housh

% -*- texinfo -*-
% @deftypefn {Function File} {[@var{housv}, @var{beta}, @var{zer}] =} housh (@var{x}, @var{j}, @var{z})
% Compute Householder reflection vector @var{housv} to reflect @var{x}
% to be the j-th column of identity, i.e.,
%
% @example
% @group
% (I - beta*housv*housv')x =  norm(x)*e(j) if x(1) < 0,
% (I - beta*housv*housv')x = -norm(x)*e(j) if x(1) >= 0
% @end group
% @end example
%
% @noindent
% Inputs
%
% @table @var
% @item x
% vector
% @item j
% index into vector
% @item z
% threshold for zero  (usually should be the number 0)
% @end table
%
% @noindent
% Outputs (see Golub and Van Loan):
%
% @table @var
% @item beta
% If beta = 0, then no reflection need be applied (zer set to 0)
% @item housv
% householder vector
% @end table
% @end deftypefn