/usr/share/octave/packages/interval-2.1.0/@infsup/det.m is in octave-interval 2.1.0-2.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 | ## Copyright 2015-2016 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} det (@var{A})
##
## Compute the determinant of matrix @var{A}.
##
## The determinant for matrices of size 3×3 or greater is computed via L-U
## decomposition and may be affected by overestimation due to the dependency
## problem.
##
## Accuracy: The result is a valid enclosure.
##
## @example
## @group
## det (infsup (magic (3)))
## @result{} ans = [-360]
## @end group
## @end example
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-10-23
function result = det (x)
if (nargin ~= 1)
print_usage ();
return
endif
if (not (issquare (x.inf)))
error ("det: argument must be a square matrix");
endif
if (any (isempty (x)(:)))
result = infsup ();
return
endif
switch (rows (x.inf))
case 0
result = infsup (1);
return
case 1
result = x;
return
case 2
## det ([1, 3; 2, 4]) = 4*1 - 3*2
## The result will be tightest.
result = mtimes (infsup ([x.inf(4), -x.sup(3)], ...
[x.sup(4), -x.inf(3)]), ...
infsup (x.inf(:, 1), x.sup(:, 1)));
return
endswitch
zero = x.inf == 0 & x.sup == 0;
if (any (all (zero, 1)) || any (all (zero, 2)))
## One column or row being zero
result = infsup (0);
return
endif
## P * x = L * U, with
## det (P) = ±1 and det (L) = 1 and det (U) = prod (diag (U))
##
## => det (x) = det (P) * det (U)
[~, U, P] = lu (x);
result = times (det (P), prod (diag (U)));
## Integer matrix, determinant must be integral
if (all (all (fix (x.inf) == x.inf & fix (x.sup) == x.sup)))
result.inf = ceil (result.inf);
result.sup = floor (result.sup);
endif
endfunction
%!# from the documentation string
%!assert (det (infsup (magic (3))) == -360);
|