Control.Monad.Bayes.Class

This module defines MonadMeasure, which can be used to represent any probabilistic program, such as the following:

import Control.Monad (when)
import Control.Monad.Bayes.Class

model :: MonadMeasure m => m Bool
model = do
  rain <- bernoulli 0.3
  sprinkler <-
    bernoulli $
    if rain
      then 0.1
      else 0.4
  let wetProb =
    case (rain, sprinkler) of
      (True,  True)  -> 0.98
      (True,  False) -> 0.80
      (False, True)  -> 0.90
      (False, False) -> 0.00
  score wetProb
  return rain

Documentation

class Monad m => MonadDistribution m

Monads that can draw random variables.

Minimal complete definition

random

Instances

MonadDistribution Enumerator

Defined in Control.Monad.Bayes.Enumerator

Methods

random :: Enumerator Double

uniform :: Double -> Double -> Enumerator Double

normal :: Double -> Double -> Enumerator Double

gamma :: Double -> Double -> Enumerator Double

beta :: Double -> Double -> Enumerator Double

bernoulli :: Double -> Enumerator Bool

categorical :: Vector v Double => v Double -> Enumerator Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Enumerator Int

uniformD :: [a] -> Enumerator a

geometric :: Double -> Enumerator Int

poisson :: Double -> Enumerator Int

dirichlet :: Vector v Double => v Double -> Enumerator (v Double)

MonadDistribution Integrator

Defined in Control.Monad.Bayes.Integrator

Methods

random :: Integrator Double

uniform :: Double -> Double -> Integrator Double

normal :: Double -> Double -> Integrator Double

gamma :: Double -> Double -> Integrator Double

beta :: Double -> Double -> Integrator Double

bernoulli :: Double -> Integrator Bool

categorical :: Vector v Double => v Double -> Integrator Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Integrator Int

uniformD :: [a] -> Integrator a

geometric :: Double -> Integrator Int

poisson :: Double -> Integrator Int

dirichlet :: Vector v Double => v Double -> Integrator (v Double)

MonadDistribution Sampler

Defined in Control.Monad.Bayes.Sampler.Lazy

Methods

random :: Sampler Double

uniform :: Double -> Double -> Sampler Double

normal :: Double -> Double -> Sampler Double

gamma :: Double -> Double -> Sampler Double

beta :: Double -> Double -> Sampler Double

bernoulli :: Double -> Sampler Bool

categorical :: Vector v Double => v Double -> Sampler Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Sampler Int

uniformD :: [a] -> Sampler a

geometric :: Double -> Sampler Int

poisson :: Double -> Sampler Int

dirichlet :: Vector v Double => v Double -> Sampler (v Double)

Monad m => MonadDistribution (Density m)

Defined in Control.Monad.Bayes.Density.Free

Methods

random :: Density m Double

uniform :: Double -> Double -> Density m Double

normal :: Double -> Double -> Density m Double

gamma :: Double -> Double -> Density m Double

beta :: Double -> Double -> Density m Double

bernoulli :: Double -> Density m Bool

categorical :: Vector v Double => v Double -> Density m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Density m Int

uniformD :: [a] -> Density m a

geometric :: Double -> Density m Int

poisson :: Double -> Density m Int

dirichlet :: Vector v Double => v Double -> Density m (v Double)

MonadDistribution m => MonadDistribution (Density m)

Defined in Control.Monad.Bayes.Density.State

Methods

random :: Density m Double

uniform :: Double -> Double -> Density m Double

normal :: Double -> Double -> Density m Double

gamma :: Double -> Double -> Density m Double

beta :: Double -> Double -> Density m Double

bernoulli :: Double -> Density m Bool

categorical :: Vector v Double => v Double -> Density m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Density m Int

uniformD :: [a] -> Density m a

geometric :: Double -> Density m Int

poisson :: Double -> Density m Int

dirichlet :: Vector v Double => v Double -> Density m (v Double)

MonadDistribution m => MonadDistribution (SMC2 m)

Defined in Control.Monad.Bayes.Inference.SMC2

Methods

random :: SMC2 m Double

uniform :: Double -> Double -> SMC2 m Double

normal :: Double -> Double -> SMC2 m Double

gamma :: Double -> Double -> SMC2 m Double

beta :: Double -> Double -> SMC2 m Double

bernoulli :: Double -> SMC2 m Bool

categorical :: Vector v Double => v Double -> SMC2 m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> SMC2 m Int

uniformD :: [a] -> SMC2 m a

geometric :: Double -> SMC2 m Int

poisson :: Double -> SMC2 m Int

dirichlet :: Vector v Double => v Double -> SMC2 m (v Double)

MonadDistribution m => MonadDistribution (Population m)

Defined in Control.Monad.Bayes.Population

Methods

random :: Population m Double

uniform :: Double -> Double -> Population m Double

normal :: Double -> Double -> Population m Double

gamma :: Double -> Double -> Population m Double

beta :: Double -> Double -> Population m Double

bernoulli :: Double -> Population m Bool

categorical :: Vector v Double => v Double -> Population m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Population m Int

uniformD :: [a] -> Population m a

geometric :: Double -> Population m Int

poisson :: Double -> Population m Int

dirichlet :: Vector v Double => v Double -> Population m (v Double)

MonadDistribution m => MonadDistribution (Sequential m)

Defined in Control.Monad.Bayes.Sequential.Coroutine

Methods

random :: Sequential m Double

uniform :: Double -> Double -> Sequential m Double

normal :: Double -> Double -> Sequential m Double

gamma :: Double -> Double -> Sequential m Double

beta :: Double -> Double -> Sequential m Double

bernoulli :: Double -> Sequential m Bool

categorical :: Vector v Double => v Double -> Sequential m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Sequential m Int

uniformD :: [a] -> Sequential m a

geometric :: Double -> Sequential m Int

poisson :: Double -> Sequential m Int

dirichlet :: Vector v Double => v Double -> Sequential m (v Double)

MonadDistribution m => MonadDistribution (Traced m)

Defined in Control.Monad.Bayes.Traced.Basic

Methods

random :: Traced m Double

uniform :: Double -> Double -> Traced m Double

normal :: Double -> Double -> Traced m Double

gamma :: Double -> Double -> Traced m Double

beta :: Double -> Double -> Traced m Double

bernoulli :: Double -> Traced m Bool

categorical :: Vector v Double => v Double -> Traced m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Traced m Int

uniformD :: [a] -> Traced m a

geometric :: Double -> Traced m Int

poisson :: Double -> Traced m Int

dirichlet :: Vector v Double => v Double -> Traced m (v Double)

MonadDistribution m => MonadDistribution (Traced m)

Defined in Control.Monad.Bayes.Traced.Dynamic

Methods

random :: Traced m Double

uniform :: Double -> Double -> Traced m Double

normal :: Double -> Double -> Traced m Double

gamma :: Double -> Double -> Traced m Double

beta :: Double -> Double -> Traced m Double

bernoulli :: Double -> Traced m Bool

categorical :: Vector v Double => v Double -> Traced m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Traced m Int

uniformD :: [a] -> Traced m a

geometric :: Double -> Traced m Int

poisson :: Double -> Traced m Int

dirichlet :: Vector v Double => v Double -> Traced m (v Double)

MonadDistribution m => MonadDistribution (Traced m)

Defined in Control.Monad.Bayes.Traced.Static

Methods

random :: Traced m Double

uniform :: Double -> Double -> Traced m Double

normal :: Double -> Double -> Traced m Double

gamma :: Double -> Double -> Traced m Double

beta :: Double -> Double -> Traced m Double

bernoulli :: Double -> Traced m Bool

categorical :: Vector v Double => v Double -> Traced m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Traced m Int

uniformD :: [a] -> Traced m a

geometric :: Double -> Traced m Int

poisson :: Double -> Traced m Int

dirichlet :: Vector v Double => v Double -> Traced m (v Double)

MonadDistribution m => MonadDistribution (Weighted m)

Defined in Control.Monad.Bayes.Weighted

Methods

random :: Weighted m Double

uniform :: Double -> Double -> Weighted m Double

normal :: Double -> Double -> Weighted m Double

gamma :: Double -> Double -> Weighted m Double

beta :: Double -> Double -> Weighted m Double

bernoulli :: Double -> Weighted m Bool

categorical :: Vector v Double => v Double -> Weighted m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Weighted m Int

uniformD :: [a] -> Weighted m a

geometric :: Double -> Weighted m Int

poisson :: Double -> Weighted m Int

dirichlet :: Vector v Double => v Double -> Weighted m (v Double)

MonadDistribution m => MonadDistribution (ListT m)

Defined in Control.Monad.Bayes.Class

Methods

random :: ListT m Double

uniform :: Double -> Double -> ListT m Double

normal :: Double -> Double -> ListT m Double

gamma :: Double -> Double -> ListT m Double

beta :: Double -> Double -> ListT m Double

bernoulli :: Double -> ListT m Bool

categorical :: Vector v Double => v Double -> ListT m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> ListT m Int

uniformD :: [a] -> ListT m a

geometric :: Double -> ListT m Int

poisson :: Double -> ListT m Int

dirichlet :: Vector v Double => v Double -> ListT m (v Double)

StatefulGen g m => MonadDistribution (Sampler g m)

Defined in Control.Monad.Bayes.Sampler.Strict

Methods

random :: Sampler g m Double

uniform :: Double -> Double -> Sampler g m Double

normal :: Double -> Double -> Sampler g m Double

gamma :: Double -> Double -> Sampler g m Double

beta :: Double -> Double -> Sampler g m Double

bernoulli :: Double -> Sampler g m Bool

categorical :: Vector v Double => v Double -> Sampler g m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> Sampler g m Int

uniformD :: [a] -> Sampler g m a

geometric :: Double -> Sampler g m Int

poisson :: Double -> Sampler g m Int

dirichlet :: Vector v Double => v Double -> Sampler g m (v Double)

MonadDistribution m => MonadDistribution (ExceptT e m)

Defined in Control.Monad.Bayes.Class

Methods

random :: ExceptT e m Double

uniform :: Double -> Double -> ExceptT e m Double

normal :: Double -> Double -> ExceptT e m Double

gamma :: Double -> Double -> ExceptT e m Double

beta :: Double -> Double -> ExceptT e m Double

bernoulli :: Double -> ExceptT e m Bool

categorical :: Vector v Double => v Double -> ExceptT e m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> ExceptT e m Int

uniformD :: [a] -> ExceptT e m a

geometric :: Double -> ExceptT e m Int

poisson :: Double -> ExceptT e m Int

dirichlet :: Vector v Double => v Double -> ExceptT e m (v Double)

MonadDistribution m => MonadDistribution (IdentityT m)

Defined in Control.Monad.Bayes.Class

Methods

random :: IdentityT m Double

uniform :: Double -> Double -> IdentityT m Double

normal :: Double -> Double -> IdentityT m Double

gamma :: Double -> Double -> IdentityT m Double

beta :: Double -> Double -> IdentityT m Double

bernoulli :: Double -> IdentityT m Bool

categorical :: Vector v Double => v Double -> IdentityT m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> IdentityT m Int

uniformD :: [a] -> IdentityT m a

geometric :: Double -> IdentityT m Int

poisson :: Double -> IdentityT m Int

dirichlet :: Vector v Double => v Double -> IdentityT m (v Double)

MonadDistribution m => MonadDistribution (ReaderT r m)

Defined in Control.Monad.Bayes.Class

Methods

random :: ReaderT r m Double

uniform :: Double -> Double -> ReaderT r m Double

normal :: Double -> Double -> ReaderT r m Double

gamma :: Double -> Double -> ReaderT r m Double

beta :: Double -> Double -> ReaderT r m Double

bernoulli :: Double -> ReaderT r m Bool

categorical :: Vector v Double => v Double -> ReaderT r m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> ReaderT r m Int

uniformD :: [a] -> ReaderT r m a

geometric :: Double -> ReaderT r m Int

poisson :: Double -> ReaderT r m Int

dirichlet :: Vector v Double => v Double -> ReaderT r m (v Double)

MonadDistribution m => MonadDistribution (StateT s m)

Defined in Control.Monad.Bayes.Class

Methods

random :: StateT s m Double

uniform :: Double -> Double -> StateT s m Double

normal :: Double -> Double -> StateT s m Double

gamma :: Double -> Double -> StateT s m Double

beta :: Double -> Double -> StateT s m Double

bernoulli :: Double -> StateT s m Bool

categorical :: Vector v Double => v Double -> StateT s m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> StateT s m Int

uniformD :: [a] -> StateT s m a

geometric :: Double -> StateT s m Int

poisson :: Double -> StateT s m Int

dirichlet :: Vector v Double => v Double -> StateT s m (v Double)

(Monoid w, MonadDistribution m) => MonadDistribution (WriterT w m)

Defined in Control.Monad.Bayes.Class

Methods

random :: WriterT w m Double

uniform :: Double -> Double -> WriterT w m Double

normal :: Double -> Double -> WriterT w m Double

gamma :: Double -> Double -> WriterT w m Double

beta :: Double -> Double -> WriterT w m Double

bernoulli :: Double -> WriterT w m Bool

categorical :: Vector v Double => v Double -> WriterT w m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> WriterT w m Int

uniformD :: [a] -> WriterT w m a

geometric :: Double -> WriterT w m Int

poisson :: Double -> WriterT w m Int

dirichlet :: Vector v Double => v Double -> WriterT w m (v Double)

MonadDistribution m => MonadDistribution (ContT r m)

Defined in Control.Monad.Bayes.Class

Methods

random :: ContT r m Double

uniform :: Double -> Double -> ContT r m Double

normal :: Double -> Double -> ContT r m Double

gamma :: Double -> Double -> ContT r m Double

beta :: Double -> Double -> ContT r m Double

bernoulli :: Double -> ContT r m Bool

categorical :: Vector v Double => v Double -> ContT r m Int

logCategorical :: (Vector v (Log Double), Vector v Double) => v (Log Double) -> ContT r m Int

uniformD :: [a] -> ContT r m a

geometric :: Double -> ContT r m Int

poisson :: Double -> ContT r m Int

dirichlet :: Vector v Double => v Double -> ContT r m (v Double)

random

Arguments

:: MonadDistribution m

=> m Double

\(\sim \mathcal{U}(0, 1)\)

Draw from a uniform distribution.

uniform

Arguments

:: MonadDistribution m

=> Double

lower bound a

-> Double

upper bound b

-> m Double

\(\sim \mathcal{U}(a, b)\).

Draw from a uniform distribution.

normal

Arguments

:: MonadDistribution m

=> Double

mean μ

-> Double

standard deviation σ

-> m Double

\(\sim \mathcal{N}(\mu, \sigma^2)\)

Draw from a normal distribution.

gamma

Arguments

:: MonadDistribution m

=> Double

shape k

-> Double

scale θ

-> m Double

\(\sim \Gamma(k, \theta)\)

Draw from a gamma distribution.

beta

Arguments

:: MonadDistribution m

=> Double

shape α

-> Double

shape β

-> m Double

\(\sim \mathrm{Beta}(\alpha, \beta)\)

Draw from a beta distribution.

bernoulli

Arguments

:: MonadDistribution m

=> Double

probability p

-> m Bool

\(\sim \mathrm{B}(1, p)\)

Draw from a Bernoulli distribution.

categorical

Arguments

:: (MonadDistribution m, Vector v Double)

=> v Double

event probabilities

-> m Int

outcome category

Draw from a categorical distribution.

logCategorical

Arguments

:: (MonadDistribution m, Vector v (Log Double), Vector v Double)

=> v (Log Double)

event probabilities

-> m Int

outcome category

Draw from a categorical distribution in the log domain.

uniformD

Arguments

:: MonadDistribution m

=> [a]

observable outcomes xs

-> m a

\(\sim \mathcal{U}\{\mathrm{xs}\}\)

Draw from a discrete uniform distribution.

geometric

Arguments

:: MonadDistribution m

=> Double

success rate p

-> m Int

\(\sim\) number of failed Bernoulli trials with success probability p before first success

Draw from a geometric distribution.

poisson

Arguments

:: MonadDistribution m

=> Double

parameter λ

-> m Int

\(\sim \mathrm{Pois}(\lambda)\)

Draw from a Poisson distribution.

dirichlet

Arguments

:: (MonadDistribution m, Vector v Double)

=> v Double

concentration parameters as

-> m (v Double)

\(\sim \mathrm{Dir}(\mathrm{as})\)

Draw from a Dirichlet distribution.

class Monad m => MonadFactor m

Monads that can score different execution paths.

Minimal complete definition

score

Instances

MonadFactor Enumerator

Defined in Control.Monad.Bayes.Enumerator

Methods

score :: Log Double -> Enumerator ()

Monad m => MonadFactor (SMC2 m)

Defined in Control.Monad.Bayes.Inference.SMC2

Methods

score :: Log Double -> SMC2 m ()

Monad m => MonadFactor (Population m)

Defined in Control.Monad.Bayes.Population

Methods

score :: Log Double -> Population m ()

MonadFactor m => MonadFactor (Sequential m)

Execution is suspended after each score.

Defined in Control.Monad.Bayes.Sequential.Coroutine

Methods

score :: Log Double -> Sequential m ()

MonadFactor m => MonadFactor (Traced m)

Defined in Control.Monad.Bayes.Traced.Basic

Methods

score :: Log Double -> Traced m ()

MonadFactor m => MonadFactor (Traced m)

Defined in Control.Monad.Bayes.Traced.Dynamic

Methods

score :: Log Double -> Traced m ()

MonadFactor m => MonadFactor (Traced m)

Defined in Control.Monad.Bayes.Traced.Static

Methods

score :: Log Double -> Traced m ()

Monad m => MonadFactor (Weighted m)

Defined in Control.Monad.Bayes.Weighted

Methods

score :: Log Double -> Weighted m ()

MonadFactor m => MonadFactor (ListT m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> ListT m ()

MonadFactor m => MonadFactor (ExceptT e m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> ExceptT e m ()

MonadFactor m => MonadFactor (IdentityT m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> IdentityT m ()

MonadFactor m => MonadFactor (ReaderT r m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> ReaderT r m ()

MonadFactor m => MonadFactor (StateT s m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> StateT s m ()

(Monoid w, MonadFactor m) => MonadFactor (WriterT w m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> WriterT w m ()

MonadFactor m => MonadFactor (ContT r m)

Defined in Control.Monad.Bayes.Class

Methods

score :: Log Double -> ContT r m ()

score

Arguments

:: MonadFactor m

=> Log Double

likelihood of the execution path

-> m ()

Record a likelihood.

factor

Arguments

:: MonadFactor m

=> Log Double

likelihood of the execution path

-> m ()

Synonym for score.

condition :: MonadFactor m => Bool -> m ()

Hard conditioning.

class (MonadDistribution m, MonadFactor m) => MonadMeasure m

Monads that support both sampling and scoring.

Instances

MonadMeasure Enumerator

Defined in Control.Monad.Bayes.Enumerator

MonadDistribution m => MonadMeasure (SMC2 m)

Defined in Control.Monad.Bayes.Inference.SMC2

MonadDistribution m => MonadMeasure (Population m)

Defined in Control.Monad.Bayes.Population

MonadMeasure m => MonadMeasure (Sequential m)

Defined in Control.Monad.Bayes.Sequential.Coroutine

MonadMeasure m => MonadMeasure (Traced m)

Defined in Control.Monad.Bayes.Traced.Basic

MonadMeasure m => MonadMeasure (Traced m)

Defined in Control.Monad.Bayes.Traced.Dynamic

MonadMeasure m => MonadMeasure (Traced m)

Defined in Control.Monad.Bayes.Traced.Static

MonadDistribution m => MonadMeasure (Weighted m)

Defined in Control.Monad.Bayes.Weighted

MonadMeasure m => MonadMeasure (ListT m)

Defined in Control.Monad.Bayes.Class

MonadMeasure m => MonadMeasure (ExceptT e m)

Defined in Control.Monad.Bayes.Class

MonadMeasure m => MonadMeasure (IdentityT m)

Defined in Control.Monad.Bayes.Class

MonadMeasure m => MonadMeasure (ReaderT r m)

Defined in Control.Monad.Bayes.Class

MonadMeasure m => MonadMeasure (StateT s m)

Defined in Control.Monad.Bayes.Class

(Monoid w, MonadMeasure m) => MonadMeasure (WriterT w m)

Defined in Control.Monad.Bayes.Class

MonadMeasure m => MonadMeasure (ContT r m)

Defined in Control.Monad.Bayes.Class

discrete :: (DiscreteDistr d, MonadDistribution m) => d -> m Int

Draw from a discrete distributions using the probability mass function.

normalPdf

Arguments

:: Double

mean μ

-> Double

standard deviation σ

-> Double

sample x

-> Log Double

relative likelihood of observing sample x in \(\mathcal{N}(\mu, \sigma^2)\)

Probability density function of the normal distribution.

data Bayesian m z o

a useful datatype for expressing bayesian models

Constructors

Bayesian

Fields

• prior :: m z
• generative :: z -> m o
• likelihood :: z -> o -> Log Double

posterior :: (MonadMeasure m, Foldable f, Functor f) => Bayesian m z o -> f o -> m z

p(z|o)

priorPredictive :: Monad m => Bayesian m a b -> m b

posteriorPredictive :: (MonadMeasure m, Foldable f, Functor f) => Bayesian m a b -> f b -> m b

independent :: Applicative m => Int -> m a -> m [a]

mvNormal :: MonadDistribution m => Vector Double -> Matrix Double -> m (Vector Double)

multivariate normal

type Histogram = Histogram BinD Double

histogram :: Int -> [(Double, Log Double)] -> Histogram

histogramToList :: Histogram -> [(Double, Double)]

type Distribution a = forall m. MonadDistribution m => m a

synonym for pretty type signatures, but note that (A -> Distribution B) won't work as intended: for that, use Kernel Also note that the use of RankNTypes means performance may take a hit: really the main point of these signatures is didactic

type Measure a = forall m. MonadMeasure m => m a

type Kernel a b = forall m. MonadMeasure m => a -> m b

newtype Log a

Log-domain Float and Double values.

Constructors

Exp

Fields

• ln :: a

Instances

Foldable Log

Defined in Numeric.Log

Methods

fold :: Monoid m => Log m -> m

foldMap :: Monoid m => (a -> m) -> Log a -> m

foldMap' :: Monoid m => (a -> m) -> Log a -> m

foldr :: (a -> b -> b) -> b -> Log a -> b

foldr' :: (a -> b -> b) -> b -> Log a -> b

foldl :: (b -> a -> b) -> b -> Log a -> b

foldl' :: (b -> a -> b) -> b -> Log a -> b

foldr1 :: (a -> a -> a) -> Log a -> a

foldl1 :: (a -> a -> a) -> Log a -> a

toList :: Log a -> [a]

null :: Log a -> Bool

length :: Log a -> Int

elem :: Eq a => a -> Log a -> Bool

maximum :: Ord a => Log a -> a

minimum :: Ord a => Log a -> a

sum :: Num a => Log a -> a

product :: Num a => Log a -> a

Eq1 Log

Defined in Numeric.Log

Methods

liftEq :: (a -> b -> Bool) -> Log a -> Log b -> Bool

Traversable Log

Defined in Numeric.Log

Methods

traverse :: Applicative f => (a -> f b) -> Log a -> f (Log b)

sequenceA :: Applicative f => Log (f a) -> f (Log a)

mapM :: Monad m => (a -> m b) -> Log a -> m (Log b)

sequence :: Monad m => Log (m a) -> m (Log a)

Applicative Log

Defined in Numeric.Log

Methods

pure :: a -> Log a

(<*>) :: Log (a -> b) -> Log a -> Log b

liftA2 :: (a -> b -> c) -> Log a -> Log b -> Log c

(*>) :: Log a -> Log b -> Log b

(<*) :: Log a -> Log b -> Log a

Functor Log

Defined in Numeric.Log

Methods

fmap :: (a -> b) -> Log a -> Log b

(<$) :: a -> Log b -> Log a

Monad Log

Defined in Numeric.Log

Methods

(>>=) :: Log a -> (a -> Log b) -> Log b

(>>) :: Log a -> Log b -> Log b

return :: a -> Log a

Serial1 Log

Defined in Numeric.Log

Methods

serializeWith :: MonadPut m => (a -> m ()) -> Log a -> m ()

deserializeWith :: MonadGet m => m a -> m (Log a)

Comonad Log

Defined in Numeric.Log

Methods

extract :: Log a -> a

duplicate :: Log a -> Log (Log a)

extend :: (Log a -> b) -> Log a -> Log b

ComonadApply Log

Defined in Numeric.Log

Methods

(<@>) :: Log (a -> b) -> Log a -> Log b

(@>) :: Log a -> Log b -> Log b

(<@) :: Log a -> Log b -> Log a

Distributive Log

Defined in Numeric.Log

Methods

distribute :: Functor f => f (Log a) -> Log (f a)

collect :: Functor f => (a -> Log b) -> f a -> Log (f b)

distributeM :: Monad m => m (Log a) -> Log (m a)

collectM :: Monad m => (a -> Log b) -> m a -> Log (m b)

Hashable1 Log

Defined in Numeric.Log

Methods

liftHashWithSalt :: (Int -> a -> Int) -> Int -> Log a -> Int

Apply Log

Defined in Numeric.Log

Methods

(<.>) :: Log (a -> b) -> Log a -> Log b

(.>) :: Log a -> Log b -> Log b

(<.) :: Log a -> Log b -> Log a

liftF2 :: (a -> b -> c) -> Log a -> Log b -> Log c

Bind Log

Defined in Numeric.Log

Methods

(>>-) :: Log a -> (a -> Log b) -> Log b

join :: Log (Log a) -> Log a

Extend Log

Defined in Numeric.Log

Methods

duplicated :: Log a -> Log (Log a)

extended :: (Log a -> b) -> Log a -> Log b

Foldable1 Log

Defined in Numeric.Log

Methods

fold1 :: Semigroup m => Log m -> m

foldMap1 :: Semigroup m => (a -> m) -> Log a -> m

toNonEmpty :: Log a -> NonEmpty a

Traversable1 Log

Defined in Numeric.Log

Methods

traverse1 :: Apply f => (a -> f b) -> Log a -> f (Log b)

sequence1 :: Apply f => Log (f b) -> f (Log b)

(RealFloat a, Unbox a) => Vector Vector (Log a)

Defined in Numeric.Log

Methods

basicUnsafeFreeze :: PrimMonad m => Mutable Vector (PrimState m) (Log a) -> m (Vector (Log a))

basicUnsafeThaw :: PrimMonad m => Vector (Log a) -> m (Mutable Vector (PrimState m) (Log a))

basicLength :: Vector (Log a) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Log a) -> Vector (Log a)

basicUnsafeIndexM :: Monad m => Vector (Log a) -> Int -> m (Log a)

basicUnsafeCopy :: PrimMonad m => Mutable Vector (PrimState m) (Log a) -> Vector (Log a) -> m ()

elemseq :: Vector (Log a) -> Log a -> b -> b

Unbox a => MVector MVector (Log a)

Defined in Numeric.Log

Methods

basicLength :: MVector s (Log a) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Log a) -> MVector s (Log a)

basicOverlaps :: MVector s (Log a) -> MVector s (Log a) -> Bool

basicUnsafeNew :: PrimMonad m => Int -> m (MVector (PrimState m) (Log a))

basicInitialize :: PrimMonad m => MVector (PrimState m) (Log a) -> m ()

basicUnsafeReplicate :: PrimMonad m => Int -> Log a -> m (MVector (PrimState m) (Log a))

basicUnsafeRead :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> m (Log a)

basicUnsafeWrite :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> Log a -> m ()

basicClear :: PrimMonad m => MVector (PrimState m) (Log a) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Log a) -> Log a -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Log a) -> MVector (PrimState m) (Log a) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Log a) -> MVector (PrimState m) (Log a) -> m ()

basicUnsafeGrow :: PrimMonad m => MVector (PrimState m) (Log a) -> Int -> m (MVector (PrimState m) (Log a))

Data a => Data (Log a)

Defined in Numeric.Log

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Log a -> c (Log a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Log a)

toConstr :: Log a -> Constr

dataTypeOf :: Log a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Log a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Log a))

gmapT :: (forall b. Data b => b -> b) -> Log a -> Log a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Log a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Log a -> r

gmapQ :: (forall d. Data d => d -> u) -> Log a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Log a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Log a -> m (Log a)

Storable a => Storable (Log a)

Defined in Numeric.Log

Methods

sizeOf :: Log a -> Int

alignment :: Log a -> Int

peekElemOff :: Ptr (Log a) -> Int -> IO (Log a)

pokeElemOff :: Ptr (Log a) -> Int -> Log a -> IO ()

peekByteOff :: Ptr b -> Int -> IO (Log a)

pokeByteOff :: Ptr b -> Int -> Log a -> IO ()

peek :: Ptr (Log a) -> IO (Log a)

poke :: Ptr (Log a) -> Log a -> IO ()

RealFloat a => Monoid (Log a)

Defined in Numeric.Log

Methods

mempty :: Log a

mappend :: Log a -> Log a -> Log a

mconcat :: [Log a] -> Log a

RealFloat a => Semigroup (Log a)

Defined in Numeric.Log

Methods

(<>) :: Log a -> Log a -> Log a

sconcat :: NonEmpty (Log a) -> Log a

stimes :: Integral b => b -> Log a -> Log a

(RealFloat a, Enum a) => Enum (Log a)

Defined in Numeric.Log

Methods

succ :: Log a -> Log a

pred :: Log a -> Log a

toEnum :: Int -> Log a

fromEnum :: Log a -> Int

enumFrom :: Log a -> [Log a]

enumFromThen :: Log a -> Log a -> [Log a]

enumFromTo :: Log a -> Log a -> [Log a]

enumFromThenTo :: Log a -> Log a -> Log a -> [Log a]

RealFloat a => Floating (Log a)

Defined in Numeric.Log

Methods

pi :: Log a

exp :: Log a -> Log a

log :: Log a -> Log a

sqrt :: Log a -> Log a

(**) :: Log a -> Log a -> Log a

logBase :: Log a -> Log a -> Log a

sin :: Log a -> Log a

cos :: Log a -> Log a

tan :: Log a -> Log a

asin :: Log a -> Log a

acos :: Log a -> Log a

atan :: Log a -> Log a

sinh :: Log a -> Log a

cosh :: Log a -> Log a

tanh :: Log a -> Log a

asinh :: Log a -> Log a

acosh :: Log a -> Log a

atanh :: Log a -> Log a

log1p :: Log a -> Log a

expm1 :: Log a -> Log a

log1pexp :: Log a -> Log a

log1mexp :: Log a -> Log a

Generic (Log a)

Defined in Numeric.Log

Associated Types

type Rep (Log a) :: Type -> Type

Methods

from :: Log a -> Rep (Log a) x

to :: Rep (Log a) x -> Log a

RealFloat a => Num (Log a)

Defined in Numeric.Log

Methods

(+) :: Log a -> Log a -> Log a

(-) :: Log a -> Log a -> Log a

(*) :: Log a -> Log a -> Log a

negate :: Log a -> Log a

abs :: Log a -> Log a

signum :: Log a -> Log a

fromInteger :: Integer -> Log a

(Floating a, Read a) => Read (Log a)

Defined in Numeric.Log

Methods

readsPrec :: Int -> ReadS (Log a)

readList :: ReadS [Log a]

readPrec :: ReadPrec (Log a)

readListPrec :: ReadPrec [Log a]

RealFloat a => Fractional (Log a)

Defined in Numeric.Log

Methods

(/) :: Log a -> Log a -> Log a

recip :: Log a -> Log a

fromRational :: Rational -> Log a

(RealFloat a, Ord a) => Real (Log a)

Defined in Numeric.Log

Methods

toRational :: Log a -> Rational

RealFloat a => RealFrac (Log a)

Defined in Numeric.Log

Methods

properFraction :: Integral b => Log a -> (b, Log a)

truncate :: Integral b => Log a -> b

round :: Integral b => Log a -> b

ceiling :: Integral b => Log a -> b

floor :: Integral b => Log a -> b

(Floating a, Show a) => Show (Log a)

Defined in Numeric.Log

Methods

showsPrec :: Int -> Log a -> ShowS

show :: Log a -> String

showList :: [Log a] -> ShowS

Binary a => Binary (Log a)

Defined in Numeric.Log

Methods

put :: Log a -> Put

get :: Get (Log a)

putList :: [Log a] -> Put

Serial a => Serial (Log a)

Defined in Numeric.Log

Methods

serialize :: MonadPut m => Log a -> m ()

deserialize :: MonadGet m => m (Log a)

Serialize a => Serialize (Log a)

Defined in Numeric.Log

Methods

put :: Putter (Log a)

get :: Get (Log a)

NFData a => NFData (Log a)

Defined in Numeric.Log

Methods

rnf :: Log a -> ()

Eq a => Eq (Log a)

Defined in Numeric.Log

Methods

(==) :: Log a -> Log a -> Bool

(/=) :: Log a -> Log a -> Bool

Ord a => Ord (Log a)

Defined in Numeric.Log

Methods

compare :: Log a -> Log a -> Ordering

(<) :: Log a -> Log a -> Bool

(<=) :: Log a -> Log a -> Bool

(>) :: Log a -> Log a -> Bool

(>=) :: Log a -> Log a -> Bool

max :: Log a -> Log a -> Log a

min :: Log a -> Log a -> Log a

Hashable a => Hashable (Log a)

Defined in Numeric.Log

Methods

hashWithSalt :: Int -> Log a -> Int

hash :: Log a -> Int

(RealFloat a, Unbox a) => Unbox (Log a)

Defined in Numeric.Log

newtype MVector s (Log a)

Defined in Numeric.Log

newtype MVector s (Log a) = MV_Log (MVector s a)

type Rep (Log a)

Defined in Numeric.Log

type Rep (Log a) = D1 ('MetaData "Log" "Numeric.Log" "log-domain-0.13.2-1s0JmBUjl1G45npr6XDBlr" 'True) (C1 ('MetaCons "Exp" 'PrefixI 'True) (S1 ('MetaSel ('Just "ln") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

newtype Vector (Log a)

Defined in Numeric.Log

newtype Vector (Log a) = V_Log (Vector a)