## 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} {} laplace_inv (@var{x})
## For each element of @var{x}, compute the quantile (the inverse of the CDF)
## at @var{x} of the Laplace distribution.
## @end deftypefn

## Author: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Quantile function of the Laplace distribution

function inv = laplace_inv (x)

  if (nargin != 1)
    print_usage ();
  endif

  if (iscomplex (x))
    error ("laplace_inv: X must not be complex");
  endif

  if (isa (x, "single"))
    inv = NaN (size (x), "single");
  else
    inv = NaN (size (x));
  endif

  k = (x >= 0) & (x <= 1);
  inv(k) = ((x(k) < 1/2) .* log (2 * x(k))
            - (x(k) > 1/2) .* log (2 * (1 - x(k))));

endfunction


%!shared x
%! x = [-1 0 0.5 1 2];
%!assert (laplace_inv (x), [NaN -Inf 0 Inf NaN])

## Test class of input preserved
%!assert (laplace_inv ([x, NaN]), [NaN -Inf 0 Inf NaN NaN])
%!assert (laplace_inv (single ([x, NaN])), single ([NaN -Inf 0 Inf NaN NaN]))

## Test input validation
%!error laplace_inv ()
%!error laplace_inv (1,2)
%!error laplace_inv (i)