/usr/share/octave/packages/interval-1.4.1/@infsupdec/power.m is in octave-interval 1.4.1-1.
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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 | ## 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
## @defop Method {@@infsupdec} power (@var{X}, @var{Y})
## @defopx Operator {@@infsupdec} {@var{X} .^ @var{Y}}
##
## Compute the general power function on intervals, which is defined for
## (1) any positive base @var{X}; (2) @code{@var{X} = 0} when @var{Y} is
## positive; (3) negative base @var{X} together with integral exponent @var{Y}.
##
## This definition complies with the common complex valued power function,
## restricted to the domain where results are real, plus limit values where
## @var{X} is zero. The complex power function is defined by
## @code{exp (@var{Y} * log (@var{X}))} with initial branch of complex
## logarithm and complex exponential function.
##
## Warning: This function is not defined by IEEE Std 1788-2015. However, it
## has been published as “pow2” in O. Heimlich, M. Nehmeier, J. Wolff von
## Gudenberg. 2013. “Variants of the general interval power function.”
## Soft Computing. Volume 17, Issue 8, pp 1357–1366.
## Springer Berlin Heidelberg. DOI 10.1007/s00500-013-1008-8.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## infsupdec (-5, 6) .^ infsupdec (2, 3)
## @result{} ans = [-125, +216]_trv
## @end group
## @end example
## @seealso{@@infsupdec/pow, @@infsupdec/pown, @@infsupdec/pow2, @@infsupdec/pow10, @@infsupdec/exp}
## @end defop
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-15
function result = power (x, y)
if (nargin ~= 2)
print_usage ();
return
endif
if (not (isa (x, "infsupdec")))
x = infsupdec (x);
endif
if (not (isa (y, "infsupdec")))
y = infsupdec (y);
endif
if (isnai (x))
result = x;
return
endif
if (isnai (y))
result = y;
return
endif
result = newdec (power (intervalpart (x), intervalpart (y)));
result.dec = min (result.dec, min (x.dec, y.dec));
## The general power function is continuous where it is defined
domain = not (isempty (result)) & (...
inf (x) > 0 | ... # defined for all x > 0
(inf (x) == 0 & inf (y) > 0) | ... # defined for x = 0 if y > 0
# defined for x < 0 only where y is integral
(issingleton (y) & fix (inf (y)) == inf (y) & ...
(inf (y) > 0 | not (ismember (0, x))))); # not defined for 0^0
result.dec (not (domain)) = _trv ();
endfunction
%!test "from the documentation string";
%! assert (isequal (infsupdec (-5, 6) .^ infsupdec (2, 3), infsupdec (-125, 216, "trv")));
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