Domain.LinearAlgebra.Matrix

Documentation

data Matrix a

Instances

Functor Matrix

Defined in Domain.LinearAlgebra.Matrix

Methods

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

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

Foldable Matrix

Defined in Domain.LinearAlgebra.Matrix

Methods

fold :: Monoid m => Matrix m -> m

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

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

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

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

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

foldr1 :: (a -> a -> a) -> Matrix a -> a

foldl1 :: (a -> a -> a) -> Matrix a -> a

toList :: Matrix a -> [a]

null :: Matrix a -> Bool

length :: Matrix a -> Int

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

maximum :: Ord a => Matrix a -> a

minimum :: Ord a => Matrix a -> a

sum :: Num a => Matrix a -> a

product :: Num a => Matrix a -> a

Traversable Matrix

Defined in Domain.LinearAlgebra.Matrix

Methods

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

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

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

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

Eq a => Eq (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

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

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

Ord a => Ord (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

compare :: Matrix a -> Matrix a -> Ordering

(<) :: Matrix a -> Matrix a -> Bool

(<=) :: Matrix a -> Matrix a -> Bool

(>) :: Matrix a -> Matrix a -> Bool

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

max :: Matrix a -> Matrix a -> Matrix a

min :: Matrix a -> Matrix a -> Matrix a

Show a => Show (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

showsPrec :: Int -> Matrix a -> ShowS

show :: Matrix a -> String

showList :: [Matrix a] -> ShowS

Arbitrary a => Arbitrary (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

arbitrary :: Gen (Matrix a)

shrink :: Matrix a -> [Matrix a]

CoArbitrary a => CoArbitrary (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

coarbitrary :: Matrix a -> Gen b -> Gen b

IsTerm a => IsTerm (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

toTerm :: Matrix a -> Term

toTermList :: [Matrix a] -> Term

fromTerm :: MonadPlus m => Term -> m (Matrix a)

fromTermList :: MonadPlus m => Term -> m [Matrix a]

Simplify a => Simplify (Matrix a)

Defined in Domain.LinearAlgebra.Matrix

Methods

simplifyWith :: SimplifyConfig -> Matrix a -> Matrix a

simplify :: Matrix a -> Matrix a

type Row a = [a]

type Column a = [a]

isRectangular :: [[a]] -> Bool

makeMatrix :: [Row a] -> Matrix a

identity :: Num a => Int -> Matrix a

mapWithPos :: ((Int, Int) -> a -> b) -> Matrix a -> Matrix b

changeEntries :: Map (Int, Int) (a -> a) -> Matrix a -> Matrix a

changeEntry :: (Int, Int) -> (a -> a) -> Matrix a -> Matrix a

setEntries :: Map (Int, Int) a -> Matrix a -> Matrix a

setEntry :: (Int, Int) -> a -> Matrix a -> Matrix a

rows :: Matrix a -> [Row a]

row :: Int -> Matrix a -> Row a

columns :: Matrix a -> [Column a]

column :: Int -> Matrix a -> Column a

dimensions :: Matrix a -> (Int, Int)

entry :: (Int, Int) -> Matrix a -> a

isEmpty :: Matrix a -> Bool

add :: Num a => Matrix a -> Matrix a -> Matrix a

scale :: Num a => a -> Matrix a -> Matrix a

multiply :: Num a => Matrix a -> Matrix a -> Matrix a

reduce :: (Eq a, Fractional a) => Matrix a -> Matrix a

forward :: (Eq a, Fractional a) => Matrix a -> Matrix a

backward :: (Eq a, Fractional a) => Matrix a -> Matrix a

inverse :: (Eq a, Fractional a) => Matrix a -> Maybe (Matrix a)

invertible :: (Eq a, Fractional a) => Matrix a -> Bool

rank :: (Eq a, Fractional a) => Matrix a -> Int

nullity :: (Eq a, Fractional a) => Matrix a -> Int

eqMatrix :: (Eq a, Fractional a) => Matrix a -> Matrix a -> Bool

switchRows :: Int -> Int -> Matrix a -> Matrix a

scaleRow :: Num a => Int -> a -> Matrix a -> Matrix a

addRow :: Num a => Int -> Int -> a -> Matrix a -> Matrix a

inRowEchelonForm :: (Eq a, Num a) => Matrix a -> Bool

inRowReducedEchelonForm :: (Eq a, Num a) => Matrix a -> Bool

nonZero :: (Eq a, Num a) => [a] -> Bool

pivot :: (Eq a, Num a) => Row a -> Maybe a

isPivotColumn :: (Eq a, Num a) => Column a -> Bool

isSquare :: Matrix a -> Bool

identityMatrix :: Num a => Int -> Matrix a

isLowerTriangular :: (Eq a, Num a) => Matrix a -> Bool

isUpperTriangular :: (Eq a, Num a) => Matrix a -> Bool