Numeric.Discretized

Discretized floating point numbers, where the scaling factor is kept as two phantom types denoting the rational number used for scaling.

Documentation

data RatioTy a

Some discretizations are of the type ln 2 / 2 (PAM matrices in Blast for example). Using this type, we can annotate as follows: Discretized (RTyLn 2 :% RTyId 2).

One may use Unknown if the scale is not known. For example, the blast matrices use different scales internally and one needs to read the header to get the scale.

Constructors

RTyExp a

RTyId a

RTyLn a

RTyPlus (RatioTy a) (RatioTy a)

RTyTimes (RatioTy a) (RatioTy a)

Unknown

Instances

KnownNat k => RatioTyConstant ('RTyExp k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyExp k) -> Ratio Integer

KnownNat k => RatioTyConstant ('RTyId k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyId k) -> Ratio Integer

KnownNat k => RatioTyConstant ('RTyLn k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyLn k) -> Ratio Integer

(RatioTyConstant a, RatioTyConstant b) => RatioTyConstant ('RTyTimes a b :: RatioTy k)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyTimes a b) -> Ratio Integer

(RatioTyConstant a, RatioTyConstant b) => RatioTyConstant ('RTyPlus a b :: RatioTy k)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyPlus a b) -> Ratio Integer

Num (Discretized ('Unknown :: RatioTy a))

Defined in Numeric.Discretized

Methods

(+) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

(-) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

(*) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

negate :: Discretized 'Unknown -> Discretized 'Unknown

abs :: Discretized 'Unknown -> Discretized 'Unknown

signum :: Discretized 'Unknown -> Discretized 'Unknown

fromInteger :: Integer -> Discretized 'Unknown

class RatioTyConstant a where

Methods

ratioTyConstant :: Proxy a -> Ratio Integer

Instances

KnownNat k => RatioTyConstant ('RTyExp k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyExp k) -> Ratio Integer

KnownNat k => RatioTyConstant ('RTyId k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyId k) -> Ratio Integer

KnownNat k => RatioTyConstant ('RTyLn k :: RatioTy Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyLn k) -> Ratio Integer

(KnownNat k, KnownNat l) => RatioTyConstant (k :% l :: Ratio Nat)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy (k :% l) -> Ratio Integer

(RatioTyConstant a, RatioTyConstant b) => RatioTyConstant ('RTyTimes a b :: RatioTy k)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyTimes a b) -> Ratio Integer

(RatioTyConstant a, RatioTyConstant b) => RatioTyConstant ('RTyPlus a b :: RatioTy k)

Defined in Numeric.Discretized

Methods

ratioTyConstant :: Proxy ('RTyPlus a b) -> Ratio Integer

newtype Discretized (b :: k)

A discretized value takes a floating point number n and produces a discretized value. The actual discretization formula is given on the type level, freeing us from having to carry around some scaling function.

Typically, one might use types likes 100, (100 :% 1), or (RTyLn 2 :% RTyId 2).

The main use of a Discretized value is to enable calculations with Int while somewhat pretending to use floating point values.

Be careful with certain operations like (*) as they will easily cause the numbers to arbitrarily wrong. (+) and (-) are fine, however.

NOTE Export and import of data is in the form of floating points, which can lead to additional loss of precision if one is careless!

TODO fast Show methods required!

TODO blaze stuff?

TODO We might want to discretize LogDomain style values. This requires some thought on in which direction to wrap. Maybe, we want to log-domain Discretized values, which probably just works.

Constructors

Discretized

Fields

• getDiscretized :: Int

Instances

Vector Vector (Discretized t)

Defined in Numeric.Discretized

Methods

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

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

basicLength :: Vector (Discretized t) -> Int

basicUnsafeSlice :: Int -> Int -> Vector (Discretized t) -> Vector (Discretized t)

basicUnsafeIndexM :: Monad m => Vector (Discretized t) -> Int -> m (Discretized t)

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

elemseq :: Vector (Discretized t) -> Discretized t -> b -> b

MVector MVector (Discretized t)

Defined in Numeric.Discretized

Methods

basicLength :: MVector s (Discretized t) -> Int

basicUnsafeSlice :: Int -> Int -> MVector s (Discretized t) -> MVector s (Discretized t)

basicOverlaps :: MVector s (Discretized t) -> MVector s (Discretized t) -> Bool

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

basicInitialize :: PrimMonad m => MVector (PrimState m) (Discretized t) -> m ()

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

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

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

basicClear :: PrimMonad m => MVector (PrimState m) (Discretized t) -> m ()

basicSet :: PrimMonad m => MVector (PrimState m) (Discretized t) -> Discretized t -> m ()

basicUnsafeCopy :: PrimMonad m => MVector (PrimState m) (Discretized t) -> MVector (PrimState m) (Discretized t) -> m ()

basicUnsafeMove :: PrimMonad m => MVector (PrimState m) (Discretized t) -> MVector (PrimState m) (Discretized t) -> m ()

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

Enum (Discretized b)

Defined in Numeric.Discretized

Methods

succ :: Discretized b -> Discretized b

pred :: Discretized b -> Discretized b

toEnum :: Int -> Discretized b

fromEnum :: Discretized b -> Int

enumFrom :: Discretized b -> [Discretized b]

enumFromThen :: Discretized b -> Discretized b -> [Discretized b]

enumFromTo :: Discretized b -> Discretized b -> [Discretized b]

enumFromThenTo :: Discretized b -> Discretized b -> Discretized b -> [Discretized b]

Eq (Discretized b)

Defined in Numeric.Discretized

Methods

(==) :: Discretized b -> Discretized b -> Bool

(/=) :: Discretized b -> Discretized b -> Bool

(KnownNat u, KnownNat l) => Fractional (Discretized (u :% l))

Defined in Numeric.Discretized

Methods

(/) :: Discretized (u :% l) -> Discretized (u :% l) -> Discretized (u :% l)

recip :: Discretized (u :% l) -> Discretized (u :% l)

fromRational :: Rational -> Discretized (u :% l)

(KnownNat u, KnownNat l) => Num (Discretized (u :% l))

Defined in Numeric.Discretized

Methods

(+) :: Discretized (u :% l) -> Discretized (u :% l) -> Discretized (u :% l)

(-) :: Discretized (u :% l) -> Discretized (u :% l) -> Discretized (u :% l)

(*) :: Discretized (u :% l) -> Discretized (u :% l) -> Discretized (u :% l)

negate :: Discretized (u :% l) -> Discretized (u :% l)

abs :: Discretized (u :% l) -> Discretized (u :% l)

signum :: Discretized (u :% l) -> Discretized (u :% l)

fromInteger :: Integer -> Discretized (u :% l)

Num (Discretized ('Unknown :: RatioTy a))

Defined in Numeric.Discretized

Methods

(+) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

(-) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

(*) :: Discretized 'Unknown -> Discretized 'Unknown -> Discretized 'Unknown

negate :: Discretized 'Unknown -> Discretized 'Unknown

abs :: Discretized 'Unknown -> Discretized 'Unknown

signum :: Discretized 'Unknown -> Discretized 'Unknown

fromInteger :: Integer -> Discretized 'Unknown

Ord (Discretized b)

Defined in Numeric.Discretized

Methods

compare :: Discretized b -> Discretized b -> Ordering

(<) :: Discretized b -> Discretized b -> Bool

(<=) :: Discretized b -> Discretized b -> Bool

(>) :: Discretized b -> Discretized b -> Bool

(>=) :: Discretized b -> Discretized b -> Bool

max :: Discretized b -> Discretized b -> Discretized b

min :: Discretized b -> Discretized b -> Discretized b

Read (Discretized b)

Defined in Numeric.Discretized

Methods

readsPrec :: Int -> ReadS (Discretized b)

readList :: ReadS [Discretized b]

readPrec :: ReadPrec (Discretized b)

readListPrec :: ReadPrec [Discretized b]

(KnownNat u, KnownNat l) => Real (Discretized (u :% l))

Defined in Numeric.Discretized

Methods

toRational :: Discretized (u :% l) -> Rational

Show (Discretized b)

Defined in Numeric.Discretized

Methods

showsPrec :: Int -> Discretized b -> ShowS

show :: Discretized b -> String

showList :: [Discretized b] -> ShowS

Generic (Discretized b)

Defined in Numeric.Discretized

Associated Types

type Rep (Discretized b) :: Type -> Type

Methods

from :: Discretized b -> Rep (Discretized b) x

to :: Rep (Discretized b) x -> Discretized b

Info (Discretized b)

Defined in Numeric.Discretized

Methods

info :: Discretized b -> String

Hashable (Discretized t)

Defined in Numeric.Discretized

Methods

hashWithSalt :: Int -> Discretized t -> Int

hash :: Discretized t -> Int

(KnownNat k, KnownNat l) => ToJSON (Discretized (k :% l))

Defined in Numeric.Discretized

Methods

toJSON :: Discretized (k :% l) -> Value

toEncoding :: Discretized (k :% l) -> Encoding

toJSONList :: [Discretized (k :% l)] -> Value

toEncodingList :: [Discretized (k :% l)] -> Encoding

(KnownNat k, KnownNat l) => FromJSON (Discretized (k :% l))

Defined in Numeric.Discretized

Methods

parseJSON :: Value -> Parser (Discretized (k :% l))

parseJSONList :: Value -> Parser [Discretized (k :% l)]

Binary (Discretized t)

Defined in Numeric.Discretized

Methods

put :: Discretized t -> Put

get :: Get (Discretized t)

putList :: [Discretized t] -> Put

Serialize (Discretized t)

Defined in Numeric.Discretized

Methods

put :: Putter (Discretized t)

get :: Get (Discretized t)

NFData (Discretized t)

Defined in Numeric.Discretized

Methods

rnf :: Discretized t -> ()

Unbox (Discretized t)

Defined in Numeric.Discretized

Num (Discretized k2) => Semiring (Discretized k2)

Defined in Numeric.Discretized

Methods

plus :: Discretized k2 -> Discretized k2 -> Discretized k2

zero :: Discretized k2

times :: Discretized k2 -> Discretized k2 -> Discretized k2

one :: Discretized k2

fromNatural :: Natural -> Discretized k2

NumericLimits (Discretized t)

Defined in Numeric.Discretized

Methods

minFinite :: Discretized t

maxFinite :: Discretized t

newtype MVector s (Discretized t)

Defined in Numeric.Discretized

newtype MVector s (Discretized t) = MV_Discretized (MVector s Int)

type Rep (Discretized b)

Defined in Numeric.Discretized

type Rep (Discretized b) = D1 ('MetaData "Discretized" "Numeric.Discretized" "SciBaseTypes-0.1.1.0-3Dyd7liFoDd1V6ph3ZjwIR" 'True) (C1 ('MetaCons "Discretized" 'PrefixI 'True) (S1 ('MetaSel ('Just "getDiscretized") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 Int)))

newtype Vector (Discretized t)

Defined in Numeric.Discretized

newtype Vector (Discretized t) = V_Discretized (Vector Int)

fromUnknown :: Discretized Unknown -> Discretized t

discretizeRatio :: forall a u l. (Real a, KnownNat u, KnownNat l) => a -> Discretized ((u :: Nat) :% (l :: Nat))

Discretizes any Real a into the Discretized value. This conversion is lossy and uses a type-level rational of u :% l!