/usr/share/octave/packages/interval-2.1.0/@infsup/abs.m is in octave-interval 2.1.0-2.
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##
## This program 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.
##
## This program 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 this program; if not, see <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @documentencoding UTF-8
## @defmethod {@@infsup} abs (@var{X})
##
## Compute the absolute value of numbers.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## abs (infsup (2.5, 3.5))
## @result{} ans = [2.5, 3.5]
## abs (infsup (-0.5, 5.5))
## @result{} ans = [0, 5.5]
## @end group
## @end example
## @seealso{@@infsup/mag, @@infsup/mig}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-04
function x = abs (x)
if (nargin ~= 1)
print_usage ();
return
endif
## This is already correct, if the interval(s) are non-negative.
l = x.inf;
u = x.sup;
## This is even correct, if the interval(s) are empty.
notpositive = (x.sup <= 0);
l(notpositive) = -x.sup(notpositive);
u(notpositive) = -x.inf(notpositive);
zerointerior = (x.inf < 0 & not (notpositive));
l(zerointerior) = -0;
u(zerointerior) = max (-x.inf(zerointerior), x.sup(zerointerior));
x.inf = l;
x.sup = u;
endfunction
%!# Empty interval
%!assert (abs (infsup ()) == infsup ());
%!# Singleton intervals
%!assert (abs (infsup (1)) == infsup (1));
%!assert (abs (infsup (0)) == infsup (0));
%!assert (abs (infsup (-1)) == infsup (1));
%!assert (abs (infsup (realmax)) == infsup (realmax));
%!assert (abs (infsup (realmin)) == infsup (realmin));
%!assert (abs (infsup (-realmin)) == infsup (realmin));
%!assert (abs (infsup (-realmax)) == infsup (realmax));
%!# Bounded intervals
%!assert (abs (infsup (1, 2)) == infsup (1, 2));
%!assert (abs (infsup (0, 1)) == infsup (0, 1));
%!assert (abs (infsup (-1, 1)) == infsup (0, 1));
%!assert (abs (infsup (-1, 0)) == infsup (0, 1));
%!assert (abs (infsup (-2, -1)) == infsup (1, 2));
%!# Unbounded intervals
%!assert (abs (infsup (0, inf)) == infsup (0, inf));
%!assert (abs (infsup (-inf, inf)) == infsup (0, inf));
%!assert (abs (infsup (-inf, 0)) == infsup (0, inf));
%!assert (abs (infsup (1, inf)) == infsup (1, inf));
%!assert (abs (infsup (-1, inf)) == infsup (0, inf));
%!assert (abs (infsup (-inf, -1)) == infsup (1, inf));
%!assert (abs (infsup (-inf, 1)) == infsup (0, inf));
%!# from the documentation string
%!assert (abs (infsup (2.5, 3.5)) == infsup (2.5, 3.5));
%!assert (abs (infsup (-0.5, 5.5)) == infsup (0, 5.5));
%!# correct use of signed zeros
%!assert (signbit (inf (abs (infsup (-1, 0)))));
%!test
%! x = abs (infsup (0));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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