{- | HasGP Gaussian Process Library. This module contains assorted functions that support GP calculations but are more general-purpose than GP-specific. 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.Support.Functions where import HasGP.Types.MainTypes import Numeric.LinearAlgebra import Numeric.GSL.Special.Erf square :: Double -> Double square x = (x * x) trace :: DMatrix -> Double trace = sum . toList . takeDiag -- | Standard delta function - 0/1 valued. delta :: (Eq a) => a -> a -> Double delta a b | (a==b) = 1.0 | otherwise = 0.0 -- | Standard delta function - boolean valued. deltaBool :: (Eq a) => a -> a -> Bool deltaBool a b = (a==b) -- | General sigmoid function with variable slope. generalSigmoid :: Double -> Double -> Double generalSigmoid theta x = 1 / (1 + (exp (-(theta * x)))) -- | Standard sigmoid function. sigmoid :: Double -> Double sigmoid = generalSigmoid 1 -- | Integral of Gaussian density of mean 0 and variance 1 -- from -infinity to x phiIntegral :: Double -> Double phiIntegral x = 1 - (erf_Q x) -- | Value of Gaussian density function for mean 0 and -- variance 1. n :: Double -> Double n x = erf_Z x -- | DANGER! You can't compute the ratio (n x) / (phiIntegral x) directly, -- as although it has sensible values for negative x the denominator gets -- small so fast that you quickly get Infinity turning up. GSL has the -- inverse Mill's function/hazard function for the Gaussian distribution, -- and the ratio is equal to hazard(-x). nOverPhi :: Double -> Double nOverPhi x = hazard(-x) -- | DANGER! See nOverPhi - you have to compute this carefully as -- well. logPhi :: Double -> Double logPhi x = log $ (n x) / (hazard (-x))