/usr/share/octave/packages/miscellaneous-1.2.1/lauchli.m is in octave-miscellaneous 1.2.1-4.
This file is owned by root:root, with mode 0o644.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 | ## -*- texinfo -*-
## @deftypefn {Function File} {@var{a}} = lauchli (@var{n})
## @deftypefnx {Function File} {@var{a}} = lauchli (@var{n},@var{mu})
## Creates the matrix [ ones(1,@var{n}); @var{mu}*eye(@var{n}) ]
## The value @var{mu} defaults to sqrt(eps).
## This is an ill-conditioned system for testing the
## accuracy of the QR routine.
##
## @example
## @group
## A = lauchli(15);
## [Q, R] = qr(A);
## norm(Q*R - A)
## norm(Q'*Q - eye(rows(Q)))
## @end group
## @end example
## @end deftypefn
## @seealso {ones,zeros,eye}
## This program is in the public domain
## Author: Paul Kienzle <pkienzle@users.sf.net>
function A = lauchli(n,mu)
if (nargin < 1 || nargin > 2)
usage("A = lauchli(n [, mu])");
endif
if (nargin < 2), mu = sqrt(eps); endif
A = [ ones(1,n); mu*eye(n) ];
endfunction
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