/usr/share/octave/packages/interval-2.1.0/@infsupdec/mulrev.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} =} mulrev (@var{B}, @var{C}, @var{X})
## @deftypemethodx {@@infsupdec} {@var{X} =} mulrev (@var{B}, @var{C})
## @deftypemethodx {@@infsupdec} {[@var{U}, @var{V}] =} mulrev (@var{B}, @var{C})
## @deftypemethodx {@@infsupdec} {[@var{U}, @var{V}] =} mulrev (@var{B}, @var{C}, @var{X})
##
## Compute the reverse multiplication function or the two-output division.
##
## That is, an enclosure of all @code{x ∈ @var{X}} where
## @code{x .* b ∈ @var{C}} for any @code{b ∈ @var{B}}.
##
## This function is similar to interval division @code{@var{C} ./ @var{B}}.
## However, it treats the case 0/0 as “any real number” instead of “undefined”.
##
## Interval division, considered as a set, can have zero, one or two disjoint
## connected components as a result. If called with two output parameters,
## this function returns the components separately. @var{U} contains the
## negative or unique component, whereas @var{V} contains the positive
## component in cases with two components.
##
## 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
## c = infsupdec (1);
## b = infsupdec (-inf, inf);
## [u, v] = mulrev (b, c)
## @result{}
## u = [-Inf, 0]_trv
## v = [0, Inf]_trv
## @end group
## @end example
## @seealso{@@infsupdec/times}
## @end deftypemethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-19
function [u, v] = mulrev (b, c, x)
if (nargin < 2 || nargin > 3)
print_usage ();
return
endif
if (nargin < 3)
x = infsupdec (-inf, inf);
endif
if (not (isa (b, "infsupdec")))
b = infsupdec (b);
endif
if (not (isa (c, "infsupdec")))
c = infsupdec (c);
endif
if (not (isa (x, "infsupdec")))
x = infsupdec (x);
endif
if (nargout < 2)
u = mulrev (b.infsup, c.infsup, x.infsup);
u = infsupdec (u, "trv");
u.dec(isnai (x) | isnai (b) | isnai (c)) = _ill ();
else
[u, v] = mulrev (b.infsup, c.infsup, x.infsup);
u = newdec (u);
u.dec(isempty (b) | isempty (c) | ismember (0, b)) = _trv ();
u.dec = min (u.dec, min (b.dec, c.dec));
u.dec(isnai (x)) = _ill ();
v = infsupdec (v, "trv");
v.dec(isnai (x) | isnai (b) | isnai (c)) = _ill ();
endif
endfunction
%!# IEEE Std 1788-2015 mulRevToPair examples
%!test
%! [u, v] = mulrev (infsupdec (0), infsupdec (1, 2));
%! assert (isempty (u) & isempty (v));
%!test
%! [u, v] = mulrev (infsupdec (0), infsupdec (0, 1));
%! assert (isentire (u) & isempty (v));
%!test
%! [u, v] = mulrev (infsupdec (1), infsupdec (1, 2));
%! assert (isequal (u, infsupdec (1, 2)) & isempty (v));
%!test
%! [u, v] = mulrev (infsupdec (1, inf), infsupdec (1));
%! assert (isequal (u, infsupdec (0, 1, "dac")) & isempty (v));
%!test
%! [u, v] = mulrev (infsupdec (-1, 1), infsupdec (1, 2));
%! assert (isequal (u, infsupdec (-inf, -1, "trv")) & isequal (v, infsupdec (1, inf, "trv")));
%!test
%! [u, v] = mulrev (infsupdec (-inf, inf), infsupdec (1));
%! assert (isequal (u, infsupdec (-inf, 0, "trv")) & isequal (v, infsupdec (0, inf, "trv")));
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