## Copyright (C) 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2005, 2007
##               Kurt Hornik
##
## This file is part of Octave.
##
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## -*- texinfo -*-
## @deftypefn {Function File} {[@var{dl}, @var{d2l}] =} logistic_regression_derivatives (@var{x}, @var{z}, @var{z1}, @var{g}, @var{g1}, @var{p})
## Called by logistic_regression.  Calculates derivates of the
## log-likelihood for ordinal logistic regression model.
## @end deftypefn

## Author: Gordon K. Smyth <gks@maths.uq.oz.au>
## Adapted-By: KH <Kurt.Hornik@wu-wien.ac.at>
## Description: Derivates of log-likelihood in logistic regression

function [dl, d2l] = logistic_regression_derivatives (x, z, z1, g, g1, p)

  ## first derivative
  v = g .* (1 - g) ./ p; v1 = g1 .* (1 - g1) ./ p;
  dlogp = [(dmult (v, z) - dmult (v1, z1)), (dmult (v - v1, x))];
  dl = sum (dlogp)';

  ## second derivative
  w = v .* (1 - 2 * g); w1 = v1 .* (1 - 2 * g1);
  d2l = [z, x]' * dmult (w, [z, x]) - [z1, x]' * dmult (w1, [z1, x]) ...
      - dlogp' * dlogp;

endfunction