/usr/share/octave/packages/interval-2.1.0/@infsup/setxor.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 {@@infsup} {} setxor (@var{A}, @var{B})
## @deftypemethodx {@@infsup} {[@var{C}, @var{C1}, @var{C2}] =} setxor (@var{A}, @var{B})
##
## Build the symmetric difference of intervals @var{A} and @var{B}.
##
## With three output arguments, return intervals @var{C1} and @var{C2} such
## that @var{C1} and @var{C2} are enclosures of disjoint sets whose union is
## enclosed by interval @var{C}.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## x = infsup (1, 3);
## y = infsup (2, 4);
## [z, z1, z2] = setxor (x, y)
## @result{}
## z = [1, 4]
## z1 = [1, 2]
## z2 = [3, 4]
## @end group
## @end example
## @seealso{@@infsup/intersect, @@infsup/union, @@infsup/setdiff}
## @end deftypemethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-04-03
function [c, c1, c2] = setxor (a, b)
if (nargin ~= 2)
print_usage ();
return
endif
if (not (isa (a, "infsup")))
a = infsup (a);
endif
if (not (isa (b, "infsup")))
b = infsup (b);
endif
## Resize, if scalar × matrix
if (not (size_equal (a.inf, b.inf)))
a.inf = ones (size (b.inf)) .* a.inf;
a.sup = ones (size (b.inf)) .* a.sup;
b.inf = ones (size (a.inf)) .* b.inf;
b.sup = ones (size (a.inf)) .* b.sup;
endif
## Sort the four boundaries in ascending order b1 <= b2 <= b3 <= b4,
## if only one empty interval is present, then [b2, b3] = [Empty],
## with two empty intervals we also have [b1, b4] = [Empty].
b1 = min (a.inf, b.inf);
b2 = max (a.inf, b.inf);
b3 = min (a.sup, b.sup);
b4 = max (a.sup, b.sup);
[b2, b3] = deal (min (b2, b3), max (b2, b3));
l = b1;
u = b4;
select = a.inf == b.inf;
l(select) = b3(select);
select = a.sup == b.sup;
u(select) = b2(select);
select = a.inf == b.inf & a.sup == b.sup;
l(select) = inf;
u(select) = -inf;
l(l == 0) = -0;
u(u == 0) = +0;
c = infsup ();
c.inf = l;
c.sup = u;
if (nargout > 1)
select = isempty (a) | isempty (b);
b1(select) = a.inf(select);
b2(select) = a.sup(select);
b3(select) = b.inf(select);
b4(select) = b.sup(select);
l1 = b1;
u1 = b2;
select = a.inf == b.inf;
l1(select) = inf;
u1(select) = -inf;
l1(l1 == 0) = -0;
u1(u1 == 0) = +0;
c1 = infsup ();
c1.inf = l1;
c1.sup = u1;
l2 = b3;
u2 = b4;
select = a.sup == b.sup;
l2(select) = inf;
u2(select) = -inf;
l2(l2 == 0) = -0;
u2(u2 == 0) = +0;
c2 = infsup ();
c2.inf = l2;
c2.sup = u2;
endif
endfunction
%!test
%! [z, z1, z2] = setxor (infsup (), infsup ());
%! assert (isempty (z));
%! assert (isempty (z1));
%! assert (isempty (z2));
%!test
%! [z, z1, z2] = setxor (infsup (-inf, inf), infsup ());
%! assert (isentire (z));
%! assert (isentire (z1));
%! assert (isempty (z2));
%!test
%! [z, z1, z2] = setxor (infsup (-inf, inf), infsup (2));
%! assert (isentire (z));
%! assert (z1 == infsup (-inf, 2));
%! assert (z2 == infsup (2, inf));
%!test
%! [z, z1, z2] = setxor (infsup (2, 3), infsup (2));
%! assert (z == infsup (2, 3));
%! assert (z1 == infsup ());
%! assert (z2 == infsup (2, 3));
%!test
%! [z, z1, z2] = setxor (infsup (2, 3), infsup (2, 2.5));
%! assert (z == infsup (2.5, 3));
%! assert (z1 == infsup ());
%! assert (z2 == infsup (2.5, 3));
%!# from the documentation string
%!test
%! [z, z1, z2] = setxor (infsup (1, 3), infsup (2, 4));
%! assert (z == infsup (1, 4));
%! assert (z1 == infsup (1, 2));
%! assert (z2 == infsup (3, 4));
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