## Copyright (C) 2022 Nicholas R. Jankowski ## Copyright (C) 2012 Rik Wehbring ## Copyright (C) 1997-2016 Kurt Hornik ## ## 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; see the file COPYING. If not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} hygeinv (@var{x}, @var{t}, @var{m}, @var{n}) ## For each element of @var{x}, compute the quantile (the inverse of the CDF) ## at @var{x} of the hypergeometric distribution with parameters ## @var{t}, @var{m}, and @var{n}. ## ## This is the probability of obtaining @var{x} marked items when randomly ## drawing a sample of size @var{n} without replacement from a population of ## total size @var{t} containing @var{m} marked items. ## ## The parameters @var{t}, @var{m}, and @var{n} must be positive integers ## with @var{m} and @var{n} not greater than @var{t}. ## @end deftypefn ## Author: KH ## Description: Random deviates from the hypergeometric distribution function inv = hygeinv (x, t, m, n) if (nargin != 4) print_usage (); endif if (! isscalar (t) || ! isscalar (m) || ! isscalar (n)) [retval, x, t, m, n] = common_size (x, t, m, n); if (retval > 0) error ("hygeinv: X, T, M, and N must be of common size or scalars"); endif endif if (iscomplex (x) || iscomplex (t) || iscomplex (m) || iscomplex (n)) error ("hygeinv: X, T, M, and N must not be complex"); endif if (isa (x, "single") || isa (t, "single") || isa (m, "single") || isa (n, "single")) inv = NaN (size (x), "single"); else inv = NaN (size (x)); endif ok = ((t >= 0) & (m >= 0) & (n > 0) & (m <= t) & (n <= t) & (t == fix (t)) & (m == fix (m)) & (n == fix (n))); if (isscalar (t)) if (ok) inv = discrete_inv (x, 0 : n, hygepdf (0 : n, t, m, n)); inv(x == 0) = 0; # Hack to return correct value for start of distribution endif else k = (x == 0); inv (ok & k) = 0; # set any x=0 to 0 if not already set to output NaN k = (x == 1); inv (ok & k) = n(ok & k); ok &= (x>0 & x<1); #remove 0's and x's outside (0,1), leave unfilled as NaN if any(ok(:)) n = n(ok); v = 0 : max (n(:)); ## manually perform discrete_inv to enable vectorizing with array input p = cumsum (hygepdf (v, t(ok), m(ok), n, "vectorexpand"), 2); sz_p = size (p); end_locs = sub2ind (sz_p, [1 : numel(n)]', n(:) + 1); ## manual row-wise vectorization of lookup, which returns index of element ## less than or equal to test value, zero if test value less than lowest ## number, and max index if greater than highest number. operated on ## flipped p, adjusting for different vector lengths in array rows. p = (p ./ p(end_locs))(:, end:-1:1) - x(ok)(:); p(p>=0) = NaN; [p_match, p_match_idx] = max (p, [], 2); p_match_idx(isnan(p_match)) = v(end) + 2; inv(ok) = v(v(end) - p_match_idx + 3); endif endif endfunction %!shared x %! x = [-1 0 0.5 1 2]; %!assert (hygeinv (x, 4*ones (1,5), 2*ones (1,5), 2*ones (1,5)), [NaN 0 1 2 NaN]) %!assert (hygeinv (x, 4*ones (1,5), 2, 2), [NaN 0 1 2 NaN]) %!assert (hygeinv (x, 4, 2*ones (1,5), 2), [NaN 0 1 2 NaN]) %!assert (hygeinv (x, 4, 2, 2*ones (1,5)), [NaN 0 1 2 NaN]) %!assert (hygeinv (x, 4*[1 -1 NaN 1.1 1], 2, 2), [NaN NaN NaN NaN NaN]) %!assert (hygeinv (x, 4, 2*[1 -1 NaN 1.1 1], 2), [NaN NaN NaN NaN NaN]) %!assert (hygeinv (x, 4, 5, 2), [NaN NaN NaN NaN NaN]) %!assert (hygeinv (x, 4, 2, 2*[1 -1 NaN 1.1 1]), [NaN NaN NaN NaN NaN]) %!assert (hygeinv (x, 4, 2, 5), [NaN NaN NaN NaN NaN]) %!assert (hygeinv ([x(1:2) NaN x(4:5)], 4, 2, 2), [NaN 0 NaN 2 NaN]) ## Test class of input preserved %!assert (hygeinv ([x, NaN], 4, 2, 2), [NaN 0 1 2 NaN NaN]) %!assert (hygeinv (single ([x, NaN]), 4, 2, 2), single ([NaN 0 1 2 NaN NaN])) %!assert (hygeinv ([x, NaN], single (4), 2, 2), single ([NaN 0 1 2 NaN NaN])) %!assert (hygeinv ([x, NaN], 4, single (2), 2), single ([NaN 0 1 2 NaN NaN])) %!assert (hygeinv ([x, NaN], 4, 2, single (2)), single ([NaN 0 1 2 NaN NaN])) ## Test input validation %!error hygeinv () %!error hygeinv (1) %!error hygeinv (1,2) %!error hygeinv (1,2,3) %!error hygeinv (1,2,3,4,5) %!error hygeinv (ones (2), ones (3), 1, 1) %!error hygeinv (1, ones (2), ones (3), 1) %!error hygeinv (1, 1, ones (2), ones (3)) %!error hygeinv (i, 2, 2, 2) %!error hygeinv (2, i, 2, 2) %!error hygeinv (2, 2, i, 2) %!error hygeinv (2, 2, 2, i)