Mercurial > hg > octave-max
changeset 7484:e7485946272b
new norm arg for cond
author | John W. Eaton <jwe@octave.org> |
---|---|
date | Fri, 15 Feb 2008 16:35:59 -0500 |
parents | fb66330b2608 |
children | fe2d956d9007 |
files | scripts/ChangeLog scripts/linear-algebra/cond.m |
diffstat | 2 files changed, 49 insertions(+), 26 deletions(-) [+] |
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--- a/scripts/ChangeLog +++ b/scripts/ChangeLog @@ -1,3 +1,8 @@ +2008-02-15 Rolf Fabian <r.fabian@jacobs-university.de> + + * linear-algebra/cond.m: New optional second argument to + specify 1-norm, inf-norm, or frobenius-norm. + 2008-02-12 Kostas Poulios <poulios.konstantinos@googlemail.com> * plot/__quiver__.m: make arrow head be in z-plane of the arrow
--- a/scripts/linear-algebra/cond.m +++ b/scripts/linear-algebra/cond.m @@ -1,5 +1,5 @@ ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2003, 2004, -## 2005, 2006, 2007 John W. Eaton +## 2005, 2006, 2007, 2008 John W. Eaton ## ## This file is part of Octave. ## @@ -18,37 +18,46 @@ ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- -## @deftypefn {Function File} {} cond (@var{a}) -## Compute the (two-norm) condition number of a matrix. @code{cond (a)} is -## defined as @code{norm (a) * norm (inv (a))}, and is computed via a -## singular value decomposition. -## @seealso{norm, svd, rank} +## @deftypefn {Function File} {} cond (@var{a},@var{p}) +## Compute the @var{p}-norm condition number of a matrix. @code{cond (@var{a})} is +## defined as @code{norm (@var{a}, @var{p}) * norm (inv (@var{a}), @var{p})}. +## 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, inf, 'Inf', 'fro'} which are generally faster. +## @seealso{norm, inv, det, svd, rank} ## @end deftypefn ## Author: jwe -function retval = cond (a) +function retval = cond (a, p) - if (nargin == 1) + if (nargin && nargin < 3) if (ndims (a) > 2) - error ("cond: Only valid on 2-D objects") + error ("cond: only valid on 2-D objects") + endif + + if (nargin <2) + p = 2; endif - [nr, nc] = size (a); - if (nr == 0 || nc == 0) - retval = 0.0; - endif - if (any (any (isinf (a) | isnan (a)))) - error ("cond: argument must not contain Inf or NaN values"); + if (! isstr (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 - sigma = svd (a); - sigma_1 = sigma(1); - sigma_n = sigma(length (sigma)); - if (sigma_1 == 0 || sigma_n == 0) - retval = Inf; - else - retval = sigma_1 / sigma_n; - endif + retval = norm (a, p) * norm (inv (a), p); endif else print_usage (); @@ -56,11 +65,20 @@ endfunction -%!assert(abs (cond ([1, 2; 2, 1]) - 3) < sqrt (eps)); +%!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(cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16); +%!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); +%!error cond (1, 2, 3);