Data.Array.Internal.Shaped

Documentation

newtype Array sh a

Constructors

A

Fields

• unA :: Array sh Vector a

Instances

Shape sh => Foldable (Array sh)

Defined in Data.Array.Internal.Shaped

Methods

fold :: Monoid m => Array sh m -> m

foldMap :: Monoid m => (a -> m) -> Array sh a -> m

foldMap' :: Monoid m => (a -> m) -> Array sh a -> m

foldr :: (a -> b -> b) -> b -> Array sh a -> b

foldr' :: (a -> b -> b) -> b -> Array sh a -> b

foldl :: (b -> a -> b) -> b -> Array sh a -> b

foldl' :: (b -> a -> b) -> b -> Array sh a -> b

foldr1 :: (a -> a -> a) -> Array sh a -> a

foldl1 :: (a -> a -> a) -> Array sh a -> a

toList :: Array sh a -> [a]

null :: Array sh a -> Bool

length :: Array sh a -> Int

elem :: Eq a => a -> Array sh a -> Bool

maximum :: Ord a => Array sh a -> a

minimum :: Ord a => Array sh a -> a

sum :: Num a => Array sh a -> a

product :: Num a => Array sh a -> a

Shape sh => Traversable (Array sh)

Defined in Data.Array.Internal.Shaped

Methods

traverse :: Applicative f => (a -> f b) -> Array sh a -> f (Array sh b)

sequenceA :: Applicative f => Array sh (f a) -> f (Array sh a)

mapM :: Monad m => (a -> m b) -> Array sh a -> m (Array sh b)

sequence :: Monad m => Array sh (m a) -> m (Array sh a)

Shape sh => Applicative (Array sh)

Defined in Data.Array.Internal.Shaped

Methods

pure :: a -> Array sh a

(<*>) :: Array sh (a -> b) -> Array sh a -> Array sh b

liftA2 :: (a -> b -> c) -> Array sh a -> Array sh b -> Array sh c

(*>) :: Array sh a -> Array sh b -> Array sh b

(<*) :: Array sh a -> Array sh b -> Array sh a

Shape sh => Functor (Array sh)

Defined in Data.Array.Internal.Shaped

Methods

fmap :: (a -> b) -> Array sh a -> Array sh b

(<$) :: a -> Array sh b -> Array sh a

(a ~ b, Shape sh) => Convert (Array a) (Array sh b)

Defined in Data.Array.Convert

Methods

convert :: Array0 a -> Array sh b

convertE :: Array0 a -> Either String (Array sh b)

(Shape sh, Arbitrary a) => Arbitrary (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

arbitrary :: Gen (Array sh a)

shrink :: Array sh a -> [Array sh a]

(Typeable sh, Data a) => Data (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Array sh a -> c (Array sh a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Array sh a)

toConstr :: Array sh a -> Constr

dataTypeOf :: Array sh a -> DataType

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Array sh a))

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Array sh a))

gmapT :: (forall b. Data b => b -> b) -> Array sh a -> Array sh a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Array sh a -> r

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Array sh a -> r

gmapQ :: (forall d. Data d => d -> u) -> Array sh a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Array sh a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Array sh a -> m (Array sh a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Array sh a -> m (Array sh a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Array sh a -> m (Array sh a)

(Shape sh, Enum a) => Enum (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

succ :: Array sh a -> Array sh a

pred :: Array sh a -> Array sh a

toEnum :: Int -> Array sh a

fromEnum :: Array sh a -> Int

enumFrom :: Array sh a -> [Array sh a]

enumFromThen :: Array sh a -> Array sh a -> [Array sh a]

enumFromTo :: Array sh a -> Array sh a -> [Array sh a]

enumFromThenTo :: Array sh a -> Array sh a -> Array sh a -> [Array sh a]

(Shape sh, Floating a) => Floating (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

pi :: Array sh a

exp :: Array sh a -> Array sh a

log :: Array sh a -> Array sh a

sqrt :: Array sh a -> Array sh a

(**) :: Array sh a -> Array sh a -> Array sh a

logBase :: Array sh a -> Array sh a -> Array sh a

sin :: Array sh a -> Array sh a

cos :: Array sh a -> Array sh a

tan :: Array sh a -> Array sh a

asin :: Array sh a -> Array sh a

acos :: Array sh a -> Array sh a

atan :: Array sh a -> Array sh a

sinh :: Array sh a -> Array sh a

cosh :: Array sh a -> Array sh a

tanh :: Array sh a -> Array sh a

asinh :: Array sh a -> Array sh a

acosh :: Array sh a -> Array sh a

atanh :: Array sh a -> Array sh a

log1p :: Array sh a -> Array sh a

expm1 :: Array sh a -> Array sh a

log1pexp :: Array sh a -> Array sh a

log1mexp :: Array sh a -> Array sh a

Generic (Array sh a)

Defined in Data.Array.Internal.Shaped

Associated Types

type Rep (Array sh a) :: Type -> Type

Methods

from :: Array sh a -> Rep (Array sh a) x

to :: Rep (Array sh a) x -> Array sh a

(Shape sh, Num a) => Num (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

(+) :: Array sh a -> Array sh a -> Array sh a

(-) :: Array sh a -> Array sh a -> Array sh a

(*) :: Array sh a -> Array sh a -> Array sh a

negate :: Array sh a -> Array sh a

abs :: Array sh a -> Array sh a

signum :: Array sh a -> Array sh a

fromInteger :: Integer -> Array sh a

(Read a, Shape sh) => Read (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

readsPrec :: Int -> ReadS (Array sh a)

readList :: ReadS [Array sh a]

readPrec :: ReadPrec (Array sh a)

readListPrec :: ReadPrec [Array sh a]

(Shape sh, Fractional a) => Fractional (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

(/) :: Array sh a -> Array sh a -> Array sh a

recip :: Array sh a -> Array sh a

fromRational :: Rational -> Array sh a

(Shape sh, Integral a) => Integral (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

quot :: Array sh a -> Array sh a -> Array sh a

rem :: Array sh a -> Array sh a -> Array sh a

div :: Array sh a -> Array sh a -> Array sh a

mod :: Array sh a -> Array sh a -> Array sh a

quotRem :: Array sh a -> Array sh a -> (Array sh a, Array sh a)

divMod :: Array sh a -> Array sh a -> (Array sh a, Array sh a)

toInteger :: Array sh a -> Integer

(Shape sh, Real a) => Real (Array sh a)

Defined in Data.Array.Shaped.Instances

Methods

toRational :: Array sh a -> Rational

(Show a, Shape sh) => Show (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

showsPrec :: Int -> Array sh a -> ShowS

show :: Array sh a -> String

showList :: [Array sh a] -> ShowS

NFData a => NFData (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

rnf :: Array sh a -> ()

Eq (Array sh Vector a) => Eq (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

(==) :: Array sh a -> Array sh a -> Bool

(/=) :: Array sh a -> Array sh a -> Bool

Ord (Array sh Vector a) => Ord (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

compare :: Array sh a -> Array sh a -> Ordering

(<) :: Array sh a -> Array sh a -> Bool

(<=) :: Array sh a -> Array sh a -> Bool

(>) :: Array sh a -> Array sh a -> Bool

(>=) :: Array sh a -> Array sh a -> Bool

max :: Array sh a -> Array sh a -> Array sh a

min :: Array sh a -> Array sh a -> Array sh a

(Pretty a, Shape sh) => Pretty (Array sh a)

Defined in Data.Array.Internal.Shaped

Methods

pPrintPrec :: PrettyLevel -> Rational -> Array sh a -> Doc

pPrint :: Array sh a -> Doc

pPrintList :: PrettyLevel -> [Array sh a] -> Doc

(a ~ b, Shape sh) => Convert (Array sh a) (Array b)

Defined in Data.Array.Convert

Methods

convert :: Array sh a -> Array0 b

convertE :: Array sh a -> Either String (Array0 b)

(a ~ b, Rank sh ~ n, Shape sh) => Convert (Array n a) (Array sh b)

Defined in Data.Array.Convert

Methods

convert :: Array0 n a -> Array sh b

convertE :: Array0 n a -> Either String (Array sh b)

(a ~ b, n ~ m, Unbox a) => Convert (Array n a) (Array m b)

Defined in Data.Array.Convert

Methods

convert :: Array0 n a -> Array m b

convertE :: Array0 n a -> Either String (Array m b)

(a ~ b, n ~ m, Unbox a) => Convert (Array n a) (Array m b)

Defined in Data.Array.Convert

Methods

convert :: Array0 n a -> Array m b

convertE :: Array0 n a -> Either String (Array m b)

(a ~ b, Rank sh ~ n, Shape sh) => Convert (Array sh a) (Array n b)

Defined in Data.Array.Convert

Methods

convert :: Array sh a -> Array0 n b

convertE :: Array sh a -> Either String (Array0 n b)

(a ~ b, n ~ m, Unbox a) => Convert (Array n a) (Array m b)

Defined in Data.Array.Convert

Methods

convert :: Array n a -> Array0 m b

convertE :: Array n a -> Either String (Array0 m b)

(a ~ b, n ~ m, Unbox a) => Convert (Array n a) (Array m b)

Defined in Data.Array.Convert

Methods

convert :: Array n a -> Array0 m b

convertE :: Array n a -> Either String (Array0 m b)

(a ~ b, s ~ t) => Convert (Array s a) (Array t Vector b)

Defined in Data.Array.Convert

Methods

convert :: Array s a -> Array0 t Vector b

convertE :: Array s a -> Either String (Array0 t Vector b)

type Rep (Array sh a)

Defined in Data.Array.Internal.Shaped

type Rep (Array sh a) = D1 ('MetaData "Array" "Data.Array.Internal.Shaped" "orthotope-0.1.6.0-7Lf71PJ1JmQsaMK9uKKpP" 'True) (C1 ('MetaCons "A" 'PrefixI 'True) (S1 ('MetaSel ('Just "unA") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (Array sh Vector a))))

class Typeable s => Shape (s :: [Nat]) where

Methods

shapeP :: Proxy s -> [Int]

sizeP :: Proxy s -> Int

Instances

Shape ('[] :: [Nat])

Defined in Data.Array.Internal.Shape

Methods

shapeP :: Proxy '[] -> [Int]

sizeP :: Proxy '[] -> Int

(Shape s, KnownNat n) => Shape (n ': s)

Defined in Data.Array.Internal.Shape

Methods

shapeP :: Proxy (n ': s) -> [Int]

sizeP :: Proxy (n ': s) -> Int

type Size (s :: [Nat]) = Size' 1 s

Compute the size, i.e., total number of elements of a type level shape.

type family Rank (s :: [Nat]) :: Nat where ...

Compute the rank, i.e., length of a type level shape.

Equations

Rank '[] = 0

Rank (n ': ns) = 1 + Rank ns

class Vector v

The Vector class is the interface to the underlying storage for the arrays. The operations map straight to operations for Vector.

Minimal complete definition

vIndex, vLength, vToList, vFromList, vSingleton, vReplicate, vMap, vZipWith, vZipWith3, vZipWith4, vZipWith5, vAppend, vConcat, vFold, vSlice, vSum, vProduct, vMaximum, vMinimum, vUpdate, vGenerate, vAll, vAny

Instances

Vector Vector

Defined in Data.Array.Internal.Dynamic

Associated Types

type VecElem Vector :: Type -> Constraint

Methods

vIndex :: VecElem Vector a => Vector a -> Int -> a

vLength :: VecElem Vector a => Vector a -> Int

vToList :: VecElem Vector a => Vector a -> [a]

vFromList :: VecElem Vector a => [a] -> Vector a

vSingleton :: VecElem Vector a => a -> Vector a

vReplicate :: VecElem Vector a => Int -> a -> Vector a

vMap :: (VecElem Vector a, VecElem Vector b) => (a -> b) -> Vector a -> Vector b

vZipWith :: (VecElem Vector a, VecElem Vector b, VecElem Vector c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c

vZipWith3 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d) => (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d

vZipWith4 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e) => (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e

vZipWith5 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e, VecElem Vector f) => (a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f

vAppend :: VecElem Vector a => Vector a -> Vector a -> Vector a

vConcat :: VecElem Vector a => [Vector a] -> Vector a

vFold :: VecElem Vector a => (a -> a -> a) -> a -> Vector a -> a

vSlice :: VecElem Vector a => Int -> Int -> Vector a -> Vector a

vSum :: (VecElem Vector a, Num a) => Vector a -> a

vProduct :: (VecElem Vector a, Num a) => Vector a -> a

vMaximum :: (VecElem Vector a, Ord a) => Vector a -> a

vMinimum :: (VecElem Vector a, Ord a) => Vector a -> a

vUpdate :: VecElem Vector a => Vector a -> [(Int, a)] -> Vector a

vGenerate :: VecElem Vector a => Int -> (Int -> a) -> Vector a

vAll :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

vAny :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

Vector Vector

Defined in Data.Array.Internal.DynamicS

Associated Types

type VecElem Vector :: Type -> Constraint

Methods

vIndex :: VecElem Vector a => Vector a -> Int -> a

vLength :: VecElem Vector a => Vector a -> Int

vToList :: VecElem Vector a => Vector a -> [a]

vFromList :: VecElem Vector a => [a] -> Vector a

vSingleton :: VecElem Vector a => a -> Vector a

vReplicate :: VecElem Vector a => Int -> a -> Vector a

vMap :: (VecElem Vector a, VecElem Vector b) => (a -> b) -> Vector a -> Vector b

vZipWith :: (VecElem Vector a, VecElem Vector b, VecElem Vector c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c

vZipWith3 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d) => (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d

vZipWith4 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e) => (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e

vZipWith5 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e, VecElem Vector f) => (a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f

vAppend :: VecElem Vector a => Vector a -> Vector a -> Vector a

vConcat :: VecElem Vector a => [Vector a] -> Vector a

vFold :: VecElem Vector a => (a -> a -> a) -> a -> Vector a -> a

vSlice :: VecElem Vector a => Int -> Int -> Vector a -> Vector a

vSum :: (VecElem Vector a, Num a) => Vector a -> a

vProduct :: (VecElem Vector a, Num a) => Vector a -> a

vMaximum :: (VecElem Vector a, Ord a) => Vector a -> a

vMinimum :: (VecElem Vector a, Ord a) => Vector a -> a

vUpdate :: VecElem Vector a => Vector a -> [(Int, a)] -> Vector a

vGenerate :: VecElem Vector a => Int -> (Int -> a) -> Vector a

vAll :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

vAny :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

Vector Vector

Defined in Data.Array.Internal.DynamicU

Associated Types

type VecElem Vector :: Type -> Constraint

Methods

vIndex :: VecElem Vector a => Vector a -> Int -> a

vLength :: VecElem Vector a => Vector a -> Int

vToList :: VecElem Vector a => Vector a -> [a]

vFromList :: VecElem Vector a => [a] -> Vector a

vSingleton :: VecElem Vector a => a -> Vector a

vReplicate :: VecElem Vector a => Int -> a -> Vector a

vMap :: (VecElem Vector a, VecElem Vector b) => (a -> b) -> Vector a -> Vector b

vZipWith :: (VecElem Vector a, VecElem Vector b, VecElem Vector c) => (a -> b -> c) -> Vector a -> Vector b -> Vector c

vZipWith3 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d) => (a -> b -> c -> d) -> Vector a -> Vector b -> Vector c -> Vector d

vZipWith4 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e) => (a -> b -> c -> d -> e) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e

vZipWith5 :: (VecElem Vector a, VecElem Vector b, VecElem Vector c, VecElem Vector d, VecElem Vector e, VecElem Vector f) => (a -> b -> c -> d -> e -> f) -> Vector a -> Vector b -> Vector c -> Vector d -> Vector e -> Vector f

vAppend :: VecElem Vector a => Vector a -> Vector a -> Vector a

vConcat :: VecElem Vector a => [Vector a] -> Vector a

vFold :: VecElem Vector a => (a -> a -> a) -> a -> Vector a -> a

vSlice :: VecElem Vector a => Int -> Int -> Vector a -> Vector a

vSum :: (VecElem Vector a, Num a) => Vector a -> a

vProduct :: (VecElem Vector a, Num a) => Vector a -> a

vMaximum :: (VecElem Vector a, Ord a) => Vector a -> a

vMinimum :: (VecElem Vector a, Ord a) => Vector a -> a

vUpdate :: VecElem Vector a => Vector a -> [(Int, a)] -> Vector a

vGenerate :: VecElem Vector a => Int -> (Int -> a) -> Vector a

vAll :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

vAny :: VecElem Vector a => (a -> Bool) -> Vector a -> Bool

Vector []

Defined in Data.Array.Internal

Associated Types

type VecElem [] :: Type -> Constraint

Methods

vIndex :: VecElem [] a => [a] -> Int -> a

vLength :: VecElem [] a => [a] -> Int

vToList :: VecElem [] a => [a] -> [a]

vFromList :: VecElem [] a => [a] -> [a]

vSingleton :: VecElem [] a => a -> [a]

vReplicate :: VecElem [] a => Int -> a -> [a]

vMap :: (VecElem [] a, VecElem [] b) => (a -> b) -> [a] -> [b]

vZipWith :: (VecElem [] a, VecElem [] b, VecElem [] c) => (a -> b -> c) -> [a] -> [b] -> [c]

vZipWith3 :: (VecElem [] a, VecElem [] b, VecElem [] c, VecElem [] d) => (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]

vZipWith4 :: (VecElem [] a, VecElem [] b, VecElem [] c, VecElem [] d, VecElem [] e) => (a -> b -> c -> d -> e) -> [a] -> [b] -> [c] -> [d] -> [e]

vZipWith5 :: (VecElem [] a, VecElem [] b, VecElem [] c, VecElem [] d, VecElem [] e, VecElem [] f) => (a -> b -> c -> d -> e -> f) -> [a] -> [b] -> [c] -> [d] -> [e] -> [f]

vAppend :: VecElem [] a => [a] -> [a] -> [a]

vConcat :: VecElem [] a => [[a]] -> [a]

vFold :: VecElem [] a => (a -> a -> a) -> a -> [a] -> a

vSlice :: VecElem [] a => Int -> Int -> [a] -> [a]

vSum :: (VecElem [] a, Num a) => [a] -> a

vProduct :: (VecElem [] a, Num a) => [a] -> a

vMaximum :: (VecElem [] a, Ord a) => [a] -> a

vMinimum :: (VecElem [] a, Ord a) => [a] -> a

vUpdate :: VecElem [] a => [a] -> [(Int, a)] -> [a]

vGenerate :: VecElem [] a => Int -> (Int -> a) -> [a]

vAll :: VecElem [] a => (a -> Bool) -> [a] -> Bool

vAny :: VecElem [] a => (a -> Bool) -> [a] -> Bool

type ShapeL = [Int]

The shape of an array is a list of its dimensions.

class Window (ws :: [Nat]) (ss :: [Nat]) (rs :: [Nat]) | ws ss -> rs

Instances

Window' ws ws ss rs => Window ws ss rs

Defined in Data.Array.Internal.Shape

class Stride (ts :: [Nat]) (ss :: [Nat]) (rs :: [Nat]) | ts ss -> rs

Instances

Stride ('[] :: [Nat]) ss ss

Defined in Data.Array.Internal.Shape

(Stride ts ss rs, DivRoundUp s t ~ r) => Stride (t ': ts) (s ': ss) (r ': rs)

Defined in Data.Array.Internal.Shape

type Permute (is :: [Nat]) (xs :: [Nat]) = Permute' is (Take (Rank is) xs) ++ Drop (Rank is) xs

class Permutation (is :: [Nat])

Instances

AllElem is (Count 0 is) => Permutation is

Defined in Data.Array.Internal.Shape

class ValidDims (rs :: [Nat]) (sh :: [Nat])

Instances

AllElem rs (Count 0 sh) => ValidDims rs sh

Defined in Data.Array.Internal.Shape

size :: forall sh a. Shape sh => Array sh a -> Int

The number of elements in the array.

shapeL :: Shape sh => Array sh a -> ShapeL

The shape of an array, i.e., a list of the sizes of its dimensions. In the linearization of the array the outermost (i.e. first list element) varies most slowly. O(1) time.

rank :: (Shape sh, KnownNat (Rank sh)) => Array sh a -> Int

The rank of an array, i.e., the number of dimensions it has, which is the n in Array n a. O(1) time.

toList :: forall sh a. Shape sh => Array sh a -> [a]

Convert to a list with the elements in the linearization order. O(n) time.

fromList :: forall sh a. (HasCallStack, Shape sh) => [a] -> Array sh a

Convert from a list with the elements given in the linearization order. Fails if the given shape does not have the same number of elements as the list. O(n) time.

toVector :: Shape sh => Array sh a -> Vector a

Convert to a vector with the elements in the linearization order. O(n) or O(1) time (the latter if the vector is already in the linearization order).

fromVector :: forall sh a. (HasCallStack, Shape sh) => Vector a -> Array sh a

Convert from a vector with the elements given in the linearization order. Fails if the given shape does not have the same number of elements as the list. O(1) time.

normalize :: Shape sh => Array sh a -> Array sh a

Make sure the underlying vector is in the linearization order. This is semantically an identity function, but can have big performance implications. O(n) or O(1) time.

scalar :: a -> Array '[] a

Convert a value to a scalar (rank 0) array. O(1) time.

unScalar :: Array '[] a -> a

Convert a scalar (rank 0) array to a value. O(1) time.

constant :: forall sh a. Shape sh => a -> Array sh a

Make an array with all elements having the same value. O(1) time.

reshape :: forall sh' sh a. (Shape sh, Shape sh', Size sh ~ Size sh') => Array sh a -> Array sh' a

Change the shape of an array. Fails if the arrays have different number of elements. O(n) or O(1) time.

stretch :: forall sh' sh a. (Shape sh, Shape sh', ValidStretch sh sh') => Array sh a -> Array sh' a

Change the size of dimensions with size 1. These dimension can be changed to any size. All other dimensions must remain the same. O(1) time.

stretchOuter :: (KnownNat s, Shape sh) => Array (1 ': sh) a -> Array (s ': sh) a

Change the size of the outermost dimension by replication.

transpose :: forall is sh a. (Permutation is, Rank is <= Rank sh, Shape sh, Shape is, KnownNat (Rank sh)) => Array sh a -> Array (Permute is sh) a

Do an arbitrary array transposition. Fails if the transposition argument is not a permutation of the numbers [0..r-1], where r is the rank of the array. O(1) time.

index :: (HasCallStack, KnownNat s) => Array (s ': sh) a -> Int -> Array sh a

Index into an array. Fails if the index is out of bounds. O(1) time.

pad :: forall ps sh' sh a. (HasCallStack, Padded ps sh sh', Shape sh) => a -> Array sh a -> Array sh' a

Pad each dimension on the low and high side with the given value. O(n) time.

mapA :: Shape sh => (a -> b) -> Array sh a -> Array sh b

Map over the array elements. O(n) time.

zipWithA :: Shape sh => (a -> b -> c) -> Array sh a -> Array sh b -> Array sh c

Map over the array elements. O(n) time.

zipWith3A :: Shape sh => (a -> b -> c -> d) -> Array sh a -> Array sh b -> Array sh c -> Array sh d

Map over the array elements. O(n) time.

append :: (Shape sh, KnownNat m, KnownNat n, KnownNat (m + n)) => Array (m ': sh) a -> Array (n ': sh) a -> Array ((m + n) ': sh) a

Append two arrays along the outermost dimension. All dimensions, except the outermost, must be the same. O(n) time.

ravel :: (Shape sh, KnownNat s) => Array '[s] (Array sh a) -> Array (s ': sh) a

Turn a rank-1 array of arrays into a single array by making the outer array into the outermost dimension of the result array. All the arrays must have the same shape. O(n) time.

unravel :: (Shape sh, KnownNat s) => Array (s ': sh) a -> Array '[s] (Array sh a)

Turn an array into a nested array, this is the inverse of ravel. I.e., ravel . unravel == id.

window :: forall ws sh' sh a. (Window ws sh sh', KnownNat (Rank ws)) => Array sh a -> Array sh' a

Make a window of the outermost dimensions. The rank increases with the length of the window list. E.g., if the shape of the array is [10,12,8] and the window size is [3,3] then the resulting array will have shape [8,10,3,3,8]. O(1) time.

stride :: forall ts sh' sh a. (Stride ts sh sh', Shape ts) => Array sh a -> Array sh' a

Stride the outermost dimensions. E.g., if the array shape is [10,12,8] and the strides are [2,2] then the resulting shape will be [5,6,8]. O(1) time.

slice :: forall sl sh' sh a. Slice sl sh sh' => Array sh a -> Array sh' a

Extract a slice of an array. The first argument is a list of (offset, length) pairs. The length of the slicing argument must not exceed the rank of the array. The extracted slice must fall within the array dimensions. E.g. slice [1,2] (fromList [4] [1,2,3,4]) == [2,3]. O(1) time.

rerank :: forall n i o sh a b. (Drop n sh ~ i, Shape sh, KnownNat n, Shape o, Shape (Take n sh ++ o)) => (Array i a -> Array o b) -> Array sh a -> Array (Take n sh ++ o) b

Apply a function to the subarrays n levels down and make the results into an array with the same n outermost dimensions. The n must not exceed the rank of the array. O(n) time.

rerank2 :: forall n i o sh a b c. (Drop n sh ~ i, Shape sh, KnownNat n, Shape o, Shape (Take n sh ++ o)) => (Array i a -> Array i b -> Array o c) -> Array sh a -> Array sh b -> Array (Take n sh ++ o) c

Apply a two-argument function to the subarrays n levels down and make the results into an array with the same n outermost dimensions. The n must not exceed the rank of the array. O(n) time.

rev :: forall rs sh a. (ValidDims rs sh, Shape rs, Shape sh) => Array sh a -> Array sh a

Reverse the given dimensions, with the outermost being dimension 0. O(1) time.

reduce :: Shape sh => (a -> a -> a) -> a -> Array sh a -> Array '[] a

Reduce all elements of an array into a rank 0 array. To reduce parts use rerank and transpose together with reduce. O(n) time.

foldrA :: Shape sh => (a -> b -> b) -> b -> Array sh a -> b

Constrained version of foldr for Arrays.

Note that this Array actually has Traversable anyway.

traverseA :: (Applicative f, Shape sh) => (a -> f b) -> Array sh a -> f (Array sh b)

Constrained version of traverse for Arrays.

Note that this Array actually has Traversable anyway.

allSameA :: (Shape sh, Eq a) => Array sh a -> Bool

Check if all elements of the array are equal.

sumA :: (Num a, Shape sh) => Array sh a -> a

Sum of all elements.

productA :: (Num a, Shape sh) => Array sh a -> a

Product of all elements.

minimumA :: (Ord a, Shape sh, 1 <= Size sh) => Array sh a -> a

Minimum of all elements.

maximumA :: (Ord a, Shape sh, 1 <= Size sh) => Array sh a -> a

Maximum of all elements.

anyA :: Shape sh => (a -> Bool) -> Array sh a -> Bool

Test if the predicate holds for any element.

allA :: Shape sh => (a -> Bool) -> Array sh a -> Bool

Test if the predicate holds for all elements.

broadcast :: forall ds sh' sh a. (Shape sh, Shape sh', Broadcast ds sh sh') => Array sh a -> Array sh' a

Put the dimensions of the argument into the specified dimensions, and just replicate the data along all other dimensions. The list of dimensions indicies must have the same rank as the argument array and it must be strictly ascending.

generate :: Shape sh => ([Int] -> a) -> Array sh a

Generate an array with a function that computes the value for each index.

iterateN :: forall n a. KnownNat n => (a -> a) -> a -> Array '[n] a

Iterate a function n times.

iota :: (KnownNat n, Enum a, Num a) => Array '[n] a

Generate a vector from 0 to n-1.