% This is a function which calculates and returns the 
% Newton polynomial of degree <= n which passes through
% the points (x(i),y(i)), for i = 1, 2, .... n + 1, where
% n+1 is the number of components in the input vectors
% x and y.
%
% Usage:   [out] = nestmult(a,nodes,x);
%
% Input:   a     = vector containing a list of the coefficients
%                 for the interpolating polynomial in Newton form.
%          nodes = vector containing a list of abscissas
%          x     = vector containing the set of points where the
%                 polynomial is to be evaluated.
%
% NOTE:    The input vectors are REQUIRED TO BE COLUMN VECTORS!!!
%
% Output:  out   = vector containing the values of the Newton 
%                  interpolating polynomial

function [out] = nestmult(a,nodes,x)

% Local Variables
% j           = loop index

%----- Here we check to see that a, nodes and x are column vectors ----%
[rx,cx] = size(x);
[ra,ca] = size(a);
[r,c]   = size(nodes);

if (cx~=1) | (ca~=1) | (c~=1)
   fprintf(1,'Your input vectors are WRONG!!!--nestmult.m\n');
end;   % end-if
%---------------------------------------------------------------%


% Initializations
out  = ones(rx,1)*a(r);     % Initializes the output vector.
                           % This is our S_j from class.

                           
% Loop to evaluate the polynomial
for j=(r-1):-1:1
    out = out.*(x-nodes(j)) + a(j);
end;   % end-j-loop