gen_hh.m

来自「求解离散病态问题的正则化方法matlab 工具箱」· M 代码 · 共 24 行

function [x1,beta,v] = gen_hh(x)
%GEN_HH Generate a Householder transformation.
%
% [x1,beta,v] = gen_hh(x)
%
% Given a vector x, gen_hh computes the scalar beta and the vector v
% determining a Householder transformation
%    H = (I - beta*v*v'),
% such that H*x = +-norm(x)*e_1. x1 is the first element of H*x.

% Per Christian Hansen, IMM, 11/11/1997.

v = x; alpha = norm(v);
if (alpha==0),
  beta = 0;
else
  beta = 1/(alpha*(alpha + abs(v(1))));
end
if (v(1) >= 0)
  v(1) = v(1) + alpha; x1 = -alpha;
else
  v(1) = v(1) - alpha; x1 = +alpha;
end