Data.Matrix.Dense.Generic

Immutable Matrix

data Matrix v a

Row-major matrix supporting efficient slice

Constructors

Matrix !Int !Int !Int !Int !(v a)

Instances

Vector v a => Matrix Matrix v a

Methods

dim :: Matrix v a -> (Int, Int)

unsafeIndex :: Matrix v a -> (Int, Int) -> a

unsafeFromVector :: (Int, Int) -> v a -> Matrix v a

flatten :: Matrix v a -> v a

unsafeTakeRow :: Matrix v a -> Int -> v a

unsafeTakeColumn :: Matrix v a -> Int -> v a

takeDiag :: Matrix v a -> v a

thaw :: PrimMonad s => Matrix v a -> s (Mutable Matrix (Mutable v) (PrimState s) a)

unsafeThaw :: PrimMonad s => Matrix v a -> s (Mutable Matrix (Mutable v) (PrimState s) a)

freeze :: PrimMonad s => Mutable Matrix (Mutable v) (PrimState s) a -> s (Matrix v a)

unsafeFreeze :: PrimMonad s => Mutable Matrix (Mutable v) (PrimState s) a -> s (Matrix v a)

Eq (v a) => Eq (Matrix v a)

Methods

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

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

Read (v a) => Read (Matrix v a)

Methods

readsPrec :: Int -> ReadS (Matrix v a)

readList :: ReadS [Matrix v a]

readPrec :: ReadPrec (Matrix v a)

readListPrec :: ReadPrec [Matrix v a]

Show (v a) => Show (Matrix v a)

Methods

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

show :: Matrix v a -> String

showList :: [Matrix v a] -> ShowS

Generic (Matrix v a)

Associated Types

type Rep (Matrix v a) :: * -> *

Methods

from :: Matrix v a -> Rep (Matrix v a) x

to :: Rep (Matrix v a) x -> Matrix v a

NFData (v a) => NFData (Matrix v a)

Methods

rnf :: Matrix v a -> ()

type Mutable Matrix

type Mutable Matrix = MMatrix

type Rep (Matrix v a)

type Rep (Matrix v a) = D1 (MetaData "Matrix" "Data.Matrix.Dense.Generic" "matrices-0.4.5-FxXj00niP442mTwOHbDHPt" False) (C1 (MetaCons "Matrix" PrefixI False) ((:*:) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int))) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int)) ((:*:) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 Int)) (S1 (MetaSel (Nothing Symbol) NoSourceUnpackedness SourceStrict DecidedStrict) (Rec0 (v a)))))))

Accessors

length information

dim :: Matrix m v a => m v a -> (Int, Int)

rows :: Matrix m v a => m v a -> Int

Derived methods

Return the number of rows

cols :: Matrix m v a => m v a -> Int

Return the number of columns

Indexing

unsafeIndex :: Matrix m v a => m v a -> (Int, Int) -> a

(!) :: Matrix m v a => m v a -> (Int, Int) -> a

Indexing

takeRow :: Matrix m v a => m v a -> Int -> v a

Extract a row.

takeColumn :: Matrix m v a => m v a -> Int -> v a

Extract a row.

takeDiag :: Matrix m v a => m v a -> v a

Extract the diagonal. Default algorithm is O(min(m,n) * O(unsafeIndex)).

Construction

unsafeFromVector :: Matrix m v a => (Int, Int) -> v a -> m v a

fromVector :: Matrix m v a => (Int, Int) -> v a -> m v a

matrix

Arguments

:: Matrix m v a

=> Int

number of columns

-> [a]

row list

-> m v a

O(m*n) Matrix construction

fromLists :: Matrix m v a => [[a]] -> m v a

O(m*n) Create matrix from list of lists, it doesn't check if the list of list is a valid matrix

fromRows :: Matrix m v a => [v a] -> m v a

O(m*n) Create matrix from rows

fromColumns :: Vector v a => [v a] -> Matrix v a

O(m*n) Create matrix from columns

empty :: Matrix m v a => m v a

Conversions

flatten :: Matrix m v a => m v a -> v a

Default algorithm is O((m*n) * O(unsafeIndex)).

toRows :: Matrix m v a => m v a -> [v a]

O(m) Return the rows

toColumns :: Matrix m v a => m v a -> [v a]

O(m*n) Return the columns

toList :: Matrix m v a => m v a -> [a]

O(m*n) Create a list by concatenating rows

toLists :: Matrix m v a => m v a -> [[a]]

O(m*n) List of lists

Different matrix types

convert :: (Vector v a, Vector w a) => Matrix v a -> Matrix w a

O(m*n) Convert different matrix type

tr :: Vector v a => Matrix v a -> Matrix v a

O(m*n) Matrix transpose

subMatrix

Arguments

:: Vector v a

=> (Int, Int)

upper left corner of the submatrix

-> (Int, Int)

bottom right corner of the submatrix

-> Matrix v a

-> Matrix v a

O(1) Extract sub matrix

ident :: (Num a, Vector v a) => Int -> Matrix v a

O(m*n) Create an identity matrix

diag

Arguments

:: (Num a, Vector v a, Foldable t)

=> t a

diagonal

-> Matrix v a

O(m*n) Create a square matrix with given diagonal, other entries default to 0

diagRect

Arguments

:: (Vector v a, Foldable t)

=> a

default value

-> (Int, Int)

-> t a

diagonal

-> Matrix v a

O(m*n) Create a rectangular matrix with default values and given diagonal

fromBlocks

Arguments

:: Vector v a

=> a

default value

-> [[Matrix v a]]

-> Matrix v a

isSymmetric :: (Eq a, Vector v a) => Matrix v a -> Bool

force :: Vector v a => Matrix v a -> Matrix v a

foldl :: Vector v b => (a -> b -> a) -> a -> Matrix v b -> a

Mapping

map :: (Vector v a, Vector v b) => (a -> b) -> Matrix v a -> Matrix v b

imap :: (Vector v a, Vector v b) => ((Int, Int) -> a -> b) -> Matrix v a -> Matrix v b

Monadic mapping

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

imapM :: (Vector v a, Vector v b, Monad m) => ((Int, Int) -> a -> m b) -> Matrix v a -> m (Matrix v b)

O(m*n) Apply the monadic action to every element and its index, yielding a matrix of results.

mapM_ :: (Vector v a, Monad m) => (a -> m b) -> Matrix v a -> m ()

imapM_ :: (Vector v a, Monad m) => ((Int, Int) -> a -> m b) -> Matrix v a -> m ()

O(m*n) Apply the monadic action to every element and its index, ignoring the results.

forM :: (Vector v a, Vector v b, Monad m) => Matrix v a -> (a -> m b) -> m (Matrix v b)

forM_ :: (Vector v a, Monad m) => Matrix v a -> (a -> m b) -> m ()

Zipping

zipWith :: (Vector v a, Vector v b, Vector v c) => (a -> b -> c) -> Matrix v a -> Matrix v b -> Matrix v c

zipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => (a -> b -> c -> d) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d

zipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => (a -> b -> c -> d -> e) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e

zipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => (a -> b -> c -> d -> e -> f) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f

zipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => (a -> b -> c -> d -> e -> f -> g) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v g

izipWith :: (Vector v a, Vector v b, Vector v c) => ((Int, Int) -> a -> b -> c) -> Matrix v a -> Matrix v b -> Matrix v c

izipWith3 :: (Vector v a, Vector v b, Vector v c, Vector v d) => ((Int, Int) -> a -> b -> c -> d) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d

izipWith4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e) => ((Int, Int) -> a -> b -> c -> d -> e) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e

izipWith5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f) => ((Int, Int) -> a -> b -> c -> d -> e -> f) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f

izipWith6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v g) => ((Int, Int) -> a -> b -> c -> d -> e -> f -> g) -> Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v g

zip :: (Vector v a, Vector v b, Vector v (a, b)) => Matrix v a -> Matrix v b -> Matrix v (a, b)

zip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v (a, b, c)

zip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v (a, b, c, d)

zip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v (a, b, c, d, e)

zip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => Matrix v a -> Matrix v b -> Matrix v c -> Matrix v d -> Matrix v e -> Matrix v f -> Matrix v (a, b, c, d, e, f)

Monadic Zipping

zipWithM :: (Monad m, Vector v a, Vector v b, Vector v c) => (a -> b -> m c) -> Matrix v a -> Matrix v b -> m (Matrix v c)

zipWithM_ :: (Monad m, Vector v a, Vector v b) => (a -> b -> m c) -> Matrix v a -> Matrix v b -> m ()

Unzipping

unzip :: (Vector v a, Vector v b, Vector v (a, b)) => Matrix v (a, b) -> (Matrix v a, Matrix v b)

unzip3 :: (Vector v a, Vector v b, Vector v c, Vector v (a, b, c)) => Matrix v (a, b, c) -> (Matrix v a, Matrix v b, Matrix v c)

unzip4 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v (a, b, c, d)) => Matrix v (a, b, c, d) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d)

unzip5 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v (a, b, c, d, e)) => Matrix v (a, b, c, d, e) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d, Matrix v e)

unzip6 :: (Vector v a, Vector v b, Vector v c, Vector v d, Vector v e, Vector v f, Vector v (a, b, c, d, e, f)) => Matrix v (a, b, c, d, e, f) -> (Matrix v a, Matrix v b, Matrix v c, Matrix v d, Matrix v e, Matrix v f)

Monadic sequencing

sequence :: (Vector v a, Vector v (m a), Monad m) => Matrix v (m a) -> m (Matrix v a)

sequence_ :: (Vector v (m a), Monad m) => Matrix v (m a) -> m ()

generate :: Vector v a => (Int, Int) -> ((Int, Int) -> a) -> Matrix v a

Mutable matrix

thaw :: (Matrix m v a, PrimMonad s) => m v a -> s (Mutable m (Mutable v) (PrimState s) a)

unsafeThaw :: (Matrix m v a, PrimMonad s) => m v a -> s (Mutable m (Mutable v) (PrimState s) a)

freeze :: (Matrix m v a, PrimMonad s) => Mutable m (Mutable v) (PrimState s) a -> s (m v a)

unsafeFreeze :: (Matrix m v a, PrimMonad s) => Mutable m (Mutable v) (PrimState s) a -> s (m v a)

create :: Matrix m v a => (forall s. ST s (Mutable m (Mutable v) s a)) -> m v a