/usr/share/octave/packages/interval-2.1.0/ctc_intersect.m is in octave-interval 2.1.0-2.
This file is owned by root:root, with mode 0o644.
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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 | ## 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
## @defun ctc_intersect (@var{C1}, @var{Y1}, @var{C2}, @var{Y2})
## @defunx ctc_intersect (@var{C1}, @var{C2})
##
## Return a contractor function for the intersection of two sets.
##
## Functions @var{C1} and @var{C2} define two sets @code{S1 = @{@var{x} |
## @var{C1} (@var{x}) ∈ @var{Y1}@}} and @code{S2 = @{@var{x} |
## @var{C2} (@var{x}) ∈ @var{Y2}@}}. The return value is a contractor function
## for the set @code{S1 ∩ S2 = @{@var{x} | @var{C1} (@var{x}) ∈ @var{Y1} and
## @var{C2} (@var{x}) ∈ @var{Y2}@}}.
##
## Parameters @var{C1} and @var{C2} must be function handles and must accept
## the same number of parameters. See @command{@@infsup/fsolve} for how to
## define contractor functions. The user manual also contains an example on
## how to use this function.
##
## Instead of solving @code{@var{C1} (@var{x}) ∈ @var{Y1}} and
## @code{@var{C2} (@var{x}) ∈ @var{Y2}} separately and then compute an
## intersection of the result, you can solve
## @code{ctc_intersect (@var{C1}, @var{Y1}, @var{C2}, @var{Y2}) = 0}.
##
## @seealso{@@infsup/fsolve, ctc_union}
## @end defun
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-12-20
function c = ctc_intersect (ctc1, y1, ctc2, y2)
## Reorder parameters
switch (nargin)
case 2
ctc2 = y1;
y1 = y2 = 0;
case 3
if (is_function_handle (y1))
y2 = ctc2;
ctc2 = y1;
y1 = 0;
else
y2 = 0;
endif
case 4
...
otherwise
print_usage ();
endswitch
## Check parameters
if (not (isa (y1, "infsup")))
y1 = infsup (y1);
endif
if (not (isa (y2, "infsup")))
y2 = infsup (y2);
endif
if (not (is_function_handle (ctc1)) && not (ischar (ctc1)))
error ("interval:InvalidOperand", ...
"ctc_intersect: Parameter C1 is no function handle")
endif
if (not (is_function_handle (ctc2)) && not (ischar (ctc2)))
error ("interval:InvalidOperand", ...
"ctc_intersect: Parameter C2 is no function handle")
endif
c = @(varargin) ctc_intersect_eval (ctc1, y1, ctc2, y2, varargin{:});
endfunction
function varargout = ctc_intersect_eval (ctc1, y1, ctc2, y2, varargin)
y = varargin{1};
x = varargin(2 : end);
## Evaluate each contractor function
fval_and_contractions1 = nthargout (1 : nargout, ctc1, y1, x{:});
fval_and_contractions2 = nthargout (1 : nargout, ctc2, y2, x{:});
## Compute fval = y if either function value is inside of its constraints
fval1 = fval_and_contractions1{1};
fval2 = fval_and_contractions2{1};
fval1 = y + y_dist (y1, fval1);
fval2 = y + y_dist (y2, fval2);
varargout{1} = union (fval1, fval2);
## Both contractors must produce a subset of y.
varargout{1}(disjoint (fval1, y) | disjoint (fval2, y)) = infsup ();
## Combine the contractions
for i = 2 : nargout
varargout{i} = intersect (fval_and_contractions1{i}, ...
fval_and_contractions2{i});
endfor
endfunction
function d = y_dist (y, fval)
d = infsup (idist (y, fval), hdist (y, fval));
d(subset (fval, y) & not (isempty (fval))) = 0;
if (columns (y) == 1)
d = sum (d, 1);
elseif (rows (y) == 1)
d = sum (d, 2);
else
d = sum (sum (d));
endif
endfunction
%!function [fval, x] = ctc_abs (y, x)
%! fval = abs (x);
%! x = absrev (intersect (fval, y), x);
%!endfunction
%!shared c
%! c = ctc_intersect (@ctc_abs, "[0, 2]", @ctc_abs, "[1, 3]");
%!test
%! [fval, x] = c (infsup (0), infsup ("[1, 3]"));
%! assert (ismember (0, fval) && 0 != fval);
%! assert (x == infsup ("[1, 2]"));
%!test
%! [fval, x] = c (infsup (0), infsup ("[1, 2]"));
%! assert (0 == fval);
%! assert (x == infsup ("[1, 2]"));
%!test
%! [fval, x] = c (infsup (0), infsup ("[entire]"));
%! assert (ismember (0, fval) && 0 != fval);
%! assert (x == infsup ("[-2, 2]"));
%!test
%! [fval, x] = c (infsup (0), infsup ("[0, inf]"));
%! assert (ismember (0, fval) && 0 != fval);
%! assert (x == infsup ("[1, 2]"));
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