/usr/share/octave/packages/interval-2.1.0/@infsup/sum.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} sum (@var{X})
## @defmethodx {@@infsup} sum (@var{X}, @var{DIM})
##
## Sum of elements along dimension @var{DIM}. If @var{DIM} is omitted, it
## defaults to the first non-singleton dimension.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## sum ([infsup(1), pow2(-1074), -1])
## @result{} ans ⊂ [4.9406e-324, 4.9407e-324]
## infsup (1) + pow2 (-1074) - 1
## @result{} ans ⊂ [0, 2.2205e-16]
## @end group
## @end example
## @seealso{@@infsup/plus, @@infsup/prod}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-26
function result = sum (x, dim)
if (nargin > 2)
print_usage ();
return
endif
if (nargin < 2)
## Try to find non-singleton dimension
dim = find (size (x.inf) > 1, 1);
if (isempty (dim))
dim = 1;
endif
endif
## Short-circuit
if (size (x.inf, dim) == 1)
result = x;
return
endif
if (dim == 1)
resultsize = [1, max(1, size (x.inf, 2))];
elseif (dim == 2)
resultsize = [max(1, size (x.inf, 1)), 1];
else
error ("interval:InvalidOperand", "sum: DIM must be a valid dimension")
endif
l = u = zeros (resultsize);
for n = 1 : size (x.inf, 3 - dim)
idx.type = "()";
idx.subs = cell (1, 2);
idx.subs{dim} = ":";
idx.subs{3 - dim} = n;
## Select current vector in matrix
if (size (x.inf, 3 - dim) == 1)
vector.x = x;
else
vector.x = subsref (x, idx);
endif
if (any (isempty (vector.x)(:)))
## One of the intervals is empty
l(n) = inf;
u(n) = -inf;
else
l(n) = mpfr_vector_sum_d (-inf, vector.x.inf);
u(n) = mpfr_vector_sum_d (+inf, vector.x.sup);
endif
endfor
result = infsup ();
result.inf = l;
result.sup = u;
endfunction
%!# from the documentation string
%!assert (sum ([infsup(1), pow2(-1074), -1]) == infsup (pow2 (-1074)));
%!assert (sum (infsup ([])) == 0);
%!# correct use of signed zeros
%!test
%! x = sum (infsup (0));
%! assert (signbit (inf (x)));
%! assert (not (signbit (sup (x))));
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