Data.Monoid.Statistics.Extra

Monoids for calculating various statistics in constant space. This module contains algorithms that should be generally avoided unless there's specific reason to use them.

Mean

data WelfordMean

Incremental calculation of mean. Note that this algorithm doesn't offer better numeric precision than plain summation. Its only advantage is protection against double overflow:

>>> calcMean $ reduceSample @MeanKBN (replicate 100 1e308) :: Maybe Double
Just NaN
>>> calcMean $ reduceSample @WelfordMean (replicate 100 1e308) :: Maybe Double
Just 1.0e308

Unless this feature is needed KBNSum should be used. Algorithm is due to Welford [Welford1962]

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

Constructors

WelfordMean !Int !Double

Instances

Eq WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

(==) :: WelfordMean -> WelfordMean -> Bool

(/=) :: WelfordMean -> WelfordMean -> Bool

Data WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

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

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

toConstr :: WelfordMean -> Constr

dataTypeOf :: WelfordMean -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> WelfordMean -> WelfordMean

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

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

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

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

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

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

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

Show WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

showsPrec :: Int -> WelfordMean -> ShowS

show :: WelfordMean -> String

showList :: [WelfordMean] -> ShowS

Generic WelfordMean

Defined in Data.Monoid.Statistics.Extra

Associated Types

type Rep WelfordMean :: Type -> Type

Methods

from :: WelfordMean -> Rep WelfordMean x

to :: Rep WelfordMean x -> WelfordMean

Semigroup WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

(<>) :: WelfordMean -> WelfordMean -> WelfordMean

sconcat :: NonEmpty WelfordMean -> WelfordMean

stimes :: Integral b => b -> WelfordMean -> WelfordMean

Monoid WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

mempty :: WelfordMean

mappend :: WelfordMean -> WelfordMean -> WelfordMean

mconcat :: [WelfordMean] -> WelfordMean

Unbox WelfordMean

Defined in Data.Monoid.Statistics.Extra

CalcMean WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => WelfordMean -> m Double

CalcCount WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

calcCount :: WelfordMean -> Int

Vector Vector WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

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

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

basicLength :: Vector WelfordMean -> Int

basicUnsafeSlice :: Int -> Int -> Vector WelfordMean -> Vector WelfordMean

basicUnsafeIndexM :: Monad m => Vector WelfordMean -> Int -> m WelfordMean

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

elemseq :: Vector WelfordMean -> WelfordMean -> b -> b

MVector MVector WelfordMean

Defined in Data.Monoid.Statistics.Extra

Methods

basicLength :: MVector s WelfordMean -> Int

basicUnsafeSlice :: Int -> Int -> MVector s WelfordMean -> MVector s WelfordMean

basicOverlaps :: MVector s WelfordMean -> MVector s WelfordMean -> Bool

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

basicInitialize :: PrimMonad m => MVector (PrimState m) WelfordMean -> m ()

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

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

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

basicClear :: PrimMonad m => MVector (PrimState m) WelfordMean -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) WelfordMean -> WelfordMean -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) WelfordMean -> MVector (PrimState m) WelfordMean -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) WelfordMean -> MVector (PrimState m) WelfordMean -> m ()

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

Real a => StatMonoid WelfordMean a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: WelfordMean -> a -> WelfordMean

singletonMonoid :: a -> WelfordMean

type Rep WelfordMean

Defined in Data.Monoid.Statistics.Extra

type Rep WelfordMean = D1 ('MetaData "WelfordMean" "Data.Monoid.Statistics.Extra" "monoid-statistics-1.1.1-Et52IJUUy4YDKplMeouIOs" 'False) (C1 ('MetaCons "WelfordMean" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Double)))

newtype Vector WelfordMean

Defined in Data.Monoid.Statistics.Extra

newtype Vector WelfordMean = V_WelfordMean (Vector (Int, Double))

newtype MVector s WelfordMean

Defined in Data.Monoid.Statistics.Extra

newtype MVector s WelfordMean = MV_WelfordMean (MVector s (Int, Double))

asWelfordMean :: WelfordMean -> WelfordMean

Type restricted id

data MeanKahan

Incremental calculation of mean. Sum of elements is calculated using compensated Kahan summation. It's provided only for sake of completeness. KBNSum should be used instead.

Constructors

MeanKahan !Int !KahanSum

Instances

Eq MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

(==) :: MeanKahan -> MeanKahan -> Bool

(/=) :: MeanKahan -> MeanKahan -> Bool

Data MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

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

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

toConstr :: MeanKahan -> Constr

dataTypeOf :: MeanKahan -> DataType

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

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

gmapT :: (forall b. Data b => b -> b) -> MeanKahan -> MeanKahan

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

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

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

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

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

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

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

Show MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

showsPrec :: Int -> MeanKahan -> ShowS

show :: MeanKahan -> String

showList :: [MeanKahan] -> ShowS

Generic MeanKahan

Defined in Data.Monoid.Statistics.Extra

Associated Types

type Rep MeanKahan :: Type -> Type

Methods

from :: MeanKahan -> Rep MeanKahan x

to :: Rep MeanKahan x -> MeanKahan

Semigroup MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

(<>) :: MeanKahan -> MeanKahan -> MeanKahan

sconcat :: NonEmpty MeanKahan -> MeanKahan

stimes :: Integral b => b -> MeanKahan -> MeanKahan

Monoid MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

mempty :: MeanKahan

mappend :: MeanKahan -> MeanKahan -> MeanKahan

mconcat :: [MeanKahan] -> MeanKahan

Unbox MeanKahan

Defined in Data.Monoid.Statistics.Extra

CalcMean MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => MeanKahan -> m Double

CalcCount MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

calcCount :: MeanKahan -> Int

Vector Vector MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

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

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

basicLength :: Vector MeanKahan -> Int

basicUnsafeSlice :: Int -> Int -> Vector MeanKahan -> Vector MeanKahan

basicUnsafeIndexM :: Monad m => Vector MeanKahan -> Int -> m MeanKahan

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

elemseq :: Vector MeanKahan -> MeanKahan -> b -> b

MVector MVector MeanKahan

Defined in Data.Monoid.Statistics.Extra

Methods

basicLength :: MVector s MeanKahan -> Int

basicUnsafeSlice :: Int -> Int -> MVector s MeanKahan -> MVector s MeanKahan

basicOverlaps :: MVector s MeanKahan -> MVector s MeanKahan -> Bool

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

basicInitialize :: PrimMonad m => MVector (PrimState m) MeanKahan -> m ()

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

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

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

basicClear :: PrimMonad m => MVector (PrimState m) MeanKahan -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) MeanKahan -> MeanKahan -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) MeanKahan -> MVector (PrimState m) MeanKahan -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) MeanKahan -> MVector (PrimState m) MeanKahan -> m ()

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

Real a => StatMonoid MeanKahan a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: MeanKahan -> a -> MeanKahan

singletonMonoid :: a -> MeanKahan

type Rep MeanKahan

Defined in Data.Monoid.Statistics.Extra

type Rep MeanKahan = D1 ('MetaData "MeanKahan" "Data.Monoid.Statistics.Extra" "monoid-statistics-1.1.1-Et52IJUUy4YDKplMeouIOs" 'False) (C1 ('MetaCons "MeanKahan" 'PrefixI 'False) (S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 Int) :*: S1 ('MetaSel ('Nothing :: Maybe Symbol) 'NoSourceUnpackedness 'SourceStrict 'DecidedStrict) (Rec0 KahanSum)))

newtype Vector MeanKahan

Defined in Data.Monoid.Statistics.Extra

newtype Vector MeanKahan = V_MeanKahan (Vector (Int, Double, Double))

newtype MVector s MeanKahan

Defined in Data.Monoid.Statistics.Extra

newtype MVector s MeanKahan = MV_MeanKahan (MVector s (Int, Double, Double))

asMeanKahan :: MeanKahan -> MeanKahan

data MeanKB2

Incremental calculation of mean which uses second-order compensated Kahan-Babuška summation. In most cases KBNSum should provide enough precision.

Constructors

MeanKB2 !Int !KB2Sum

Instances

Eq MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

(==) :: MeanKB2 -> MeanKB2 -> Bool

(/=) :: MeanKB2 -> MeanKB2 -> Bool

Show MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

showsPrec :: Int -> MeanKB2 -> ShowS

show :: MeanKB2 -> String

showList :: [MeanKB2] -> ShowS

Semigroup MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

(<>) :: MeanKB2 -> MeanKB2 -> MeanKB2

sconcat :: NonEmpty MeanKB2 -> MeanKB2

stimes :: Integral b => b -> MeanKB2 -> MeanKB2

Monoid MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

mempty :: MeanKB2

mappend :: MeanKB2 -> MeanKB2 -> MeanKB2

mconcat :: [MeanKB2] -> MeanKB2

CalcMean MeanKB2

Defined in Data.Monoid.Statistics.Extra

Methods

calcMean :: MonadThrow m => MeanKB2 -> m Double

Real a => StatMonoid MeanKB2 a

Defined in Data.Monoid.Statistics.Extra

Methods

addValue :: MeanKB2 -> a -> MeanKB2

singletonMonoid :: a -> MeanKB2

asMeanKB2 :: MeanKB2 -> MeanKB2

• [Welford1962] Welford, B.P. (1962) Note on a method for calculating corrected sums of squares and products. Technometrics 4(3):419-420. http://www.jstor.org/stable/1266577