/usr/share/octave/packages/interval-2.1.0/@infsup/dilog.m is in octave-interval 2.1.0-2.
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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 | ## 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} dilog (@var{X})
##
## Compute the real part of the dilogarithm function.
##
## @tex
## $$
## {\rm dilog} (x) = -\Re \int_0^x {{\log (1-t)} \over t} dt
## $$
## @end tex
## @ifnottex
## @group
## @verbatim
## x
## / log (1 - t)
## dilog (x) = - Re | ------------- dt
## / t
## 0
## @end verbatim
## @end group
## @end ifnottex
##
## Accuracy: The result is a tight enclosure.
##
## @example
## @group
## dilog (infsup (1))
## @result{} ans ⊂ [1.6449, 1.645]
## @end group
## @end example
## @end defmethod
## Author: Oliver Heimlich
## Keywords: interval
## Created: 2015-02-29
function x = dilog (x)
if (nargin ~= 1)
print_usage ();
return
endif
l = inf (size (x.inf));
u = -l;
## Monotonically increasing for x1
x1 = intersect (x, infsup (-inf, 2));
select = not (isempty (x1));
if (any (select(:)))
l(select) = mpfr_function_d ('dilog', -inf, x1.inf(select));
u(select) = mpfr_function_d ('dilog', +inf, x1.sup(select));
endif
## Monotonically decreasing for x2
x2 = intersect (x, infsup (2, inf));
select = not (isempty (x2));
if (any (select(:)))
l(select) = min (l(select), ...
mpfr_function_d ('dilog', -inf, x2.sup(select)));
u(select) = mpfr_function_d ('dilog', +inf, x2.inf(select));
endif
x.inf = l;
x.sup = u;
endfunction
%!assert (dilog (infsup (-inf, inf)) == "[-Inf, +0x1.3BD3CC9BE45DFp1]");
%!# from the documentation string
%!assert (dilog (infsup (1)) == "[0x1.A51A6625307D3, 0x1.A51A6625307D4]");
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