## Copyright (C) 2012 Rik Wehbring
## Copyright (C) 1995-2015 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)