update packages

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

diff --git a/octave_packages/m/statistics/distributions/tinv.m b/octave_packages/m/statistics/distributions/tinv.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} {} tinv (@var{x}, @var{n})
+## For each element of @var{x}, compute the quantile (the inverse of
+## the CDF) at @var{x} of the t (Student) distribution with @var{n} 
+## degrees of freedom.  This function is analogous to looking in a table
+## for the t-value of a single-tailed distribution.
+## @end deftypefn
+
+## For very large n, the "correct" formula does not really work well,
+## and the quantiles of the standard normal distribution are used
+## directly.
+
+## Author: KH <Kurt.Hornik@wu-wien.ac.at>
+## Description: Quantile function of the t distribution
+
+function inv = tinv (x, n)
+
+  if (nargin != 2)
+    print_usage ();
+  endif
+
+  if (!isscalar (n))
+    [retval, x, n] = common_size (x, n);
+    if (retval > 0)
+      error ("tinv: X and N must be of common size or scalars");
+    endif
+  endif
+
+  if (iscomplex (x) || iscomplex (n))
+    error ("tinv: X and N must not be complex");
+  endif
+
+  if (isa (x, "single") || isa (n, "single"))
+    inv = NaN (size (x), "single");
+  else
+    inv = NaN (size (x));
+  endif
+
+  k = (x == 0) & (n > 0);
+  inv(k) = -Inf;
+
+  k = (x == 1) & (n > 0);
+  inv(k) = Inf;
+
+  if (isscalar (n))
+    k = (x > 0) & (x < 1);
+    if ((n > 0) && (n < 10000))
+      inv(k) = (sign (x(k) - 1/2)
+                .* sqrt (n * (1 ./ betainv (2*min (x(k), 1 - x(k)),
+                                            n/2, 1/2) - 1)));
+    elseif (n >= 10000)
+      ## For large n, use the quantiles of the standard normal
+      inv(k) = stdnormal_inv (x(k));
+    endif
+  else
+    k = (x > 0) & (x < 1) & (n > 0) & (n < 10000);
+    inv(k) = (sign (x(k) - 1/2)
+              .* sqrt (n(k) .* (1 ./ betainv (2*min (x(k), 1 - x(k)),
+                                              n(k)/2, 1/2) - 1)));
+
+    ## For large n, use the quantiles of the standard normal
+    k = (x > 0) & (x < 1) & (n >= 10000);
+    inv(k) = stdnormal_inv (x(k));
+  endif
+
+endfunction
+
+
+%!shared x
+%! x = [-1 0 0.5 1 2];
+%!assert(tinv (x, ones(1,5)), [NaN -Inf 0 Inf NaN]);
+%!assert(tinv (x, 1), [NaN -Inf 0 Inf NaN], eps);
+%!assert(tinv (x, [1 0 NaN 1 1]), [NaN NaN NaN Inf NaN], eps);
+%!assert(tinv ([x(1:2) NaN x(4:5)], 1), [NaN -Inf NaN Inf NaN]);
+
+%% Test class of input preserved
+%!assert(tinv ([x, NaN], 1), [NaN -Inf 0 Inf NaN NaN], eps);
+%!assert(tinv (single([x, NaN]), 1), single([NaN -Inf 0 Inf NaN NaN]), eps("single"));
+%!assert(tinv ([x, NaN], single(1)), single([NaN -Inf 0 Inf NaN NaN]), eps("single"));
+
+%% Test input validation
+%!error tinv ()
+%!error tinv (1)
+%!error tinv (1,2,3)
+%!error tinv (ones(3),ones(2))
+%!error tinv (ones(2),ones(3))
+%!error tinv (i, 2)
+%!error tinv (2, i)
+