Data.Monoid.Statistics.Class

Type class and helpers

class Monoid m => StatMonoid m a where

This type class is used to express parallelizable constant space algorithms for calculation of statistics. By definitions statistic is some measure of sample which doesn't depend on order of elements (for example: mean, sum, number of elements, variance, etc).

For many statistics it's possible to possible to construct constant space algorithm which is expressed as fold. Additionally it's usually possible to write function which combine state of fold accumulator to get statistic for union of two samples.

Thus for such algorithm we have value which corresponds to empty sample, merge function which which corresponds to merging of two samples, and single step of fold. Last one allows to evaluate statistic given data sample and first two form a monoid and allow parallelization: split data into parts, build estimate for each by folding and then merge them using mappend.

Instance must satisfy following laws. If floating point arithmetics is used then equality should be understood as approximate.

1. addValue (addValue y mempty) x  == addValue mempty x <> addValue mempty y
2. x <> y == y <> x

Minimal complete definition

addValue | singletonMonoid

Methods

addValue :: m -> a -> m

Add one element to monoid accumulator. It's step of fold.

singletonMonoid :: a -> m

State of accumulator corresponding to 1-element sample.

Instances

Real a => StatMonoid KBNSum a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: KBNSum -> a -> KBNSum

singletonMonoid :: a -> KBNSum

Real a => StatMonoid KahanSum a

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: KahanSum -> a -> KahanSum

singletonMonoid :: a -> KahanSum

StatMonoid BinomAcc Bool

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: BinomAcc -> Bool -> BinomAcc

singletonMonoid :: Bool -> BinomAcc

a ~ Double => StatMonoid MaxD a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MaxD -> a -> MaxD

singletonMonoid :: a -> MaxD

a ~ Double => StatMonoid MinD a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MinD -> a -> MinD

singletonMonoid :: a -> MinD

Real a => StatMonoid Variance a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Variance -> a -> Variance

singletonMonoid :: a -> Variance

Real a => StatMonoid WelfordMean a

\[ s_n = s_{n-1} + \frac{x_n - s_{n-1}}{n} \]

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: WelfordMean -> a -> WelfordMean

singletonMonoid :: a -> WelfordMean

Real a => StatMonoid MeanKBN a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MeanKBN -> a -> MeanKBN

singletonMonoid :: a -> MeanKBN

Real a => StatMonoid MeanKahan a

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: MeanKahan -> a -> MeanKahan

singletonMonoid :: a -> MeanKahan

(Num a, a ~ a') => StatMonoid (Sum a) a'

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Sum a -> a' -> Sum a

singletonMonoid :: a' -> Sum a

(Num a, a ~ a') => StatMonoid (Product a) a'

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Product a -> a' -> Product a

singletonMonoid :: a' -> Product a

(Ord a, a ~ a') => StatMonoid (Max a) a'

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Max a -> a' -> Max a

singletonMonoid :: a' -> Max a

(Ord a, a ~ a') => StatMonoid (Min a) a'

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: Min a -> a' -> Min a

singletonMonoid :: a' -> Min a

Integral a => StatMonoid (CountG a) b

Defined in Data.Monoid.Statistics.Numeric

Methods

addValue :: CountG a -> b -> CountG a

singletonMonoid :: b -> CountG a

(StatMonoid a x, StatMonoid b x) => StatMonoid (Pair a b) x

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Pair a b -> x -> Pair a b

singletonMonoid :: x -> Pair a b

reduceSample :: (Foldable f, StatMonoid m a) => f a -> m

Calculate statistic over Foldable. It's implemented in terms of foldl'.

reduceSampleVec :: (Vector v a, StatMonoid m a) => v a -> m

Calculate statistic over vector. It's implemented in terms of foldl'.

Data types

data Pair a b

Strict pair. It allows to calculate two statistics in parallel

Constructors

Pair !a !b

Instances

(Unbox a, Unbox b) => Vector Vector (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

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

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

basicLength :: Vector (Pair a b) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Pair a b) -> Vector (Pair a b)

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

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

elemseq :: Vector (Pair a b) -> Pair a b -> b0 -> b0

(Unbox a, Unbox b) => MVector MVector (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

basicLength :: MVector s (Pair a b) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Pair a b) -> MVector s (Pair a b)

basicOverlaps :: MVector s (Pair a b) -> MVector s (Pair a b) -> Bool

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

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

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

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

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

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

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

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

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

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

(Eq a, Eq b) => Eq (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

(==) :: Pair a b -> Pair a b -> Bool

(/=) :: Pair a b -> Pair a b -> Bool

(Data a, Data b) => Data (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

gfoldl :: (forall d b0. Data d => c (d -> b0) -> d -> c b0) -> (forall g. g -> c g) -> Pair a b -> c (Pair a b)

gunfold :: (forall b0 r. Data b0 => c (b0 -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Pair a b)

toConstr :: Pair a b -> Constr

dataTypeOf :: Pair a b -> DataType

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

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

gmapT :: (forall b0. Data b0 => b0 -> b0) -> Pair a b -> Pair a b

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

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

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

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

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

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

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

(Ord a, Ord b) => Ord (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

compare :: Pair a b -> Pair a b -> Ordering

(<) :: Pair a b -> Pair a b -> Bool

(<=) :: Pair a b -> Pair a b -> Bool

(>) :: Pair a b -> Pair a b -> Bool

(>=) :: Pair a b -> Pair a b -> Bool

max :: Pair a b -> Pair a b -> Pair a b

min :: Pair a b -> Pair a b -> Pair a b

(Show a, Show b) => Show (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

showsPrec :: Int -> Pair a b -> ShowS

show :: Pair a b -> String

showList :: [Pair a b] -> ShowS

Generic (Pair a b)

Defined in Data.Monoid.Statistics.Class

Associated Types

type Rep (Pair a b) :: Type -> Type

Methods

from :: Pair a b -> Rep (Pair a b) x

to :: Rep (Pair a b) x -> Pair a b

(Semigroup a, Semigroup b) => Semigroup (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

(<>) :: Pair a b -> Pair a b -> Pair a b

sconcat :: NonEmpty (Pair a b) -> Pair a b

stimes :: Integral b0 => b0 -> Pair a b -> Pair a b

(Monoid a, Monoid b) => Monoid (Pair a b)

Defined in Data.Monoid.Statistics.Class

Methods

mempty :: Pair a b

mappend :: Pair a b -> Pair a b -> Pair a b

mconcat :: [Pair a b] -> Pair a b

(Unbox a, Unbox b) => Unbox (Pair a b)

Defined in Data.Monoid.Statistics.Class

(StatMonoid a x, StatMonoid b x) => StatMonoid (Pair a b) x

Defined in Data.Monoid.Statistics.Class

Methods

addValue :: Pair a b -> x -> Pair a b

singletonMonoid :: x -> Pair a b

newtype MVector s (Pair a b)

Defined in Data.Monoid.Statistics.Class

newtype MVector s (Pair a b) = MV_Pair (MVector s (a, b))

type Rep (Pair a b)

Defined in Data.Monoid.Statistics.Class

type Rep (Pair a b) = D1 (MetaData "Pair" "Data.Monoid.Statistics.Class" "monoid-statistics-1.0.1.0-1S6uCZlndwKGUT6ITei8nH" False) (C1 (MetaCons "Pair" PrefixI False) (S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 a) :*: S1 (MetaSel (Nothing :: Maybe Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 b)))

newtype Vector (Pair a b)

Defined in Data.Monoid.Statistics.Class

newtype Vector (Pair a b) = V_Pair (Vector (a, b))