update packages

[CreaPhase.git] / octave_packages / m / statistics / distributions / betainv.m

diff --git a/octave_packages/m/statistics/distributions/betainv.m b/octave_packages/m/statistics/distributions/betainv.m
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+## Copyright (C) 2012 Rik Wehbring
+## Copyright (C) 1995-2012 Kurt Hornik
+##
+## 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
+## <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {} betainv (@var{x}, @var{a}, @var{b})
+## For each element of @var{x}, compute the quantile (the inverse of
+## the CDF) at @var{x} of the Beta distribution with parameters @var{a}
+## and @var{b}.
+## @end deftypefn
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Quantile function of the Beta distribution
+
+function inv = betainv (x, a, b)
+
+  if (nargin != 3)
+    print_usage ();
+  endif
+
+  if (!isscalar (a) || !isscalar (b))
+    [retval, x, a, b] = common_size (x, a, b);
+    if (retval > 0)
+      error ("betainv: X, A, and B must be of common size or scalars");
+    endif
+  endif
+
+  if (iscomplex (x) || iscomplex (a) || iscomplex (b))
+    error ("betainv: X, A, and B must not be complex");
+  endif
+
+  if (isa (x, "single") || isa (a, "single") || isa (b, "single"))
+    inv = zeros (size (x), "single");
+  else
+    inv = zeros (size (x));
+  endif
+
+  k = (x < 0) | (x > 1) | !(a > 0) | !(b > 0) | isnan (x);
+  inv(k) = NaN;
+
+  k = (x == 1) & (a > 0) & (b > 0);
+  inv(k) = 1;
+
+  k = find ((x > 0) & (x < 1) & (a > 0) & (b > 0));
+  if (any (k))
+    if (!isscalar (a) || !isscalar (b))
+      a = a(k);
+      b = b(k);
+      y = a ./ (a + b);
+    else
+      y = a / (a + b) * ones (size (k));
+    endif
+    x = x(k);
+
+    if (isa (y, "single"))
+      myeps = eps ("single");
+    else
+      myeps = eps;
+    endif
+
+    l = find (y < myeps);
+    if (any (l))
+      y(l) = sqrt (myeps) * ones (length (l), 1);
+    endif
+    l = find (y > 1 - myeps);
+    if (any (l))
+      y(l) = 1 - sqrt (myeps) * ones (length (l), 1);
+    endif
+
+    y_old = y;
+    for i = 1 : 10000
+      h     = (betacdf (y_old, a, b) - x) ./ betapdf (y_old, a, b);
+      y_new = y_old - h;
+      ind   = find (y_new <= myeps);
+      if (any (ind))
+        y_new (ind) = y_old (ind) / 10;
+      endif
+      ind = find (y_new >= 1 - myeps);
+      if (any (ind))
+        y_new (ind) = 1 - (1 - y_old (ind)) / 10;
+      endif
+      h = y_old - y_new;
+      if (max (abs (h)) < sqrt (myeps))
+        break;
+      endif
+      y_old = y_new;
+    endfor
+
+    inv(k) = y_new;
+  endif
+
+endfunction
+
+
+%!shared x
+%! x = [-1 0 0.75 1 2];
+%!assert(betainv (x, ones(1,5), 2*ones(1,5)), [NaN 0 0.5 1 NaN]);
+%!assert(betainv (x, 1, 2*ones(1,5)), [NaN 0 0.5 1 NaN]);
+%!assert(betainv (x, ones(1,5), 2), [NaN 0 0.5 1 NaN]);
+%!assert(betainv (x, [1 0 NaN 1 1], 2), [NaN NaN NaN 1 NaN]);
+%!assert(betainv (x, 1, 2*[1 0 NaN 1 1]), [NaN NaN NaN 1 NaN]);
+%!assert(betainv ([x(1:2) NaN x(4:5)], 1, 2), [NaN 0 NaN 1 NaN]);
+
+%% Test class of input preserved
+%!assert(betainv ([x, NaN], 1, 2), [NaN 0 0.5 1 NaN NaN]);
+%!assert(betainv (single([x, NaN]), 1, 2), single([NaN 0 0.5 1 NaN NaN]));
+%!assert(betainv ([x, NaN], single(1), 2), single([NaN 0 0.5 1 NaN NaN]));
+%!assert(betainv ([x, NaN], 1, single(2)), single([NaN 0 0.5 1 NaN NaN]));
+
+%% Test input validation
+%!error betainv ()
+%!error betainv (1)
+%!error betainv (1,2)
+%!error betainv (1,2,3,4)
+%!error betainv (ones(3),ones(2),ones(2))
+%!error betainv (ones(2),ones(3),ones(2))
+%!error betainv (ones(2),ones(2),ones(3))
+%!error betainv (i, 2, 2)
+%!error betainv (2, i, 2)
+%!error betainv (2, 2, i)
+