random-fu-0.3.0.1: Random number generation

Safe Haskell | Safe-Inferred
Language | Haskell2010

Data.Random.RVar

Synopsis

- type RVar = RVarT Identity
- runRVar :: StatefulGen g m => RVar a -> g -> m a
- data RVarT (m :: Type -> Type) a
- runRVarT :: forall (n :: Type -> Type) m g a. (Lift n m, StatefulGen g m) => RVarT n a -> g -> m a
- runRVarTWith :: forall m n g a. StatefulGen g m => (forall t. n t -> m t) -> RVarT n a -> g -> m a
- data RGen = RGen
- uniformRVarT :: forall a (m :: Type -> Type). Uniform a => RVarT m a
- uniformRangeRVarT :: forall a (m :: Type -> Type). UniformRange a => (a, a) -> RVarT m a

# Documentation

type RVar = RVarT Identity Source #

An opaque type modeling a "random variable" - a value which depends on the outcome of some random event. `RVar`s can be conveniently defined by an imperative-looking style:

    normalPair =  do
        u <- stdUniform
        t <- stdUniform
        let r = sqrt (-2 * log u)
            theta = (2 * pi) * t

            x = r * cos theta
            y = r * sin theta
        return (x,y)

OR by a more applicative style:

    logNormal = exp <$> stdNormal

Once defined (in any style), there are several ways to sample `RVar`s:

- Using an immutable pseudo-random number generator that has an instance for `RandomGen` with `StateT` monad:

    >>> import qualified Data.Random as Fu (uniform)
    >>> import System.Random (mkStdGen)
    >>> import Control.Monad.State (runState)
    >>> runState (sampleStateRVar (Fu.uniform 1 (100 :: Integer))) (mkStdGen 2021)
    (79,StdGen {unStdGen = SMGen 4687568268719557181 4805600293067301895})

- Using a mutable pseud-random number generator that has an instance for `StatefulGen` with `ReaderT` monad.

    >>> import qualified Data.Random as Fu (uniform)
    >>> import System.Random.MWC (create)
    >>> import Control.Monad.Reader (runReaderT)
    >>> import qualified Data.Vector.Storable as VS
    >>> initialize (VS.singleton 2021) >>= runReaderT (sampleReaderRVar (uniform 1 (100 :: Integer)))
    8

runRVar :: StatefulGen g m => RVar a -> g -> m a Source #

"Run" an `RVar` - samples the random variable from the provided source of entropy.

data RVarT (m :: Type -> Type) a Source #

A random variable with access to operations in an underlying monad. Useful examples include any form of state for implementing random processes with hysteresis, or writer monads for implementing tracing of complicated algorithms.

For example, a simple random walk can be implemented as an `RVarT` `IO` value:

    rwalkIO :: IO (RVarT IO Double)
    rwalkIO d = do
        lastVal <- newIORef 0

        let x = do
                prev    <- lift (readIORef lastVal)
                change  <- rvarT StdNormal

                let new = prev + change
                lift (writeIORef lastVal new)
                return new

        return x

To run the random walk it must first be initialized, after which it can be sampled as usual:

    do
        rw <- rwalkIO
        x <- sampleRVarT rw
        y <- sampleRVarT rw
        ...

The same random-walk process as above can be implemented using MTL types as follows (using `import Control.Monad.Trans as MTL`):

    rwalkState :: RVarT (State Double) Double
    rwalkState = do
        prev <- MTL.lift get
        change  <- rvarT StdNormal

        let new = prev + change
        MTL.lift (put new)
        return new

Invocation is straightforward (although a bit noisy) if you're used to MTL:

    rwalk :: Int -> Double -> StdGen -> ([Double], StdGen)
    rwalk count start gen =
        flip evalState start .
            flip runStateT gen .
                sampleRVarTWith MTL.lift $
                    replicateM count rwalkState

#### Instances

Instances details

MonadTrans RVarT |
Instance details Defined in Data.RVar Methods lift :: Monad m => m a -> RVarT m a Source #
MonadPrompt Prim (RVarT n) |
Instance details Defined in Data.RVar Methods prompt :: Prim a -> RVarT n a
StatefulGen RGen (RVarT m) |

Instance details

Defined in Data.RVar

Methods

uniformWord32R :: Word32 -> RGen -> RVarT m Word32 Source #

uniformWord64R :: Word64 -> RGen -> RVarT m Word64 Source #

uniformWord8 :: RGen -> RVarT m Word8 Source #

uniformWord16 :: RGen -> RVarT m Word16 Source #

uniformWord32 :: RGen -> RVarT m Word32 Source #

uniformWord64 :: RGen -> RVarT m Word64 Source #

uniformShortByteString :: Int -> RGen -> RVarT m ShortByteString Source #

MonadIO m => MonadIO (RVarT m) |
Instance details Defined in Data.RVar Methods liftIO :: IO a -> RVarT m a Source #
Applicative (RVarT n) |
Instance details Defined in Data.RVar Methods pure :: a -> RVarT n a Source # (<*>) :: RVarT n (a -> b) -> RVarT n a -> RVarT n b Source # liftA2 :: (a -> b -> c) -> RVarT n a -> RVarT n b -> RVarT n c Source # (*>) :: RVarT n a -> RVarT n b -> RVarT n b Source # (<*) :: RVarT n a -> RVarT n b -> RVarT n a Source #
Functor (RVarT n) |
Instance details Defined in Data.RVar Methods fmap :: (a -> b) -> RVarT n a -> RVarT n b Source # (<$) :: a -> RVarT n b -> RVarT n a Source #
Monad (RVarT n) |
Instance details Defined in Data.RVar Methods (>>=) :: RVarT n a -> (a -> RVarT n b) -> RVarT n b Source # (>>) :: RVarT n a -> RVarT n b -> RVarT n b Source # return :: a -> RVarT n a Source #
Lift m n => Sampleable (RVarT m) n t Source # |
Instance details Defined in Data.Random.Sample Methods sampleFrom :: StatefulGen g n => g -> RVarT m t -> n t Source #
Lift (RVarT Identity) (RVarT m) Source # |
Instance details Defined in Data.Random.Lift Methods lift :: RVarT Identity a -> RVarT m a Source #

runRVarT :: forall (n :: Type -> Type) m g a. (Lift n m, StatefulGen g m) => RVarT n a -> g -> m a Source #

Like `runRVarTWith`, but using an implicit lifting (provided by the `Lift` class)

runRVarTWith :: forall m n g a. StatefulGen g m => (forall t. n t -> m t) -> RVarT n a -> g -> m a Source #

"Runs" an `RVarT`, sampling the random variable it defines.

The first argument lifts the base monad into the sampling monad. This operation must obey the "monad transformer" laws:

    lift . return = return
    lift (x >>= f) = (lift x) >>= (lift . f)

One example of a useful non-standard lifting would be one that takes `State s` to another monad with a different state representation (such as `IO` with the state mapped to an `IORef`):

    embedState :: (Monad m) => m s -> (s -> m ()) -> State s a -> m a
    embedState get put = \m -> do
        s <- get
        (res,s) <- return (runState m s)
        put s
        return res

The ability to lift is very important - without it, every `RVar` would have to either be given access to the full capability of the monad in which it will eventually be sampled (which, incidentally, would also have to be monomorphic so you couldn't sample one `RVar` in more than one monad) or functions manipulating `RVar`s would have to use higher-ranked types to enforce the same kind of isolation and polymorphism.

data RGen Source #

Constructors

RGen |

#### Instances

Instances details

StatefulGen RGen (RVarT m) |

Instance details

Defined in Data.RVar

Methods

uniformWord32R :: Word32 -> RGen -> RVarT m Word32 Source #

uniformWord64R :: Word64 -> RGen -> RVarT m Word64 Source #

uniformWord8 :: RGen -> RVarT m Word8 Source #

uniformWord16 :: RGen -> RVarT m Word16 Source #

uniformWord32 :: RGen -> RVarT m Word32 Source #

uniformWord64 :: RGen -> RVarT m Word64 Source #

uniformShortByteString :: Int -> RGen -> RVarT m ShortByteString Source #

uniformRVarT :: forall a (m :: Type -> Type). Uniform a => RVarT m a Source #

uniformRangeRVarT :: forall a (m :: Type -> Type). UniformRange a => (a, a) -> RVarT m a Source #