/usr/share/octave/packages/interval-2.1.0/@infsupdec/absrev.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
## @deftypemethod {@@infsupdec} {@var{X} =} absrev (@var{C}, @var{X})
## @deftypemethodx {@@infsupdec} {@var{X} =} absrev (@var{C})
##
## Compute the reverse absolute value function.
##
## That is, an enclosure of all @code{x ∈ @var{X}} where
## @code{abs (x) ∈ @var{C}}.
##
## Accuracy: The result is a tight enclosure.
##
## @comment DO NOT SYNCHRONIZE DOCUMENTATION STRING
## No one way of decorating this operations gives useful information in all
## contexts. Therefore, the result will carry a @code{trv} decoration at best.
##
## @example
## @group
## absrev (infsupdec (-2, 1))
## @result{} ans = [-1, +1]_trv
## @end group
## @end example
## @seealso{@@infsupdec/abs}
## @end deftypemethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-19
function result = absrev (c, x)
if (nargin > 2)
print_usage ();
return
endif
if (nargin < 2)
x = infsupdec (-inf, inf);
endif
if (not (isa (c, "infsupdec")))
c = infsupdec (c);
endif
if (not (isa (x, "infsupdec")))
x = infsupdec (x);
endif
result = infsupdec (absrev (c.infsup, x.infsup), "trv");
result.dec(isnai (c) | isnai (x)) = _ill ();
endfunction
%!# Empty interval
%!assert (isequal (absrev (infsupdec ()), infsupdec ()));
%!assert (isequal (absrev (infsupdec (0, 1), infsupdec ()), infsupdec ()));
%!assert (isequal (absrev (infsupdec (0, 1), infsupdec (7, 9)), infsupdec ()));
%!assert (isequal (absrev (infsupdec (), infsupdec (0, 1)), infsupdec ()));
%!assert (isequal (absrev (infsupdec (-2, -1)), infsupdec ()));
%!# Singleton intervals
%!assert (isequal (absrev (infsupdec (1)), infsupdec (-1, 1, "trv")));
%!assert (isequal (absrev (infsupdec (0)), infsupdec (0, "trv")));
%!assert (isequal (absrev (infsupdec (-1)), infsupdec ()));
%!assert (isequal (absrev (infsupdec (realmax)), infsupdec (-realmax, realmax, "trv")));
%!assert (isequal (absrev (infsupdec (realmin)), infsupdec (-realmin, realmin, "trv")));
%!assert (isequal (absrev (infsupdec (-realmin)), infsupdec ()));
%!assert (isequal (absrev (infsupdec (-realmax)), infsupdec ()));
%!# Bound intervals
%!assert (isequal (absrev (infsupdec (1, 2)), infsupdec (-2, 2, "trv")));
%!assert (isequal (absrev (infsupdec (1, 2), infsupdec (0, 2)), infsupdec (1, 2, "trv")));
%!assert (isequal (absrev (infsupdec (0, 1), infsupdec (-0.5, 2)), infsupdec (-0.5, 1, "trv")));
%!assert (isequal (absrev (infsupdec (-1, 1)), infsupdec (-1, 1, "trv")));
%!assert (isequal (absrev (infsupdec (-1, 0)), infsupdec (0, "trv")));
%!# Unbound intervals
%!assert (isequal (absrev (infsupdec (0, inf)), infsupdec (-inf, inf, "trv")));
%!assert (isequal (absrev (infsupdec (-inf, inf)), infsupdec (-inf, inf, "trv")));
%!assert (isequal (absrev (infsupdec (-inf, 0)), infsupdec (0, "trv")));
%!assert (isequal (absrev (infsupdec (1, inf), infsupdec (-inf, 0)), infsupdec (-inf, -1, "trv")));
%!assert (isequal (absrev (infsupdec (-1, inf)), infsupdec (-inf, inf, "trv")));
%!assert (isequal (absrev (infsupdec (-inf, -1)), infsupdec ()));
%!assert (isequal (absrev (infsupdec (-inf, 1)), infsupdec (-1, 1, "trv")));
%!# from the documentation string
%!assert (isequal (absrev (infsupdec (-2, 1)), infsupdec (-1, 1, "trv")));
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