/usr/share/octave/packages/interval-2.1.0/@infsup/csc.m is in octave-interval 2.1.0-2.
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##
## 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} csc (@var{X})
##
## Compute the cosecant in radians, that is the reciprocal sine.
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## csc (infsup (1))
## @result{} ans ⊂ [1.1883, 1.1884]
## @end group
## @end example
## @seealso{@@infsup/sin, @@infsup/sec, @@infsup/cot}
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-03-15
function x = csc (x)
if (nargin ~= 1)
print_usage ();
return
endif
l = u = derivl = derivu = zeros (size (x.inf));
## Check, if wid (x) is certainly greater than 2*pi. This can save the
## computation if some values.
width = mpfr_function_d ('minus', -inf, x.sup, x.inf);
persistent pi = infsup ("pi");
certainlysingularity = width >= sup (pi);
## We simply compute the cosecant for both endpoints.
x.inf(x.inf == 0) = +0;
x.sup(x.sup == 0) = -0;
select = not (certainlysingularity);
l(select) = min (...
mpfr_function_d ('csc', -inf, x.inf(select)), ...
mpfr_function_d ('csc', -inf, x.sup(select)));
u(select) = max (...
mpfr_function_d ('csc', inf, x.inf(select)), ...
mpfr_function_d ('csc', inf, x.sup(select)));
## A change of sign is a sufficient singularity indicator
certainlysingularity = certainlysingularity | (select & sign (l) ~= sign (u));
l(certainlysingularity) = -inf;
u(certainlysingularity) = inf;
## Check, whether the interval contains a local extremum using the derivative
select = not (certainlysingularity);
derivl(select) = -mpfr_function_d ('csc', 0, x.inf(select)) .* ...
mpfr_function_d ('cot', 0, x.inf(select));
derivu(select) = -mpfr_function_d ('csc', 0, x.sup(select)) .* ...
mpfr_function_d ('cot', 0, x.sup(select));
hasextremum = select & ((derivl <= 0 & derivu >= 0) | ...
(derivl >= 0 & derivu <= 0));
l(hasextremum & l > 0) = 1;
u(hasextremum & u < 0) = -1;
emptyresult = isempty (x) | (x.inf == 0 & x.sup == 0);
l(emptyresult) = inf;
u(emptyresult) = -inf;
x.inf = l;
x.sup = u;
endfunction
%!# from the documentation string
%!assert (csc (infsup (1)) == "[0x1.303AA9620B223, 0x1.303AA9620B224]");
|