/usr/share/octave/packages/interval-3.1.0/@infsup/mid.m is in octave-interval 3.1.0-5.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 | ## Copyright 2014-2016 Oliver Heimlich
##
## 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} mid (@var{X})
##
## Get the midpoint of interval @var{X}.
##
## If @var{X} is empty, @code{mid (@var{X})} is NaN.
## If @var{X} is entire, @code{mid (@var{X})} is 0.
## If @var{X} is unbounded in one direction, @code{mid (@var{X})} is positive
## or negative @code{realmax ()}.
##
## Accuracy: The result is rounded to the nearest floating point number and
## may thus be exact or not. However, it is guaranteed that the interval
## @var{X} is tightly enclosed by
## @code{[mid (@var{X}) - rad (@var{X}), mid (@var{X}) + rad (@var{X})]}.
##
## @example
## @group
## mid (infsup (2.5, 3.5))
## @result{} ans = 3
## @end group
## @end example
## @seealso{@@infsup/inf, @@infsup/sup, @@infsup/rad}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-05
function result = mid (x)
if (nargin ~= 1)
print_usage ();
return
endif
## First divide by 2 and then add, because this will prevent overflow.
## The different rounding modes for division will make errors of 2^-1075
## with subnormal numbers cancel each other out, or will make the round
## to nearest prefer the side that had an underflow error.
l = mpfr_function_d ('rdivide', -inf, x.inf, 2);
u = mpfr_function_d ('rdivide', +inf, x.sup, 2);
result = l + u;
result(x.inf == -inf) = -realmax ();
result(x.sup == inf) = realmax ();
result(isentire (x)) = 0;
result(isempty (x)) = nan ();
endfunction
%!assert (mid (infsup (-inf, inf)), 0);
%!# from the documentation string
%!assert (mid (infsup (2.5, 3.5)), 3);
%!shared testdata
%! # Load compiled test data (from src/test/*.itl)
%! testdata = load (file_in_loadpath ("test/itl.mat"));
%!test
%! # Scalar evaluation
%! testcases = testdata.NoSignal.infsup.mid;
%! for testcase = [testcases]'
%! assert (isequaln (...
%! mid (testcase.in{1}), ...
%! testcase.out));
%! endfor
%!test
%! # Vector evaluation
%! testcases = testdata.NoSignal.infsup.mid;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! out = vertcat (testcases.out);
%! assert (isequaln (mid (in1), out));
%!test
%! # N-dimensional array evaluation
%! testcases = testdata.NoSignal.infsup.mid;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! out = vertcat (testcases.out);
%! # Reshape data
%! i = -1;
%! do
%! i = i + 1;
%! testsize = factor (numel (in1) + i);
%! until (numel (testsize) > 2)
%! in1 = reshape ([in1; in1(1:i)], testsize);
%! out = reshape ([out; out(1:i)], testsize);
%! assert (isequaln (mid (in1), out));
%!test
%! # Decorated scalar evaluation
%! testcases = testdata.NoSignal.infsupdec.mid;
%! for testcase = [testcases]'
%! assert (isequaln (...
%! mid (testcase.in{1}), ...
%! testcase.out));
%! endfor
%!test
%! # Decorated vector evaluation
%! testcases = testdata.NoSignal.infsupdec.mid;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! out = vertcat (testcases.out);
%! assert (isequaln (mid (in1), out));
%!test
%! # Decorated N-dimensional array evaluation
%! testcases = testdata.NoSignal.infsupdec.mid;
%! in1 = vertcat (vertcat (testcases.in){:, 1});
%! out = vertcat (testcases.out);
%! # Reshape data
%! i = -1;
%! do
%! i = i + 1;
%! testsize = factor (numel (in1) + i);
%! until (numel (testsize) > 2)
%! in1 = reshape ([in1; in1(1:i)], testsize);
%! out = reshape ([out; out(1:i)], testsize);
%! assert (isequaln (mid (in1), out));
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