update packages

[CreaPhase.git] / octave_packages / m / linear-algebra / cond.m

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+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- 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);
+