function Qb = formqb(W,b)
% FUNCTION Q = formqb(W,b)
% takes the matrix W produced by house.m as input,
% and implicitly calculates Q'b
%  
% INPUT:  W  -- an m x n lower triangular matrix 
%               containing the vectors of successive
%               Householder reflections  
%         b  -- m x 1 vector  
% OUTPUT: Qb -- n x 1 vector satisfying Qb = Q'b
    
  [m,n] = size(W);
  
  for k = 1:n
    b(k:m) = b(k:m) - 2*W(k:m,k)*(W(k:m,k)'*b(k:m));
  end
  
  Qb = b;