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

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
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.LogPhi
(
LogPhi(..)
) where

import Numeric.LinearAlgebra

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

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

instance LogLikelihood LogPhi where
likelihood    LogPhi y f = logPhi (y * f)
dLikelihood   LogPhi y f = y * nOverP
where
nOverP = (n f) / (phiIntegral (y * f))
ddLikelihood  LogPhi y f = -(((nOverP)^2) + ((y * f) * nOverP))
where
nOverP = (n f) / (phiIntegral (y * f))
dddLikelihood LogPhi y f =
(2 * y * (nOverP^3)) + (((2 * f) + (y^2)) *
(nOverP ^2)) - (y * (1 - (f^2)) * nOverP)
where
nOverP = (n f) / (phiIntegral (y * f))

```