function R = housemovie(A);
% HOUSEMOVIE shows in-place Householder triangularization to give R,
%            but it throws away the v_k needed to form Q or use "A=QR"

[m n] = size(A);
scal = max(max(abs(A)));

disp('hit any key to show next stage')
A, pause

for k=1:n  % alg 10.1
    clear v
    v = A(k:m,k); % called 'x' in alg 10.1
    if v(1,1) < 0,   v(1,1) = -norm(v,2) + v(1,1);
    else,            v(1,1) =  norm(v,2) + v(1,1);   end
    r = norm(v,2);
    if abs(r) / scal < 2*eps, error('Householder reflector nearly zero'), end
    v = v/r;
    A(k:m,k:n)=A(k:m,k:n)-2*v*(v'*A(k:m,k:n));
    
    A, pause
end    

R = A;