## Copyright (C) 2012 Rik Wehbring
## Copyright (C) 1995-2016 Kurt Hornik
## Copyright (C) 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{y} =} poisspdf (@var{x}, @var{lambda})
##
## Poisson probability density function (PDF).
##
## For each element of @var{x}, compute the probability density function (PDF)
## of the Poisson distribution with rate parameter @var{lambda}.  The size of
## @var{y} is the common size of @var{x} and @var{lambda}.  A scalar input
## functions as a constant matrix of the same size as the other inputs.
##
## Further information about the Poisson distribution can be found at
## @url{https://en.wikipedia.org/wiki/Poisson_distribution}
##
## Input arguments must be @qcode{double}, @qcode{single}, or an integer type;
## logical and character arrays are rejected.  Integer input is promoted to
## @qcode{double}, so the result is always a probability.  MATLAB is
## inconsistent here: for several of the discrete distributions it returns the
## result in the integer class of the input, truncating a probability to
## @math{0} or @math{1}.
##
##
## The density at an infinite abscissa is @math{0}, no proper distribution
## placing mass there.  MATLAB returns @qcode{NaN} here, as it does for
## @code{raylpdf} and for no other density, which is an inconsistency there rather
## than a convention: it returns @math{0} at @math{Inf} for every other
## distribution of the same support.
## @seealso{poisscdf, poissinv, poissrnd, poissfit, poisslike, poisstat}
## @end deftypefn

function y = poisspdf (x, lambda)

  ## Check for valid number of input arguments
  if (nargin < 2)
    error ("poisspdf: function called with too few input arguments.");
  endif

  ## Check for common size of X and LAMBDA
  if (! isscalar (x) || ! isscalar (lambda))
    [retval, x, lambda] = common_size (x, lambda);
    if (retval > 0)
      error ("poisspdf: X and LAMBDA must be of common size or scalars.");
    endif
  endif

  ## Check for X and LAMBDA being double, single, or integer
  if (! (isnumeric (x) && isnumeric (lambda)))
    error ("poisspdf: X and LAMBDA must be double, single, or integer.");
  endif

  ## Integer input is promoted to double, so the result is a probability
  ## rather than a value truncated to the input's integer type.
  if (isinteger (x))
    x = double (x);
  endif
  if (isinteger (lambda))
    lambda = double (lambda);
  endif

  ## Check for X and LAMBDA being reals
  if (iscomplex (x) || iscomplex (lambda))
    error ("poisspdf: X and LAMBDA must not be complex.");
  endif

  ## Check for class type
  if (isa (x, 'single') || isa (lambda, 'single'))
    y = zeros (size (x), 'single');
  else
    y = zeros (size (x));
  endif

  ## Force NaN for out of range parameters or missing data NaN
  k = isnan (x) | ! (lambda > 0);
  y(k) = NaN;

  k = (x >= 0) & (x < Inf) & (x == fix (x)) & (lambda > 0);
  if (isscalar (lambda))
    y(k) = exp (x(k) * log (lambda) - lambda - gammaln (x(k) + 1));
  else
    y(k) = exp (x(k) .* log (lambda(k)) - lambda(k) - gammaln (x(k) + 1));
  endif

endfunction

%!demo
%! ## Plot various PDFs from the Poisson distribution
%! x = 0:20;
%! y1 = poisspdf (x, 1);
%! y2 = poisspdf (x, 4);
%! y3 = poisspdf (x, 10);
%! plot (x, y1, '*b', x, y2, '*g', x, y3, '*r')
%! grid on
%! ylim ([0, 0.4])
%! legend ({'λ = 1', 'λ = 4', 'λ = 10'}, 'location', 'northeast')
%! title ('Poisson PDF')
%! xlabel ('values in x (number of occurrences)')
%! ylabel ('density')

## Test output
%!shared x, y
%! x = [-1 0 1 2 Inf];
%! y = [0, exp(-1)*[1 1 0.5], 0];
%!assert_equal (poisspdf (x, ones (1,5)), y, eps)
%!assert_equal (poisspdf (x, 1), y, eps)
%!assert_equal (poisspdf (x, [1 0 NaN 1 1]), [y(1) NaN NaN y(4:5)], eps)
%!assert_equal (poisspdf ([x, NaN], 1), [y, NaN], eps)

## Test class of input preserved
%!assert_equal (poisspdf (single ([x, NaN]), 1), single ([y, NaN]), eps ('single'))
%!assert_equal (poisspdf ([x, NaN], single (1)), single ([y, NaN]), eps ('single'))

## Test input validation
%!error<poisspdf: function called with too few input arguments.> poisspdf ()
%!error<poisspdf: function called with too few input arguments.> poisspdf (1)
%!error<poisspdf: X and LAMBDA must be of common size or scalars.> ...
%! poisspdf (ones (3), ones (2))
%!error<poisspdf: X and LAMBDA must be of common size or scalars.> ...
%! poisspdf (ones (2), ones (3))
%!error<poisspdf: X and LAMBDA must be double, single, or integer.> poisspdf (true, 2)
%!error<poisspdf: X and LAMBDA must be double, single, or integer.> poisspdf ('a', 2)
%!assert_equal (class (poisspdf (int32 (2), 2)), 'double')
%!error<poisspdf: X and LAMBDA must not be complex.> poisspdf (i, 2)
%!error<poisspdf: X and LAMBDA must not be complex.> poisspdf (2, i)
