MathObj.Matrix

Routines and abstractions for Matrices and basic linear algebra over fields or rings.

We stick to simple Int indices. Although advanced indices would be nice e.g. for matrices with sub-matrices, this is not easily implemented since arrays do only support a lower and an upper bound but no additional parameters.

ToDo: - Matrix inverse, determinant (see htam:Matrix)

Documentation

data T a

A matrix is a twodimensional array, indexed by integers.

Instances

Functor T

Methods

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

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

C T

Methods

zero :: C a => T a

(<+>) :: C a => T a -> T a -> T a

(*>) :: C a => a -> T a -> T a

C a b => C a (T b)

Methods

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

Eq a => Eq (T a)

Methods

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

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

Ord a => Ord (T a)

Methods

compare :: T a -> T a -> Ordering

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

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

(>) :: T a -> T a -> Bool

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

max :: T a -> T a -> T a

min :: T a -> T a -> T a

Read a => Read (T a)

Methods

readsPrec :: Int -> ReadS (T a)

readList :: ReadS [T a]

readPrec :: ReadPrec (T a)

readListPrec :: ReadPrec [T a]

Show a => Show (T a)

Methods

showsPrec :: Int -> T a -> ShowS

show :: T a -> String

showList :: [T a] -> ShowS

C a => C (T a)

Methods

zero :: T a

(+) :: T a -> T a -> T a

(-) :: T a -> T a -> T a

negate :: T a -> T a

C a => C (T a)

Methods

(*) :: T a -> T a -> T a

one :: T a

fromInteger :: Integer -> T a

(^) :: T a -> Integer -> T a

type Dimension = Int

format :: Show a => T a -> String

transpose :: T a -> T a

Transposition of matrices is just transposition in the sense of Data.List.

rows :: T a -> [[a]]

columns :: T a -> [[a]]

index :: T a -> Dimension -> Dimension -> a

fromRows :: Dimension -> Dimension -> [[a]] -> T a

fromColumns :: Dimension -> Dimension -> [[a]] -> T a

fromList :: Dimension -> Dimension -> [a] -> T a

dimension :: T a -> (Dimension, Dimension)

numRows :: T a -> Dimension

numColumns :: T a -> Dimension

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

zero :: C a => Dimension -> Dimension -> T a

one :: C a => Dimension -> T a

diagonal :: C a => [a] -> T a

scale :: C a => a -> T a -> T a

random :: (RandomGen g, Random a) => Dimension -> Dimension -> g -> (T a, g)

randomR :: (RandomGen g, Random a) => Dimension -> Dimension -> (a, a) -> g -> (T a, g)