gen_hh

(PublicToolbox/regutools/gen_hh.m in BrainStorm 2.0 (Alpha))

Function Synopsis

[x1,beta,v] = gen_hh(x)

Help Text

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.

Cross-Reference Information

bidiag                             C:\BrainStorm_2001\PublicToolbox\regutools\bidiag.m
lanc_b                             C:\BrainStorm_2001\PublicToolbox\regutools\lanc_b.m
lsqr                               C:\BrainStorm_2001\PublicToolbox\regutools\lsqr.m
plsqr                              C:\BrainStorm_2001\PublicToolbox\regutools\plsqr.m

Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\gen_hh.m

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, UNI-C, 05/13/1989.

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