:
%    x     vector of x coordinates of given points.
%    y     vector of y coordinates of given points.
%    xint  the x coordinate at which y is to be interpolated
%
%
%  Output parameters:
%    yint       the interpolated value at xint. 
%
%  Kartik Sivaramakrishnan
%  Department of  Mathematics
%  North Carolina State University
%  September 7, 2007
%

n = length(x);
for i=1:n,
  L(i) = 1;
  for j=1:n,
    if j~=i,
      L(i) = L(i)*(xint-x(j))/(x(i)-x(j));
    end
  end
end
L = L(:);
yint = y'*L;