```{- | HasGP Gaussian Process Library. This module contains the definition
for the standard log logistic likelihood function.

Copyright (C) 2011 Sean Holden. sbh11\@cl.cam.ac.uk.
-}
{- This file is part of HasGP.

HasGP 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.

HasGP 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 HasGP.  If not, see <http://www.gnu.org/licenses/>.
-}
module HasGP.Likelihood.LogLogistic
(
LogLogistic(..)
) where

import Numeric.LinearAlgebra

import HasGP.Types.MainTypes
import HasGP.Support.Functions
import HasGP.Likelihood.Basic

{- | Value and first three derivatives of log sigmoid with respect to its
parameter f. log p(y|f) = log sigmoid (yf) where y is +1 or -1.
-}
data LogLogistic = LogLogistic

instance LogLikelihood LogLogistic where
likelihood    LogLogistic y f = log (1 / (1 + (exp (-(f * y)))))
dLikelihood   LogLogistic y f = ((y + 1) / 2) - (sigmoid f)
ddLikelihood  LogLogistic y f = (-x) * (1 - x)
where x = sigmoid f
dddLikelihood LogLogistic y f = (exp (-f)) * (x^2) * ((2 * x) - 1)
where x = sigmoid f

```