diff --git a/ChangeLog.md b/ChangeLog.md new file mode 100644 --- /dev/null +++ b/ChangeLog.md @@ -0,0 +1,5 @@ +# Revision history for stat-sampling + +## 0.1.0.0 -- 2016-08-19 + +* First version. Released on an unsuspecting world. diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. 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If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.hs b/Setup.hs new file mode 100644 --- /dev/null +++ b/Setup.hs @@ -0,0 +1,2 @@ +import Distribution.Simple +main = defaultMain diff --git a/src/Data/Stochastic.hs b/src/Data/Stochastic.hs new file mode 100644 --- /dev/null +++ b/src/Data/Stochastic.hs @@ -0,0 +1,226 @@ +{-| + Module : Data.Stochastic + Description : Main module containing functions for interacting with Samples and StochProcesses. + License : GPL-3 + Maintainer : hackage@mail.kevinl.io + Stability : experimental + + This module contains convenience functions to + construct 'Sample's or 'StochProcess'es corresponding + to several probability distributions. + + It also contains functions that can be used for + running the constructed 'StochProcess'es and generating + datapoints, or sampling from a constructed 'Sample'. + + Some examples for usage can be found here: +-} + +module Data.Stochastic ( + -- * Constructing a Sample + certain +, uniform +, discrete +, bernoulli +, normal + -- * Sampling from a Sample +, sample +, sample_ +, sampleN +, sampleIO +, sampleIO_ +, sampleION + -- * Constructing a StochProcess +, certainProcess +, uniformProcess +, discreteProcess +, normalProcess + -- * Running a StochProcess +, runProcess +, runProcess_ +, runProcessN + -- * Sampling from a StochProcess +, sampleProcess +, sampleProcess_ +, sampleProcessN +, sampleProcessIO +, sampleProcessION + -- * The types +, module Data.Stochastic.Types + -- * Internal functions for your viewing pleasure +, module Data.Stochastic.Internal +) where + +import Control.Monad.Trans +import Control.Monad.Writer + +import Data.Stochastic.Internal +import Data.Stochastic.Types + +import qualified Data.Sequence as S + +import System.Random + +-- | Function to construct a 'StochProcess' computation +-- given an initial computation, a 'StochProcess' function, +-- and number of times to apply the function with bind. +composeProcess :: Integral i => i -> StochProcess -> (Double -> StochProcess) -> StochProcess +composeProcess i pr f = if i <= 0 then pr + else (composeProcess (i-1) pr f) >>= f + +-- | Sample from the 'StochProcess' computation, discarding +-- the new 'RandomGen'. +sampleProcess_ :: StochProcess -> StdGen -> Double +sampleProcess_ ma g = flip sample_ g $ liftM fst $ runWriterT ma + +-- | Sample from the 'StochProcess' computation, returning +-- the value of type a and a new 'RandomGen'. +sampleProcess :: StochProcess -> StdGen -> (Double, StdGen) +sampleProcess ma g = flip sample g $ liftM fst $ runWriterT ma + +-- | Sample from the 'StochProcess' computation +-- in the IO monad, returning a 'Double' +-- and a 'RandomGen' created in the IO monad. +sampleProcessIO :: StochProcess -> IO (Double, StdGen) +sampleProcessIO ma = do + gen <- newStdGen + return $ sampleProcess ma gen + +-- | Sample from the 'StochProcess' computation +-- in the IO monad, returning a 'Double' +-- and discarding the 'RandomGen'. +sampleProcessIO_ :: StochProcess -> IO Double +sampleProcessIO_ ma = fst <$> sampleProcessIO ma + +-- | Get a certain number of samples from the 'StochProcess' computation in the IO monad. +sampleProcessION :: (Integral i) => i -> StochProcess -> IO (S.Seq Double) +sampleProcessION i ma = do + gen <- newStdGen + return $ sampleProcessN i ma gen + +-- | Get a certain number of samples from the 'StochProcess' computation. +sampleProcessN :: (Integral i) => i -> StochProcess -> StdGen -> S.Seq Double +sampleProcessN i ma g = if i <= 0 then S.empty + else let (a, gen) = sampleProcess ma g + in a S.<| sampleProcessN (i-1) ma gen + +-- | Run a 'StochProcess' computation and retrieve the recorded +-- results along with a new 'RandomGen'. +runProcess :: StochProcess -> StdGen -> (S.Seq Double, StdGen) +runProcess ma g = flip sample g $ execWriterT ma + +-- | Run a 'StochProcess' computation and retrieve the recorded +-- results, discarding the new 'RandomGen'. +runProcess_ :: StochProcess -> StdGen -> S.Seq Double +runProcess_ ma g = fst $ runProcess ma g + +-- | Runs a 'StochProcess' computation a given number times +-- and produces a 'Sequence' of 'Sequence's of Doubles. +runProcessN :: (Integral i) => i -> StochProcess -> StdGen -> S.Seq (S.Seq Double) +runProcessN n pr gen = if n <= 0 then S.empty + else let (seq, gen') = runProcess pr gen + in seq S.<| runProcessN (n-1) pr gen' + +-- | 'StochProcess' sample for a normal distribution that records +-- the value sampled from the normal distribution. +normalProcess :: Mean -> StDev -> StochProcess +normalProcess mean std = do + sample <- lift $ normal mean std + tell $ S.singleton sample + return sample + +-- | 'StochProcess' sample for a distribution over 'Double's that always +-- returns the same value when sampled, and records that value. +certainProcess :: Double -> StochProcess +certainProcess a = do + sample <- lift $ certain a + tell $ S.singleton sample + return sample + +-- | 'StochProcess' sample for a discrete distribution over 'Double's +-- that records the value sampled from the normal distribution. +discreteProcess :: [(Double, Double)] -> StochProcess +discreteProcess a = do + sample <- lift $ discrete a + tell $ S.singleton sample + return sample + +-- | 'StochProcess' sample for a uniform distribution over 'Double's +-- that records the value sampled from it. +uniformProcess :: [Double] -> StochProcess +uniformProcess l = do + sample <- lift $ uniform l + tell $ S.singleton sample + return sample + +-- | 'Sample' for a normal distribution with given +-- 'StdGen', 'Mean', and 'StDev'. +normal :: RandomGen g => Mean -> StDev -> Sample g Distribution Double +normal m s = mkSample $ Normal m $ abs s + +-- | 'Sample' for a Bernoulli distribution with given +-- probability to produce True. +bernoulli :: RandomGen g => Double -> Sample g Distribution Bool +bernoulli f = mkSample $ Bernoulli f + +-- | 'Sample' for a discrete distribution with given +-- list of tuples of values of type a and 'Double's +-- representing the probability of producing each +-- value when sampling from this distribution. +discrete :: RandomGen g => [(a, Double)] -> Sample g Distribution a +discrete [] = error "do not construct empty discrete distributions" +discrete l = mkSample $ Discrete l + +-- | 'Sample' for a uniform distribution +-- given a list of provided values. +uniform :: (RandomGen g) => [a] -> Sample g Distribution a +uniform l = mkSample $ Uniform l + +-- | 'Sample' for a distribution where we always sample +-- the same value. +certain :: (RandomGen g, Sampleable d) => a -> Sample g d a +certain = mkSample . certainDist + +-- | Get one sample of type a from the 'Sample' along with +-- a new 'StdGen'. +-- +-- We do an extra 'next' in order to get one more +-- 'RandomGen' because when we sample from normal +-- distributions, we consume one extra 'RandomGen'. +sample :: (RandomGen g, Sampleable d) => Sample g d a -> g -> (a, g) +sample s g = let (dist, g') = runSample s g + (a, g'') = sampleFrom dist g' + in (a, snd $ next g'') + +-- | Get one sample of type a from the 'Sample', +-- discarding the 'RandomGen' +sample_ :: (RandomGen g, Sampleable d) => Sample g d a -> g -> a +sample_ s g = fst $ sample s g + +-- | Get a certain number of samples from the 'Sample' +sampleN :: (RandomGen g, Sampleable d, Integral i) => i -> Sample g d a -> g -> S.Seq a +sampleN i s g = if i <= 0 then S.empty + else let (a, g') = sample s g + in a S.<| sampleN (i - 1) s g' + +-- | Sample from a 'Sample' of type a using the global +-- random number generator provided by 'newStdGen', +-- returning a new 'StdGen' with the sampled value. +sampleIO :: Sampleable d => Sample StdGen d a -> IO (a, StdGen) +sampleIO s = sample s <$> newStdGen + +-- | Sample from a 'Sample' of type a using the global +-- random number generator provided by 'newStdGen', +-- discarding the new 'StdGen'. +sampleIO_ :: Sampleable d => Sample StdGen d a -> IO a +sampleIO_ s = fst <$> (sample s <$> newStdGen) + +-- | Produce several samples from the 'Sample' using the random number generator +-- in the IO monad. +sampleION :: (Sampleable d, Integral i) => i -> Sample StdGen d a -> IO (S.Seq a) +sampleION i s = sampleN i s <$> newStdGen + +-- | Function to make a 'Sample' out of a provided +-- 'Distribution'. +mkSample :: (RandomGen g, Sampleable d) => d a -> Sample g d a +mkSample d = Sample $ \g -> (d, snd $ next g) diff --git a/src/Data/Stochastic/Internal.hs b/src/Data/Stochastic/Internal.hs new file mode 100644 --- /dev/null +++ b/src/Data/Stochastic/Internal.hs @@ -0,0 +1,28 @@ +{-| + Module : Data.Stochastic.Internal + Description : Internal utility functions for Sample types. + License : GPL-3 + Maintainer : hackage@mail.kevinl.io + Stability : experimental + +-} +module Data.Stochastic.Internal ( + boxMuller +, decentRandom +) where + +import System.Random + +import Numeric.MathFunctions.Constants + +-- | Function to convert values sampled from uniform distribution +-- to a value sampled from a standard normal distribution. +boxMuller :: (Floating a) => a -> a -> a +boxMuller u1 u2 = cos (2 * pi * u2) * (sqrt $ (-2) * (log u1)) + +-- | Randoms that aren't too small or equal to 1. +decentRandom :: (RandomGen g) => g -> (Double, g) +decentRandom gen = let (sampled, newG) = randomR (0, 1.0) gen + in if sampled <= m_epsilon || sampled == 1 + then decentRandom newG + else (sampled, newG) diff --git a/src/Data/Stochastic/Types.hs b/src/Data/Stochastic/Types.hs new file mode 100644 --- /dev/null +++ b/src/Data/Stochastic/Types.hs @@ -0,0 +1,138 @@ +{-#LANGUAGE GADTs#-} +{-#LANGUAGE RankNTypes#-} +{-#LANGUAGE FlexibleInstances#-} + +{-| + Module : Data.Stochastic.Types + Description : Types used for the stochastic package. + License : GPL-3 + Maintainer : hackage@mail.kevinl.io + Stability : experimental + + This module contains the types used + for the stochastic package. + + WARNING: In its current state, care should be + taken when using discrete distributions + as it is never checked that the probabilities + sum to 1. As is, execution of sampling may fail at run-time + if probabilities aren't normalized. +-} + +module Data.Stochastic.Types ( + Distribution (..) +, Sampleable (..) +, Sample (..) +, StochProcess (..) +, Sampler (..) +, Mean (..) +, StDev (..) +) where + +import Control.Monad +import Control.Monad.Writer + +import Data.Stochastic.Internal + +import qualified Data.Sequence as S + +import System.Random + +-- | Datatype representing parameterized probability distributions +-- over values of type a. GADTs are used to restrict types +-- of certain distributions (e.g. normal distributions can +-- only be defined over floating point numbers) +data Distribution a where + Normal :: Mean -> StDev -> Distribution Double + Bernoulli :: Double -> Distribution Bool + Discrete :: [(a, Double)] -> Distribution a + Uniform :: [a] -> Distribution a + Certain :: a -> Distribution a + +-- | Class of types from which samples can be obtained. +class Sampleable d where + -- | Constructor for a datatype from which we always + -- sample the same value. + certainDist :: a -> d a + -- | Sample from the sampleable datatype using a 'RandomGen' + -- returning a new 'RandomGen'. + sampleFrom :: (RandomGen g) => d a -> g -> (a, g) + +-- | 'Sampleable' instance for 'Distribution'. We ensure +-- that we always pass the *next* 'RandomGen' provided +-- to sampleFrom. This lets us obey the monad laws. +instance Sampleable Distribution where + sampleFrom da g + = case da of + Normal mean stdev + -> let (a, g') = decentRandom g + (a', g'') = decentRandom g' + s = (stdev * (boxMuller a a')) + mean + in (s, g') + Bernoulli prob + -> let (a, g') = decentRandom g + in (a <= prob, g') + Discrete l + -> let (a, g') = decentRandom g + in (scan a l, g') + where scan lim [] = + if lim <= 0 then error $ "not normalized discrete dist" + else error "empty discrete dist" + scan lim (x:xs) = + if lim <= snd x then fst x + else scan (lim - snd x) xs + Uniform l + -> let (a, g') = decentRandom g + prob = 1 / (fromIntegral $ length l) + in (l !! (floor $ a / prob), g') + Certain val + -> (val, snd $ decentRandom g) + -- Seemingly unnecessary, but important to obey the monad laws to always produce the same RandomGen each time we sample. + certainDist = Certain + +-- | Show instance for 'Distribution's. +instance (Show a) => Show (Distribution a) where + show da = case da of + Normal mean stdev -> "Normal " ++ show mean ++ " " ++ show stdev + Bernoulli prob -> "Bernoulli " ++ show prob + Discrete l -> "Discrete " ++ show l + Uniform l -> "Uniform " ++ show l + Certain val -> "Certain " ++ show val + +-- | 'Sample' monad containing a random number generator plus a type from which +-- we can sample values of type a +newtype Sample g d a + = Sample { runSample :: (RandomGen g, Sampleable d) => g -> (d a, g) } + +-- | Monad that represents a stochastic process. +-- It allows us to record numeric values as we sample. +type StochProcess + = WriterT (S.Seq Double) (Sample StdGen Distribution) Double + +-- | Monad instance for Sample. +instance (RandomGen g, Sampleable d) => Monad (Sample g d) where + return x = Sample $ \g -> (certainDist x, snd $ next g) + (>>=) ma f = Sample $ \g -> + let (dist, g') = runSample ma g + (a, g'') = sampleFrom dist g' + in runSample (f a) g'' + +-- | Trivial 'Functor' instance for 'Sample' 'StdGen' 'Distribution'. +instance (RandomGen g, Sampleable s) => Functor (Sample g s) where + fmap = liftM + +-- | Trivial 'Applicative' instance for 'Sample' 'StdGen' 'Distribution'. +instance (RandomGen g, Sampleable s) => Applicative (Sample g s) where + pure = return + (<*>) = ap + +-- | Type synonym for shorter type annotations for 'Sample'. +type Sampler a = Sample StdGen Distribution a + +-- | Type synonym for 'Double' so that the +-- type annotation for the 'Normal' constructor is more informative. +type Mean = Double + +-- | Type synonyms for 'Double' so that the +-- type annotation for the 'Normal' constructor is more informative. +type StDev = Double diff --git a/stochastic.cabal b/stochastic.cabal new file mode 100644 --- /dev/null +++ b/stochastic.cabal @@ -0,0 +1,180 @@ +-- Initial stochastic.cabal generated by cabal init. For further +-- documentation, see http://haskell.org/cabal/users-guide/ + +-- The name of the package. +name: stochastic + +-- The package version. See the Haskell package versioning policy (PVP) +-- for standards guiding when and how versions should be incremented. +-- https://wiki.haskell.org/Package_versioning_policy +-- PVP summary: +-+------- breaking API changes +-- | | +----- non-breaking API additions +-- | | | +--- code changes with no API change +version: 0.1.0.0 + +-- A short (one-line) description of the package. +synopsis: Monadic composition of probabilistic functions and sampling. + +-- A longer description of the package. +description: This package allows the user to perform monadic composition of + probabilistic functions (i.e. functions that take values + and return distributions over values). These functions + can then be sampled from to generate datapoints. + +-- URL for the project homepage or repository. +homepage: http://kevinl.io/posts/2016-08-17-sampling-monad.html + +-- The license under which the package is released. +license: GPL-3 + +-- The file containing the license text. +license-file: LICENSE + +-- The package author(s). +author: Kevin Li + +-- An email address to which users can send suggestions, bug reports, and +-- patches. +maintainer: hackage@mail.kevinl.io + +-- A copyright notice. +-- copyright: + +category: Math + +build-type: Simple + +-- Extra files to be distributed with the package, such as examples or a +-- README. +extra-source-files: ChangeLog.md + +-- Constraint on the version of Cabal needed to build this package. +cabal-version: >=1.10 + + +library + -- Modules exported by the library. + exposed-modules: Data.Stochastic + -- Data.Sample.Chart + Data.Stochastic.Types + Data.Stochastic.Internal + + -- Modules included in this library but not exported. + -- other-modules: + + -- LANGUAGE extensions used by modules in this package. + -- other-extensions: + + -- Other library packages from which modules are imported. + build-depends: base >=4.9 && <4.10, + -- Chart >=1.8 && <1.9, + -- Chart-cairo >=1.8 && <1.9, + containers >= 0.5 && <0.6, + random >=1.1 && <2, + math-functions >=0.2 && <0.3, + mtl >=2.2 && <2.3 + + -- Directories containing source files. + hs-source-dirs: src + + -- Base language which the package is written in. + default-language: Haskell2010 + + -- | Options to pass to ghc + -- ghc-options: -O2 + +source-repository head + type: git + location: git://github.com/kevin-li-195/stochastic.git + +test-suite shadyGambler + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Test.hs + build-depends: base, stochastic, containers + default-language: Haskell2010 + -- | Options to pass to ghc +-- ghc-options: -O2 +-- -threaded +-- "-with-rtsopts=-N -p -s -h -i0.1" + +test-suite monadLaws + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: MonadLaws.hs + build-depends: base, stochastic, random + default-language: Haskell2010 + -- | Options to pass to ghc +-- ghc-options: -O2 +-- -threaded +-- "-with-rtsopts=-N -pa-s -h -i0.1" + +test-suite normal3 + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Normal3.hs + build-depends: base, stochastic, random + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded + "-with-rtsopts=-N -pa -s -h -i0.1" +test-suite normal10 + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Normal10.hs + build-depends: base, stochastic, random + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded + "-with-rtsopts=-N -pa -s -h -i0.1" + +test-suite chart + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: ChartTest.hs + build-depends: base, stochastic, random, Chart-cairo, Chart, containers, mtl + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded +test-suite coolCharts + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: CoolCharts.hs + build-depends: base, stochastic, random, Chart-cairo, Chart, containers, mtl + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded + +test-suite swindler + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: Swindler.hs + build-depends: base, stochastic, containers, random + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded + +test-suite montyHall + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: MontyHall.hs + build-depends: base, stochastic, containers, random + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded + +test-suite contrivedGambler + type: exitcode-stdio-1.0 + hs-source-dirs: test + main-is: ContrivedGambler.hs + build-depends: base, stochastic, random, Chart-cairo, Chart, containers, mtl + default-language: Haskell2010 + -- | Options to pass to ghc + ghc-options: -O2 + -threaded diff --git a/test/ChartTest.hs b/test/ChartTest.hs new file mode 100644 --- /dev/null +++ b/test/ChartTest.hs @@ -0,0 +1,46 @@ +{-#LANGUAGE FlexibleContexts#-} + +import Control.Monad.Trans + +import Data.Sample +import Data.Sample.Types +import Data.Sample.Lib +import Data.Sample.Chart + +import qualified Data.Sequence as S + +import System.Random +import Graphics.Rendering.Chart.Backend.Cairo +import Graphics.Rendering.Chart.Easy + +normalInit :: StochProcess +normalInit = normalProcess 0 1 + +skew :: Sampler Double +skew = normal 0 1 + +skewProcess :: StochProcess +skewProcess = normalProcess 0 1 + +f :: Double -> StochProcess +f d = do + sk <- lift skew + normalProcess (d + sk) 1 + +testChart :: S.Seq (S.Seq Double) -> EC (Layout Integer Double) () +testChart ss = processToChart "Test Monte Carlo Chart" ss + +normal1 :: StochProcess +normal1 = composeProcess 10000 normalInit f + +mean :: S.Seq Double -> Double +mean ss = (foldr (+) 0 ss) / fromIntegral (S.length ss) + +main = do + gen <- newStdGen + let a = runProcessN 100 normal1 gen + fs = fmap (\x -> case S.viewr x of + S.EmptyR -> 0 + xs S.:> val -> val) a + toFile def "chart.png" $ testChart a + print $ mean fs diff --git a/test/ContrivedGambler.hs b/test/ContrivedGambler.hs new file mode 100644 --- /dev/null +++ b/test/ContrivedGambler.hs @@ -0,0 +1,29 @@ +import Data.Foldable + +import Data.Sample +import Data.Sample.Lib +import Data.Sample.Types +import Data.Sample.Chart + +import qualified Data.Sequence as S + +import System.Random + +import Graphics.Rendering.Chart.Backend.Cairo +import Graphics.Rendering.Chart.Easy + +contrivedGambler :: Bool -> Sampler Double +contrivedGambler b = if b + then normal 100 20 + else normal (-100) 10 + +fairCoin :: Sampler Bool +fairCoin = bernoulli 0.5 + +gamblerWithCoin :: Sampler Double +gamblerWithCoin = fairCoin >>= contrivedGambler + +main = do + gen <- newStdGen + let winnings = sampleN 100000 gamblerWithCoin gen + renderableToFile def "contrived.png" $ toRenderable $ histogram "Contrived Gambler" $ toList winnings diff --git a/test/CoolCharts.hs b/test/CoolCharts.hs new file mode 100644 --- /dev/null +++ b/test/CoolCharts.hs @@ -0,0 +1,34 @@ +import Control.Monad.Trans + +import Data.Sample +import Data.Sample.Types +import Data.Sample.Lib +import Data.Sample.Chart + +import qualified Data.Sequence as S + +import System.Random +import Graphics.Rendering.Chart.Backend.Cairo +import Graphics.Rendering.Chart.Easy + +normalInit :: StochProcess +normalInit = normalProcess 0 1 + +drift :: Sampler Double +drift = normal 0 1 + +f :: Double -> StochProcess +f samp = do + dr <- lift drift + normalProcess (dr + samp) 1 + +testChart :: S.Seq (S.Seq Double) -> EC (Layout Integer Double) () +testChart ss = processToChart "Random Walk" ss + +normal1 :: StochProcess +normal1 = composeProcess 10000 normalInit f + +main = do + gen <- newStdGen + let a = runProcess_ normal1 gen + toFile def "chart.png" $ testChart $ S.singleton a diff --git a/test/MonadLaws.hs b/test/MonadLaws.hs new file mode 100644 --- /dev/null +++ b/test/MonadLaws.hs @@ -0,0 +1,62 @@ +import Data.Sample +import Data.Sample.Lib +import Data.Sample.Types + +import System.Random +import System.Exit + +f :: Double -> Sampler Double +f d = if d == 3 then normal 5 2 + else normal 4 1 + +g :: Double -> Sampler Double +g d = if d < 10 then normal 33 10 + else normal 2.5 0.5 + +leftId :: Sampler Double +leftId = f 3 + +leftId' :: Sampler Double +leftId' = return 3 >>= f + +rightId :: Sampler Double +rightId = normal 10 3 + +rightId' :: Sampler Double +rightId' = rightId >>= return + +rightId'' :: Sampler Double +rightId'' = rightId' >>= return + +rightId''' :: Sampler Double +rightId''' = rightId'' >>= return + +assoc :: Sampler Double +assoc = (rightId >>= f) >>= g + +assoc' :: Sampler Double +assoc' = rightId >>= (\x -> f x >>= g) + +main :: IO Int +main = do + gen <- getStdGen + let l = sampleN 1000 leftId gen + l'= sampleN 1000 leftId' gen + r = sampleN 1000 rightId gen + r'= sampleN 1000 rightId' gen + r'' = sampleN 1000 rightId'' gen + r'''= sampleN 1000 rightId''' gen + a = sampleN 1000 assoc gen + a'= sampleN 1000 assoc' gen + print "Left" + print l + print l' + print "Right" + print r + print r' + print "Assoc" + print a + print a' + + if (l /= l') || (r' /= r'') || (r /= r''') || (r /= r') || (r'' /= r''') || (a /= a') then exitFailure + else return 0 diff --git a/test/MontyHall.hs b/test/MontyHall.hs new file mode 100644 --- /dev/null +++ b/test/MontyHall.hs @@ -0,0 +1,37 @@ +import Data.Sample +import Data.Sample.Lib +import Data.Sample.Types + +import qualified Data.Sequence as S + +import System.Random + +data Prize = Goat | Car + deriving Eq + +doorInit :: Int -> Sampler Prize +doorInit n = uniform $ Car : (take (n-1) $ repeat Goat) + +removeDoor :: Prize -> Sampler Prize -> Sampler Prize +removeDoor b sa = let (da, g) = runSample sa $ mkStdGen 0 + in case da of + Uniform l -> uniform $ removeFst b l + _ -> error "not monty hall" + where removeFst b [] = [] + removeFst b (x:xs) = if x == b then xs + else x : removeFst b xs + +montyHall :: Sampler Prize +montyHall = do + let doors = doorInit 3 + firstPick <- doors + let remainingDoors = removeDoor firstPick doors + removeDoor Goat remainingDoors + +main = do + gen <- newStdGen + let a = sampleN 100000 montyHall gen + a' = S.filter (== Car) a + a'' = S.filter (== Goat) a + print $ "Number of cars won: " ++ (show $ length a') + print $ "Number of goats won: " ++ (show $ length a'') diff --git a/test/Normal10.hs b/test/Normal10.hs new file mode 100644 --- /dev/null +++ b/test/Normal10.hs @@ -0,0 +1,21 @@ +import Data.Sample +import Data.Sample.Types +import Data.Sample.Lib + +import System.Random + +normalInit :: StochProcess +normalInit = normalProcess 10 3 + +f :: Double -> StochProcess +f d = if d < 7 then normalProcess (0.9 * d) (0.3 * d) + else if d > 13 then normalProcess (1.1 * d) (0.3 * d) + else normalProcess d (0.3 * d) + +normal10 :: StochProcess +normal10 = composeProcess 10 normalInit f + +main = do + gen <- newStdGen + print "normal10" + print $ runProcessN 100000 normal10 gen diff --git a/test/Normal3.hs b/test/Normal3.hs new file mode 100644 --- /dev/null +++ b/test/Normal3.hs @@ -0,0 +1,21 @@ +import Data.Sample +import Data.Sample.Types +import Data.Sample.Lib + +import System.Random + +normalInit :: StochProcess +normalInit = normalProcess 10 3 + +f :: Double -> StochProcess +f d = if d < 7 then normalProcess (0.9 * d) (0.3 * d) + else if d > 13 then normalProcess (1.1 * d) (0.3 * d) + else normalProcess d (0.3 * d) + +normal3 :: StochProcess +normal3 = composeProcess 3 normalInit f + +main = do + gen <- newStdGen + print "normal3" + print $ runProcessN 100000 normal3 gen diff --git a/test/Swindler.hs b/test/Swindler.hs new file mode 100644 --- /dev/null +++ b/test/Swindler.hs @@ -0,0 +1,26 @@ +import Data.Sample +import Data.Sample.Lib +import Data.Sample.Types + +import qualified Data.Sequence as S + +import System.Random + +swindler :: Int -> Bool +swindler i = i == 1 + +die :: Sampler Int +die = uniform [1, 2, 3, 4, 5, 6] + +swindlersDice :: Sampler Bool +swindlersDice = do + s1 <- die + s2 <- die + s3 <- die + return (swindler s1 || swindler s2 || swindler s3) + +main = do + gen <- newStdGen + let a = sampleN 100000 swindlersDice gen + print $ length $ S.filter id a + print $ length $ S.filter (not . id) a diff --git a/test/Test.hs b/test/Test.hs new file mode 100644 --- /dev/null +++ b/test/Test.hs @@ -0,0 +1,24 @@ +module Main where + +import Data.Sample +import Data.Sample.Lib +import Data.Sample.Types + +import qualified Data.Sequence as S + +fairCoin :: Sampler Bool +fairCoin = bernoulli 0.5 + +shadyGambler :: Bool -> Sampler Double +shadyGambler b = if b then discrete [(100, 0.9), (-100, 0.1)] + else certain (-100) + +gamblerGivenCoin :: Sampler Bool -> Sampler Double +gamblerGivenCoin coin = coin >>= shadyGambler + +main = do + s <- sampleION 1000000 $ gamblerGivenCoin fairCoin + let wins = S.filter (== 100) s + losses = S.filter (== (-100)) s + print $ "Wins with fair coin: " ++ (show $ length wins) + print $ "Losses with fair coin: " ++ (show $ length losses)