Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / miscellaneous-1.1.0 / lauchli.m

diff --git a/octave_packages/miscellaneous-1.1.0/lauchli.m b/octave_packages/miscellaneous-1.1.0/lauchli.m
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+## -*- 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