MacFormat 1994 August/August CD.bin/Shareware/Education/numericalmethods Folder/chap_11/house2.m

Text File | 1994-06-05 | 697 b | 27 lines | [MATF/MATL]

function A = house2(A,show)
% A = house2(A,show)
% To reduce a symmetric matrix to tridigonal form.
% Householder`s method is employed.
% A is an n x n symmetric matrix, input.
% A is the tridiagonal matrix, output.
if nargin==1, show = 0; end
[n,n] = size(A);
for k = 2:n-1
  U = A(:,k-1);
  U(1:k-1) = zeros(k-1,1);
  U = U/norm(U);
  if U(k) < 0, U = -U; end
  U(k) = U(k) + 1;
  beta = -U(k);       % beta is  -(norm(U)^2)/2
  V = A*U/beta;
  gamma = V'*U/(2*beta);
  V = V + gamma*U;
  A  =  A + U*V' + V*U';
  A(k-1,k+1:n) = zeros(1,n-k);
  if show==1,
    home, clc
    disp(''),disp(['Householder similarity transformation No. ',...
    int2str(k-1)]),disp(''),disp(A),pause(1);
  end
end