Safe Haskell	None
Language	GHC2021

NumHask.Algebra.Metric

Description

Metric classes

Synopsis

class Distributive (Mag a) => Basis a where
- type Mag a
- type Base a
- magnitude :: a -> Mag a
- basis :: a -> Base a
type Absolute a = (Basis a, Mag a ~ a)
type Sign a = (Basis a, Base a ~ a)
type EndoBased a = (Basis a, Mag a ~ a, Base a ~ a)
abs :: Absolute a => a -> a
signum :: Sign a => a -> a
distance :: (Basis a, Subtractive a) => a -> a -> Mag a
class (Distributive coord, Distributive (Dir coord)) => Direction coord where
- type Dir coord
- angle :: coord -> Dir coord
- ray :: Dir coord -> coord
data Polar a = Polar {
- radial :: a
- azimuth :: a
}
polar :: (Dir (Base a) ~ Mag a, Basis a, Direction (Base a)) => a -> Polar (Mag a)
coord :: (Scalar m ~ Dir m, MultiplicativeAction m, Direction m) => Polar (Scalar m) -> m
class (Eq a, Additive a) => Epsilon a where
- epsilon :: a
nearZero :: (Epsilon a, Lattice a, Subtractive a) => a -> Bool
aboutEqual :: (Epsilon a, Lattice a, Subtractive a) => a -> a -> Bool
(~=) :: (Epsilon a, Lattice a, Subtractive a) => a -> a -> Bool
newtype EuclideanPair a = EuclideanPair {
- euclidPair :: (a, a)
}

Documentation

class Distributive (Mag a) => Basis a where Source #

Basis encapsulates the notion of magnitude (intuitively the quotienting of a higher-kinded number to a scalar one) and the basis on which the magnitude quotienting was performed. An instance needs to satisfy these laws:

\a -> magnitude a >= zero
\a -> magnitude zero == zero
\a -> a == magnitude a *| basis a
\a -> magnitude (basis a) == one

The names chosen are meant to represent the spiritual idea of a basis rather than a specific mathematics. See https://en.wikipedia.org/wiki/Basis_(linear_algebra) & https://en.wikipedia.org/wiki/Norm_(mathematics) for some mathematical motivations.

>>> magnitude (-0.5 :: Double)
0.5

>>> basis (-0.5 :: Double)
-1.0

Since: 0.11

Associated Types

type Mag a Source #

type Base a Source #

Methods

magnitude :: a -> Mag a Source #

or length, or ||v||

basis :: a -> Base a Source #

or direction, or v-hat

Instances

Instances details

Basis Int16 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int16
Instance details Defined in NumHask.Algebra.Metric type Mag Int16 = Int16
type Base Int16
Instance details Defined in NumHask.Algebra.Metric type Base Int16 = Int16

Methods

magnitude :: Int16 -> Mag Int16 Source #

basis :: Int16 -> Base Int16 Source #

Basis Int32 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int32
Instance details Defined in NumHask.Algebra.Metric type Mag Int32 = Int32
type Base Int32
Instance details Defined in NumHask.Algebra.Metric type Base Int32 = Int32

Methods

magnitude :: Int32 -> Mag Int32 Source #

basis :: Int32 -> Base Int32 Source #

Basis Int64 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int64
Instance details Defined in NumHask.Algebra.Metric type Mag Int64 = Int64
type Base Int64
Instance details Defined in NumHask.Algebra.Metric type Base Int64 = Int64

Methods

magnitude :: Int64 -> Mag Int64 Source #

basis :: Int64 -> Base Int64 Source #

Basis Int8 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int8
Instance details Defined in NumHask.Algebra.Metric type Mag Int8 = Int8
type Base Int8
Instance details Defined in NumHask.Algebra.Metric type Base Int8 = Int8

Methods

magnitude :: Int8 -> Mag Int8 Source #

basis :: Int8 -> Base Int8 Source #

Basis Word16 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word16
Instance details Defined in NumHask.Algebra.Metric type Mag Word16 = Word16
type Base Word16
Instance details Defined in NumHask.Algebra.Metric type Base Word16 = Word16

Methods

magnitude :: Word16 -> Mag Word16 Source #

basis :: Word16 -> Base Word16 Source #

Basis Word32 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word32
Instance details Defined in NumHask.Algebra.Metric type Mag Word32 = Word32
type Base Word32
Instance details Defined in NumHask.Algebra.Metric type Base Word32 = Word32

Methods

magnitude :: Word32 -> Mag Word32 Source #

basis :: Word32 -> Base Word32 Source #

Basis Word64 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word64
Instance details Defined in NumHask.Algebra.Metric type Mag Word64 = Word64
type Base Word64
Instance details Defined in NumHask.Algebra.Metric type Base Word64 = Word64

Methods

magnitude :: Word64 -> Mag Word64 Source #

basis :: Word64 -> Base Word64 Source #

Basis Word8 Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word8
Instance details Defined in NumHask.Algebra.Metric type Mag Word8 = Word8
type Base Word8
Instance details Defined in NumHask.Algebra.Metric type Base Word8 = Word8

Methods

magnitude :: Word8 -> Mag Word8 Source #

basis :: Word8 -> Base Word8 Source #

Basis Integer Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Integer
Instance details Defined in NumHask.Algebra.Metric type Mag Integer = Integer
type Base Integer
Instance details Defined in NumHask.Algebra.Metric type Base Integer = Integer

Methods

magnitude :: Integer -> Mag Integer Source #

basis :: Integer -> Base Integer Source #

Basis Natural Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Natural
Instance details Defined in NumHask.Algebra.Metric type Mag Natural = Natural
type Base Natural
Instance details Defined in NumHask.Algebra.Metric type Base Natural = Natural

Methods

magnitude :: Natural -> Mag Natural Source #

basis :: Natural -> Base Natural Source #

Basis Double Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Double
Instance details Defined in NumHask.Algebra.Metric type Mag Double = Double
type Base Double
Instance details Defined in NumHask.Algebra.Metric type Base Double = Double

Methods

magnitude :: Double -> Mag Double Source #

basis :: Double -> Base Double Source #

Basis Float Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Float
Instance details Defined in NumHask.Algebra.Metric type Mag Float = Float
type Base Float
Instance details Defined in NumHask.Algebra.Metric type Base Float = Float

Methods

magnitude :: Float -> Mag Float Source #

basis :: Float -> Base Float Source #

Basis Int Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Int
Instance details Defined in NumHask.Algebra.Metric type Mag Int = Int
type Base Int
Instance details Defined in NumHask.Algebra.Metric type Base Int = Int

Methods

magnitude :: Int -> Mag Int Source #

basis :: Int -> Base Int Source #

Basis Word Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag Word
Instance details Defined in NumHask.Algebra.Metric type Mag Word = Word
type Base Word
Instance details Defined in NumHask.Algebra.Metric type Base Word = Word

Methods

magnitude :: Word -> Mag Word Source #

basis :: Word -> Base Word Source #

(ExpField a, Eq a) => Basis (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Mag (EuclideanPair a) = a
type Base (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Base (EuclideanPair a) = EuclideanPair a

Methods

magnitude :: EuclideanPair a -> Mag (EuclideanPair a) Source #

basis :: EuclideanPair a -> Base (EuclideanPair a) Source #

(Additive a, Multiplicative a) => Basis (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Mag (Polar a) = a
type Base (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Base (Polar a) = a

Methods

magnitude :: Polar a -> Mag (Polar a) Source #

basis :: Polar a -> Base (Polar a) Source #

(ExpField a, Eq a) => Basis (Complex a) Source #

Instance details

Defined in NumHask.Data.Complex

Associated Types

type Mag (Complex a)
Instance details Defined in NumHask.Data.Complex type Mag (Complex a) = Mag (EuclideanPair a)
type Base (Complex a)
Instance details Defined in NumHask.Data.Complex type Base (Complex a) = Base (EuclideanPair a)

Methods

magnitude :: Complex a -> Mag (Complex a) Source #

basis :: Complex a -> Base (Complex a) Source #

Basis a => Basis (Positive a) Source #

Instance details

Defined in NumHask.Data.Positive

Associated Types

type Mag (Positive a)
Instance details Defined in NumHask.Data.Positive type Mag (Positive a) = Mag (Wrapped a)
type Base (Positive a)
Instance details Defined in NumHask.Data.Positive type Base (Positive a) = Base (Wrapped a)

Methods

magnitude :: Positive a -> Mag (Positive a) Source #

basis :: Positive a -> Base (Positive a) Source #

(Ord a, EndoBased a, Integral a, Ring a) => Basis (Ratio a) Source #

Instance details

Defined in NumHask.Data.Rational

Associated Types

type Mag (Ratio a)
Instance details Defined in NumHask.Data.Rational type Mag (Ratio a) = Ratio a
type Base (Ratio a)
Instance details Defined in NumHask.Data.Rational type Base (Ratio a) = Ratio a

Methods

magnitude :: Ratio a -> Mag (Ratio a) Source #

basis :: Ratio a -> Base (Ratio a) Source #

Basis a => Basis (Wrapped a) Source #

Instance details

Defined in NumHask.Data.Wrapped

Associated Types

type Mag (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Mag (Wrapped a) = Mag a
type Base (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Base (Wrapped a) = Base a

Methods

magnitude :: Wrapped a -> Mag (Wrapped a) Source #

basis :: Wrapped a -> Base (Wrapped a) Source #

type Absolute a = (Basis a, Mag a ~ a) Source #

Basis where the domain and magnitude codomain are the same.

Since: 0.11

type Sign a = (Basis a, Base a ~ a) Source #

Basis where the domain and basis codomain are the same.

Since: 0.11

type EndoBased a = (Basis a, Mag a ~ a, Base a ~ a) Source #

Basis where the domain, magnitude codomain and basis codomain are the same.

Since: 0.11

abs :: Absolute a => a -> a Source #

The absolute value of a number.

\a -> abs a * signum a ~= a

>>> abs (-1)
1

signum :: Sign a => a -> a Source #

The sign of a number.

>>> signum (-1)
-1

abs zero == zero, so any value for signum zero is ok. We choose lawful neutral:

>>> signum zero == zero
True

Since: 0.11

distance :: (Basis a, Subtractive a) => a -> a -> Mag a Source #

Distance, which combines the Subtractive notion of difference, with Basis.

distance a b >= zero
distance a a == zero
distance a b *| basis (a - b) == a - b

class (Distributive coord, Distributive (Dir coord)) => Direction coord where Source #

Convert between a "co-ordinated" or "higher-kinded" number and a direction.

ray . angle == basis
magnitude (ray x) == one

Since: 0.7

Associated Types

type Dir coord Source #

Methods

angle :: coord -> Dir coord Source #

ray :: Dir coord -> coord Source #

Instances

Instances details

TrigField a => Direction (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Dir (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Dir (EuclideanPair a) = a

Methods

angle :: EuclideanPair a -> Dir (EuclideanPair a) Source #

ray :: Dir (EuclideanPair a) -> EuclideanPair a Source #

TrigField a => Direction (Complex a) Source #

Instance details

Defined in NumHask.Data.Complex

Associated Types

type Dir (Complex a)
Instance details Defined in NumHask.Data.Complex type Dir (Complex a) = Dir (EuclideanPair a)

Methods

angle :: Complex a -> Dir (Complex a) Source #

ray :: Dir (Complex a) -> Complex a Source #

Direction a => Direction (Positive a) Source #

Instance details

Defined in NumHask.Data.Positive

Associated Types

type Dir (Positive a)
Instance details Defined in NumHask.Data.Positive type Dir (Positive a) = Dir (Wrapped a)

Methods

angle :: Positive a -> Dir (Positive a) Source #

ray :: Dir (Positive a) -> Positive a Source #

Direction a => Direction (Wrapped a) Source #

Instance details

Defined in NumHask.Data.Wrapped

Associated Types

type Dir (Wrapped a)
Instance details Defined in NumHask.Data.Wrapped type Dir (Wrapped a) = Dir a

Methods

angle :: Wrapped a -> Dir (Wrapped a) Source #

ray :: Dir (Wrapped a) -> Wrapped a Source #

data Polar a Source #

Something that has a magnitude and a direction, with both expressed as the same type.

See Polar coordinate system

Since: 0.7

Constructors

Polar
Fields radial :: a azimuth :: a

Instances

Instances details

Data a => Data (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

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

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

toConstr :: Polar a -> Constr #

dataTypeOf :: Polar a -> DataType #

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

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

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

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

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

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

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

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

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

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

Generic (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Rep (Polar a)

Instance details

Defined in NumHask.Algebra.Metric

type Rep (Polar a) = D1 ('MetaData "Polar" "NumHask.Algebra.Metric" "numhask-0.13.1.0-4JL3km17UUX2ZsRg2smvA0" 'False) (C1 ('MetaCons "Polar" 'PrefixI 'True) (S1 ('MetaSel ('Just "radial") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "azimuth") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Methods

from :: Polar a -> Rep (Polar a) x #

to :: Rep (Polar a) x -> Polar a #

Show a => Show (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

showsPrec :: Int -> Polar a -> ShowS #

show :: Polar a -> String #

showList :: [Polar a] -> ShowS #

Eq a => Eq (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(==) :: Polar a -> Polar a -> Bool #

(/=) :: Polar a -> Polar a -> Bool #

(Additive a, Multiplicative a) => Basis (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Mag (Polar a) = a
type Base (Polar a)
Instance details Defined in NumHask.Algebra.Metric type Base (Polar a) = a

Methods

magnitude :: Polar a -> Mag (Polar a) Source #

basis :: Polar a -> Base (Polar a) Source #

type Rep (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

type Rep (Polar a) = D1 ('MetaData "Polar" "NumHask.Algebra.Metric" "numhask-0.13.1.0-4JL3km17UUX2ZsRg2smvA0" 'False) (C1 ('MetaCons "Polar" 'PrefixI 'True) (S1 ('MetaSel ('Just "radial") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a) :*: S1 ('MetaSel ('Just "azimuth") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

type Base (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

type Base (Polar a) = a

type Mag (Polar a) Source #

Instance details

Defined in NumHask.Algebra.Metric

type Mag (Polar a) = a

polar :: (Dir (Base a) ~ Mag a, Basis a, Direction (Base a)) => a -> Polar (Mag a) Source #

Convert a higher-kinded number that has direction, to a Polar

Since: 0.7

coord :: (Scalar m ~ Dir m, MultiplicativeAction m, Direction m) => Polar (Scalar m) -> m Source #

Convert a Polar to a (higher-kinded) number that has a direction.

Since: 0.7

class (Eq a, Additive a) => Epsilon a where Source #

A small number, especially useful for approximate equality.

Minimal complete definition

Nothing

Methods

epsilon :: a Source #

Instances

Instances details

Epsilon Int16 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Int16 Source #
Epsilon Int32 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Int32 Source #
Epsilon Int64 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Int64 Source #
Epsilon Int8 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Int8 Source #
Epsilon Word16 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Word16 Source #
Epsilon Word32 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Word32 Source #
Epsilon Word64 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Word64 Source #
Epsilon Word8 Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Word8 Source #
Epsilon Integer Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Integer Source #
Epsilon Double Source #	1e-14
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Double Source #
Epsilon Float Source #	1e-6
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Float Source #
Epsilon Int Source #	0
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Int Source #
Epsilon Word Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: Word Source #
Epsilon a => Epsilon (EuclideanPair a) Source #
Instance details Defined in NumHask.Algebra.Metric Methods epsilon :: EuclideanPair a Source #
Epsilon a => Epsilon (Complex a) Source #
Instance details Defined in NumHask.Data.Complex Methods epsilon :: Complex a Source #
Epsilon a => Epsilon (Positive a) Source #
Instance details Defined in NumHask.Data.Positive Methods epsilon :: Positive a Source #
(Ord a, EndoBased a, Integral a, Ring a, MeetSemiLattice a) => Epsilon (Ratio a) Source #
Instance details Defined in NumHask.Data.Rational Methods epsilon :: Ratio a Source #
Epsilon a => Epsilon (Wrapped a) Source #
Instance details Defined in NumHask.Data.Wrapped Methods epsilon :: Wrapped a Source #

nearZero :: (Epsilon a, Lattice a, Subtractive a) => a -> Bool Source #

Note that the constraint is Lattice rather than Ord allowing broader usage.

>>> nearZero (epsilon :: Double)
True

>>> nearZero (epsilon :: EuclideanPair Double)
True

aboutEqual :: (Epsilon a, Lattice a, Subtractive a) => a -> a -> Bool Source #

Approximate equality

>>> aboutEqual zero (epsilon :: Double)
True

(~=) :: (Epsilon a, Lattice a, Subtractive a) => a -> a -> Bool infixl 4 Source #

About equal operator.

>>> (1.0 + epsilon) ~= (1.0 :: Double)
True

newtype EuclideanPair a Source #

Two dimensional cartesian coordinates.

Since: 0.11

Constructors

EuclideanPair
Fields euclidPair :: (a, a)

Instances

Instances details

Applicative EuclideanPair Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

pure :: a -> EuclideanPair a #

(<*>) :: EuclideanPair (a -> b) -> EuclideanPair a -> EuclideanPair b #

liftA2 :: (a -> b -> c) -> EuclideanPair a -> EuclideanPair b -> EuclideanPair c #

(*>) :: EuclideanPair a -> EuclideanPair b -> EuclideanPair b #

(<*) :: EuclideanPair a -> EuclideanPair b -> EuclideanPair a #

Functor EuclideanPair Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

fmap :: (a -> b) -> EuclideanPair a -> EuclideanPair b #

(<$) :: a -> EuclideanPair b -> EuclideanPair a #

Data a => Data (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

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

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

toConstr :: EuclideanPair a -> Constr #

dataTypeOf :: EuclideanPair a -> DataType #

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

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

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

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

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

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

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

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

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

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

Generic (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Rep (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Rep (EuclideanPair a) = D1 ('MetaData "EuclideanPair" "NumHask.Algebra.Metric" "numhask-0.13.1.0-4JL3km17UUX2ZsRg2smvA0" 'True) (C1 ('MetaCons "EuclideanPair" 'PrefixI 'True) (S1 ('MetaSel ('Just "euclidPair") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (a, a))))

Methods

from :: EuclideanPair a -> Rep (EuclideanPair a) x #

to :: Rep (EuclideanPair a) x -> EuclideanPair a #

Show a => Show (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

showsPrec :: Int -> EuclideanPair a -> ShowS #

show :: EuclideanPair a -> String #

showList :: [EuclideanPair a] -> ShowS #

Eq a => Eq (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(==) :: EuclideanPair a -> EuclideanPair a -> Bool #

(/=) :: EuclideanPair a -> EuclideanPair a -> Bool #

Divisive a => DivisiveAction (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(|/) :: EuclideanPair a -> Scalar (EuclideanPair a) -> EuclideanPair a Source #

Multiplicative a => MultiplicativeAction (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Scalar (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Scalar (EuclideanPair a) = a

Methods

(|*) :: EuclideanPair a -> Scalar (EuclideanPair a) -> EuclideanPair a Source #

Additive a => Additive (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(+) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

zero :: EuclideanPair a Source #

Subtractive a => Subtractive (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

negate :: EuclideanPair a -> EuclideanPair a Source #

(-) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

(Ord a, TrigField a, ExpField a) => ExpField (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

exp :: EuclideanPair a -> EuclideanPair a Source #

log :: EuclideanPair a -> EuclideanPair a Source #

(**) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

logBase :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

sqrt :: EuclideanPair a -> EuclideanPair a Source #

(QuotientField a, Subtractive a) => QuotientField (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Whole (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Whole (EuclideanPair a) = EuclideanPair (Whole a)

Methods

properFraction :: EuclideanPair a -> (Whole (EuclideanPair a), EuclideanPair a) Source #

round :: EuclideanPair a -> Whole (EuclideanPair a) Source #

ceiling :: EuclideanPair a -> Whole (EuclideanPair a) Source #

floor :: EuclideanPair a -> Whole (EuclideanPair a) Source #

truncate :: EuclideanPair a -> Whole (EuclideanPair a) Source #

JoinSemiLattice a => JoinSemiLattice (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(\/) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

LowerBounded a => LowerBounded (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

bottom :: EuclideanPair a Source #

MeetSemiLattice a => MeetSemiLattice (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

(/\) :: EuclideanPair a -> EuclideanPair a -> EuclideanPair a Source #

UpperBounded a => UpperBounded (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Methods

top :: EuclideanPair a Source #

(ExpField a, Eq a) => Basis (EuclideanPair a) Source #

Instance details

Defined in NumHask.Algebra.Metric

Associated Types

type Mag (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Mag (EuclideanPair a) = a
type Base (EuclideanPair a)
Instance details Defined in NumHask.Algebra.Metric type Base (EuclideanPair a) = EuclideanPair a