/usr/share/octave/packages/interval-1.4.1/@infsup/pownrev.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 | ## 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
## @deftypemethod {@@infsup} {@var{X} =} pownrev (@var{C}, @var{X}, @var{P})
## @deftypemethodx {@@infsup} {@var{X} =} pownrev (@var{C}, @var{P})
##
## Compute the reverse monomial @code{x^@var{P}}.
##
## That is, an enclosure of all @code{x ∈ @var{X}} where
## @code{pown (x, @var{P}) ∈ @var{C}}.
##
## Accuracy: The result is a valid enclosure. The result is a tight
## enclosure for @var{P} ≥ -2. The result also is a tight enclosure if the
## reciprocal of @var{P} can be computed exactly in double-precision.
##
## @seealso{@@infsup/pown}
## @end deftypemethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-13
function result = pownrev (c, x, p)
if (nargin < 2 || nargin > 3)
print_usage ();
return
endif
if (nargin < 3)
p = x;
x = infsup (-inf, inf);
endif
if (not (isa (c, "infsup")))
c = infsup (c);
endif
if (not (isa (x, "infsup")))
x = infsup (x);
endif
if (not (isnumeric (p)) || fix (p) ~= p)
error ("interval:InvalidOperand", "pownrev: exponent is not an integer");
endif
## Resize, if scalar × matrix
if (isscalar (x.inf) ~= isscalar (c.inf))
x.inf = x.inf (ones (size (c.inf)));
x.sup = x.sup (ones (size (c.inf)));
c.inf = c.inf (ones (size (x.inf)));
c.sup = c.sup (ones (size (x.inf)));
endif
if (p == 0) # x^p == 1
result = x;
emptyresult = c.inf > 1 | c.sup < 1;
result.inf (emptyresult) = inf;
result.sup (emptyresult) = -inf;
else
even = mod (p, 2) == 0;
if (even)
result = union (...
intersect (x, nthroot (intersect (c, infsup (0, inf)), p)), ...
intersect (x, -nthroot (intersect (c, infsup (0, inf)), p)));
else
result = union (...
intersect (x, nthroot (intersect (c, infsup (0, inf)), p)), ...
intersect (x, nthroot (intersect (c, infsup (-inf, 0)), p)));
endif
endif
endfunction
%!assert (pownrev (infsup (25, 36), infsup (0, inf), 2) == infsup (5, 6));
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