X-Git-Url: https://git.creatis.insa-lyon.fr/pubgit/?p=CreaPhase.git;a=blobdiff_plain;f=octave_packages%2Fm%2Flinear-algebra%2Fcond.m;fp=octave_packages%2Fm%2Flinear-algebra%2Fcond.m;h=eaa226646b4fdf77dff55e41f15aa65a1b4f361f;hp=0000000000000000000000000000000000000000;hb=1c0469ada9531828709108a4882a751d2816994a;hpb=63de9f36673d49121015e3695f2c336ea92bc278 diff --git a/octave_packages/m/linear-algebra/cond.m b/octave_packages/m/linear-algebra/cond.m new file mode 100644 index 0000000..eaa2266 --- /dev/null +++ b/octave_packages/m/linear-algebra/cond.m @@ -0,0 +1,93 @@ +## Copyright (C) 1993-2012 John W. Eaton +## +## This file is part of Octave. +## +## Octave is free software; you can redistribute it and/or modify it +## under the terms of the GNU General Public License as published by +## the Free Software Foundation; either version 3 of the License, or (at +## your option) any later version. +## +## Octave is distributed in the hope that it will be useful, but +## WITHOUT ANY WARRANTY; without even the implied warranty of +## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU +## General Public License for more details. +## +## You should have received a copy of the GNU General Public License +## along with Octave; see the file COPYING. If not, see +## . + +## -*- texinfo -*- +## @deftypefn {Function File} {} cond (@var{A}) +## @deftypefnx {Function File} {} cond (@var{A}, @var{p}) +## Compute the @var{p}-norm condition number of a matrix. +## +## @code{cond (@var{A})} is ## defined as +## @tex +## $ {\parallel A \parallel_p * \parallel A^{-1} \parallel_p .} $ +## @end tex +## @ifnottex +## @code{norm (@var{A}, @var{p}) * norm (inv (@var{A}), @var{p})}. +## @end ifnottex +## +## By default @code{@var{p} = 2} is used which implies a (relatively slow) +## singular value decomposition. Other possible selections are +## @code{@var{p} = 1, Inf, "fro"} which are generally faster. See +## @code{norm} for a full discussion of possible @var{p} values. +## @seealso{condest, rcond, norm, svd} +## @end deftypefn + +## Author: jwe + +function retval = cond (A, p) + + if (nargin && nargin < 3) + if (ndims (A) > 2) + error ("cond: only valid on 2-D objects"); + endif + + if (nargin <2) + p = 2; + endif + + if (! ischar (p) && p == 2) + [nr, nc] = size (A); + if (nr == 0 || nc == 0) + retval = 0.0; + elseif (any (any (isinf (A) | isnan (A)))) + error ("cond: argument must not contain Inf or NaN values"); + else + sigma = svd (A); + sigma_1 = sigma(1); + sigma_n = sigma(end); + if (sigma_1 == 0 || sigma_n == 0) + retval = Inf; + else + retval = sigma_1 / sigma_n; + endif + endif + else + retval = norm (A, p) * norm (inv (A), p); + endif + else + print_usage (); + endif + +endfunction + +%!test +%! y= [7, 2, 3; 1, 3, 4; 6, 4, 5]; +%! tol = 1e-6; +%! type = {1, 2, 'fro', 'inf', inf}; +%! for n = 1:numel(type) +%! rcondition(n) = 1 / cond (y, type{n}); +%! endfor +%! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol); + +%!assert (abs (cond ([1, 2; 2, 1]) - 3) < sqrt (eps)); + +%!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16); + +%!error cond (); + +%!error cond (1, 2, 3); +