function p = tcdf(x,n)
% TCDF returns student cumulative distribtion function
%
% cdf = tcdf(x,DF);
%
% Computes the CDF of the students distribution
%    with DF degrees of freedom
% x,DF must be matrices of same size, or any one can be a scalar.
%
% see also: NORMCDF, TPDF, TINV

% Reference(s):

%       $Id: tcdf.m 9033 2011-11-08 20:58:07Z schloegl $

%   Copyright (C) 2000-2003,2009 by Alois Schloegl <alois.schloegl@gmail.com>
%   Copyright (C) 2014-2017 Dynare Team
%
%       This is part of the NaN-toolbox. For more details see
%       http://pub.ist.ac.at/~schloegl/matlab/NaN/

%    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; If not, see <http://www.gnu.org/licenses/>.


% check size of arguments
if all(size(x)==1)
    x = repmat(x,size(n));
elseif all(size(n)==1)
    n = repmat(n,size(x));
elseif all(size(x)==size(n))
    % OK, do nothing
else
    error('size of input arguments must be equal or scalar')
end

% allocate memory
p = zeros(size(x));
p((x==Inf) & (n>0)) = 1;

% workaround for invalid arguments in BETAINC
ix   = isnan(x) | ~(n>0);
p(ix)= NaN;

ix    = (x > -Inf) & (x < Inf) & (n > 0);
p(ix) = betainc (n(ix) ./ (n(ix) + x(ix).^2), n(ix)/2, 1/2) / 2;

ix    = find(x>0);
p(ix) = 1 - p(ix);

% shape output
p = reshape(p,size(x));

%!assert(tcdf(NaN,4),NaN)