```{- | Demonstration of Gaussian process regression using the simple
data from "Neural Networks for Pattern Recognition," by Chris
Bishop. This version estimates the hyperparameters using the
optimization algorithm from HMatrix.

For details of the algorithms involved see www.gaussianprocesses.org.

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.Demos.RegressionDemo1 where

import Numeric.LinearAlgebra
import Numeric.GSL.Minimization

import HasGP.Data.BishopData
import HasGP.Types.MainTypes
import HasGP.Support.Linear
import HasGP.Support.Random
import HasGP.Regression.Regression
import HasGP.Covariance.SquaredExp

demo = do
putStrLn "Generating the training data..."

let (inputs, targets) = bishopData
saveMatrix "inputs.txt" "%g" inputs
fprintfVector "targets.txt" "%g" targets

putStrLn "Searching for best hyperparameters..."
let f = gpRLogHyperToEvidence (SquaredExponential 0 0) inputs targets
let ev = fst . f
let gev = snd . f
let (solution, path) =
minimizeVD ConjugatePR 0.0001 50 0.01 0.1 ev gev
(constant (log 0.1) 3)

putStrLn \$ "Found: " ++ (show solution)
putStrLn \$ "Path: "
putStrLn \$ show path

putStrLn "Learning and predicting..."

let newPoints = fromColumns \$ [linspace 100 (0.0,1.0)]

let (newOuts, var) =
gpRPredict' (SquaredExponential (solution @> 1) (solution @> 2))
(solution @> 0) inputs targets newPoints

fprintfVector "outputs.txt" "%g" newOuts
fprintfVector "variances.txt" "%g" var

putStrLn "Done"
return ()

```