Synapse.Tensors.Vec

Implementation of mathematical vector.

Vec is only a newtype wrapper around Vector, which implements several mathematical operations on itself.

Vec offers meaningful abstraction and easy interface (you can unwrap it to perform more complex tasks).

Vec datatype and simple getters.

newtype Vec a

Mathematical vector (collection of elements).

Constructors

Vec

Fields

• unVec :: Vector a

  Internal representation.

Instances

Foldable Vec

Defined in Synapse.Tensors.Vec

Methods

fold :: Monoid m => Vec m -> m

foldMap :: Monoid m => (a -> m) -> Vec a -> m

foldMap' :: Monoid m => (a -> m) -> Vec a -> m

foldr :: (a -> b -> b) -> b -> Vec a -> b

foldr' :: (a -> b -> b) -> b -> Vec a -> b

foldl :: (b -> a -> b) -> b -> Vec a -> b

foldl' :: (b -> a -> b) -> b -> Vec a -> b

foldr1 :: (a -> a -> a) -> Vec a -> a

foldl1 :: (a -> a -> a) -> Vec a -> a

toList :: Vec a -> [a]

null :: Vec a -> Bool

length :: Vec a -> Int

elem :: Eq a => a -> Vec a -> Bool

maximum :: Ord a => Vec a -> a

minimum :: Ord a => Vec a -> a

sum :: Num a => Vec a -> a

product :: Num a => Vec a -> a

Traversable Vec

Defined in Synapse.Tensors.Vec

Methods

traverse :: Applicative f => (a -> f b) -> Vec a -> f (Vec b)

sequenceA :: Applicative f => Vec (f a) -> f (Vec a)

mapM :: Monad m => (a -> m b) -> Vec a -> m (Vec b)

sequence :: Monad m => Vec (m a) -> m (Vec a)

Applicative Vec

Defined in Synapse.Tensors.Vec

Methods

pure :: a -> Vec a

(<*>) :: Vec (a -> b) -> Vec a -> Vec b

liftA2 :: (a -> b -> c) -> Vec a -> Vec b -> Vec c

(*>) :: Vec a -> Vec b -> Vec b

(<*) :: Vec a -> Vec b -> Vec a

Functor Vec

Defined in Synapse.Tensors.Vec

Methods

fmap :: (a -> b) -> Vec a -> Vec b

(<$) :: a -> Vec b -> Vec a

Floating a => Floating (Vec a)

Defined in Synapse.Tensors.Vec

Methods

pi :: Vec a

exp :: Vec a -> Vec a

log :: Vec a -> Vec a

sqrt :: Vec a -> Vec a

(**) :: Vec a -> Vec a -> Vec a

logBase :: Vec a -> Vec a -> Vec a

sin :: Vec a -> Vec a

cos :: Vec a -> Vec a

tan :: Vec a -> Vec a

asin :: Vec a -> Vec a

acos :: Vec a -> Vec a

atan :: Vec a -> Vec a

sinh :: Vec a -> Vec a

cosh :: Vec a -> Vec a

tanh :: Vec a -> Vec a

asinh :: Vec a -> Vec a

acosh :: Vec a -> Vec a

atanh :: Vec a -> Vec a

log1p :: Vec a -> Vec a

expm1 :: Vec a -> Vec a

log1pexp :: Vec a -> Vec a

log1mexp :: Vec a -> Vec a

Num a => Num (Vec a)

Defined in Synapse.Tensors.Vec

Methods

(+) :: Vec a -> Vec a -> Vec a

(-) :: Vec a -> Vec a -> Vec a

(*) :: Vec a -> Vec a -> Vec a

negate :: Vec a -> Vec a

abs :: Vec a -> Vec a

signum :: Vec a -> Vec a

fromInteger :: Integer -> Vec a

Read a => Read (Vec a)

Defined in Synapse.Tensors.Vec

Methods

readsPrec :: Int -> ReadS (Vec a)

readList :: ReadS [Vec a]

readPrec :: ReadPrec (Vec a)

readListPrec :: ReadPrec [Vec a]

Fractional a => Fractional (Vec a)

Defined in Synapse.Tensors.Vec

Methods

(/) :: Vec a -> Vec a -> Vec a

recip :: Vec a -> Vec a

fromRational :: Rational -> Vec a

Show a => Show (Vec a)

Defined in Synapse.Tensors.Vec

Methods

showsPrec :: Int -> Vec a -> ShowS

show :: Vec a -> String

showList :: [Vec a] -> ShowS

Eq a => Eq (Vec a)

Defined in Synapse.Tensors.Vec

Methods

(==) :: Vec a -> Vec a -> Bool

(/=) :: Vec a -> Vec a -> Bool

Symbolic a => Symbolic (Vec a)

Defined in Synapse.Autograd

Methods

symbolicZero :: Vec a -> Vec a

symbolicOne :: Vec a -> Vec a

symbolicN :: Int -> Vec a -> Vec a

Symbolic a => ElementwiseScalarOps (Symbol (Vec a))

Defined in Synapse.Autograd

Methods

(+.) :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

(-.) :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

(*.) :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

(/.) :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

(**.) :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

elementsMin :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

elementsMax :: Symbol (Vec a) -> DType (Symbol (Vec a)) -> Symbol (Vec a)

ElementwiseScalarOps (Vec a)

Defined in Synapse.Tensors.Vec

Methods

(+.) :: Vec a -> DType (Vec a) -> Vec a

(-.) :: Vec a -> DType (Vec a) -> Vec a

(*.) :: Vec a -> DType (Vec a) -> Vec a

(/.) :: Vec a -> DType (Vec a) -> Vec a

(**.) :: Vec a -> DType (Vec a) -> Vec a

elementsMin :: Vec a -> DType (Vec a) -> Vec a

elementsMax :: Vec a -> DType (Vec a) -> Vec a

Indexable (Vec a)

Defined in Synapse.Tensors.Vec

Associated Types

type Index (Vec a)

Methods

unsafeIndex :: Vec a -> Index (Vec a) -> DType (Vec a)

(!) :: Vec a -> Index (Vec a) -> DType (Vec a)

(!?) :: Vec a -> Index (Vec a) -> Maybe (DType (Vec a))

Symbolic a => SingletonOps (SymbolVec a)

Defined in Synapse.Autograd

Methods

singleton :: DType (SymbolVec a) -> SymbolVec a

isSingleton :: SymbolVec a -> Bool

unSingleton :: SymbolVec a -> DType (SymbolVec a)

extendSingleton :: SymbolVec a -> SymbolVec a -> SymbolVec a

elementsSum :: SymbolVec a -> SymbolVec a

elementsProduct :: SymbolVec a -> SymbolVec a

mean :: SymbolVec a -> SymbolVec a

norm :: SymbolVec a -> SymbolVec a

SingletonOps (Vec a)

Defined in Synapse.Tensors.Vec

Methods

singleton :: DType (Vec a) -> Vec a

isSingleton :: Vec a -> Bool

unSingleton :: Vec a -> DType (Vec a)

extendSingleton :: Vec a -> Vec a -> Vec a

elementsSum :: Vec a -> Vec a

elementsProduct :: Vec a -> Vec a

mean :: Vec a -> Vec a

norm :: Vec a -> Vec a

Symbolic a => VecOps (SymbolVec a)

Defined in Synapse.Autograd

Methods

dot :: SymbolVec a -> SymbolVec a -> SymbolVec a

Num a => VecOps (Vec a)

Defined in Synapse.Tensors.Vec

Methods

dot :: Vec a -> Vec a -> Vec a

type DType (SymbolVec a)

Defined in Synapse.Autograd

type DType (SymbolVec a) = a

type DType (Vec a)

Defined in Synapse.Tensors.Vec

type DType (Vec a) = a

type Index (Vec a)

Defined in Synapse.Tensors.Vec

type Index (Vec a) = Int

size :: Vec a -> Int

Size of a vector - number of elements.

Constructors

empty :: Vec a

Creates empty Vec.

singleton :: SingletonOps f => DType f -> f

Initializes singleton container.

fromList :: [a] -> Vec a

Creates Vec from list.

generate :: Int -> (Int -> a) -> Vec a

Creates Vec of given length using generating function.

replicate :: Int -> a -> Vec a

Creates Vec of given length filled with given element.

Concatenation and splitting

cons :: a -> Vec a -> Vec a

Prepend Vec with given element.

snoc :: Vec a -> a -> Vec a

Append Vec with given element.

(++) :: Vec a -> Vec a -> Vec a infixr 5

Concatenate two Vecs.

concat :: [Vec a] -> Vec a

Concatenate all Vecs.

splitAt :: Int -> Vec a -> (Vec a, Vec a)

Splits Vec into two Vecs at a given index.

Combining

map :: (a -> b) -> Vec a -> Vec b

Map a function over a Vec.

imap :: (Int -> a -> b) -> Vec a -> Vec b

Apply a function to every element of a Vec and its index.

for :: Vec a -> (a -> b) -> Vec b

map with its arguments flipped.

zipWith :: (a -> b -> c) -> Vec a -> Vec b -> Vec c

Zips two Vecs with the given function.

zip :: Vec a -> Vec b -> Vec (a, b)

Zips two Vecs.

Mathematics

zeroes :: Num a => Int -> Vec a

Creates Vec of given length filled with zeroes.

ones :: Num a => Int -> Vec a

Creates Vec of given length filled with ones.

squaredMagnitude :: Num a => Vec a -> a

Squared magnitude of a Vec.

magnitude :: Floating a => Vec a -> a

Magnitude of a Vec.

clampMagnitude :: (Floating a, Ord a) => a -> Vec a -> Vec a

Clamps Vec magnitude.

normalized :: Floating a => Vec a -> Vec a

Normalizes Vec by dividing each component by Vec magnitude.

linearCombination :: Num a => [(a, Vec a)] -> Vec a

Computes linear combination of Vecs. Returns empty Vec if empty list was passed to this function.

dot :: (VecOps f, Num (DType f)) => f -> f -> f

Calculates dot product of two vectors.

angleBetween :: Floating a => Vec a -> Vec a -> a

Calculates an angle between two Vecs.

lerp :: (Floating a, Ord a) => a -> Vec a -> Vec a -> Vec a

Linearly interpolates between two Vecs. Given parameter will be clamped between [0.0, 1.0].