/usr/share/octave/packages/interval-3.1.0/@infsup/mpower.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 | ## 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 {@@infsup} mpower (@var{X}, @var{Y})
## @defopx Operator {@@infsup} {@var{X} ^ @var{Y}}
##
## Return the matrix power operation of @var{X} raised to the @var{Y} power.
##
## If @var{X} is a scalar, this function and @code{power} are equivalent.
## Otherwise, @var{X} must be a square matrix and @var{Y} must be a single
## integer.
##
## Warning: This function is not defined by IEEE Std 1788-2015.
##
## Accuracy: The result is a valid enclosure. The result is tightest for
## @var{Y} in @{0, 1, 2@}.
##
## @example
## @group
## infsup (magic (3)) ^ 2
## @result{} ans = 3×3 interval matrix
## [91] [67] [67]
## [67] [91] [67]
## [67] [67] [91]
## @end group
## @end example
## @seealso{@@infsup/pow, @@infsup/pown, @@infsup/pow2, @@infsup/pow10, @@infsup/exp}
## @end defop
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2014-10-31
function result = mpower (x, y)
if (nargin ~= 2)
print_usage ();
return
endif
if (not (isa (x, "infsup")))
x = infsup (x);
endif
if (isscalar (x))
## Short-circuit for scalars
result = power (x, y);
return
endif
if (not (isreal (y)) || fix (y) ~= y)
error ("interval:InvalidOperand", ...
"mpower: only integral powers can be computed");
endif
if (not (issquare (x.inf)))
error ("interval:InvalidOperand", ...
"mpower: must be square matrix");
endif
## Implements log-time algorithm A.1 in
## Heimlich, Oliver. 2011. “The General Interval Power Function.”
## Diplomarbeit, Institute for Computer Science, University of Würzburg.
## http://exp.ln0.de/heimlich-power-2011.htm.
result = infsup (eye (length (x)));
while (y ~= 0)
if (rem (y, 2) == 0) # y is even
[x.inf, x.sup] = mpfr_matrix_sqr_d (x.inf, x.sup);
y /= 2;
else # y is odd
result = mtimes (result, x);
if (all (vec (isempty (result))) || all (vec (isentire (result))))
## We can stop the computation here, this is a fixed point
break
endif
if (y > 0)
y --;
else
y ++;
if (y == 0)
## Inversion after computation of a negative power.
## Inversion should be the last step, because it is not
## tightest and would otherwise increase rounding errors.
result = inv (result);
endif
endif
endif
endwhile
endfunction
%!# from the documentation string
%!assert (isequal (infsup (magic (3)) ^ 2, infsup (magic (3) ^ 2)));
%!# correct use of signed zeros
%!test
%! x = mpower (infsup (eye (2)), 2);
%! assert (signbit (inf (x(1, 2))));
%! assert (not (signbit (sup (x(1, 2)))));
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