function A = house(A,show)
%---------------------------------------------------------------------------
%HOUSE Householder`s method is used to reduce
% a symmetric matrix to tridigonal form.
% Sample call
% A = house(A,show)
% Inputs
% A symmetric matrix
% Return
% A solution: tridiagonal matrix
 %--------------------------------------------
 if nargin==1, show = 0; end
[n,n] = size(A);
for k=1:(n-2),
s = norm(A(k+1:n,k));                  % Start of Form_W
if (A(k+1,k)<0), s = -s; end
r = sqrt(2*(A(k+1,k) + s)*s);
W(1:k) = zeros(1,k);                   % First K elements are 0
W(k+1) = (A(k+1,k) + s)/r;  
W(k+2:n) = A(k+2:n,k)'/r;              % End of Form_W
V(1:k) = zeros(1,k); % Start of Form_V, First K elements are 0
V(k+1:n) =  A(k+1:n,k+1:n)*W(k+1:n)';  % End of Form_V
c = W(k+1:n)*V(k+1:n)';                % Start of Form_Q
Q(1:k) = zeros(1,k);                   % First K elements are 0
Q(k+1:n) = V(k+1:n) - c*W(k+1:n); % End of Form_Q
A(k+2:n,k) = zeros(n-k-1,1);           % Start of Form_A
A(k,k+2:n) = zeros(1,n-k-1);

A(k+1,k) = -s;
A(k,k+1) = -s;
A(k+1:n,k+1:n) = A(k+1:n,k+1:n) ...
- 2*W(k+1:n)'*Q(k+1:n) - 2*Q(k+1:n)'*W(k+1:n); 
% End of Form_A
if show==1,
home; if k==1, clc; end; 
Mx1 = 'Scalar s         Scalar r        Scalar c';
Pts= [s r c];
Vts= [W;V;Q]';
Mx2 = 'Vector W         Vector V          Vector Q';
disp(' '),disp(Mx1),disp(Pts),...
disp(' '),disp(Mx2),disp(Vts),...
disp(' '),disp('Transformed matrix  A = '),disp(A)
pause(1.5);
end
end
end