function Q = formq(W)
% FUNCTION Q = formq(W)
% takes the matrix W produced by house.m as input,
% and generates a corresponding m x m orthogonal
% matrix Q.  Note, most people normally don't 
% construct Q explicitly because it is expensive
% and redundant. 
%  
% INPUT:  W -- an m x n lower triangular matrix 
%              containing the vectors of successive
%              Householder reflections  
% OUTPUT: Q -- corresponding orthogonal matrix
    
  [m,n] = size(W);
  Q = eye(m);
  
  for k = 1:m
    for j = n:-1:1
      Q(j:m,k) = Q(j:m,k) - 2*W(j:m,j)*(W(j:m,j)'*Q(j:m,k));
    end
  end