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########################################################################
##
## Copyright (C) 1996-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## This file is part of Octave.
##
## Octave 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.
##
## Octave 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 Octave; see the file COPYING. If not, see
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{q} =} discrete_inv (@var{x}, @var{v}, @var{p})
## For each element of @var{x}, compute the quantile (the inverse of the CDF)
## at @var{x} of the univariate distribution which assumes the values in
## @var{v} with probabilities @var{p}.
## @end deftypefn
function q = discrete_inv (x, v, p)
if (nargin != 3)
print_usage ();
endif
if (! isvector (v))
error ("discrete_inv: V must be a vector");
elseif (! isvector (p) || (length (p) != length (v)))
error ("discrete_inv: P must be a vector with length (V) elements");
elseif (any (isnan (p)))
error ("discrete_rnd: P must not have any NaN elements");
elseif (! (all (p >= 0) && any (p)))
error ("discrete_inv: P must be a nonzero, non-negative vector");
endif
if (isa (x, "single") || isa (v, "single") || isa (p, "single"))
q = NaN (size (x), "single");
else
q = NaN (size (x));
endif
## FIXME: This isn't elegant. But cumsum and lookup together produce
## different results when called with a single or a double.
if (isa (p, "single"))
p = double (p);
endif
[v, idx] = sort (v);
p = cumsum (p(idx)(:)) / sum (p); # Reshape and normalize probability vector
k = (x == 0);
q(k) = v(1);
k = (x == 1);
q(k) = v(end);
k = (x > 0) & (x < 1);
q(k) = v(length (p) - lookup (sort (p, "descend"), x(k)) + 1);
endfunction
%!shared x,v,p,y
%! x = [-1 0 0.1 0.5 1 2];
%! v = 0.1:0.2:1.9;
%! p = 1/length (v) * ones (1, length (v));
%! y = [NaN v(1) v(1) v(end/2) v(end) NaN];
%!assert (discrete_inv ([x, NaN], v, p), [y, NaN], eps)
## Test class of input preserved
%!assert (discrete_inv (single ([x, NaN]), v, p),
%! single ([y, NaN]), eps ("single"))
%!assert (discrete_inv ([x, NaN], single (v), p),
%! single ([y, NaN]), eps ("single"))
%!assert (discrete_inv ([x, NaN], v, single (p)),
%! single ([y, NaN]), eps ("single"))
## Test input validation
%!error <Invalid call> discrete_inv ()
%!error <Invalid call> discrete_inv (1)
%!error <Invalid call> discrete_inv (1,2)
%!error discrete_inv (1, ones (2), ones (2,1))
%!error discrete_inv (1, ones (2,1), ones (1,1))
%!error discrete_inv (1, ones (2,1), [1 NaN])
%!error discrete_inv (1, ones (2,1), [1 -1])
%!error discrete_inv (1, ones (2,1), [0 0])
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