Data.Monoid.Additive

Documentation

class AdditiveMonoid h where

Minimal complete definition

Nothing

Methods

zeroHV :: h

default zeroHV :: (Generic h, AdditiveMonoid (AMRep h)) => h

addHVs :: h -> h -> h

default addHVs :: (Generic h, AdditiveMonoid (AMRep h)) => h -> h -> h

Instances

AdditiveMonoid Int16

Defined in Data.Monoid.Additive

Methods

zeroHV :: Int16

addHVs :: Int16 -> Int16 -> Int16

AdditiveMonoid Int32

Defined in Data.Monoid.Additive

Methods

zeroHV :: Int32

addHVs :: Int32 -> Int32 -> Int32

AdditiveMonoid Int64

Defined in Data.Monoid.Additive

Methods

zeroHV :: Int64

addHVs :: Int64 -> Int64 -> Int64

AdditiveMonoid Int8

Defined in Data.Monoid.Additive

Methods

zeroHV :: Int8

addHVs :: Int8 -> Int8 -> Int8

AdditiveMonoid Word16

Defined in Data.Monoid.Additive

Methods

zeroHV :: Word16

addHVs :: Word16 -> Word16 -> Word16

AdditiveMonoid Word32

Defined in Data.Monoid.Additive

Methods

zeroHV :: Word32

addHVs :: Word32 -> Word32 -> Word32

AdditiveMonoid Word64

Defined in Data.Monoid.Additive

Methods

zeroHV :: Word64

addHVs :: Word64 -> Word64 -> Word64

AdditiveMonoid Word8

Defined in Data.Monoid.Additive

Methods

zeroHV :: Word8

addHVs :: Word8 -> Word8 -> Word8

AdditiveMonoid Integer

Defined in Data.Monoid.Additive

Methods

zeroHV :: Integer

addHVs :: Integer -> Integer -> Integer

AdditiveMonoid Double

Defined in Data.Monoid.Additive

Methods

zeroHV :: Double

addHVs :: Double -> Double -> Double

AdditiveMonoid Float

Defined in Data.Monoid.Additive

Methods

zeroHV :: Float

addHVs :: Float -> Float -> Float

AdditiveMonoid Int

Defined in Data.Monoid.Additive

Methods

zeroHV :: Int

addHVs :: Int -> Int -> Int

AdditiveMonoid Word

Defined in Data.Monoid.Additive

Methods

zeroHV :: Word

addHVs :: Word -> Word -> Word

Num k => AdditiveMonoid (Cℝay (ZeroDim k))

Defined in Data.Monoid.Additive

Methods

zeroHV :: Cℝay (ZeroDim k)

addHVs :: Cℝay (ZeroDim k) -> Cℝay (ZeroDim k) -> Cℝay (ZeroDim k)

AdditiveGroup (Needle (Rep a Void)) => AdditiveMonoid (GenericNeedle a)

Defined in Data.Monoid.Additive

Methods

zeroHV :: GenericNeedle a

addHVs :: GenericNeedle a -> GenericNeedle a -> GenericNeedle a

AdditiveMonoid (ZeroDim k)

Defined in Data.Monoid.Additive

Methods

zeroHV :: ZeroDim k

addHVs :: ZeroDim k -> ZeroDim k -> ZeroDim k

(AdditiveMonoid h, AdditiveMonoid i) => AdditiveMonoid (h, i)

Defined in Data.Monoid.Additive

Methods

zeroHV :: (h, i)

addHVs :: (h, i) -> (h, i) -> (h, i)

AdditiveMonoid h => AdditiveMonoid (Rec0 h s)

Defined in Data.Monoid.Additive

Methods

zeroHV :: Rec0 h s

addHVs :: Rec0 h s -> Rec0 h s -> Rec0 h s

(AdditiveMonoid h, AdditiveMonoid i, AdditiveMonoid j) => AdditiveMonoid (h, i, j)

Defined in Data.Monoid.Additive

Methods

zeroHV :: (h, i, j)

addHVs :: (h, i, j) -> (h, i, j) -> (h, i, j)

(AdditiveMonoid (f p), AdditiveMonoid (g p)) => AdditiveMonoid ((f :*: g) p)

Defined in Data.Monoid.Additive

Methods

zeroHV :: (f :*: g) p

addHVs :: (f :*: g) p -> (f :*: g) p -> (f :*: g) p

AdditiveMonoid (f p) => AdditiveMonoid (M1 i c f p)

Defined in Data.Monoid.Additive

Methods

zeroHV :: M1 i c f p

addHVs :: M1 i c f p -> M1 i c f p -> M1 i c f p

class AdditiveMonoid h => HalfSpace h where

Minimal complete definition

Nothing

Associated Types

type FullSubspace h :: Type

type FullSubspace h = GenericFullSubspace h

type Ray h :: Type

type Ray h = Ray (AMRep h)

type MirrorJoin h :: Type

type MirrorJoin h = GenericMirrorJoin h

Methods

scaleNonNeg :: Ray h -> h -> h

default scaleNonNeg :: (Generic h, HalfSpace (AMRep h), FullSubspace h ~ GenericFullSubspace h, Ray h ~ Ray (AMRep h)) => Ray h -> h -> h

fromFullSubspace :: FullSubspace h -> h

default fromFullSubspace :: (Generic h, HalfSpace (AMRep h), FullSubspace h ~ GenericFullSubspace h, Ray h ~ Ray (AMRep h)) => FullSubspace h -> h

projectToFullSubspace :: h -> FullSubspace h

default projectToFullSubspace :: (Generic h, HalfSpace (AMRep h), FullSubspace h ~ GenericFullSubspace h, Ray h ~ Ray (AMRep h)) => h -> FullSubspace h

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace h), ScalarSpace (Scalar (FullSubspace h)), Scalar (FullSubspace h) ~ MirrorJoin (Ray h)) => r) -> r

default fullSubspaceIsVectorSpace :: (VectorSpace (FullSubspace h), ScalarSpace (Scalar (FullSubspace h)), Scalar (FullSubspace h) ~ MirrorJoin (Ray h)) => ((VectorSpace (FullSubspace h), ScalarSpace (Scalar (FullSubspace h)), Scalar (FullSubspace h) ~ MirrorJoin (Ray h)) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray h) => r) -> r

default rayIsHalfSpace :: HalfSpace (Ray h) => (HalfSpace (Ray h) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin h), Scalar (MirrorJoin h) ~ MirrorJoin (Ray h)) => r) -> r

default mirrorJoinIsVectorSpace :: (VectorSpace (MirrorJoin h), Scalar (MirrorJoin h) ~ MirrorJoin (Ray h)) => ((VectorSpace (MirrorJoin h), Scalar (MirrorJoin h) ~ MirrorJoin (Ray h)) => r) -> r

fromPositiveHalf :: h -> MirrorJoin h

default fromPositiveHalf :: (Generic h, HalfSpace (AMRep h), MirrorJoin h ~ GenericMirrorJoin h, Ray h ~ Ray (AMRep h)) => h -> MirrorJoin h

fromNegativeHalf :: h -> MirrorJoin h

default fromNegativeHalf :: (Generic h, HalfSpace (AMRep h), MirrorJoin h ~ GenericMirrorJoin h, Ray h ~ Ray (AMRep h)) => h -> MirrorJoin h

Instances

(Num k, VectorSpace k, Scalar k ~ k) => HalfSpace (Cℝay (ZeroDim k))

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace (Cℝay (ZeroDim k))

type Ray (Cℝay (ZeroDim k))

type MirrorJoin (Cℝay (ZeroDim k))

Methods

scaleNonNeg :: Ray (Cℝay (ZeroDim k)) -> Cℝay (ZeroDim k) -> Cℝay (ZeroDim k)

fromFullSubspace :: FullSubspace (Cℝay (ZeroDim k)) -> Cℝay (ZeroDim k)

projectToFullSubspace :: Cℝay (ZeroDim k) -> FullSubspace (Cℝay (ZeroDim k))

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (Cℝay (ZeroDim k))), ScalarSpace (Scalar (FullSubspace (Cℝay (ZeroDim k)))), Scalar (FullSubspace (Cℝay (ZeroDim k))) ~ MirrorJoin (Ray (Cℝay (ZeroDim k)))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray (Cℝay (ZeroDim k))) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (Cℝay (ZeroDim k))), Scalar (MirrorJoin (Cℝay (ZeroDim k))) ~ MirrorJoin (Ray (Cℝay (ZeroDim k)))) => r) -> r

fromPositiveHalf :: Cℝay (ZeroDim k) -> MirrorJoin (Cℝay (ZeroDim k))

fromNegativeHalf :: Cℝay (ZeroDim k) -> MirrorJoin (Cℝay (ZeroDim k))

ScalarSpace k => HalfSpace (ZeroDim k)

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace (ZeroDim k)

type Ray (ZeroDim k)

type MirrorJoin (ZeroDim k)

Methods

scaleNonNeg :: Ray (ZeroDim k) -> ZeroDim k -> ZeroDim k

fromFullSubspace :: FullSubspace (ZeroDim k) -> ZeroDim k

projectToFullSubspace :: ZeroDim k -> FullSubspace (ZeroDim k)

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (ZeroDim k)), ScalarSpace (Scalar (FullSubspace (ZeroDim k))), Scalar (FullSubspace (ZeroDim k)) ~ MirrorJoin (Ray (ZeroDim k))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray (ZeroDim k)) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (ZeroDim k)), Scalar (MirrorJoin (ZeroDim k)) ~ MirrorJoin (Ray (ZeroDim k))) => r) -> r

fromPositiveHalf :: ZeroDim k -> MirrorJoin (ZeroDim k)

fromNegativeHalf :: ZeroDim k -> MirrorJoin (ZeroDim k)

(HalfSpace x, VectorSpace y, AdditiveMonoid y, Ray x ~ Cℝay (ZeroDim (Scalar y))) => HalfSpace (x, y)

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace (x, y)

type Ray (x, y)

type MirrorJoin (x, y)

Methods

scaleNonNeg :: Ray (x, y) -> (x, y) -> (x, y)

fromFullSubspace :: FullSubspace (x, y) -> (x, y)

projectToFullSubspace :: (x, y) -> FullSubspace (x, y)

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (x, y)), ScalarSpace (Scalar (FullSubspace (x, y))), Scalar (FullSubspace (x, y)) ~ MirrorJoin (Ray (x, y))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray (x, y)) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (x, y)), Scalar (MirrorJoin (x, y)) ~ MirrorJoin (Ray (x, y))) => r) -> r

fromPositiveHalf :: (x, y) -> MirrorJoin (x, y)

fromNegativeHalf :: (x, y) -> MirrorJoin (x, y)

HalfSpace h => HalfSpace (Rec0 h s)

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace (Rec0 h s)

type Ray (Rec0 h s)

type MirrorJoin (Rec0 h s)

Methods

scaleNonNeg :: Ray (Rec0 h s) -> Rec0 h s -> Rec0 h s

fromFullSubspace :: FullSubspace (Rec0 h s) -> Rec0 h s

projectToFullSubspace :: Rec0 h s -> FullSubspace (Rec0 h s)

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (Rec0 h s)), ScalarSpace (Scalar (FullSubspace (Rec0 h s))), Scalar (FullSubspace (Rec0 h s)) ~ MirrorJoin (Ray (Rec0 h s))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray (Rec0 h s)) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (Rec0 h s)), Scalar (MirrorJoin (Rec0 h s)) ~ MirrorJoin (Ray (Rec0 h s))) => r) -> r

fromPositiveHalf :: Rec0 h s -> MirrorJoin (Rec0 h s)

fromNegativeHalf :: Rec0 h s -> MirrorJoin (Rec0 h s)

(HalfSpace (f p), VectorSpace (g p), AdditiveMonoid (g p), Ray (f p) ~ Cℝay (ZeroDim (Scalar (g p)))) => HalfSpace ((f :*: g) p)

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace ((f :*: g) p)

type Ray ((f :*: g) p)

type MirrorJoin ((f :*: g) p)

Methods

scaleNonNeg :: Ray ((f :*: g) p) -> (f :*: g) p -> (f :*: g) p

fromFullSubspace :: FullSubspace ((f :*: g) p) -> (f :*: g) p

projectToFullSubspace :: (f :*: g) p -> FullSubspace ((f :*: g) p)

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace ((f :*: g) p)), ScalarSpace (Scalar (FullSubspace ((f :*: g) p))), Scalar (FullSubspace ((f :*: g) p)) ~ MirrorJoin (Ray ((f :*: g) p))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray ((f :*: g) p)) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin ((f :*: g) p)), Scalar (MirrorJoin ((f :*: g) p)) ~ MirrorJoin (Ray ((f :*: g) p))) => r) -> r

fromPositiveHalf :: (f :*: g) p -> MirrorJoin ((f :*: g) p)

fromNegativeHalf :: (f :*: g) p -> MirrorJoin ((f :*: g) p)

HalfSpace (f p) => HalfSpace (M1 i c f p)

Defined in Data.Monoid.Additive

Associated Types

type FullSubspace (M1 i c f p)

type Ray (M1 i c f p)

type MirrorJoin (M1 i c f p)

Methods

scaleNonNeg :: Ray (M1 i c f p) -> M1 i c f p -> M1 i c f p

fromFullSubspace :: FullSubspace (M1 i c f p) -> M1 i c f p

projectToFullSubspace :: M1 i c f p -> FullSubspace (M1 i c f p)

fullSubspaceIsVectorSpace :: ((VectorSpace (FullSubspace (M1 i c f p)), ScalarSpace (Scalar (FullSubspace (M1 i c f p))), Scalar (FullSubspace (M1 i c f p)) ~ MirrorJoin (Ray (M1 i c f p))) => r) -> r

rayIsHalfSpace :: (HalfSpace (Ray (M1 i c f p)) => r) -> r

mirrorJoinIsVectorSpace :: ((VectorSpace (MirrorJoin (M1 i c f p)), Scalar (MirrorJoin (M1 i c f p)) ~ MirrorJoin (Ray (M1 i c f p))) => r) -> r

fromPositiveHalf :: M1 i c f p -> MirrorJoin (M1 i c f p)

fromNegativeHalf :: M1 i c f p -> MirrorJoin (M1 i c f p)