Algebra.Linear

Documentation

type VectorSpace scalar a = (Field scalar, Module scalar a, Group a)

class (Finite (Rep v), Representable v, Foldable v, Applicative v) => VectorR v where

Representation of vector as traversable functor ... but this is missing the link with *^ for module. We should be able to add forall s. PreRing s => Module s (v s), but this creates problems when defining instances.

Minimal complete definition

Nothing

Methods

vectorSplit :: v ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: v ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

Instances

VectorR Id

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). Id ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). Id ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

VectorR a => VectorR (VNext a)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). VNext a ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). VNext a ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

VectorR (One :: Type -> Type)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). One ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). One ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

VectorR f => VectorR (Euclid f)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f0 :: Type -> Type) (g :: Type -> Type). Euclid f ~ (f0 ⊗ g) => Dict (VectorR f0, VectorR g)

vectorCut :: forall (f0 :: Type -> Type) (g :: Type -> Type). Euclid f ~ (f0 ⊕ g) => Dict (VectorR f0, VectorR g)

(VectorR v, VectorR w) => VectorR (v ⊗ w)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). (v ⊗ w) ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). (v ⊗ w) ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

(VectorR v, VectorR w) => VectorR (v ∘ w)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). (v ∘ w) ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). (v ∘ w) ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

class VectorR v => InnerProdSpace v where

Methods

inner :: Field s => v s -> v s -> s

Instances

VectorR f => InnerProdSpace (Euclid f)

Defined in Algebra.Linear

Methods

inner :: Field s => Euclid f s -> Euclid f s -> s

type VZero x = Zero x

data VNext v a

Constructors

VNext

Fields

• vnextInit :: !(v a)
• vnextLast :: !a

Instances

Representable a => Representable (VNext a)

Defined in Algebra.Linear

Associated Types

type Rep (VNext a)

Methods

tabulate :: (Rep (VNext a) -> a0) -> VNext a a0

index :: VNext a a0 -> Rep (VNext a) -> a0

Foldable v => Foldable (VNext v)

Defined in Algebra.Linear

Methods

fold :: Monoid m => VNext v m -> m

foldMap :: Monoid m => (a -> m) -> VNext v a -> m

foldMap' :: Monoid m => (a -> m) -> VNext v a -> m

foldr :: (a -> b -> b) -> b -> VNext v a -> b

foldr' :: (a -> b -> b) -> b -> VNext v a -> b

foldl :: (b -> a -> b) -> b -> VNext v a -> b

foldl' :: (b -> a -> b) -> b -> VNext v a -> b

foldr1 :: (a -> a -> a) -> VNext v a -> a

foldl1 :: (a -> a -> a) -> VNext v a -> a

toList :: VNext v a -> [a]

null :: VNext v a -> Bool

length :: VNext v a -> Int

elem :: Eq a => a -> VNext v a -> Bool

maximum :: Ord a => VNext v a -> a

minimum :: Ord a => VNext v a -> a

sum :: Num a => VNext v a -> a

product :: Num a => VNext v a -> a

Traversable v => Traversable (VNext v)

Defined in Algebra.Linear

Methods

traverse :: Applicative f => (a -> f b) -> VNext v a -> f (VNext v b)

sequenceA :: Applicative f => VNext v (f a) -> f (VNext v a)

mapM :: Monad m => (a -> m b) -> VNext v a -> m (VNext v b)

sequence :: Monad m => VNext v (m a) -> m (VNext v a)

Applicative v => Applicative (VNext v)

Defined in Algebra.Linear

Methods

pure :: a -> VNext v a

(<*>) :: VNext v (a -> b) -> VNext v a -> VNext v b

liftA2 :: (a -> b -> c) -> VNext v a -> VNext v b -> VNext v c

(*>) :: VNext v a -> VNext v b -> VNext v b

(<*) :: VNext v a -> VNext v b -> VNext v a

Functor v => Functor (VNext v)

Defined in Algebra.Linear

Methods

fmap :: (a -> b) -> VNext v a -> VNext v b

(<$) :: a -> VNext v b -> VNext v a

Distributive v => Distributive (VNext v)

Defined in Algebra.Linear

Methods

distribute :: Functor f => f (VNext v a) -> VNext v (f a)

collect :: Functor f => (a -> VNext v b) -> f a -> VNext v (f b)

distributeM :: Monad m => m (VNext v a) -> VNext v (m a)

collectM :: Monad m => (a -> VNext v b) -> m a -> VNext v (m b)

IsVec f => IsVec (VNext f)

Defined in Algebra.Linear

Methods

reifyVec :: VNext f a -> V (VNext f) a

VectorR a => VectorR (VNext a)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f :: Type -> Type) (g :: Type -> Type). VNext a ~ (f ⊗ g) => Dict (VectorR f, VectorR g)

vectorCut :: forall (f :: Type -> Type) (g :: Type -> Type). VNext a ~ (f ⊕ g) => Dict (VectorR f, VectorR g)

(Show a, Show (v a)) => Show (VNext v a)

Defined in Algebra.Linear

Methods

showsPrec :: Int -> VNext v a -> ShowS

show :: VNext v a -> String

showList :: [VNext v a] -> ShowS

(Eq a, Eq (v a)) => Eq (VNext v a)

Defined in Algebra.Linear

Methods

(==) :: VNext v a -> VNext v a -> Bool

(/=) :: VNext v a -> VNext v a -> Bool

(Ord a, Ord (v a)) => Ord (VNext v a)

Defined in Algebra.Linear

Methods

compare :: VNext v a -> VNext v a -> Ordering

(<) :: VNext v a -> VNext v a -> Bool

(<=) :: VNext v a -> VNext v a -> Bool

(>) :: VNext v a -> VNext v a -> Bool

(>=) :: VNext v a -> VNext v a -> Bool

max :: VNext v a -> VNext v a -> VNext v a

min :: VNext v a -> VNext v a -> VNext v a

type Rep (VNext a)

Defined in Algebra.Linear

type Rep (VNext a) = (One :: Type) ⊕ Rep a

data V f a where

Constructors

V0 :: V One a

(:/) :: !(V f a) -> !a -> V (VNext f) a

Instances

Foldable (V f)

Defined in Algebra.Linear

Methods

fold :: Monoid m => V f m -> m

foldMap :: Monoid m => (a -> m) -> V f a -> m

foldMap' :: Monoid m => (a -> m) -> V f a -> m

foldr :: (a -> b -> b) -> b -> V f a -> b

foldr' :: (a -> b -> b) -> b -> V f a -> b

foldl :: (b -> a -> b) -> b -> V f a -> b

foldl' :: (b -> a -> b) -> b -> V f a -> b

foldr1 :: (a -> a -> a) -> V f a -> a

foldl1 :: (a -> a -> a) -> V f a -> a

toList :: V f a -> [a]

null :: V f a -> Bool

length :: V f a -> Int

elem :: Eq a => a -> V f a -> Bool

maximum :: Ord a => V f a -> a

minimum :: Ord a => V f a -> a

sum :: Num a => V f a -> a

product :: Num a => V f a -> a

Traversable (V f)

Defined in Algebra.Linear

Methods

traverse :: Applicative f0 => (a -> f0 b) -> V f a -> f0 (V f b)

sequenceA :: Applicative f0 => V f (f0 a) -> f0 (V f a)

mapM :: Monad m => (a -> m b) -> V f a -> m (V f b)

sequence :: Monad m => V f (m a) -> m (V f a)

IsVec f => Applicative (V f)

Defined in Algebra.Linear

Methods

pure :: a -> V f a

(<*>) :: V f (a -> b) -> V f a -> V f b

liftA2 :: (a -> b -> c) -> V f a -> V f b -> V f c

(*>) :: V f a -> V f b -> V f b

(<*) :: V f a -> V f b -> V f a

Functor (V f)

Defined in Algebra.Linear

Methods

fmap :: (a -> b) -> V f a -> V f b

(<$) :: a -> V f b -> V f a

Show a => Show (V f a)

Defined in Algebra.Linear

Methods

showsPrec :: Int -> V f a -> ShowS

show :: V f a -> String

showList :: [V f a] -> ShowS

Eq a => Eq (V f a)

Defined in Algebra.Linear

Methods

(==) :: V f a -> V f a -> Bool

(/=) :: V f a -> V f a -> Bool

class (Foldable f, Applicative f) => IsVec f where

Methods

reifyVec :: f a -> V f a

Instances

IsVec f => IsVec (VNext f)

Defined in Algebra.Linear

Methods

reifyVec :: VNext f a -> V (VNext f) a

IsVec (One :: Type -> Type)

Defined in Algebra.Linear

Methods

reifyVec :: One a -> V One a

fromV :: V f a -> f a

type V1' = VNext One

type V2' = VNext V1'

type V3' = VNext V2'

pattern V1' :: a -> V1' a

pattern V2' :: forall a. a -> a -> V2' a

pattern V3' :: forall a. a -> a -> a -> V3' a

newtype Euclid f a

Make a Euclidean vector out of a traversable functor. (The p)

Constructors

Euclid

Fields

• fromEuclid :: f a

Instances

(Functor f, Scalable s a) => Scalable s (Euclid f a)

Defined in Algebra.Linear

Methods

(*^) :: s -> Euclid f a -> Euclid f a

Representable f => Representable (Euclid f)

Defined in Algebra.Linear

Associated Types

type Rep (Euclid f)

Methods

tabulate :: (Rep (Euclid f) -> a) -> Euclid f a

index :: Euclid f a -> Rep (Euclid f) -> a

Foldable f => Foldable (Euclid f)

Defined in Algebra.Linear

Methods

fold :: Monoid m => Euclid f m -> m

foldMap :: Monoid m => (a -> m) -> Euclid f a -> m

foldMap' :: Monoid m => (a -> m) -> Euclid f a -> m

foldr :: (a -> b -> b) -> b -> Euclid f a -> b

foldr' :: (a -> b -> b) -> b -> Euclid f a -> b

foldl :: (b -> a -> b) -> b -> Euclid f a -> b

foldl' :: (b -> a -> b) -> b -> Euclid f a -> b

foldr1 :: (a -> a -> a) -> Euclid f a -> a

foldl1 :: (a -> a -> a) -> Euclid f a -> a

toList :: Euclid f a -> [a]

null :: Euclid f a -> Bool

length :: Euclid f a -> Int

elem :: Eq a => a -> Euclid f a -> Bool

maximum :: Ord a => Euclid f a -> a

minimum :: Ord a => Euclid f a -> a

sum :: Num a => Euclid f a -> a

product :: Num a => Euclid f a -> a

Traversable f => Traversable (Euclid f)

Defined in Algebra.Linear

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Euclid f a -> f0 (Euclid f b)

sequenceA :: Applicative f0 => Euclid f (f0 a) -> f0 (Euclid f a)

mapM :: Monad m => (a -> m b) -> Euclid f a -> m (Euclid f b)

sequence :: Monad m => Euclid f (m a) -> m (Euclid f a)

Applicative f => Applicative (Euclid f)

Defined in Algebra.Linear

Methods

pure :: a -> Euclid f a

(<*>) :: Euclid f (a -> b) -> Euclid f a -> Euclid f b

liftA2 :: (a -> b -> c) -> Euclid f a -> Euclid f b -> Euclid f c

(*>) :: Euclid f a -> Euclid f b -> Euclid f b

(<*) :: Euclid f a -> Euclid f b -> Euclid f a

Functor f => Functor (Euclid f)

Defined in Algebra.Linear

Methods

fmap :: (a -> b) -> Euclid f a -> Euclid f b

(<$) :: a -> Euclid f b -> Euclid f a

Distributive f => Distributive (Euclid f)

Defined in Algebra.Linear

Methods

distribute :: Functor f0 => f0 (Euclid f a) -> Euclid f (f0 a)

collect :: Functor f0 => (a -> Euclid f b) -> f0 a -> Euclid f (f0 b)

distributeM :: Monad m => m (Euclid f a) -> Euclid f (m a)

collectM :: Monad m => (a -> Euclid f b) -> m a -> Euclid f (m b)

VectorR f => InnerProdSpace (Euclid f)

Defined in Algebra.Linear

Methods

inner :: Field s => Euclid f s -> Euclid f s -> s

VectorR f => VectorR (Euclid f)

Defined in Algebra.Linear

Methods

vectorSplit :: forall (f0 :: Type -> Type) (g :: Type -> Type). Euclid f ~ (f0 ⊗ g) => Dict (VectorR f0, VectorR g)

vectorCut :: forall (f0 :: Type -> Type) (g :: Type -> Type). Euclid f ~ (f0 ⊕ g) => Dict (VectorR f0, VectorR g)

Show (f a) => Show (Euclid f a)

Defined in Algebra.Linear

Methods

showsPrec :: Int -> Euclid f a -> ShowS

show :: Euclid f a -> String

showList :: [Euclid f a] -> ShowS

(Applicative f, Additive a) => Additive (Euclid f a)

Defined in Algebra.Linear

Methods

(+) :: Euclid f a -> Euclid f a -> Euclid f a

zero :: Euclid f a

times :: Natural -> Euclid f a -> Euclid f a

(Applicative f, Group a) => Group (Euclid f a)

Defined in Algebra.Linear

Methods

(-) :: Euclid f a -> Euclid f a -> Euclid f a

subtract :: Euclid f a -> Euclid f a -> Euclid f a

negate :: Euclid f a -> Euclid f a

mult :: Integer -> Euclid f a -> Euclid f a

Eq (f a) => Eq (Euclid f a)

Defined in Algebra.Linear

Methods

(==) :: Euclid f a -> Euclid f a -> Bool

(/=) :: Euclid f a -> Euclid f a -> Bool

Ord (f a) => Ord (Euclid f a)

Defined in Algebra.Linear

Methods

compare :: Euclid f a -> Euclid f a -> Ordering

(<) :: Euclid f a -> Euclid f a -> Bool

(<=) :: Euclid f a -> Euclid f a -> Bool

(>) :: Euclid f a -> Euclid f a -> Bool

(>=) :: Euclid f a -> Euclid f a -> Bool

max :: Euclid f a -> Euclid f a -> Euclid f a

min :: Euclid f a -> Euclid f a -> Euclid f a

type Rep (Euclid f)

Defined in Algebra.Linear

type Rep (Euclid f) = Rep f

type V3 = Euclid V3'

type V2 = Euclid V2'

pattern V2 :: forall a. a -> a -> Euclid V2' a

pattern V3 :: forall a. a -> a -> a -> Euclid V3' a

pureMat :: (Applicative v, Applicative w) => s -> Mat s v w

(⊙) :: Applicative v => Multiplicative s => v s -> v s -> v s

Hadamard product

(·) :: Field s => InnerProdSpace v => v s -> v s -> s

sqNorm :: Field s => InnerProdSpace v => v s -> s

norm :: Algebraic s => InnerProdSpace v => v s -> s

normalize :: VectorSpace s (v s) => Algebraic s => InnerProdSpace v => v s -> v s

(×) :: Ring a => V3 a -> V3 a -> V3 a

Cross product in 3 dimensions https://en.wikipedia.org/wiki/Cross_product

type SqMat v s = Mat s v v

newtype Mat s w v

Matrix type. (w s) is a column. (v s) is a row.

Constructors

Mat

Fields

• fromMat :: w (v s)

Instances

(Functor f, Functor g, Scalable s a) => Scalable s (Mat a f g)

Defined in Algebra.Linear

Methods

(*^) :: s -> Mat a f g -> Mat a f g

Ring s => Braided ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

swap :: forall (a :: k) (b :: k). (Obj (Mat s) a, Obj (Mat s) b) => Mat s (a ⊗ b) (b ⊗ a)

swap_ :: forall (a :: k) (b :: k). (Obj (Mat s) a, Obj (Mat s) b) => Mat s (a ⊗ b) (b ⊗ a)

Ring s => Cartesian ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

exl :: forall (a :: k) (b :: k). O2 (Mat s) a b => Mat s (a ⊗ b) a

exr :: forall (a :: k) (b :: k). O2 (Mat s) a b => Mat s (a ⊗ b) b

dis :: forall (a :: k). Obj (Mat s) a => Mat s a One

dup :: forall (a :: k). Obj (Mat s) a => Mat s a (a ⊗ a)

(▵) :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s a b -> Mat s a c -> Mat s a (b ⊗ c)

Ring s => CoCartesian ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

inl :: forall (a :: k) (b :: k). O2 (Mat s) a b => Mat s a (a ⊗ b)

inr :: forall (a :: k) (b :: k). O2 (Mat s) a b => Mat s b (a ⊗ b)

new :: forall (a :: k). Obj (Mat s) a => Mat s One a

jam :: forall (a :: k). Obj (Mat s) a => Mat s (a ⊗ a) a

(▿) :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s b a -> Mat s c a -> Mat s (b ⊗ c) a

Ring s => Monoidal ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

(⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c, Obj (Mat s) d) => Mat s a b -> Mat s c d -> Mat s (a ⊗ c) (b ⊗ d)

assoc :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s ((a ⊗ b) ⊗ c) (a ⊗ (b ⊗ c))

assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s (a ⊗ (b ⊗ c)) ((a ⊗ b) ⊗ c)

unitorR :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) One) => Mat s a (a ⊗ One)

unitorR_ :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) One) => Mat s (a ⊗ One) a

unitorL :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) One) => Mat s a (One ⊗ a)

unitorL_ :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) One) => Mat s (One ⊗ a) a

Ring s => Symmetric ((⊗) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) (One :: Type -> Type) (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Ring s => Braided ((∘) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Id (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

swap :: forall (a :: k) (b :: k). (Obj (Mat s) a, Obj (Mat s) b) => Mat s (a ∘ b) (b ∘ a)

swap_ :: forall (a :: k) (b :: k). (Obj (Mat s) a, Obj (Mat s) b) => Mat s (a ∘ b) (b ∘ a)

Ring s => Monoidal ((∘) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Id (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

(⊗) :: forall (a :: k) (b :: k) (c :: k) (d :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c, Obj (Mat s) d) => Mat s a b -> Mat s c d -> Mat s (a ∘ c) (b ∘ d)

assoc :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s ((a ∘ b) ∘ c) (a ∘ (b ∘ c))

assoc_ :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s (a ∘ (b ∘ c)) ((a ∘ b) ∘ c)

unitorR :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) Id) => Mat s a (a ∘ Id)

unitorR_ :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) Id) => Mat s (a ∘ Id) a

unitorL :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) Id) => Mat s a (Id ∘ a)

unitorL_ :: forall (a :: k). (Obj (Mat s) a, Obj (Mat s) Id) => Mat s (Id ∘ a) a

Ring s => Symmetric ((∘) :: (Type -> Type) -> (Type -> Type) -> Type -> Type) Id (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Ring s => Category (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Associated Types

type Obj (Mat s) :: k -> Constraint

Methods

(.) :: forall (a :: k) (b :: k) (c :: k). (Obj (Mat s) a, Obj (Mat s) b, Obj (Mat s) c) => Mat s b c -> Mat s a b -> Mat s a c

id :: forall (a :: k). Obj (Mat s) a => Mat s a a

Ring s => Dagger (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

Methods

dagger :: forall (a :: k) (b :: k). O2 (Mat s) a b => Mat s a b -> Mat s b a

(Arbitrary s, Arbitrary1 a, Arbitrary1 b) => Arbitrary (Mat s a b)

Defined in Algebra.Linear

Methods

arbitrary :: Gen (Mat s a b)

shrink :: Mat s a b -> [Mat s a b]

Show (w (v s)) => Show (Mat s w v)

Defined in Algebra.Linear

Methods

showsPrec :: Int -> Mat s w v -> ShowS

show :: Mat s w v -> String

showList :: [Mat s w v] -> ShowS

(Applicative f, Applicative g, AbelianAdditive a) => AbelianAdditive (Mat a f g)

Defined in Algebra.Linear

(Applicative f, Applicative g, Additive a) => Additive (Mat a f g)

Defined in Algebra.Linear

Methods

(+) :: Mat a f g -> Mat a f g -> Mat a f g

zero :: Mat a f g

times :: Natural -> Mat a f g -> Mat a f g

(Applicative f, Applicative g, Group a) => Group (Mat a f g)

Defined in Algebra.Linear

Methods

(-) :: Mat a f g -> Mat a f g -> Mat a f g

subtract :: Mat a f g -> Mat a f g -> Mat a f g

negate :: Mat a f g -> Mat a f g

mult :: Integer -> Mat a f g -> Mat a f g

(TestEqual s, Arbitrary s, Arbitrary1 a, Arbitrary1 b, Show (a (b s)), VectorR b, VectorR a) => TestEqual (Mat s a b)

Defined in Algebra.Linear

Methods

(=.=) :: Mat s a b -> Mat s a b -> Property

type Obj (Mat s :: (Type -> Type) -> (Type -> Type) -> Type)

Defined in Algebra.Linear

type Obj (Mat s :: (Type -> Type) -> (Type -> Type) -> Type) = VectorR

newtype Flat w v s

View of the matrix as a composition of functors.

Constructors

Flat

Fields

• fromFlat :: w (v s)

Instances

(Foldable w, Foldable v) => Foldable (Flat w v)

Defined in Algebra.Linear

Methods

fold :: Monoid m => Flat w v m -> m

foldMap :: Monoid m => (a -> m) -> Flat w v a -> m

foldMap' :: Monoid m => (a -> m) -> Flat w v a -> m

foldr :: (a -> b -> b) -> b -> Flat w v a -> b

foldr' :: (a -> b -> b) -> b -> Flat w v a -> b

foldl :: (b -> a -> b) -> b -> Flat w v a -> b

foldl' :: (b -> a -> b) -> b -> Flat w v a -> b

foldr1 :: (a -> a -> a) -> Flat w v a -> a

foldl1 :: (a -> a -> a) -> Flat w v a -> a

toList :: Flat w v a -> [a]

null :: Flat w v a -> Bool

length :: Flat w v a -> Int

elem :: Eq a => a -> Flat w v a -> Bool

maximum :: Ord a => Flat w v a -> a

minimum :: Ord a => Flat w v a -> a

sum :: Num a => Flat w v a -> a

product :: Num a => Flat w v a -> a

(Applicative w, Applicative v) => Applicative (Flat w v)

Defined in Algebra.Linear

Methods

pure :: a -> Flat w v a

(<*>) :: Flat w v (a -> b) -> Flat w v a -> Flat w v b

liftA2 :: (a -> b -> c) -> Flat w v a -> Flat w v b -> Flat w v c

(*>) :: Flat w v a -> Flat w v b -> Flat w v b

(<*) :: Flat w v a -> Flat w v b -> Flat w v a

(Functor w, Functor v) => Functor (Flat w v)

Defined in Algebra.Linear

Methods

fmap :: (a -> b) -> Flat w v a -> Flat w v b

(<$) :: a -> Flat w v b -> Flat w v a

Show (w (v s)) => Show (Flat w v s)

Defined in Algebra.Linear

Methods

showsPrec :: Int -> Flat w v s -> ShowS

show :: Flat w v s -> String

showList :: [Flat w v s] -> ShowS

flatMat :: Mat s w v -> Flat w v s

matFlat :: Flat w v s -> Mat s w v

fromRel :: (VectorR a, VectorR b) => Rel s (Rep a) (Rep b) -> Mat s a b

type Mat3x3 s = SqMat V3 s

type Mat2x2 s = SqMat V2 s

pattern Mat2x2 :: forall s. s -> s -> s -> s -> Mat s V2 V2

pattern Mat3x3 :: forall s. s -> s -> s -> s -> s -> s -> s -> s -> s -> Mat s V3 V3

rotation2d :: Transcendental a => a -> Mat2x2 a

crossProductMatrix :: Group a => V3 a -> Mat3x3 a

outerWith :: (Applicative v, Applicative w) => (s -> t -> u) -> w s -> v t -> Mat u v w

outer :: (Applicative v, Applicative w, Multiplicative s) => Euclid w s -> Euclid v s -> Mat s (Euclid w) (Euclid v)

Outer product

diagonal :: Eq (Rep v) => Representable v => Ring s => Applicative v => v s -> SqMat v s

rotation3d :: Transcendental a => a -> V3 a -> Mat3x3 a

3d rotation around given axis

rotationFromTo :: forall a. Algebraic a => V3 a -> V3 a -> Mat3x3 a

3d rotation mapping the direction of from to that of to

transpose :: Functor f => Distributive g => Mat a f g -> Mat a g f

Transposition as distribution

matMul :: (Foldable u, Ring s, Applicative w, Applicative v, Applicative u) => Mat s u w -> Mat s v u -> Mat s v w

(<+>) :: (Applicative f, Additive b) => f b -> f b -> f b

matVecMul :: forall s v w. (Ring s, Foldable v, Applicative v, Applicative w) => Mat s v w -> v s -> w s

prop_linear_with_functor_laws :: Property

runTests :: IO Bool