## Copyright (C) 2012 Rik Wehbring
## Copyright (C) 1995-2016 Kurt Hornik
## Copyright (C) 2022-2023 Andreas Bertsatos <abertsatos@biol.uoa.gr>
##
## This file is part of the statistics package for GNU Octave.
##
## 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/>.

## -*- texinfo -*-
## @deftypefn  {statistics} {@var{r} =} trnd (@var{df})
## @deftypefnx {statistics} {@var{r} =} trnd (@var{df}, @var{rows})
## @deftypefnx {statistics} {@var{r} =} trnd (@var{df}, @var{rows}, @var{cols}, @dots{})
## @deftypefnx {statistics} {@var{r} =} trnd (@var{df}, [@var{sz}])
##
## Random arrays from the Student's T distribution.
##
## Return a matrix of random samples from the Students's T distribution with
## @var{df} degrees of freedom.
##
## @code{@var{r} = trnd (@var{df})} returns an array of random numbers chosen
## from the Student's T distribution with @var{df} degrees of freedom.  The size
## of @var{r} is the size of @var{df}.  A scalar input functions as a constant
## matrix of the same size as the other inputs.  @var{df} must be a finite real
## number greater than 0, otherwise NaN is returned.
##
## When called with a single size argument, @code{trnd} returns a square matrix
## with the dimension specified.  When called with more than one scalar
## argument, the first two arguments are taken as the number of rows and columns
## and any further arguments specify additional matrix dimensions.  The size may
## also be specified with a row vector of dimensions, @var{sz}.
##
## Further information about the Student's T distribution can be found at
## @url{https://en.wikipedia.org/wiki/Student%27s_t-distribution}
##
## @seealso{tcdf, tinv, tpdf, tstat}
## @end deftypefn

function r = trnd (df, varargin)

  ## Check for valid number of input arguments
  if (nargin < 1)
    error ("trnd: function called with too few input arguments.");
  endif

  ## Check for DF being real
  if (iscomplex (df))
    error ("trnd: DF must not be complex.");
  endif

  ## Parse and check SIZE arguments
  if (nargin == 1)
    sz = size (df);
  elseif (nargin == 2)
    if (isscalar (varargin{1}) && varargin{1} == fix (varargin{1}))
      sz = [varargin{1}, varargin{1}];
    elseif (isrow (varargin{1}) && all (varargin{1} == fix (varargin{1})))
      sz = varargin{1};
    elseif (isempty (varargin{1}))
      r = [];
      return;
    else
      error (strcat ("trnd: SZ must be a scalar or a row vector", ...
                     " of integers."));
    endif
  elseif (nargin > 2)
    notint = cellfun (@(x) (! isscalar (x) || x != fix (x)), varargin);
    if (any (notint))
      error ("trnd: dimensions must be integers.");
    endif
    sz = [varargin{:}];
  endif

  ## Negative dimensions are treated as zero, as in core Octave and MATLAB
  sz = max (sz, 0);

  ## Check that parameters match requested dimensions in size
  ## Use 'size (ones (sz))' to ignore any trailing singleton dimensions in SZ
  if (! isscalar (df) && ! isequal (size (df), size (ones (sz))))
    error ("trnd: DF must be scalar or of size SZ.");
  endif

  ## Check for class type
  if (isa (df, 'single'))
    cls = 'single';
  else
    cls = 'double';
  endif

  if (isscalar (df))
    if ((df > 0) && (df < Inf))
      r = randn (sz, cls) ./ sqrt (2*randg (df/2, sz, cls) / df);
    elseif (isinf (df))
      r = randn (sz, cls);
    else
      r = NaN (sz, cls);
    endif
  else
    r = NaN (sz, cls);

    k = (df > 0) & (df < Inf);
    kinf = isinf (df);
    r(k) = randn (sum (k(:)), 1, cls) ./ ...
           sqrt (2*randg (df(k)/2, cls) ./ df(k))(:);
    r(kinf) = randn (sum (kinf(:)), 1, cls);
  endif

endfunction

## Test output
%!assert_equal (size (trnd (2)), [1, 1])
%!assert_equal (size (trnd (ones (2, 1))), [2, 1])
%!assert_equal (size (trnd (ones (2, 2))), [2, 2])
%!assert_equal (size (trnd (1, 3)), [3, 3])
%!assert_equal (size (trnd (1, [4, 1])), [4, 1])
%!assert_equal (size (trnd (1, 4, 1)), [4, 1])
%!assert_equal (size (trnd (1, 4, 1)), [4, 1])
%!assert_equal (size (trnd (1, 4, 1, 5)), [4, 1, 5])
%!assert_equal (size (trnd (1, 0, 1)), [0, 1])
%!assert_equal (size (trnd (1, 1, 0)), [1, 0])
%!assert_equal (size (trnd (1, 1, 2, 0, 5)), [1, 2, 0, 5])
%!assert_equal (size (trnd (1, [])), [0, 0])
%!assert_equal (size (trnd (1, [2, 0, 2, 1])), [2, 0, 2])
%!assert_equal (size (trnd (1, -1)), [0, 0])
%!assert_equal (size (trnd (1, [2, -1, 2])), [2, 0, 2])
%!assert_equal (size (trnd (1, 2, -1, 5)), [2, 0, 5])
%!assert_equal (trnd (0, 1, 1), NaN)
%!assert_equal (trnd ([0, 0, 0], [1, 3]), [NaN, NaN, NaN])

## Test class of input preserved
%!assert_equal (class (trnd (2)), "double")
%!assert_equal (class (trnd (single (2))), "single")
%!assert_equal (class (trnd (single ([2, 2]))), "single")

## Test input validation
%!error<trnd: function called with too few input arguments.> trnd ()
%!error<trnd: DF must not be complex.> trnd (i)
%!error<trnd: SZ must be a scalar or a row vector of integers.> ...
%! trnd (1, 1.2)
%!error<trnd: SZ must be a scalar or a row vector of integers.> ...
%! trnd (1, ones (2))
%!error<trnd: SZ must be a scalar or a row vector of integers.> ...
%! trnd (1, [2 0 2.5])
%!error<trnd: SZ must be a scalar or a row vector of integers.> ...
%! trnd (ones (2), ones (2))
%!error<trnd: dimensions must be integers.> ...
%! trnd (1, 2, 1.5, 5)
%!error<trnd: DF must be scalar or of size SZ.> trnd (ones (2,2), 3)
%!error<trnd: DF must be scalar or of size SZ.> trnd (ones (2,2), [3, 2])
%!error<trnd: DF must be scalar or of size SZ.> trnd (ones (2,2), 2, 3)
