function x = forwardsubs(R,b)
% FUNCTION x = forwardsubs(R,b)
% solve the system Rx = b given that R is 
% lower triangular. 
% INPUT:  R -- lower triangular m x n matrix 
%         b -- m x 1 vector
% OUTPUT: x -- n x 1 vector satisfying Rx = b
  
  [m,n] = size(R);
  x = zeros(n,1);
  
  x(1) = b(1)/R(1,1);
  
  for j = 2:n
    x(j) = (b(j)-R(j,1:j-1)*x(1:j-1))/R(j,j);
  end