Number.Physical.UnitDatabase

Tools for creating a data base of physical units and for extracting data from it

Documentation

type T i a = [UnitSet i a]

data InitUnitSet i a

Constructors

InitUnitSet

Fields

• initUnit :: T i
• initIndependent :: Bool
• initScales :: [InitScale a]

data InitScale a

Constructors

InitScale

Fields

• initSymbol :: String
• initMag :: a
• initIsUnit :: Bool
• initDefault :: Bool

data UnitSet i a

An entry for a unit and there scalings.

Constructors

UnitSet

Fields

• unit :: T i
• independent :: Bool
• defScaleIx :: Int
• reciprocal :: Bool

  If True the symbols must be preceded with a /. Though it sounds like an attribute of Scale it must be the same for all scales and we need it to sort positive powered unitsets to the front of the list of unit components.

• scales :: [Scale a]

Instances

(Show a, Show i) => Show (UnitSet i a)

Methods

showsPrec :: Int -> UnitSet i a -> ShowS

show :: UnitSet i a -> String

showList :: [UnitSet i a] -> ShowS

data Scale a

A common scaling for a unit.

Constructors

Scale

Fields

• symbol :: String
• magnitude :: a

Instances

Show a => Show (Scale a)

Methods

showsPrec :: Int -> Scale a -> ShowS

show :: Scale a -> String

showList :: [Scale a] -> ShowS

extractOne :: [a] -> a

initScale :: String -> a -> Bool -> Bool -> InitScale a

initUnitSet :: T i -> Bool -> [InitScale a] -> InitUnitSet i a

createScale :: InitScale a -> Scale a

createUnitSet :: InitUnitSet i a -> UnitSet i a

showableUnit :: InitUnitSet i a -> Maybe (InitUnitSet i a)

powerOfUnitSet :: (Ord i, C a) => Int -> UnitSet i a -> UnitSet i a

Raise all scales of a unit and the unit itself to the n-th power

powerOfScale :: C a => Int -> Scale a -> Scale a

showExp :: Int -> String

positiveToFront :: [UnitSet i a] -> [UnitSet i a]

Reorder the unit components in a way that the units with positive exponents lead the list.

decompose :: (Ord i, C a) => T i -> T i a -> [UnitSet i a]

Decompose a complex unit into common ones

findIndep :: Eq i => T i -> T i a -> Maybe (UnitSet i a)

findClosest :: (Ord i, C a) => T i -> T i a -> UnitSet i a

evalDist

Arguments

:: (Ord i, C a)

=> T i

-> T i a

-> [(UnitSet i a, Int)]

(UnitSet,distance) the UnitSet may contain powered units

findBestExp :: Ord i => T i -> T i -> (Int, Int)

findMinExp :: [(Int, Int)] -> (Int, Int)

Find the exponent that lead to minimal distance Since the list is infinite maximum will fail but the sequence is convex and thus we can abort when the distance stop falling

distLE :: (Int, Int) -> (Int, Int) -> Bool

distances :: Ord i => T i -> [(Int, T i)] -> [(Int, Int)]

listMultiples :: (T i -> T i) -> Int -> [(Int, T i)]