Numeric.LinearAlgebra.Class

Additive ring

class Functor f => Additive f where

Minimal complete definition

zero, (^+^)

Methods

zero :: Num a => f a

Ring zero element

(^+^) :: Num a => f a -> f a -> f a

Ring +

Instances

Additive SpVector

Methods

zero :: Num a => SpVector a

(^+^) :: Num a => SpVector a -> SpVector a -> SpVector a

Additive SpMatrix

Methods

zero :: Num a => SpMatrix a

(^+^) :: Num a => SpMatrix a -> SpMatrix a -> SpMatrix a

negated :: (Num a, Functor f) => f a -> f a

negate the values in a functor

(^-^) :: (Additive f, Num a) => f a -> f a -> f a

subtract two Additive objects

Vector space

class Additive f => VectorSpace f where

Minimal complete definition

(.*)

Methods

(.*) :: Num a => a -> f a -> f a

multiplication by a scalar

Instances

VectorSpace SpVector

Methods

(.*) :: Num a => a -> SpVector a -> SpVector a

lerp :: (VectorSpace f, Num a) => a -> f a -> f a -> f a

linear interpolation

Hilbert space (inner product)

class VectorSpace f => Hilbert f where

Minimal complete definition

dot

Methods

dot :: Num a => f a -> f a -> a

inner product

Instances

Hilbert SpVector

Methods

dot :: Num a => SpVector a -> SpVector a -> a

Hilbert-space distance function

hilbertDistSq :: (Hilbert f, Num a) => f a -> f a -> a

`hilbertDistSq x y = || x - y ||^2`

Normed vector space

class Hilbert f => Normed f where

Minimal complete definition

norm

Methods

norm :: (Floating a, Eq a) => a -> f a -> a

Instances

Normed SpVector

Methods

norm :: (Floating a, Eq a) => a -> SpVector a -> a

Norms and related results

normSq :: (Hilbert f, Num a) => f a -> a

Squared 2-norm

norm1 :: (Foldable t, Num a, Functor t) => t a -> a

L1 norm

norm2 :: (Hilbert f, Floating a) => f a -> a

Euclidean norm

normP :: (Foldable t, Functor t, Floating a) => a -> t a -> a

Lp norm (p > 0)

normInfty :: (Foldable t, Ord a) => t a -> a

Infinity-norm

normalize :: (Normed f, Floating a, Eq a) => a -> f a -> f a

Normalize w.r.t. p-norm (p finite)

dotLp :: (Set t, Foldable t, Floating a) => a -> t a -> t a -> a

Lp inner product (p > 0)

reciprocal :: (Functor f, Fractional b) => f b -> f b

Reciprocal

scale :: (Num b, Functor f) => b -> f b -> f b

Scale

FiniteDim : finite-dimensional objects

class Additive f => FiniteDim f where

Minimal complete definition

dim

Associated Types

type FDSize f :: *

Methods

dim :: f a -> FDSize f

Instances

FiniteDim SpVector

Associated Types

type FDSize (SpVector :: * -> *) :: *

Methods

dim :: SpVector a -> FDSize SpVector

FiniteDim SpMatrix

Associated Types

type FDSize (SpMatrix :: * -> *) :: *

Methods

dim :: SpMatrix a -> FDSize SpMatrix

withDim :: (FiniteDim f, Show e) => f a -> (FDSize f -> f a -> Bool) -> (f a -> c) -> String -> (f a -> e) -> c

unary dimension-checking bracket

withDim2 :: (FiniteDim f, FiniteDim g, Show e) => f a -> g b -> (FDSize f -> FDSize g -> f a -> g b -> Bool) -> (f a -> g b -> c) -> String -> (f a -> g b -> e) -> c

binary dimension-checking bracket

HasData : accessing inner data (do not export)

class Additive f => HasData f a where

Minimal complete definition

dat

Associated Types

type HDData f a :: *

Methods

dat :: f a -> HDData f a

Instances

HasData SpVector a

Associated Types

type HDData (SpVector :: * -> *) a :: *

Methods

dat :: SpVector a -> HDData SpVector a

HasData SpMatrix a

Associated Types

type HDData (SpMatrix :: * -> *) a :: *

Methods

dat :: SpMatrix a -> HDData SpMatrix a

Sparse : sparse datastructures

class (FiniteDim f, HasData f a) => Sparse f a where

Minimal complete definition

spy

Methods

spy :: Fractional b => f a -> b

Instances

Sparse SpVector a

Methods

spy :: Fractional b => SpVector a -> b

Sparse SpMatrix a

Methods

spy :: Fractional b => SpMatrix a -> b

Set : types that behave as sets

class Functor f => Set f where

Minimal complete definition

liftU2, liftI2

Methods

liftU2 :: (a -> a -> a) -> f a -> f a -> f a

union binary lift : apply function on _union_ of two Sets

liftI2 :: (a -> b -> c) -> f a -> f b -> f c

intersection binary lift : apply function on _intersection_ of two Sets

Instances

Set SpVector

Methods

liftU2 :: (a -> a -> a) -> SpVector a -> SpVector a -> SpVector a

liftI2 :: (a -> b -> c) -> SpVector a -> SpVector b -> SpVector c

Set SpMatrix

Methods

liftU2 :: (a -> a -> a) -> SpMatrix a -> SpMatrix a -> SpMatrix a

liftI2 :: (a -> b -> c) -> SpMatrix a -> SpMatrix b -> SpMatrix c

IxContainer : indexed container types

class IxContainer c a where

Minimal complete definition

ixcLookup, ixcLookupDefault, ixcFilter, ixcIfilter, ixcInsert, ixcFromList, ixcToList

Associated Types

type Ix c :: *

Methods

ixcLookup :: Ix c -> c a -> Maybe a

ixcLookupDefault :: a -> Ix c -> c a -> a

ixcFilter :: (a -> Bool) -> c a -> c a

ixcIfilter :: (Ix c -> a -> Bool) -> c a -> c a

ixcInsert :: Ix c -> a -> c a -> c a

ixcFromList :: [(Ix c, a)] -> c a

ixcToList :: c a -> [(Ix c, a)]