Copyright  (c) Alexey Kuleshevich 20182019 

License  BSD3 
Maintainer  Alexey Kuleshevich <lehins@yandex.ru> 
Stability  experimental 
Portability  nonportable 
Safe Haskell  None 
Language  Haskell2010 
Massiv is a library, that allows creation and manipulation of arrays in parallel and
sequentially. Depending on the representation (r
), an
will have
certain properties that are unique to that particular representation, but all of them will share
the same trait, that an array is simply a mapping from an index (Array
r ix eix
) of an arbitrary
dimension to an element (e
) of some value. Which means that some representations describe
classic arrays and are backed by a contiguous chunk of memory reserved for the elements (or
pointers to elements), namely arrays with Manifest
representations:
B
 The most basic type of array that can hold any type of element in a boxed form, i.e. each element is a pointer to the actual value, therefore it is also the slowest representation. Elements are kept in a Weak Head Normal Form (WHNF).N
 Similar toB
, is also a boxed type, except it's elements are always kept in a Normal Form (NF). This property is very useful for parallel processing, i.e. when callingcompute
you do want all of your elements to be fully evaluated.S
 Is a type of array that is backed by pinned memory, therefore pointers to those arrays can be passed to FFI calls, because Garbage Collector (GC) is guaranteed not to move it. Elements must be an instance ofStorable
class. It is just as efficient asP
andU
arrays, except it is subject to fragmentation.U
 Unboxed representation. Elements must be an instance ofUnbox
class.P
 Array that can hold Haskell primitives, such asInt
,Word
,Double
, etc. Any element must be an instance ofPrim
class.M
 General manifest array type, that any of the above representations can be converted to in constant time usingtoManifest
.
There are also array representations that only describe how values for its elements can be computed or loaded into memory, as such, they are represented by functions and do not impose the memory overhead, that is normally associated with arrays. They are needed for proper fusion and parallelization of computation.
D
 delayed array that is a mere function from an index to an element. Also known as Pull array. Crucial representation for fusing computation. UsecomputeAs
in order to load array intoManifest
representation.DL
 delayed load array representation that describes how an array can be loaded. Also known as Push array. Useful for fusing various array combining functions. UsecomputeAs
in order to load array intoManifest
representation.DS
 delayed stream vector representation that describes how to handle a vector with possibility of unknown length. Useful for filtering and unfolding. UsecomputeAs
in order to load such vector intoManifest
representation.DI
 delayed interleaved array. Same asD
, but performs better with unbalanced computation, when evaluation of one element takes much longer than of its neighbor.DW
 delayed windowed array. This peculiar representation allows for very fastStencil
computation.
Other Array types:
L
andLN
 those types aren't particularly useful on their own, but because of their unique ability to be converted to and from nested lists in constant time, provide a perfect intermediary for lists <> array conversion.
Most of the Manifest
arrays are capable of inplace mutation. Check out
Data.Massiv.Array.Mutable module for available functionality.
Many of the function names exported by this package will clash with the ones from Prelude, hence it can be more convenient to import like this:
import Prelude as P import Data.Massiv.Array as A
Synopsis
 empty :: forall r ix e. Construct r ix e => Array r ix e
 singleton :: forall r ix e. Construct r ix e => e > Array r ix e
 replicate :: forall ix e. Index ix => Comp > Sz ix > e > Array DL ix e
 makeArray :: Construct r ix e => Comp > Sz ix > (ix > e) > Array r ix e
 makeArrayLinear :: Construct r ix e => Comp > Sz ix > (Int > e) > Array r ix e
 makeArrayR :: Construct r ix e => r > Comp > Sz ix > (ix > e) > Array r ix e
 makeArrayLinearR :: Construct r ix e => r > Comp > Sz ix > (Int > e) > Array r ix e
 makeVectorR :: Construct r Ix1 e => r > Comp > Sz1 > (Ix1 > e) > Array r Ix1 e
 iterateN :: forall ix e. Index ix => Sz ix > (e > e) > e > Array DL ix e
 iiterateN :: forall ix e. Index ix => Sz ix > (e > ix > e) > e > Array DL ix e
 unfoldlS_ :: Construct DL ix e => Sz ix > (a > (a, e)) > a > Array DL ix e
 iunfoldlS_ :: forall ix e a. Construct DL ix e => Sz ix > (ix > a > (a, e)) > a > Array DL ix e
 unfoldrS_ :: forall ix e a. Construct DL ix e => Sz ix > (a > (e, a)) > a > Array DL ix e
 iunfoldrS_ :: forall ix e a. Construct DL ix e => Sz ix > (a > ix > (e, a)) > a > Array DL ix e
 randomArray :: forall ix e g. Index ix => g > (g > (g, g)) > (g > (e, g)) > Comp > Sz ix > Array DL ix e
 randomArrayS :: forall r ix e g. Mutable r ix e => g > Sz ix > (g > (e, g)) > (g, Array r ix e)
 randomArrayWS :: forall r ix e g m. (Mutable r ix e, MonadUnliftIO m, PrimMonad m) => WorkerStates g > Sz ix > (g > m e) > m (Array r ix e)
 makeArrayA :: forall r ix e f. (Mutable r ix e, Applicative f) => Sz ix > (ix > f e) > f (Array r ix e)
 makeArrayAR :: forall r ix e f. (Mutable r ix e, Applicative f) => r > Sz ix > (ix > f e) > f (Array r ix e)
 makeArrayLinearA :: forall r ix e f. (Mutable r ix e, Applicative f) => Sz ix > (Int > f e) > f (Array r ix e)
 (...) :: Index ix => ix > ix > Array D ix ix
 (..:) :: Index ix => ix > ix > Array D ix ix
 range :: Index ix => Comp > ix > ix > Array D ix ix
 rangeStepM :: (Index ix, MonadThrow m) => Comp > ix > ix > ix > m (Array D ix ix)
 rangeStep' :: Index ix => Comp > ix > ix > ix > Array D ix ix
 rangeInclusive :: Index ix => Comp > ix > ix > Array D ix ix
 rangeStepInclusiveM :: (MonadThrow m, Index ix) => Comp > ix > ix > ix > m (Array D ix ix)
 rangeStepInclusive' :: Index ix => Comp > ix > ix > ix > Array D ix ix
 rangeSize :: Index ix => Comp > ix > Sz ix > Array D ix ix
 rangeStepSize :: Index ix => Comp > ix > ix > Sz ix > Array D ix ix
 enumFromN :: Num e => Comp > e > Sz1 > Vector D e
 enumFromStepN :: Num e => Comp > e > e > Sz1 > Vector D e
 expandWithin :: forall ix e r n a. (IsIndexDimension ix n, Manifest r (Lower ix) a) => Dimension n > Sz1 > (a > Ix1 > e) > Array r (Lower ix) a > Array D ix e
 expandWithinM :: (Index ix, Manifest r (Lower ix) a, MonadThrow m) => Dim > Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > m (Array D ix b)
 expandWithin' :: (Index ix, Manifest r (Lower ix) a) => Dim > Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b
 expandOuter :: (Index ix, Manifest r (Lower ix) a) => Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b
 expandInner :: (Index ix, Manifest r (Lower ix) a) => Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b
 getComp :: Load r ix e => Array r ix e > Comp
 setComp :: Construct r ix e => Comp > Array r ix e > Array r ix e
 compute :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e
 computeS :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e
 computeP :: forall r ix e r'. (Mutable r ix e, Construct r' ix e, Load r' ix e) => Array r' ix e > Array r ix e
 computeIO :: forall r ix e r' m. (Mutable r ix e, Load r' ix e, MonadIO m) => Array r' ix e > m (Array r ix e)
 computePrimM :: forall r ix e r' m. (Mutable r ix e, Load r' ix e, PrimMonad m) => Array r' ix e > m (Array r ix e)
 computeAs :: (Mutable r ix e, Load r' ix e) => r > Array r' ix e > Array r ix e
 computeProxy :: (Mutable r ix e, Load r' ix e) => proxy r > Array r' ix e > Array r ix e
 computeSource :: forall r ix e r'. (Mutable r ix e, Source r' ix e) => Array r' ix e > Array r ix e
 computeWithStride :: forall r ix e r'. (Mutable r ix e, StrideLoad r' ix e) => Stride ix > Array r' ix e > Array r ix e
 computeWithStrideAs :: (Mutable r ix e, StrideLoad r' ix e) => r > Stride ix > Array r' ix e > Array r ix e
 clone :: Mutable r ix e => Array r ix e > Array r ix e
 convert :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e
 convertAs :: (Mutable r ix e, Load r' ix e) => r > Array r' ix e > Array r ix e
 convertProxy :: (Mutable r ix e, Load r' ix e) => proxy r > Array r' ix e > Array r ix e
 fromRaggedArrayM :: forall r ix e r' m. (Mutable r ix e, Ragged r' ix e, Load r' ix e, MonadThrow m) => Array r' ix e > m (Array r ix e)
 fromRaggedArray' :: forall r ix e r'. (Mutable r ix e, Load r' ix e, Ragged r' ix e) => Array r' ix e > Array r ix e
 module Data.Massiv.Vector
 size :: Load r ix e => Array r ix e > Sz ix
 elemsCount :: Load r ix e => Array r ix e > Int
 isEmpty :: Load r ix e => Array r ix e > Bool
 isNotEmpty :: Load r ix e => Array r ix e > Bool
 (!?) :: (Manifest r ix e, MonadThrow m) => Array r ix e > ix > m e
 (!) :: Manifest r ix e => Array r ix e > ix > e
 (??) :: (Manifest r ix e, MonadThrow m) => m (Array r ix e) > ix > m e
 indexM :: (Manifest r ix e, MonadThrow m) => Array r ix e > ix > m e
 index :: Manifest r ix e => Array r ix e > ix > Maybe e
 index' :: Manifest r ix e => Array r ix e > ix > e
 defaultIndex :: Manifest r ix e => e > Array r ix e > ix > e
 borderIndex :: Manifest r ix e => Border e > Array r ix e > ix > e
 evaluateM :: (Source r ix e, MonadThrow m) => Array r ix e > ix > m e
 evaluate' :: Source r ix e => Array r ix e > ix > e
 map :: Source r ix e' => (e' > e) > Array r ix e' > Array D ix e
 imap :: Source r ix e' => (ix > e' > e) > Array r ix e' > Array D ix e
 traverseA :: forall r ix e r' a f. (Source r' ix a, Mutable r ix e, Applicative f) => (a > f e) > Array r' ix a > f (Array r ix e)
 traverseA_ :: forall r ix e a f. (Source r ix e, Applicative f) => (e > f a) > Array r ix e > f ()
 itraverseA :: forall r ix e r' a f. (Source r' ix a, Mutable r ix e, Applicative f) => (ix > a > f e) > Array r' ix a > f (Array r ix e)
 itraverseA_ :: forall r ix e a f. (Source r ix a, Applicative f) => (ix > a > f e) > Array r ix a > f ()
 sequenceA :: forall r ix e r' f. (Source r' ix (f e), Mutable r ix e, Applicative f) => Array r' ix (f e) > f (Array r ix e)
 sequenceA_ :: forall r ix e f. (Source r ix (f e), Applicative f) => Array r ix (f e) > f ()
 traversePrim :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, PrimMonad m) => (a > m b) > Array r' ix a > m (Array r ix b)
 itraversePrim :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, PrimMonad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b)
 mapM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => (a > m b) > Array r' ix a > m (Array r ix b)
 forM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => Array r' ix a > (a > m b) > m (Array r ix b)
 imapM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b)
 iforM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => Array r' ix a > (ix > a > m b) > m (Array r ix b)
 mapM_ :: (Source r ix a, Monad m) => (a > m b) > Array r ix a > m ()
 forM_ :: (Source r ix a, Monad m) => Array r ix a > (a > m b) > m ()
 imapM_ :: (Source r ix a, Monad m) => (ix > a > m b) > Array r ix a > m ()
 iforM_ :: (Source r ix a, Monad m) => Array r ix a > (ix > a > m b) > m ()
 mapIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => (a > m b) > Array r' ix a > m (Array r ix b)
 mapWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > (a > s > m b) > Array r' ix a > m (Array r ix b)
 mapIO_ :: (Source r b e, MonadUnliftIO m) => (e > m a) > Array r b e > m ()
 imapIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b)
 imapWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > (ix > a > s > m b) > Array r' ix a > m (Array r ix b)
 imapIO_ :: (Source r ix e, MonadUnliftIO m) => (ix > e > m a) > Array r ix e > m ()
 forIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => Array r' ix a > (a > m b) > m (Array r ix b)
 forWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > Array r' ix a > (a > s > m b) > m (Array r ix b)
 forIO_ :: (Source r ix e, MonadUnliftIO m) => Array r ix e > (e > m a) > m ()
 iforIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => Array r' ix a > (ix > a > m b) > m (Array r ix b)
 iforWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > Array r' ix a > (ix > a > s > m b) > m (Array r ix b)
 iforIO_ :: (Source r ix a, MonadUnliftIO m) => Array r ix a > (ix > a > m b) > m ()
 imapSchedulerM_ :: (Source r ix e, Monad m) => Scheduler m () > (ix > e > m a) > Array r ix e > m ()
 iforSchedulerM_ :: (Source r ix e, Monad m) => Scheduler m () > Array r ix e > (ix > e > m a) > m ()
 zip :: (Source r1 ix e1, Source r2 ix e2) => Array r1 ix e1 > Array r2 ix e2 > Array D ix (e1, e2)
 zip3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix (e1, e2, e3)
 zip4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix (e1, e2, e3, e4)
 unzip :: Source r ix (e1, e2) => Array r ix (e1, e2) > (Array D ix e1, Array D ix e2)
 unzip3 :: Source r ix (e1, e2, e3) => Array r ix (e1, e2, e3) > (Array D ix e1, Array D ix e2, Array D ix e3)
 unzip4 :: Source r ix (e1, e2, e3, e4) => Array r ix (e1, e2, e3, e4) > (Array D ix e1, Array D ix e2, Array D ix e3, Array D ix e4)
 zipWith :: (Source r1 ix e1, Source r2 ix e2) => (e1 > e2 > e) > Array r1 ix e1 > Array r2 ix e2 > Array D ix e
 zipWith3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => (e1 > e2 > e3 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix e
 zipWith4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => (e1 > e2 > e3 > e4 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix e
 izipWith :: (Source r1 ix e1, Source r2 ix e2) => (ix > e1 > e2 > e) > Array r1 ix e1 > Array r2 ix e2 > Array D ix e
 izipWith3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => (ix > e1 > e2 > e3 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix e
 izipWith4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => (ix > e1 > e2 > e3 > e4 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix e
 liftArray2 :: (Source r1 ix a, Source r2 ix b) => (a > b > e) > Array r1 ix a > Array r2 ix b > Array D ix e
 zipWithA :: (Source r1 ix e1, Source r2 ix e2, Applicative f, Mutable r ix e) => (e1 > e2 > f e) > Array r1 ix e1 > Array r2 ix e2 > f (Array r ix e)
 izipWithA :: (Source r1 ix e1, Source r2 ix e2, Applicative f, Mutable r ix e) => (ix > e1 > e2 > f e) > Array r1 ix e1 > Array r2 ix e2 > f (Array r ix e)
 zipWith3A :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Applicative f, Mutable r ix e) => (e1 > e2 > e3 > f e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > f (Array r ix e)
 izipWith3A :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Applicative f, Mutable r ix e) => (ix > e1 > e2 > e3 > f e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > f (Array r ix e)
 fold :: (Monoid e, Source r ix e) => Array r ix e > e
 ifoldMono :: (Source r ix e, Monoid m) => (ix > e > m) > Array r ix e > m
 foldMono :: (Source r ix e, Monoid m) => (e > m) > Array r ix e > m
 ifoldSemi :: (Source r ix e, Semigroup m) => (ix > e > m) > m > Array r ix e > m
 foldSemi :: (Source r ix e, Semigroup m) => (e > m) > m > Array r ix e > m
 foldOuterSlice :: (OuterSlice r ix e, Monoid m) => (Elt r ix e > m) > Array r ix e > m
 ifoldOuterSlice :: (OuterSlice r ix e, Monoid m) => (Ix1 > Elt r ix e > m) > Array r ix e > m
 foldInnerSlice :: (InnerSlice r ix e, Monoid m) => (Elt r ix e > m) > Array r ix e > m
 ifoldInnerSlice :: (InnerSlice r ix e, Monoid m) => (Ix1 > Elt r ix e > m) > Array r ix e > m
 minimumM :: (MonadThrow m, Source r ix e, Ord e) => Array r ix e > m e
 minimum' :: (Source r ix e, Ord e) => Array r ix e > e
 maximumM :: (MonadThrow m, Source r ix e, Ord e) => Array r ix e > m e
 maximum' :: (Source r ix e, Ord e) => Array r ix e > e
 sum :: (Source r ix e, Num e) => Array r ix e > e
 product :: (Source r ix e, Num e) => Array r ix e > e
 and :: Source r ix Bool => Array r ix Bool > Bool
 or :: Source r ix Bool => Array r ix Bool > Bool
 all :: Source r ix e => (e > Bool) > Array r ix e > Bool
 any :: Source r ix e => (e > Bool) > Array r ix e > Bool
 ifoldlInner :: (Index (Lower ix), Source r ix e) => (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a
 foldlInner :: (Index (Lower ix), Source r ix e) => (a > e > a) > a > Array r ix e > Array D (Lower ix) a
 ifoldrInner :: (Index (Lower ix), Source r ix e) => (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldrInner :: (Index (Lower ix), Source r ix e) => (e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldInner :: (Monoid e, Index (Lower ix), Source r ix e) => Array r ix e > Array D (Lower ix) e
 ifoldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a
 foldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (a > e > a) > a > Array r ix e > Array D (Lower ix) a
 ifoldrWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldrWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldWithin :: (Source r ix a, Monoid a, Index (Lower ix), IsIndexDimension ix n) => Dimension n > Array r ix a > Array D (Lower ix) a
 ifoldlWithin' :: (Index (Lower ix), Source r ix e) => Dim > (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a
 foldlWithin' :: (Index (Lower ix), Source r ix e) => Dim > (a > e > a) > a > Array r ix e > Array D (Lower ix) a
 ifoldrWithin' :: (Index (Lower ix), Source r ix e) => Dim > (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldrWithin' :: (Index (Lower ix), Source r ix e) => Dim > (e > a > a) > a > Array r ix e > Array D (Lower ix) a
 foldWithin' :: (Source r ix a, Monoid a, Index (Lower ix)) => Dim > Array r ix a > Array D (Lower ix) a
 foldlS :: Source r ix e => (a > e > a) > a > Array r ix e > a
 foldrS :: Source r ix e => (e > a > a) > a > Array r ix e > a
 ifoldlS :: Source r ix e => (a > ix > e > a) > a > Array r ix e > a
 ifoldrS :: Source r ix e => (ix > e > a > a) > a > Array r ix e > a
 foldlM :: (Source r ix e, Monad m) => (a > e > m a) > a > Array r ix e > m a
 foldrM :: (Source r ix e, Monad m) => (e > a > m a) > a > Array r ix e > m a
 foldlM_ :: (Source r ix e, Monad m) => (a > e > m a) > a > Array r ix e > m ()
 foldrM_ :: (Source r ix e, Monad m) => (e > a > m a) > a > Array r ix e > m ()
 ifoldlM :: (Source r ix e, Monad m) => (a > ix > e > m a) > a > Array r ix e > m a
 ifoldrM :: (Source r ix e, Monad m) => (ix > e > a > m a) > a > Array r ix e > m a
 ifoldlM_ :: (Source r ix e, Monad m) => (a > ix > e > m a) > a > Array r ix e > m ()
 ifoldrM_ :: (Source r ix e, Monad m) => (ix > e > a > m a) > a > Array r ix e > m ()
 foldrFB :: Source r ix e => (e > b > b) > b > Array r ix e > b
 lazyFoldlS :: Source r ix e => (a > e > a) > a > Array r ix e > a
 lazyFoldrS :: Source r ix e => (e > a > a) > a > Array r ix e > a
 foldlP :: (MonadIO m, Source r ix e) => (a > e > a) > a > (b > a > b) > b > Array r ix e > m b
 foldrP :: (MonadIO m, Source r ix e) => (e > a > a) > a > (a > b > b) > b > Array r ix e > m b
 ifoldlP :: (MonadIO m, Source r ix e) => (a > ix > e > a) > a > (b > a > b) > b > Array r ix e > m b
 ifoldrP :: (MonadIO m, Source r ix e) => (ix > e > a > a) > a > (a > b > b) > b > Array r ix e > m b
 ifoldlIO :: (MonadUnliftIO m, Source r ix e) => (a > ix > e > m a) > a > (b > a > m b) > b > Array r ix e > m b
 ifoldrIO :: (MonadUnliftIO m, Source r ix e) => (ix > e > a > m a) > a > (a > b > m b) > b > Array r ix e > m b
 transpose :: Source r Ix2 e => Array r Ix2 e > Array D Ix2 e
 transposeInner :: (Index (Lower ix), Source r' ix e) => Array r' ix e > Array D ix e
 transposeOuter :: (Index (Lower ix), Source r' ix e) => Array r' ix e > Array D ix e
 reverse :: (IsIndexDimension ix n, Source r ix e) => Dimension n > Array r ix e > Array D ix e
 reverse' :: Source r ix e => Dim > Array r ix e > Array D ix e
 reverseM :: (MonadThrow m, Source r ix e) => Dim > Array r ix e > m (Array D ix e)
 backpermuteM :: forall r ix e r' ix' m. (Mutable r ix e, Source r' ix' e, MonadUnliftIO m, PrimMonad m, MonadThrow m) => Sz ix > (ix > ix') > Array r' ix' e > m (Array r ix e)
 backpermute' :: (Source r' ix' e, Index ix) => Sz ix > (ix > ix') > Array r' ix' e > Array D ix e
 resizeM :: (MonadThrow m, Index ix', Load r ix e, Resize r ix) => Sz ix' > Array r ix e > m (Array r ix' e)
 resize' :: (Index ix', Load r ix e, Resize r ix) => Sz ix' > Array r ix e > Array r ix' e
 flatten :: (Load r ix e, Resize r ix) => Array r ix e > Array r Ix1 e
 extractM :: (MonadThrow m, Extract r ix e) => ix > Sz ix > Array r ix e > m (Array (R r) ix e)
 extract' :: Extract r ix e => ix > Sz ix > Array r ix e > Array (R r) ix e
 extractFromToM :: (MonadThrow m, Extract r ix e) => ix > ix > Array r ix e > m (Array (R r) ix e)
 extractFromTo' :: Extract r ix e => ix > ix > Array r ix e > Array (R r) ix e
 deleteRowsM :: (MonadThrow m, Extract r ix e, Source (R r) ix e, Index (Lower ix)) => Ix1 > Sz Ix1 > Array r ix e > m (Array DL ix e)
 deleteColumnsM :: (MonadThrow m, Extract r ix e, Source (R r) ix e) => Ix1 > Sz Ix1 > Array r ix e > m (Array DL ix e)
 deleteRegionM :: (MonadThrow m, Extract r ix e, Source (R r) ix e) => Dim > Ix1 > Sz Ix1 > Array r ix e > m (Array DL ix e)
 appendOuterM :: forall ix e m. (Index ix, MonadThrow m) => Array DL ix e > Array DL ix e > m (Array DL ix e)
 appendM :: forall r1 r2 ix e m. (MonadThrow m, Source r1 ix e, Source r2 ix e) => Dim > Array r1 ix e > Array r2 ix e > m (Array DL ix e)
 append' :: (Source r1 ix e, Source r2 ix e) => Dim > Array r1 ix e > Array r2 ix e > Array DL ix e
 concatOuterM :: forall ix e m. (Index ix, MonadThrow m) => [Array DL ix e] > m (Array DL ix e)
 concatM :: forall r ix e f m. (MonadThrow m, Foldable f, Source r ix e) => Dim > f (Array r ix e) > m (Array DL ix e)
 concat' :: (Foldable f, Source r ix e) => Dim > f (Array r ix e) > Array DL ix e
 stackSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => Dim > f (Array r (Lower ix) e) > m (Array DL ix e)
 stackOuterSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => f (Array r (Lower ix) e) > m (Array DL ix e)
 stackInnerSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => f (Array r (Lower ix) e) > m (Array DL ix e)
 splitAtM :: (MonadThrow m, Extract r ix e) => Dim > Int > Array r ix e > m (Array (R r) ix e, Array (R r) ix e)
 splitAt' :: Extract r ix e => Dim > Int > Array r ix e > (Array (R r) ix e, Array (R r) ix e)
 splitExtractM :: (MonadThrow m, Extract r ix e, Source (R r) ix e) => Dim > Ix1 > Sz Ix1 > Array r ix e > m (Array (R r) ix e, Array (R r) ix e, Array (R r) ix e)
 upsample :: forall r ix e. Load r ix e => e > Stride ix > Array r ix e > Array DL ix e
 downsample :: forall r ix e. Source r ix e => Stride ix > Array r ix e > Array DL ix e
 zoom :: forall r ix e. Source r ix e => Stride ix > Array r ix e > Array DL ix e
 zoomWithGrid :: forall r ix e. Source r ix e => e > Stride ix > Array r ix e > Array DL ix e
 transformM :: forall r ix e r' ix' e' a m. (Mutable r ix e, Source r' ix' e', MonadUnliftIO m, PrimMonad m, MonadThrow m) => (Sz ix' > m (Sz ix, a)) > (a > (ix' > m e') > ix > m e) > Array r' ix' e' > m (Array r ix e)
 transform' :: (Source r' ix' e', Index ix) => (Sz ix' > (Sz ix, a)) > (a > (ix' > e') > ix > e) > Array r' ix' e' > Array D ix e
 transform2M :: (Mutable r ix e, Source r1 ix1 e1, Source r2 ix2 e2, MonadUnliftIO m, PrimMonad m, MonadThrow m) => (Sz ix1 > Sz ix2 > m (Sz ix, a)) > (a > (ix1 > m e1) > (ix2 > m e2) > ix > m e) > Array r1 ix1 e1 > Array r2 ix2 e2 > m (Array r ix e)
 transform2' :: (Source r1 ix1 e1, Source r2 ix2 e2, Index ix) => (Sz ix1 > Sz ix2 > (Sz ix, a)) > (a > (ix1 > e1) > (ix2 > e2) > ix > e) > Array r1 ix1 e1 > Array r2 ix2 e2 > Array D ix e
 (!>) :: OuterSlice r ix e => Array r ix e > Int > Elt r ix e
 (!?>) :: (MonadThrow m, OuterSlice r ix e) => Array r ix e > Int > m (Elt r ix e)
 (??>) :: (MonadThrow m, OuterSlice r ix e) => m (Array r ix e) > Int > m (Elt r ix e)
 (<!) :: InnerSlice r ix e => Array r ix e > Int > Elt r ix e
 (<!?) :: (MonadThrow m, InnerSlice r ix e) => Array r ix e > Int > m (Elt r ix e)
 (<??) :: (MonadThrow m, InnerSlice r ix e) => m (Array r ix e) > Int > m (Elt r ix e)
 (<!>) :: Slice r ix e => Array r ix e > (Dim, Int) > Elt r ix e
 (<!?>) :: (MonadThrow m, Slice r ix e) => Array r ix e > (Dim, Int) > m (Elt r ix e)
 (<??>) :: (MonadThrow m, Slice r ix e) => m (Array r ix e) > (Dim, Int) > m (Elt r ix e)
 outerSlices :: OuterSlice r ix e => Array r ix e > Array D Ix1 (Elt r ix e)
 innerSlices :: InnerSlice r ix e => Array r ix e > Array D Ix1 (Elt r ix e)
 withinSlices :: (IsIndexDimension ix n, Slice r ix e) => Dimension n > Array r ix e > Array D Ix1 (Elt r ix e)
 withinSlicesM :: (MonadThrow m, Slice r ix e) => Dim > Array r ix e > m (Array D Ix1 (Elt r ix e))
 quicksort :: (Mutable r Ix1 e, Ord e) => Array r Ix1 e > Array r Ix1 e
 tally :: (Mutable r Ix1 e, Resize r ix, Load r ix e, Ord e) => Array r ix e > Array DS Ix1 (e, Int)
 iterateUntil :: (Load r' ix e, Mutable r ix e) => (Int > Array r ix e > Array r ix e > Bool) > (Int > Array r ix e > Array r' ix e) > Array r ix e > Array r ix e
 fromList :: forall r e. Mutable r Ix1 e => Comp > [e] > Array r Ix1 e
 fromListsM :: forall r ix e m. (Nested LN ix e, Ragged L ix e, Mutable r ix e, MonadThrow m) => Comp > [ListItem ix e] > m (Array r ix e)
 fromLists' :: forall r ix e. (Nested LN ix e, Ragged L ix e, Mutable r ix e) => Comp > [ListItem ix e] > Array r ix e
 toList :: Source r ix e => Array r ix e > [e]
 toLists :: (Nested LN ix e, Construct L ix e, Source r ix e) => Array r ix e > [ListItem ix e]
 toLists2 :: (Source r ix e, Index (Lower ix)) => Array r ix e > [[e]]
 toLists3 :: (Index (Lower (Lower ix)), Index (Lower ix), Source r ix e) => Array r ix e > [[[e]]]
 toLists4 :: (Index (Lower (Lower (Lower ix))), Index (Lower (Lower ix)), Index (Lower ix), Source r ix e) => Array r ix e > [[[[e]]]]
 module Data.Massiv.Array.Mutable
 module Data.Massiv.Core
 module Data.Massiv.Array.Delayed
 module Data.Massiv.Array.Manifest
 module Data.Massiv.Array.Stencil
 module Data.Massiv.Array.Numeric
Construct
With constant value
empty :: forall r ix e. Construct r ix e => Array r ix e Source #
Create an Array with no elements. By itself it is not particularly useful, but it serves as a nice base for constructing larger arrays.
Examples
>>>
import Data.Massiv.Array as A
>>>
:set XTypeApplications
>>>
xs = empty @DL @Ix1 @Double
>>>
snoc (cons 4 (cons 5 xs)) 22
Array DL Seq (Sz1 3) [ 4.0, 5.0, 22.0 ]
Since: 0.3.0
Create an Array with a single element.
Examples
>>>
import Data.Massiv.Array as A
>>>
singleton 7 :: Array D Ix4 Double
Array D Seq (Sz (1 :> 1 :> 1 :. 1)) [ [ [ [ 7.0 ] ] ] ]
Instead of specifying type signature we could use TypeApplications
>>>
:set XTypeApplications
>>>
singleton @U @Ix4 @Double 7
Array U Seq (Sz (1 :> 1 :> 1 :. 1)) [ [ [ [ 7.0 ] ] ] ]
Since: 0.1.0
replicate :: forall ix e. Index ix => Comp > Sz ix > e > Array DL ix e Source #
Replicate the same element
Since: 0.3.0
With a function
:: Construct r ix e  
=> Comp  
> Sz ix  Size of the result array. 
> (ix > e)  Function to generate elements at a particular index 
> Array r ix e 
Construct an Array. Resulting type either has to be unambiguously inferred or restricted manually, like in the example below. Use "Data.Massiv.Array.makeArrayR" if you'd like to specify representation as an argument.
>>>
import Data.Massiv.Array
>>>
makeArray Seq (Sz (3 :. 4)) (\ (i :. j) > if i == j then i else 0) :: Array D Ix2 Int
Array D Seq (Sz (3 :. 4)) [ [ 0, 0, 0, 0 ] , [ 0, 1, 0, 0 ] , [ 0, 0, 2, 0 ] ]
Instead of restricting the full type manually we can use TypeApplications
as convenience:
>>>
:set XTypeApplications
>>>
makeArray @P @_ @Double Seq (Sz2 3 4) $ \(i :. j) > logBase (fromIntegral i) (fromIntegral j)
Array P Seq (Sz (3 :. 4)) [ [ NaN, 0.0, 0.0, 0.0 ] , [ Infinity, NaN, Infinity, Infinity ] , [ Infinity, 0.0, 1.0, 1.5849625007211563 ] ]
Since: 0.1.0
makeArrayLinear :: Construct r ix e => Comp > Sz ix > (Int > e) > Array r ix e Source #
Same as makeArray
, but produce elements using linear rowmajor index.
>>>
import Data.Massiv.Array
>>>
makeArrayLinear Seq (Sz (2 :. 4)) id :: Array D Ix2 Int
Array D Seq (Sz (2 :. 4)) [ [ 0, 1, 2, 3 ] , [ 4, 5, 6, 7 ] ]
Since: 0.3.0
makeArrayR :: Construct r ix e => r > Comp > Sz ix > (ix > e) > Array r ix e Source #
Just like makeArray
but with ability to specify the result representation as an
argument. Note the U
nboxed type constructor in the below example.
Examples
>>>
import Data.Massiv.Array
>>>
makeArrayR U Par (Sz (2 :> 3 :. 4)) (\ (i :> j :. k) > i * i + j * j == k * k)
Array U Par (Sz (2 :> 3 :. 4)) [ [ [ True, False, False, False ] , [ False, True, False, False ] , [ False, False, True, False ] ] , [ [ False, True, False, False ] , [ False, False, False, False ] , [ False, False, False, False ] ] ]
Since: 0.1.0
makeArrayLinearR :: Construct r ix e => r > Comp > Sz ix > (Int > e) > Array r ix e Source #
Same as makeArrayLinear
, but with ability to supply resulting representation
Since: 0.3.0
makeVectorR :: Construct r Ix1 e => r > Comp > Sz1 > (Ix1 > e) > Array r Ix1 e Source #
Same as makeArrayR
, but restricted to 1dimensional arrays.
Since: 0.1.0
Iterating
iterateN :: forall ix e. Index ix => Sz ix > (e > e) > e > Array DL ix e Source #
Sequentially iterate over each cell in the array in the rowmajor order while continuously aplying the accumulator at each step.
Example
>>>
import Data.Massiv.Array
>>>
iterateN (Sz2 2 10) succ (10 :: Int)
Array DL Seq (Sz (2 :. 10)) [ [ 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 ] , [ 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 ] ]
Since: 0.3.0
iiterateN :: forall ix e. Index ix => Sz ix > (e > ix > e) > e > Array DL ix e Source #
Same as iterateN
, but with index aware function.
Since: 0.3.0
Unfolding
unfoldlS_ :: Construct DL ix e => Sz ix > (a > (a, e)) > a > Array DL ix e Source #
Unfold sequentially from the end. There is no way to save the accumulator after
unfolding is done, since resulting array is delayed, but it's possible to use
unfoldlPrimM
to achive such effect.
Since: 0.3.0
iunfoldlS_ :: forall ix e a. Construct DL ix e => Sz ix > (ix > a > (a, e)) > a > Array DL ix e Source #
Unfold sequentially from the right with an index aware function.
Since: 0.3.0
unfoldrS_ :: forall ix e a. Construct DL ix e => Sz ix > (a > (e, a)) > a > Array DL ix e Source #
Right unfold into a delayed load array. For the opposite direction use unfoldlS_
.
Examples
>>>
import Data.Massiv.Array
>>>
unfoldrS_ (Sz1 10) (\xs > (Prelude.head xs, Prelude.tail xs)) ([10 ..] :: [Int])
Array DL Seq (Sz1 10) [ 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 ]
Since: 0.3.0
iunfoldrS_ :: forall ix e a. Construct DL ix e => Sz ix > (a > ix > (e, a)) > a > Array DL ix e Source #
Right unfold of a delayed load array with index aware function
Since: 0.3.0
Random
:: Index ix  
=> g  Initial random value generator 
> (g > (g, g))  A function that can split a generator in two independent generators 
> (g > (e, g))  A function that produces a random value and the next generator 
> Comp  Computation strategy. 
> Sz ix  Resulting size of the array. 
> Array DL ix e 
Create an array with random values by using a pure splittable random number generator
such as one provided by either splitmix or
random packages. If you don't have a
splittable generator consider using randomArrayS
or randomArrayWS
instead.
Because of the pure nature of the generator and its splitability we are not only able to parallelize the random value generation, but also guarantee that it will be deterministic, granted none of the arguments have changed.
Examples
>>>
import Data.Massiv.Array
>>>
import System.Random.SplitMix as SplitMix
>>>
gen = SplitMix.mkSMGen 217
>>>
randomArray gen SplitMix.splitSMGen SplitMix.nextDouble (ParN 2) (Sz2 2 3) :: Array DL Ix2 Double
Array DL (ParN 2) (Sz (2 :. 3)) [ [ 0.7383156058619669, 0.39904053166835896, 0.5617584038393628 ] , [ 0.7218718218678238, 0.7006722805067258, 0.7225894731396042 ] ]
>>>
import Data.Massiv.Array
>>>
import System.Random as System
>>>
gen = System.mkStdGen 217
>>>
randomArray gen System.split System.random (ParN 2) (Sz2 2 3) :: Array DL Ix2 Double
Array DL (ParN 2) (Sz (2 :. 3)) [ [ 0.15191527341922206, 0.2045537167404079, 0.9635356052820256 ] , [ 9.308278528094238e2, 0.7200934018606843, 0.23173694193083583 ] ]
Since: 0.3.3
:: Mutable r ix e  
=> g  Initial random value generator 
> Sz ix  Resulting size of the array. 
> (g > (e, g))  A function that produces a random value and the next generator 
> (g, Array r ix e) 
Similar to randomArray
but performs generation sequentially, which means it doesn't
require splitability property. Another consequence is that it returns the new generator
together with manifest array of random values.
Examples
>>>
import Data.Massiv.Array
>>>
import System.Random.SplitMix as SplitMix
>>>
gen = SplitMix.mkSMGen 217
>>>
snd $ randomArrayS gen (Sz2 2 3) SplitMix.nextDouble :: Array P Ix2 Double
Array P Seq (Sz (2 :. 3)) [ [ 0.8878273949359751, 0.11290807610140963, 0.7383156058619669 ] , [ 0.39904053166835896, 0.5617584038393628, 0.16248374266020216 ] ]
>>>
import Data.Massiv.Array
>>>
import System.Random.Mersenne.Pure64 as MT
>>>
gen = MT.pureMT 217
>>>
snd $ randomArrayS gen (Sz2 2 3) MT.randomDouble :: Array P Ix2 Double
Array P Seq (Sz (2 :. 3)) [ [ 0.5504018416543631, 0.22504666452851707, 0.4480480867867128 ] , [ 0.7139711572975297, 0.49401087853770953, 0.9397201599368645 ] ]
>>>
import Data.Massiv.Array
>>>
import System.Random as System
>>>
gen = System.mkStdGen 217
>>>
snd $ randomArrayS gen (Sz2 2 3) System.random :: Array P Ix2 Double
Array P Seq (Sz (2 :. 3)) [ [ 0.7972230393466304, 0.4485860543300083, 0.257773196880671 ] , [ 0.19115043859955794, 0.33784788936970034, 3.479381605706322e2 ] ]
Since: 0.3.4
:: (Mutable r ix e, MonadUnliftIO m, PrimMonad m)  
=> WorkerStates g  Use 
> Sz ix  Resulting size of the array 
> (g > m e)  Generate the value using the per thread generator. 
> m (Array r ix e) 
This is a stateful approach of generating random values. If your generator is pure
and splittable, it is better to use randomArray
instead, which will give you a pure,
deterministic and parallelizable generation of arrays. On the other hand, if your
generator is not thread safe, which is most likely the case, instead of using some sort
of global mutex, WorkerStates
allows you to keep track of individual state per worker
(thread), which fits parallelization of random value generation perfectly. All that
needs to be done is generators need to be initialized once per worker and then they can
be reused as many times as necessary.
Examples
In the example below we take a stateful random generator from wmcrandom, which is not thread safe, and safely parallelize it by giving each thread it's own generator:
λ> import Data.Massiv.Array λ> import System.Random.MWC (createSystemRandom, uniformR) λ> import System.Random.MWC.Distributions (standard) λ> gens < initWorkerStates Par (\_ > createSystemRandom) λ> randomArrayWS gens (Sz2 2 3) standard :: IO (Array P Ix2 Double) Array P Par (Sz (2 :. 3)) [ [ 0.9066144845415213, 0.5264323240310042, 1.320943607597422 ] , [ 0.6837929005619592, 0.3041255565826211, 6.53353089112833e2 ] ] λ> randomArrayWS gens (Sz1 10) (uniformR (0, 9)) :: IO (Array P Ix1 Int) Array P Par (Sz1 10) [ 3, 6, 1, 2, 1, 7, 6, 0, 8, 8 ]
Since: 0.3.4
Applicative
makeArrayA :: forall r ix e f. (Mutable r ix e, Applicative f) => Sz ix > (ix > f e) > f (Array r ix e) Source #
Similar to makeArray
, but construct the array sequentially using an Applicative
interface.
Note  using generateArray
or
generateArrayS
will always be faster, althought not always possible.
Since: 0.2.6
makeArrayAR :: forall r ix e f. (Mutable r ix e, Applicative f) => r > Sz ix > (ix > f e) > f (Array r ix e) Source #
Same as makeArrayA
, but with ability to supply result array representation.
Since: 0.2.6
makeArrayLinearA :: forall r ix e f. (Mutable r ix e, Applicative f) => Sz ix > (Int > f e) > f (Array r ix e) Source #
Same as makeArrayA
, but with linear index.
Since: 0.4.5
Enumeration
(...) :: Index ix => ix > ix > Array D ix ix infix 4 Source #
Handy synonym for
. Similar to rangeInclusive
Seq
..
for list.
>>>
Ix1 4 ... 10
Array D Seq (Sz1 7) [ 4, 5, 6, 7, 8, 9, 10 ]
Since: 0.3.0
range :: Index ix => Comp > ix > ix > Array D ix ix Source #
Create an array of indices with a range from start to finish (notincluding), where indices are incremeted by one.
Examples
>>>
import Data.Massiv.Array
>>>
range Seq (Ix1 1) 6
Array D Seq (Sz1 5) [ 1, 2, 3, 4, 5 ]>>>
fromIx2 <$> range Seq (1) (2 :. 2)
Array D Seq (Sz (3 :. 3)) [ [ (1,1), (1,0), (1,1) ] , [ (0,1), (0,0), (0,1) ] , [ (1,1), (1,0), (1,1) ] ]
Since: 0.1.0
:: (Index ix, MonadThrow m)  
=> Comp  Computation strategy 
> ix  Start 
> ix  Step (Can't have zeros) 
> ix  End 
> m (Array D ix ix) 
Same as range
, but with a custom step.
Throws Exceptions: IndexZeroException
Examples
>>>
import Data.Massiv.Array
>>>
rangeStepM Seq (Ix1 1) 2 8
Array D Seq (Sz1 4) [ 1, 3, 5, 7 ]>>>
rangeStepM Seq (Ix1 1) 0 8
*** Exception: IndexZeroException: 0
Since: 0.3.0
rangeStep' :: Index ix => Comp > ix > ix > ix > Array D ix ix Source #
Same as rangeStepM
, but will throw an error whenever step
contains zeros.
Example
>>>
import Data.Massiv.Array
>>>
rangeStep' Seq (Ix1 1) 2 6
Array D Seq (Sz1 3) [ 1, 3, 5 ]
Since: 0.3.0
rangeInclusive :: Index ix => Comp > ix > ix > Array D ix ix Source #
Just like range
, except the finish index is included.
Since: 0.3.0
rangeStepInclusiveM :: (MonadThrow m, Index ix) => Comp > ix > ix > ix > m (Array D ix ix) Source #
Just like rangeStep
, except the finish index is included.
Since: 0.3.0
rangeStepInclusive' :: Index ix => Comp > ix > ix > ix > Array D ix ix Source #
Just like range
, except the finish index is included.
Since: 0.3.1
:: Index ix  
=> Comp  Computation strategy 
> ix 

> Sz ix 

> Array D ix ix 
Create an array of specified size with indices starting with some index at position 0
and
incremented by 1
until the end of the array is reached
Since: 0.3.0
:: Index ix  
=> Comp  Computation strategy 
> ix 

> ix 

> Sz ix 

> Array D ix ix 
Same as rangeSize
, but with ability to specify the step.
Since: 0.3.0
Same as enumFromStepN
with step dx = 1
.
Related: senumFromN
, senumFromStepN
,
enumFromStepN
, rangeSize
, rangeStepSize
, range
Examples
>>>
import Data.Massiv.Array
>>>
enumFromN Seq (5 :: Double) 3
Array D Seq (Sz1 3) [ 5.0, 6.0, 7.0 ]
Similar:
Prelude.
enumFromTo
 Very similar to
[i .. i + n  1]
, except thatsenumFromN
is faster, but it only works forNum
and not forEnum
elements Data.Vector.Generic.
enumFromN
Since: 0.1.0
:: Num e  
=> Comp  
> e 

> e 

> Sz1 

> Vector D e 
Enumerate from a starting number x
exactly n
times with a custom step value
dx
. Unlike senumFromStepN
, there is no dependency on neigboring
elements therefore enumFromStepN
is parallelizable.
Related: senumFromN
, senumFromStepN
,
enumFromN
, rangeSize
, rangeStepSize
, range
, rangeStepM
Examples
>>>
import Data.Massiv.Array
>>>
enumFromStepN Seq 1 (0.1 :: Double) 5
Array D Seq (Sz1 5) [ 1.0, 1.1, 1.2, 1.3, 1.4 ]>>>
enumFromStepN Seq (pi :: Float) (pi/4) 9
Array D Seq (Sz1 9) [ 3.1415927, 2.3561945, 1.5707964, 0.78539824, 0.0, 0.78539824, 1.5707963, 2.3561947, 3.1415927 ]
Similar:
Prelude.
enumFrom
 Similar to
take n [x, x + dx ..]
, except thatenumFromStepN
is parallelizable and it only works forNum
and not forEnum
elements. Floating point value will be slightly different as well. Data.Vector.Generic.
enumFromStepN
 Similar in the outcome, but very different in the way it works.
Since: 0.1.0
Expansion
expandWithin :: forall ix e r n a. (IsIndexDimension ix n, Manifest r (Lower ix) a) => Dimension n > Sz1 > (a > Ix1 > e) > Array r (Lower ix) a > Array D ix e Source #
Function that expands an array to one with a higher dimension.
This is useful for constructing arrays where there is shared computation between multiple cells. The makeArray method of constructing arrays:
makeArray :: Construct r ix e => Comp > ix > (ix > e) > Array r ix e
...runs a function ix > e
at every array index. This is inefficient if
there is a substantial amount of repeated computation that could be shared
while constructing elements on the same dimension. The expand functions make
this possible. First you construct an Array r (Lower ix) a
of one fewer
dimensions where a
is something like
or Array
r Ix1
a
. Then
you use Array
r Ix2
aexpandWithin
and a creation function a > Int > b
to create an
or Array
D
Ix2
b
respectfully.Array
D
Ix3
b
Examples
>>>
import Data.Massiv.Array
>>>
a = makeArrayR U Seq (Sz1 6) (+10)  Imagine (+10) is some expensive function
>>>
a
Array U Seq (Sz1 6) [ 10, 11, 12, 13, 14, 15 ]>>>
expandWithin Dim1 5 (\ e j > (j + 1) * 100 + e) a :: Array D Ix2 Int
Array D Seq (Sz (6 :. 5)) [ [ 110, 210, 310, 410, 510 ] , [ 111, 211, 311, 411, 511 ] , [ 112, 212, 312, 412, 512 ] , [ 113, 213, 313, 413, 513 ] , [ 114, 214, 314, 414, 514 ] , [ 115, 215, 315, 415, 515 ] ]>>>
expandWithin Dim2 5 (\ e j > (j + 1) * 100 + e) a :: Array D Ix2 Int
Array D Seq (Sz (5 :. 6)) [ [ 110, 111, 112, 113, 114, 115 ] , [ 210, 211, 212, 213, 214, 215 ] , [ 310, 311, 312, 313, 314, 315 ] , [ 410, 411, 412, 413, 414, 415 ] , [ 510, 511, 512, 513, 514, 515 ] ]
Since: 0.2.6
expandWithinM :: (Index ix, Manifest r (Lower ix) a, MonadThrow m) => Dim > Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > m (Array D ix b) Source #
Similar to expandWithin
, except that dimension is specified at a value level, which means it
will throw an exception on an invalid dimension.
Since: 0.4.0
expandWithin' :: (Index ix, Manifest r (Lower ix) a) => Dim > Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b Source #
Similar to expandWithin
, except that dimension is specified at a value level, which means it
will throw an exception on an invalid dimension.
Since: 0.2.6
expandOuter :: (Index ix, Manifest r (Lower ix) a) => Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b Source #
Similar to expandWithin
, except it uses the outermost dimension.
Since: 0.2.6
expandInner :: (Index ix, Manifest r (Lower ix) a) => Sz1 > (a > Ix1 > b) > Array r (Lower ix) a > Array D ix b Source #
Similar to expandWithin
, except it uses the innermost dimension.
Since: 0.2.6
Compute
getComp :: Load r ix e => Array r ix e > Comp Source #
Get computation strategy of this array
Since: 0.1.0
setComp :: Construct r ix e => Comp > Array r ix e > Array r ix e Source #
Set computation strategy for this array
Example
>>>
:set XTypeApplications
>>>
import Data.Massiv.Array
>>>
a = singleton @DL @Ix1 @Int 0
>>>
a
Array DL Seq (Sz1 1) [ 0 ]>>>
setComp (ParN 6) a  use 6 capabilities
Array DL (ParN 6) (Sz1 1) [ 0 ]
compute :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e Source #
computeS :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e Source #
Compute array sequentially disregarding predefined computation strategy. Very much
the same as computePrimM
, but executed in ST
, thus pure.
Since: 0.1.0
computeP :: forall r ix e r'. (Mutable r ix e, Construct r' ix e, Load r' ix e) => Array r' ix e > Array r ix e Source #
Compute array in parallel using all cores disregarding predefined computation strategy. Computation stategy of the resulting array will match the source, despite that it is diregarded.
Since: 0.5.4
computeIO :: forall r ix e r' m. (Mutable r ix e, Load r' ix e, MonadIO m) => Array r' ix e > m (Array r ix e) Source #
computePrimM :: forall r ix e r' m. (Mutable r ix e, Load r' ix e, PrimMonad m) => Array r' ix e > m (Array r ix e) Source #
Compute an array in PrimMonad
sequentially disregarding predefined computation
strategy.
Since: 0.4.5
computeAs :: (Mutable r ix e, Load r' ix e) => r > Array r' ix e > Array r ix e Source #
Just as compute
, but let's you supply resulting representation type as an argument.
Examples
>>>
import Data.Massiv.Array
>>>
computeAs P $ range Seq (Ix1 0) 10
Array P Seq (Sz1 10) [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ]
computeProxy :: (Mutable r ix e, Load r' ix e) => proxy r > Array r' ix e > Array r ix e Source #
Same as compute
and computeAs
, but let's you supply resulting representation type as a proxy
argument.
Examples
Useful only really for cases when representation constructor or TypeApplications
extension
aren't desireable for some reason:
>>>
import Data.Proxy
>>>
import Data.Massiv.Array
>>>
computeProxy (Proxy :: Proxy P) $ (^ (2 :: Int)) <$> range Seq (Ix1 0) 10
Array P Seq (Sz1 10) [ 0, 1, 4, 9, 16, 25, 36, 49, 64, 81 ]
Since: 0.1.1
computeSource :: forall r ix e r'. (Mutable r ix e, Source r' ix e) => Array r' ix e > Array r ix e Source #
computeWithStride :: forall r ix e r'. (Mutable r ix e, StrideLoad r' ix e) => Stride ix > Array r' ix e > Array r ix e Source #
computeWithStrideAs :: (Mutable r ix e, StrideLoad r' ix e) => r > Stride ix > Array r' ix e > Array r ix e Source #
Same as computeWithStride
, but with ability to specify resulting array representation.
Since: 0.3.0
clone :: Mutable r ix e => Array r ix e > Array r ix e Source #
O(n)  Make an exact immutable copy of an Array.
Since: 0.1.0
convert :: forall r ix e r'. (Mutable r ix e, Load r' ix e) => Array r' ix e > Array r ix e Source #
O(n)  conversion between array types. A full copy will occur, unless when the source and result arrays are of the same representation, in which case it is an O(1) operation.
Since: 0.1.0
convertAs :: (Mutable r ix e, Load r' ix e) => r > Array r' ix e > Array r ix e Source #
Same as convert
, but let's you supply resulting representation type as an argument.
Since: 0.1.0
fromRaggedArrayM :: forall r ix e r' m. (Mutable r ix e, Ragged r' ix e, Load r' ix e, MonadThrow m) => Array r' ix e > m (Array r ix e) Source #
Convert a ragged array into a common array with rectangular shape. Throws ShapeException
whenever supplied ragged array does not have a rectangular shape.
Since: 0.4.0
fromRaggedArray' :: forall r ix e r'. (Mutable r ix e, Load r' ix e, Ragged r' ix e) => Array r' ix e > Array r ix e Source #
Same as fromRaggedArrayM
, but will throw a pure exception if its shape is not
rectangular.
Since: 0.1.1
Vector
module Data.Massiv.Vector
Size
isEmpty :: Load r ix e => Array r ix e > Bool Source #
O(1)  Check if an array has no elements.
Examples
>>>
import Data.Massiv.Array
>>>
isEmpty $ range Seq (Ix2 10 20) (11 :. 21)
False>>>
isEmpty $ range Seq (Ix2 10 20) (10 :. 21)
True
Since: 0.1.0
isNotEmpty :: Load r ix e => Array r ix e > Bool Source #
O(1)  Check if array has elements.
Examples
>>>
import Data.Massiv.Array
>>>
isNotEmpty (singleton 1 :: Array D Ix2 Int)
True>>>
isNotEmpty (empty :: Array D Ix2 Int)
False
Since: 0.5.1
Indexing
(!?) :: (Manifest r ix e, MonadThrow m) => Array r ix e > ix > m e infixl 4 Source #
O(1)  Infix version of indexM
.
Exceptions: IndexOutOfBoundsException
Examples
>>>
import Data.Massiv.Array as A
>>>
:set XTypeApplications
>>>
a < fromListsM @U @Ix2 @Int Seq [[1,2,3],[4,5,6]]
>>>
a
Array U Seq (Sz (2 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ]>>>
a !? 0 :. 2
3>>>
a !? 0 :. 3
*** Exception: IndexOutOfBoundsException: (0 :. 3) is not safe for (Sz (2 :. 3))>>>
a !? 0 :. 3 :: Maybe Int
Nothing
Since: 0.1.0
(!) :: Manifest r ix e => Array r ix e > ix > e infixl 4 Source #
O(1)  Infix version of index'
.
Examples
>>>
import Data.Massiv.Array as A
>>>
a = computeAs U $ iterateN (Sz (2 :. 3)) succ (0 :: Int)
>>>
a
Array U Seq (Sz (2 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ]>>>
a ! 0 :. 2
3>>>
a ! 0 :. 3
*** Exception: IndexOutOfBoundsException: (0 :. 3) is not safe for (Sz (2 :. 3))
Since: 0.1.0
(??) :: (Manifest r ix e, MonadThrow m) => m (Array r ix e) > ix > m e infixl 4 Source #
O(1)  Lookup an element in the array, where array itself is wrapped with
MonadThrow
. This operator is useful when used together with slicing or other
functions that can fail.
Exceptions: IndexOutOfBoundsException
Examples
>>>
import Data.Massiv.Array as A
>>>
:set XTypeApplications
>>>
ma = fromListsM @U @Ix3 @Int @Maybe Seq [[[1,2,3]],[[4,5,6]]]
>>>
ma
Just (Array U Seq (Sz (2 :> 1 :. 3)) [ [ [ 1, 2, 3 ] ] , [ [ 4, 5, 6 ] ] ] )>>>
ma ??> 1
Just (Array M Seq (Sz (1 :. 3)) [ [ 4, 5, 6 ] ] )>>>
ma ??> 1 ?? 0 :. 2
Just 6>>>
ma ?? 1 :> 0 :. 2
Just 6
Since: 0.1.0
index' :: Manifest r ix e => Array r ix e > ix > e Source #
O(1)  Lookup an element in the array. This is a partial function and it can throw
IndexOutOfBoundsException
inside pure code. It is safer to use index
instead.
Examples
>>>
import Data.Massiv.Array
>>>
:set XOverloadedLists
>>>
xs = [0..100] :: Array U Ix1 Int
>>>
index' xs 50
50>>>
index' xs 150
*** Exception: IndexOutOfBoundsException: 150 is not safe for (Sz1 101)
Since: 0.1.0
defaultIndex :: Manifest r ix e => e > Array r ix e > ix > e Source #
O(1)  Lookup an element in the array, while using default element when index is out of bounds.
Examples
>>>
import Data.Massiv.Array
>>>
:set XOverloadedLists
>>>
xs = [0..100] :: Array P Ix1 Int
>>>
defaultIndex 999 xs 100
100>>>
defaultIndex 999 xs 101
999
Since: 0.1.0
borderIndex :: Manifest r ix e => Border e > Array r ix e > ix > e Source #
O(1)  Lookup an element in the array. Use a border resolution technique when index is out of bounds.
Examples
>>>
import Data.Massiv.Array as A
>>>
:set XOverloadedLists
>>>
xs = [0..100] :: Array U Ix1 Int
>>>
borderIndex Wrap xs <$> range Seq 99 104
Array D Seq (Sz1 5) [ 99, 100, 0, 1, 2 ]
Since: 0.1.0
evaluateM :: (Source r ix e, MonadThrow m) => Array r ix e > ix > m e Source #
This is just like indexM
function, but it allows getting values from
delayed arrays as well as Manifest
. As the name suggests, indexing into a
delayed array at the same index multiple times will cause evaluation of the
value each time and can destroy the performace if used without care.
Examples
>>>
import Control.Exception
>>>
import Data.Massiv.Array
>>>
evaluateM (range Seq (Ix2 10 20) (100 :. 210)) 50 :: Either SomeException Ix2
Right (60 :. 70)>>>
evaluateM (range Seq (Ix2 10 20) (100 :. 210)) 150 :: Either SomeException Ix2
Left (IndexOutOfBoundsException: (150 :. 150) is not safe for (Sz (90 :. 190)))
Since: 0.3.0
evaluate' :: Source r ix e => Array r ix e > ix > e Source #
Similar to evaluateM
, but will throw an exception in pure code.
Examples
>>>
import Data.Massiv.Array
>>>
evaluate' (range Seq (Ix2 10 20) (100 :. 210)) 50
60 :. 70>>>
evaluate' (range Seq (Ix2 10 20) (100 :. 210)) 150
*** Exception: IndexOutOfBoundsException: (150 :. 150) is not safe for (Sz (90 :. 190))
Since: 0.3.0
Mapping
map :: Source r ix e' => (e' > e) > Array r ix e' > Array D ix e Source #
Map a function over an array
imap :: Source r ix e' => (ix > e' > e) > Array r ix e' > Array D ix e Source #
Map an index aware function over an array
Traversing
Applicative
traverseA :: forall r ix e r' a f. (Source r' ix a, Mutable r ix e, Applicative f) => (a > f e) > Array r' ix a > f (Array r ix e) Source #
Traverse with an Applicative
action over an array sequentially.
Note  using traversePrim
will always be faster, althought not always possible.
Since: 0.2.6
traverseA_ :: forall r ix e a f. (Source r ix e, Applicative f) => (e > f a) > Array r ix e > f () Source #
Traverse sequentially over a source array, while discarding the result.
Since: 0.3.0
itraverseA :: forall r ix e r' a f. (Source r' ix a, Mutable r ix e, Applicative f) => (ix > a > f e) > Array r' ix a > f (Array r ix e) Source #
Traverse with an Applicative
index aware action over an array sequentially.
Since: 0.2.6
itraverseA_ :: forall r ix e a f. (Source r ix a, Applicative f) => (ix > a > f e) > Array r ix a > f () Source #
Traverse with an Applicative
index aware action over an array sequentially.
Since: 0.2.6
sequenceA :: forall r ix e r' f. (Source r' ix (f e), Mutable r ix e, Applicative f) => Array r' ix (f e) > f (Array r ix e) Source #
Sequence actions in a source array.
Since: 0.3.0
sequenceA_ :: forall r ix e f. (Source r ix (f e), Applicative f) => Array r ix (f e) > f () Source #
Sequence actions in a source array, while discarding the result.
Since: 0.3.0
PrimMonad
traversePrim :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, PrimMonad m) => (a > m b) > Array r' ix a > m (Array r ix b) Source #
Traverse sequentially within PrimMonad
over an array with an action.
Since: 0.3.0
itraversePrim :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, PrimMonad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b) Source #
Same as traversePrim
, but traverse with index aware action.
Since: 0.3.0
Monadic mapping
Sequential
:: (Source r' ix a, Mutable r ix b, Monad m)  
=> (a > m b)  Mapping action 
> Array r' ix a  Source array 
> m (Array r ix b) 
Map a monadic action over an array sequentially.
Since: 0.2.6
forM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => Array r' ix a > (a > m b) > m (Array r ix b) Source #
Same as mapM
except with arguments flipped.
Since: 0.2.6
imapM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b) Source #
Map an index aware monadic action over an array sequentially.
Since: 0.2.6
iforM :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, Monad m) => Array r' ix a > (ix > a > m b) > m (Array r ix b) Source #
Same as forM
, except with an index aware action.
Since: 0.5.1
mapM_ :: (Source r ix a, Monad m) => (a > m b) > Array r ix a > m () Source #
Map a monadic function over an array sequentially, while discarding the result.
Examples
>>>
import Data.Massiv.Array as A
>>>
rangeStepM Par (Ix1 10) 12 60 >>= A.mapM_ print
10 22 34 46 58
Since: 0.1.0
forM_ :: (Source r ix a, Monad m) => Array r ix a > (a > m b) > m () Source #
Just like mapM_
, except with flipped arguments.
Examples
Here is a common way of iterating N times using a for loop in an imperative language with mutation being an obvious side effect:
>>>
import Data.Massiv.Array as A
>>>
import Data.IORef
>>>
ref < newIORef 0 :: IO (IORef Int)
>>>
A.forM_ (range Seq (Ix1 0) 1000) $ \ i > modifyIORef' ref (+i)
>>>
readIORef ref
499500
imapM_ :: (Source r ix a, Monad m) => (ix > a > m b) > Array r ix a > m () Source #
Map a monadic index aware function over an array sequentially, while discarding the result.
Examples
>>>
import Data.Massiv.Array
>>>
imapM_ (curry print) $ range Seq (Ix1 10) 15
(0,10) (1,11) (2,12) (3,13) (4,14)
Since: 0.1.0
iforM_ :: (Source r ix a, Monad m) => Array r ix a > (ix > a > m b) > m () Source #
Just like imapM_
, except with flipped arguments.
Parallelizable
mapIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => (a > m b) > Array r' ix a > m (Array r ix b) Source #
mapWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > (a > s > m b) > Array r' ix a > m (Array r ix b) Source #
Same as imapWS
, but without the index.
Since: 0.3.4
imapIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => (ix > a > m b) > Array r' ix a > m (Array r ix b) Source #
Same as mapIO
but map an index aware action instead. Respects computation strategy.
Since: 0.2.6
imapWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > (ix > a > s > m b) > Array r' ix a > m (Array r ix b) Source #
Same as imapIO
, but ignores the inner computation strategy and uses stateful
workers during computation instead. Use initWorkerStates
for the WorkerStates
initialization.
Since: 0.3.4
imapIO_ :: (Source r ix e, MonadUnliftIO m) => (ix > e > m a) > Array r ix e > m () Source #
Same as mapIO_
, but map an index aware action instead.
Since: 0.2.6
forIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => Array r' ix a > (a > m b) > m (Array r ix b) Source #
Same as mapIO
but with arguments flipped.
Since: 0.2.6
forWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > Array r' ix a > (a > s > m b) > m (Array r ix b) Source #
Same as iforWS
, but without the index.
Since: 0.3.4
forIO_ :: (Source r ix e, MonadUnliftIO m) => Array r ix e > (e > m a) > m () Source #
Same as mapIO_
but with arguments flipped.
Example
This is the same example as in forM_
, with important difference that accumulator ref
will be
modified concurrently by as many threads as there are capabilities.
>>>
import Data.Massiv.Array
>>>
import Data.IORef
>>>
ref < newIORef 0 :: IO (IORef Int)
>>>
forIO_ (range Par (Ix1 0) 1000) $ \ i > atomicModifyIORef' ref (\v > (v+i, ()))
>>>
readIORef ref
499500
Since: 0.2.6
iforIO :: forall r ix b r' a m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => Array r' ix a > (ix > a > m b) > m (Array r ix b) Source #
Same as imapIO
but with arguments flipped.
Since: 0.2.6
iforWS :: forall r ix b r' a s m. (Source r' ix a, Mutable r ix b, MonadUnliftIO m, PrimMonad m) => WorkerStates s > Array r' ix a > (ix > a > s > m b) > m (Array r ix b) Source #
Same as imapWS
, but with source array and mapping action arguments flipped.
Since: 0.3.4
iforIO_ :: (Source r ix a, MonadUnliftIO m) => Array r ix a > (ix > a > m b) > m () Source #
Same as imapIO_
but with arguments flipped.
Since: 0.2.6
imapSchedulerM_ :: (Source r ix e, Monad m) => Scheduler m () > (ix > e > m a) > Array r ix e > m () Source #
Same as imapM_
, but will use the supplied scheduler.
Since: 0.3.1
iforSchedulerM_ :: (Source r ix e, Monad m) => Scheduler m () > Array r ix e > (ix > e > m a) > m () Source #
Same as imapM_
, but will use the supplied scheduler.
Since: 0.3.1
Zipping
zip :: (Source r1 ix e1, Source r2 ix e2) => Array r1 ix e1 > Array r2 ix e2 > Array D ix (e1, e2) Source #
Zip two arrays
zip3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix (e1, e2, e3) Source #
Zip three arrays
zip4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix (e1, e2, e3, e4) Source #
Zip four arrays
Since: 0.5.4
unzip :: Source r ix (e1, e2) => Array r ix (e1, e2) > (Array D ix e1, Array D ix e2) Source #
Unzip two arrays
unzip3 :: Source r ix (e1, e2, e3) => Array r ix (e1, e2, e3) > (Array D ix e1, Array D ix e2, Array D ix e3) Source #
Unzip three arrays
unzip4 :: Source r ix (e1, e2, e3, e4) => Array r ix (e1, e2, e3, e4) > (Array D ix e1, Array D ix e2, Array D ix e3, Array D ix e4) Source #
Unzip four arrays
Since: 0.5.4
zipWith :: (Source r1 ix e1, Source r2 ix e2) => (e1 > e2 > e) > Array r1 ix e1 > Array r2 ix e2 > Array D ix e Source #
Zip two arrays with a function. Resulting array will be an intersection of source arrays in case their dimensions do not match.
zipWith3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => (e1 > e2 > e3 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix e Source #
Just like zipWith
, except zip three arrays with a function.
zipWith4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => (e1 > e2 > e3 > e4 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix e Source #
Just like zipWith
, except zip four arrays with a function.
Since: 0.5.4
izipWith :: (Source r1 ix e1, Source r2 ix e2) => (ix > e1 > e2 > e) > Array r1 ix e1 > Array r2 ix e2 > Array D ix e Source #
Just like zipWith
, except with an index aware function.
izipWith3 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3) => (ix > e1 > e2 > e3 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array D ix e Source #
Just like zipWith3
, except with an index aware function.
izipWith4 :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Source r4 ix e4) => (ix > e1 > e2 > e3 > e4 > e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > Array r4 ix e4 > Array D ix e Source #
Just like zipWith4
, except with an index aware function.
Since: 0.5.4
liftArray2 :: (Source r1 ix a, Source r2 ix b) => (a > b > e) > Array r1 ix a > Array r2 ix b > Array D ix e Source #
Applicative
zipWithA :: (Source r1 ix e1, Source r2 ix e2, Applicative f, Mutable r ix e) => (e1 > e2 > f e) > Array r1 ix e1 > Array r2 ix e2 > f (Array r ix e) Source #
Similar to zipWith
, except does it sequentially and using the Applicative
. Note that
resulting array has Mutable representation.
Since: 0.3.0
izipWithA :: (Source r1 ix e1, Source r2 ix e2, Applicative f, Mutable r ix e) => (ix > e1 > e2 > f e) > Array r1 ix e1 > Array r2 ix e2 > f (Array r ix e) Source #
Similar to zipWith
, except does it sequentiall and using the Applicative
. Note that
resulting array has Mutable representation.
Since: 0.3.0
zipWith3A :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Applicative f, Mutable r ix e) => (e1 > e2 > e3 > f e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > f (Array r ix e) Source #
Same as zipWithA
, but for three arrays.
Since: 0.3.0
izipWith3A :: (Source r1 ix e1, Source r2 ix e2, Source r3 ix e3, Applicative f, Mutable r ix e) => (ix > e1 > e2 > e3 > f e) > Array r1 ix e1 > Array r2 ix e2 > Array r3 ix e3 > f (Array r ix e) Source #
Same as izipWithA
, but for three arrays.
Since: 0.3.0
Folding
All folding is done in a rowmajor order.
Unstructured folds
Functions in this section will fold any Source
array with respect to the inner
Comp
utation strategy setting.
O(n)  Unstructured fold of an array.
Since: 0.3.0
:: (Source r ix e, Monoid m)  
=> (ix > e > m)  Convert each element of an array to an appropriate 
> Array r ix e  Source array 
> m 
O(n)  Monoidal fold over an array with an index aware function. Also known as reduce.
Since: 0.2.4
:: (Source r ix e, Semigroup m)  
=> (ix > e > m)  Convert each element of an array to an appropriate 
> m  Initial element that must be neutral to the ( 
> Array r ix e  Source array 
> m 
O(n)  Semigroup fold over an array with an index aware function.
Since: 0.2.4
:: (Source r ix e, Semigroup m)  
=> (e > m)  Convert each element of an array to an appropriate 
> m  Initial element that must be neutral to the ( 
> Array r ix e  Source array 
> m 
O(n)  Semigroup fold over an array.
Since: 0.1.6
foldOuterSlice :: (OuterSlice r ix e, Monoid m) => (Elt r ix e > m) > Array r ix e > m Source #
Reduce each outer slice into a monoid and mappend results together
Example
>>>
import Data.Massiv.Array as A
>>>
import Data.Monoid (Product(..))
>>>
arr = computeAs P $ iterateN (Sz2 2 3) (+1) (10 :: Int)
>>>
arr
Array P Seq (Sz (2 :. 3)) [ [ 11, 12, 13 ] , [ 14, 15, 16 ] ]>>>
getProduct $ foldOuterSlice (\row > Product (A.sum row)) arr
1620>>>
(11 + 12 + 13) * (14 + 15 + 16) :: Int
1620
Since: 0.4.3
ifoldOuterSlice :: (OuterSlice r ix e, Monoid m) => (Ix1 > Elt r ix e > m) > Array r ix e > m Source #
Reduce each outer slice into a monoid with an index aware function and mappend results together
Since: 0.4.3
foldInnerSlice :: (InnerSlice r ix e, Monoid m) => (Elt r ix e > m) > Array r ix e > m Source #
Reduce each inner slice into a monoid and mappend results together
Example
>>>
import Data.Massiv.Array as A
>>>
import Data.Monoid (Product(..))
>>>
arr = computeAs P $ iterateN (Sz2 2 3) (+1) (10 :: Int)
>>>
arr
Array P Seq (Sz (2 :. 3)) [ [ 11, 12, 13 ] , [ 14, 15, 16 ] ]>>>
getProduct $ foldInnerSlice (\column > Product (A.sum column)) arr
19575>>>
(11 + 14) * (12 + 15) * (13 + 16) :: Int
19575
Since: 0.4.3
ifoldInnerSlice :: (InnerSlice r ix e, Monoid m) => (Ix1 > Elt r ix e > m) > Array r ix e > m Source #
Reduce each inner slice into a monoid with an index aware function and mappend results together
Since: 0.4.3
minimumM :: (MonadThrow m, Source r ix e, Ord e) => Array r ix e > m e Source #
O(n)  Compute minimum of all elements.
Since: 0.3.0
minimum' :: (Source r ix e, Ord e) => Array r ix e > e Source #
O(n)  Compute minimum of all elements.
Since: 0.3.0
maximumM :: (MonadThrow m, Source r ix e, Ord e) => Array r ix e > m e Source #
O(n)  Compute maximum of all elements.
Since: 0.3.0
maximum' :: (Source r ix e, Ord e) => Array r ix e > e Source #
O(n)  Compute maximum of all elements.
Since: 0.3.0
sum :: (Source r ix e, Num e) => Array r ix e > e Source #
O(n)  Compute sum of all elements.
Since: 0.1.0
product :: (Source r ix e, Num e) => Array r ix e > e Source #
O(n)  Compute product of all elements.
Since: 0.1.0
and :: Source r ix Bool => Array r ix Bool > Bool Source #
O(n)  Compute conjunction of all elements.
Since: 0.1.0
or :: Source r ix Bool => Array r ix Bool > Bool Source #
O(n)  Compute disjunction of all elements.
Since: 0.1.0
all :: Source r ix e => (e > Bool) > Array r ix e > Bool Source #
O(n)  Determines whether all element of the array satisfy the predicate.
Since: 0.1.0
any :: Source r ix e => (e > Bool) > Array r ix e > Bool Source #
O(n)  Determines whether any element of the array satisfies the predicate.
Since: 0.1.0
Single dimension folds
Safe inner most
ifoldlInner :: (Index (Lower ix), Source r ix e) => (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Left fold over the inner most dimension with index aware function.
Since: 0.2.4
foldlInner :: (Index (Lower ix), Source r ix e) => (a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Left fold over the inner most dimension.
Since: 0.2.4
ifoldrInner :: (Index (Lower ix), Source r ix e) => (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Right fold over the inner most dimension with index aware function.
Since: 0.2.4
foldrInner :: (Index (Lower ix), Source r ix e) => (e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Right fold over the inner most dimension.
Since: 0.2.4
foldInner :: (Monoid e, Index (Lower ix), Source r ix e) => Array r ix e > Array D (Lower ix) e Source #
Monoidal fold over the inner most dimension.
Since: 0.4.3
Type safe within
ifoldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Left fold along a specified dimension with an index aware function.
Since: 0.2.4
foldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Left fold along a specified dimension.
Example
>>>
import Data.Massiv.Array
>>>
:set XTypeApplications
>>>
arr = makeArrayLinear @U Seq (Sz (2 :. 5)) id
>>>
arr
Array U Seq (Sz (2 :. 5)) [ [ 0, 1, 2, 3, 4 ] , [ 5, 6, 7, 8, 9 ] ]>>>
foldlWithin Dim1 (flip (:)) [] arr
Array D Seq (Sz1 2) [ [4,3,2,1,0], [9,8,7,6,5] ]>>>
foldlWithin Dim2 (flip (:)) [] arr
Array D Seq (Sz1 5) [ [5,0], [6,1], [7,2], [8,3], [9,4] ]
Since: 0.2.4
ifoldrWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Right fold along a specified dimension with an index aware function.
Since: 0.2.4
foldrWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r ix e) => Dimension n > (e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Right fold along a specified dimension.
Since: 0.2.4
foldWithin :: (Source r ix a, Monoid a, Index (Lower ix), IsIndexDimension ix n) => Dimension n > Array r ix a > Array D (Lower ix) a Source #
Monoidal fold over some internal dimension.
Since: 0.4.3
Partial within
ifoldlWithin' :: (Index (Lower ix), Source r ix e) => Dim > (ix > a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Similar to ifoldlWithin
, except that dimension is specified at a value level, which means it
will throw an exception on an invalid dimension.
Since: 0.2.4
foldlWithin' :: (Index (Lower ix), Source r ix e) => Dim > (a > e > a) > a > Array r ix e > Array D (Lower ix) a Source #
Similar to foldlWithin
, except that dimension is specified at a value level, which means it will
throw an exception on an invalid dimension.
Since: 0.2.4
ifoldrWithin' :: (Index (Lower ix), Source r ix e) => Dim > (ix > e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Similar to ifoldrWithin
, except that dimension is specified at a value level, which means it
will throw an exception on an invalid dimension.
Since: 0.2.4
foldrWithin' :: (Index (Lower ix), Source r ix e) => Dim > (e > a > a) > a > Array r ix e > Array D (Lower ix) a Source #
Similar to foldrWithin
, except that dimension is specified at a value level, which means it
will throw an exception on an invalid dimension.
Since: 0.2.4
foldWithin' :: (Source r ix a, Monoid a, Index (Lower ix)) => Dim > Array r ix a > Array D (Lower ix) a Source #
Monoidal fold over some internal dimension. This is a pratial function and will
result in IndexDimensionException
if supplied dimension is invalid.
Since: 0.4.3
Sequential folds
Functions in this section will fold any Source
array sequentially, regardless of the inner
Comp
utation strategy setting.
foldlS :: Source r ix e => (a > e > a) > a > Array r ix e > a Source #
O(n)  Left fold, computed sequentially.
Since: 0.1.0
foldrS :: Source r ix e => (e > a > a) > a > Array r ix e > a Source #
O(n)  Right fold, computed sequentially.
Since: 0.1.0
ifoldlS :: Source r ix e => (a > ix > e > a) > a > Array r ix e > a Source #
O(n)  Left fold with an index aware function, computed sequentially.
Since: 0.1.0
ifoldrS :: Source r ix e => (ix > e > a > a) > a > Array r ix e > a Source #
O(n)  Right fold with an index aware function, computed sequentially.
Since: 0.1.0
Monadic
foldlM :: (Source r ix e, Monad m) => (a > e > m a) > a > Array r ix e > m a Source #
O(n)  Monadic left fold.
Since: 0.1.0
foldrM :: (Source r ix e, Monad m) => (e > a > m a) > a > Array r ix e > m a Source #
O(n)  Monadic right fold.
Since: 0.1.0
foldlM_ :: (Source r ix e, Monad m) => (a > e > m a) > a > Array r ix e > m () Source #
O(n)  Monadic left fold, that discards the result.
Since: 0.1.0
foldrM_ :: (Source r ix e, Monad m) => (e > a > m a) > a > Array r ix e > m () Source #
O(n)  Monadic right fold, that discards the result.
Since: 0.1.0
ifoldlM :: (Source r ix e, Monad m) => (a > ix > e > m a) > a > Array r ix e > m a Source #
O(n)  Monadic left fold with an index aware function.
Since: 0.1.0
ifoldrM :: (Source r ix e, Monad m) => (ix > e > a > m a) > a > Array r ix e > m a Source #
O(n)  Monadic right fold with an index aware function.
Since: 0.1.0
ifoldlM_ :: (Source r ix e, Monad m) => (a > ix > e > m a) > a > Array r ix e > m () Source #
O(n)  Monadic left fold with an index aware function, that discards the result.
Since: 0.1.0
ifoldrM_ :: (Source r ix e, Monad m) => (ix > e > a > m a) > a > Array r ix e > m () Source #
O(n)  Monadic right fold with an index aware function, that discards the result.
Since: 0.1.0
Special folds
foldrFB :: Source r ix e => (e > b > b) > b > Array r ix e > b Source #
Version of foldr that supports foldr/build
list fusion implemented by GHC.
Since: 0.1.0
lazyFoldlS :: Source r ix e => (a > e > a) > a > Array r ix e > a Source #
O(n)  Left fold, computed sequentially with lazy accumulator.
Since: 0.1.0
lazyFoldrS :: Source r ix e => (e > a > a) > a > Array r ix e > a Source #
O(n)  Right fold, computed sequentially with lazy accumulator.
Since: 0.1.0
Parallel folds
Note It is important to compile with threaded withrtsopts=N
flags, otherwise there will be
no parallelization.
Functions in this section will fold any Source
array in parallel, regardless of the inner
Comp
utation strategy setting. All of the parallel structured folds are performed inside IO
monad, because referential transparency can't generally be preserved and results will depend on the
number of cores/capabilities that computation is being performed on.
In contrast to sequential folds, each parallel folding function accepts two functions and two initial elements as arguments. This is necessary because an array is first split into chunks, which folded individually on separate cores with the first function, and the results of those folds are further folded with the second function.
:: (MonadIO m, Source r ix e)  
=> (a > e > a)  Folding function 
> a  Accumulator. Will be applied to 
> (b > a > b)  Chunk results folding function 
> b  Accumulator for results of chunks folding. 
> Array r ix e  
> m b 
O(n)  Left fold, computed with respect of array's computation strategy. Because we do
potentially split the folding among many threads, we also need a combining function and an
accumulator for the results. Depending on the number of threads being used, results can be
different, hence is the MonadIO
constraint.
Examples
>>>
import Data.Massiv.Array
>>>
foldlP (flip (:)) [] (flip (:)) [] $ makeArrayR D Seq (Sz1 6) id
[[5,4,3,2,1,0]]>>>
foldlP (flip (:)) [] (++) [] $ makeArrayR D Seq (Sz1 6) id
[5,4,3,2,1,0]>>>
foldlP (flip (:)) [] (flip (:)) [] $ makeArrayR D (ParN 3) (Sz1 6) id
[[5,4],[3,2],[1,0]]>>>
foldlP (flip (:)) [] (++) [] $ makeArrayR D (ParN 3) (Sz1 6) id
[1,0,3,2,5,4]
Since: 0.1.0
foldrP :: (MonadIO m, Source r ix e) => (e > a > a) > a > (a > b > b) > b > Array r ix e > m b Source #
O(n)  Right fold, computed with respect to computation strategy. Same as foldlP
, except
directed from the last element in the array towards beginning.
Examples
>>>
import Data.Massiv.Array
>>>
foldrP (:) [] (++) [] $ makeArrayR D (ParN 2) (Sz2 2 3) fromIx2
[(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]>>>
foldrP (:) [] (:) [] $ makeArrayR D Seq (Sz1 6) id
[[0,1,2,3,4,5]]>>>
foldrP (:) [] (:) [] $ makeArrayR D (ParN 3) (Sz1 6) id
[[0,1],[2,3],[4,5]]
Since: 0.1.0
ifoldlP :: (MonadIO m, Source r ix e) => (a > ix > e > a) > a > (b > a > b) > b > Array r ix e > m b Source #
O(n)  Left fold with an index aware function, computed in parallel. Just
like foldlP
, except that folding function will receive an index of an
element it is being applied to.
Since: 0.1.0
ifoldrP :: (MonadIO m, Source r ix e) => (ix > e > a > a) > a > (a > b > b) > b > Array r ix e > m b Source #
O(n)  Right fold with an index aware function, while respecting the computation strategy.
Same as ifoldlP
, except directed from the last element in the array towards
beginning, but also rowmajor.
Since: 0.1.0
:: (MonadUnliftIO m, Source r ix e)  
=> (a > ix > e > m a)  Index aware folding IO action 
> a  Accumulator 
> (b > a > m b)  Folding action that is applied to the results of a parallel fold 
> b  Accumulator for chunks folding 
> Array r ix e  
> m b 
Similar to ifoldlP
, except that folding functions themselves do live in IO
Since: 0.1.0
ifoldrIO :: (MonadUnliftIO m, Source r ix e) => (ix > e > a > m a) > a > (a > b > m b) > b > Array r ix e > m b Source #
Similar to ifoldrP
, except that folding functions themselves do live in IO
Since: 0.1.0
Transforming
Transpose
transpose :: Source r Ix2 e => Array r Ix2 e > Array D Ix2 e Source #
Transpose a 2dimensional array
Examples
>>>
import Data.Massiv.Array
>>>
arr = makeArrayLinearR D Seq (Sz (2 :. 3)) id
>>>
arr
Array D Seq (Sz (2 :. 3)) [ [ 0, 1, 2 ] , [ 3, 4, 5 ] ]>>>
transpose arr
Array D Seq (Sz (3 :. 2)) [ [ 0, 3 ] , [ 1, 4 ] , [ 2, 5 ] ]
Since: 0.1.0
transposeInner :: (Index (Lower ix), Source r' ix e) => Array r' ix e > Array D ix e Source #
Transpose inner two dimensions of at least rank2 array.
Examples
>>>
import Data.Massiv.Array
>>>
arr = makeArrayLinearR U Seq (Sz (2 :> 3 :. 4)) id
>>>
arr
Array U Seq (Sz (2 :> 3 :. 4)) [ [ [ 0, 1, 2, 3 ] , [ 4, 5, 6, 7 ] , [ 8, 9, 10, 11 ] ] , [ [ 12, 13, 14, 15 ] , [ 16, 17, 18, 19 ] , [ 20, 21, 22, 23 ] ] ]>>>
transposeInner arr
Array D Seq (Sz (3 :> 2 :. 4)) [ [ [ 0, 1, 2, 3 ] , [ 12, 13, 14, 15 ] ] , [ [ 4, 5, 6, 7 ] , [ 16, 17, 18, 19 ] ] , [ [ 8, 9, 10, 11 ] , [ 20, 21, 22, 23 ] ] ]
Since: 0.1.0
transposeOuter :: (Index (Lower ix), Source r' ix e) => Array r' ix e > Array D ix e Source #
Transpose outer two dimensions of at least rank2 array.
Examples
>>>
import Data.Massiv.Array
>>>
:set XTypeApplications
>>>
arr = makeArrayLinear @U Seq (Sz (2 :> 3 :. 4)) id
>>>
arr
Array U Seq (Sz (2 :> 3 :. 4)) [ [ [ 0, 1, 2, 3 ] , [ 4, 5, 6, 7 ] , [ 8, 9, 10, 11 ] ] , [ [ 12, 13, 14, 15 ] , [ 16, 17, 18, 19 ] , [ 20, 21, 22, 23 ] ] ]>>>
transposeOuter arr
Array D Seq (Sz (2 :> 4 :. 3)) [ [ [ 0, 4, 8 ] , [ 1, 5, 9 ] , [ 2, 6, 10 ] , [ 3, 7, 11 ] ] , [ [ 12, 16, 20 ] , [ 13, 17, 21 ] , [ 14, 18, 22 ] , [ 15, 19, 23 ] ] ]
Since: 0.1.0
Reverse
reverse :: (IsIndexDimension ix n, Source r ix e) => Dimension n > Array r ix e > Array D ix e Source #
Reverse an array along some dimension. Dimension supplied is checked at compile time.
Example
>>>
import Data.Massiv.Array as A
>>>
arr = makeArrayLinear Seq (Sz2 4 5) (+10) :: Array D Ix2 Int
>>>
arr
Array D Seq (Sz (4 :. 5)) [ [ 10, 11, 12, 13, 14 ] , [ 15, 16, 17, 18, 19 ] , [ 20, 21, 22, 23, 24 ] , [ 25, 26, 27, 28, 29 ] ]>>>
A.reverse Dim1 arr
Array D Seq (Sz (4 :. 5)) [ [ 14, 13, 12, 11, 10 ] , [ 19, 18, 17, 16, 15 ] , [ 24, 23, 22, 21, 20 ] , [ 29, 28, 27, 26, 25 ] ]>>>
A.reverse Dim2 arr
Array D Seq (Sz (4 :. 5)) [ [ 25, 26, 27, 28, 29 ] , [ 20, 21, 22, 23, 24 ] , [ 15, 16, 17, 18, 19 ] , [ 10, 11, 12, 13, 14 ] ]
Since: 0.4.1
reverse' :: Source r ix e => Dim > Array r ix e > Array D ix e Source #
Reverse an array along some dimension. Same as reverseM
, but throws the
IndexDimensionException
from pure code.
Since: 0.4.1
reverseM :: (MonadThrow m, Source r ix e) => Dim > Array r ix e > m (Array D ix e) Source #
Similarly to reverse
, flip an array along a particular dimension, but throws
IndexDimensionException
for an incorrect dimension.
Since: 0.4.1
Backpermute
:: (Mutable r ix e, Source r' ix' e, MonadUnliftIO m, PrimMonad m, MonadThrow m)  
=> Sz ix  Size of the result array 
> (ix > ix')  A function that maps indices of the new array into the source one. 
> Array r' ix' e  Source array. 
> m (Array r ix e) 
Rearrange elements of an array into a new one by using a function that maps indices of the
newly created one into the old one. This function can throw IndexOutOfBoundsException
.
Examples
>>>
import Data.Massiv.Array
>>>
:set XTypeApplications
>>>
arr = makeArrayLinear @D Seq (Sz (2 :> 3 :. 4)) id
>>>
arr
Array D Seq (Sz (2 :> 3 :. 4)) [ [ [ 0, 1, 2, 3 ] , [ 4, 5, 6, 7 ] , [ 8, 9, 10, 11 ] ] , [ [ 12, 13, 14, 15 ] , [ 16, 17, 18, 19 ] , [ 20, 21, 22, 23 ] ] ]>>>
backpermuteM @U (Sz (4 :. 2)) (\(i :. j) > j :> j :. i) arr
Array U Seq (Sz (4 :. 2)) [ [ 0, 16 ] , [ 1, 17 ] , [ 2, 18 ] , [ 3, 19 ] ]
Since: 0.3.0
:: (Source r' ix' e, Index ix)  
=> Sz ix  Size of the result array 
> (ix > ix')  A function that maps indices of the new array into the source one. 
> Array r' ix' e  Source array. 
> Array D ix e 
Similar to backpermuteM
, with a few notable differences:
 Creates a delayed array, instead of manifest, therefore it can be fused
 Respects computation strategy, so it can be parallelized
 Throws a runtime
IndexOutOfBoundsException
from pure code.
Since: 0.3.0
Resize
resizeM :: (MonadThrow m, Index ix', Load r ix e, Resize r ix) => Sz ix' > Array r ix e > m (Array r ix' e) Source #
O(1)  Changes the shape of an array. Returns Nothing
if total
number of elements does not match the source array.
Since: 0.3.0
resize' :: (Index ix', Load r ix e, Resize r ix) => Sz ix' > Array r ix e > Array r ix' e Source #
Same as resizeM
, but will throw an error if supplied dimensions are incorrect.
Since: 0.1.0
flatten :: (Load r ix e, Resize r ix) => Array r ix e > Array r Ix1 e Source #
O(1)  Reduce a multidimensional array into a flat vector
Since: 0.3.1
Extract
:: (MonadThrow m, Extract r ix e)  
=> ix  Starting index 
> Sz ix  Size of the resulting array 
> Array r ix e  Source array 
> m (Array (R r) ix e) 
Extract a subarray from within a larger source array. Array that is being extracted must be
fully encapsulated in a source array, otherwise SizeSubregionException
will be thrown.
:: Extract r ix e  
=> ix  Starting index 
> Sz ix  Size of the resulting array 
> Array r ix e  Source array 
> Array (R r) ix e 
Same as extractM
, but will throw a runtime exception from pure code if supplied dimensions
are incorrect.
Since: 0.1.0
:: (MonadThrow m, Extract r ix e)  
=> ix  Starting index 
> ix  Index up to which elements should be extracted. 
> Array r ix e  Source array. 
> m (Array (R r) ix e) 
Similar to extractM
, except it takes starting and ending index. Result array will not include
the ending index.
Since: 0.3.0
:: Extract r ix e  
=> ix  Starting index 
> ix  Index up to which elmenets should be extracted. 
> Array r ix e  Source array. 
> Array (R r) ix e 
Same as extractFromTo
, but throws an error on invalid indices.
Since: 0.2.4
deleteRowsM :: (MonadThrow m, Extract r ix e, Source (R r) ix e, Index (Lower ix)) => Ix1 > Sz Ix1 > Array r ix e > m (Array DL ix e) Source #
Similar to deleteRegionM
, but drop a specified number of rows from an array that
has at least 2 dimensions.
Example
>>>
import Data.Massiv.Array
>>>
arr = fromIx2 <$> (0 :. 0 ..: 3 :. 6)
>>>
arr
Array D Seq (Sz (3 :. 6)) [ [ (0,0), (0,1), (0,2), (0,3), (0,4), (0,5) ] , [ (1,0), (1,1), (1,2), (1,3), (1,4), (1,5) ] , [ (2,0), (2,1), (2,2), (2,3), (2,4), (2,5) ] ]>>>
deleteRowsM 1 1 arr
Array DL Seq (Sz (2 :. 6)) [ [ (0,0), (0,1), (0,2), (0,3), (0,4), (0,5) ] , [ (2,0), (2,1), (2,2), (2,3), (2,4), (2,5) ] ]
Since: 0.3.5
deleteColumnsM :: (MonadThrow m, Extract r ix e, Source (R r) ix e) => Ix1 > Sz Ix1 > Array r ix e > m (Array DL ix e) Source #
Similar to deleteRegionM
, but drop a specified number of columns an array.
Example
>>>
import Data.Massiv.Array
>>>
arr = fromIx2 <$> (0 :. 0 ..: 3 :. 6)
>>>
arr
Array D Seq (Sz (3 :. 6)) [ [ (0,0), (0,1), (0,2), (0,3), (0,4), (0,5) ] , [ (1,0), (1,1), (1,2), (1,3), (1,4), (1,5) ] , [ (2,0), (2,1), (2,2), (2,3), (2,4), (2,5) ] ]>>>
deleteColumnsM 2 3 arr
Array DL Seq (Sz (3 :. 3)) [ [ (0,0), (0,1), (0,5) ] , [ (1,0), (1,1), (1,5) ] , [ (2,0), (2,1), (2,5) ] ]
Since: 0.3.5
:: (MonadThrow m, Extract r ix e, Source (R r) ix e)  
=> Dim  Along which axis should the removal happen 
> Ix1  At which index to start dropping slices 
> Sz Ix1  Number of slices to drop 
> Array r ix e  Array that will have it's subarray removed 
> m (Array DL ix e) 
Delete a region from an array along the specified dimension.
Examples
>>>
import Data.Massiv.Array
>>>
arr = fromIx3 <$> (0 :> 0 :. 0 ..: 3 :> 2 :. 6)
>>>
deleteRegionM 1 2 3 arr
Array DL Seq (Sz (3 :> 2 :. 3)) [ [ [ (0,0,0), (0,0,1), (0,0,5) ] , [ (0,1,0), (0,1,1), (0,1,5) ] ] , [ [ (1,0,0), (1,0,1), (1,0,5) ] , [ (1,1,0), (1,1,1), (1,1,5) ] ] , [ [ (2,0,0), (2,0,1), (2,0,5) ] , [ (2,1,0), (2,1,1), (2,1,5) ] ] ]>>>
v = Ix1 0 ... 10
>>>
deleteRegionM 1 3 5 v
Array DL Seq (Sz1 6) [ 0, 1, 2, 8, 9, 10 ]
Since: 0.3.5
Append/Split
appendOuterM :: forall ix e m. (Index ix, MonadThrow m) => Array DL ix e > Array DL ix e > m (Array DL ix e) Source #
Append two arrays together along the outer most dimension. Inner dimensions must
agree, otherwise SizeMismatchException
.
Since: 0.4.4
appendM :: forall r1 r2 ix e m. (MonadThrow m, Source r1 ix e, Source r2 ix e) => Dim > Array r1 ix e > Array r2 ix e > m (Array DL ix e) Source #
Append two arrays together along a particular dimension. Sizes of both arrays must match, with
an allowed exception of the dimension they are being appended along, otherwise Nothing
is
returned.
Examples
Append two 2D arrays along both dimensions. Note that they do agree on inner dimensions.
>>>
import Data.Massiv.Array
>>>
arrA = makeArrayR U Seq (Sz2 2 3) (\(i :. j) > ('A', i, j))
>>>
arrB = makeArrayR U Seq (Sz2 2 3) (\(i :. j) > ('B', i, j))
>>>
appendM 1 arrA arrB
Array DL Seq (Sz (2 :. 6)) [ [ ('A',0,0), ('A',0,1), ('A',0,2), ('B',0,0), ('B',0,1), ('B',0,2) ] , [ ('A',1,0), ('A',1,1), ('A',1,2), ('B',1,0), ('B',1,1), ('B',1,2) ] ]>>>
appendM 2 arrA arrB
Array DL Seq (Sz (4 :. 3)) [ [ ('A',0,0), ('A',0,1), ('A',0,2) ] , [ ('A',1,0), ('A',1,1), ('A',1,2) ] , [ ('B',0,0), ('B',0,1), ('B',0,2) ] , [ ('B',1,0), ('B',1,1), ('B',1,2) ] ]
Now appending arrays with different sizes:
>>>
arrC = makeArrayR U Seq (Sz (2 :. 4)) (\(i :. j) > ('C', i, j))
>>>
appendM 1 arrA arrC
Array DL Seq (Sz (2 :. 7)) [ [ ('A',0,0), ('A',0,1), ('A',0,2), ('C',0,0), ('C',0,1), ('C',0,2), ('C',0,3) ] , [ ('A',1,0), ('A',1,1), ('A',1,2), ('C',1,0), ('C',1,1), ('C',1,2), ('C',1,3) ] ]>>>
appendM 2 arrA arrC
*** Exception: SizeMismatchException: (Sz (2 :. 3)) vs (Sz (2 :. 4))
Since: 0.3.0
append' :: (Source r1 ix e, Source r2 ix e) => Dim > Array r1 ix e > Array r2 ix e > Array DL ix e Source #
Same as appendM
, but will throw an exception in pure code on mismatched sizes.
Since: 0.3.0
concatOuterM :: forall ix e m. (Index ix, MonadThrow m) => [Array DL ix e] > m (Array DL ix e) Source #
Concat arrays together along the outer most dimension. Inner dimensions must agree
for all arrays in the list, otherwise SizeMismatchException
.
Since: 0.4.4
concatM :: forall r ix e f m. (MonadThrow m, Foldable f, Source r ix e) => Dim > f (Array r ix e) > m (Array DL ix e) Source #
Concatenate many arrays together along some dimension. It is important that all sizes are equal, with an exception of the dimensions along which concatenation happens.
Exceptions: IndexDimensionException
, SizeMismatchException
Since: 0.3.0
concat' :: (Foldable f, Source r ix e) => Dim > f (Array r ix e) > Array DL ix e Source #
Concat many arrays together along some dimension.
Since: 0.3.0
stackSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => Dim > f (Array r (Lower ix) e) > m (Array DL ix e) Source #
Stack slices on top of each other along the specified dimension.
Exceptions: IndexDimensionException
, SizeMismatchException
Examples
Here are the three different ways to stack up two 2D Matrix pages into a 3D array.
>>>
import Data.Massiv.Array as A
>>>
x = compute (iterateN 3 succ 0) :: Matrix P Int
>>>
y = compute (iterateN 3 succ 9) :: Matrix P Int
>>>
x
Array P Seq (Sz (3 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]>>>
y
Array P Seq (Sz (3 :. 3)) [ [ 10, 11, 12 ] , [ 13, 14, 15 ] , [ 16, 17, 18 ] ]>>>
stackSlicesM 1 [x, y] :: IO (Array DL Ix3 Int)
Array DL Seq (Sz (3 :> 3 :. 2)) [ [ [ 1, 10 ] , [ 2, 11 ] , [ 3, 12 ] ] , [ [ 4, 13 ] , [ 5, 14 ] , [ 6, 15 ] ] , [ [ 7, 16 ] , [ 8, 17 ] , [ 9, 18 ] ] ]>>>
stackSlicesM 2 [x, y] :: IO (Array DL Ix3 Int)
Array DL Seq (Sz (3 :> 2 :. 3)) [ [ [ 1, 2, 3 ] , [ 10, 11, 12 ] ] , [ [ 4, 5, 6 ] , [ 13, 14, 15 ] ] , [ [ 7, 8, 9 ] , [ 16, 17, 18 ] ] ]>>>
stackSlicesM 3 [x, y] :: IO (Array DL Ix3 Int)
Array DL Seq (Sz (2 :> 3 :. 3)) [ [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ] , [ [ 10, 11, 12 ] , [ 13, 14, 15 ] , [ 16, 17, 18 ] ] ]
Since: 0.5.4
stackOuterSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => f (Array r (Lower ix) e) > m (Array DL ix e) Source #
Specialized stackOuterM
to handling stacking from the outside. It is the inverse of
outerSlices
.
Exceptions: SizeMismatchException
Examples
In this example we stack vectors as row of a matrix from top to bottom:
>>>
import Data.Massiv.Array as A
>>>
x = compute (iterateN 3 succ 0) :: Matrix P Int
>>>
x
Array P Seq (Sz (3 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]>>>
rows = outerSlices x
>>>
A.mapM_ print rows
Array M Seq (Sz1 3) [ 1, 2, 3 ] Array M Seq (Sz1 3) [ 4, 5, 6 ] Array M Seq (Sz1 3) [ 7, 8, 9 ]>>>
stackOuterSlicesM rows :: IO (Matrix DL Int)
Array DL Seq (Sz (3 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]
Since: 0.5.4
stackInnerSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Source r (Lower ix) e, Index ix) => f (Array r (Lower ix) e) > m (Array DL ix e) Source #
Specialized stackOuterM
to handling stacking from the inside. It is the inverse of
outerSlices
.
Exceptions: SizeMismatchException
Examples
In this example we stack vectors as columns of a matrix from left to right:
>>>
import Data.Massiv.Array as A
>>>
x = compute (iterateN 3 succ 0) :: Matrix P Int
>>>
x
Array P Seq (Sz (3 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]>>>
columns = innerSlices x
>>>
A.mapM_ print columns
Array M Seq (Sz1 3) [ 1, 4, 7 ] Array M Seq (Sz1 3) [ 2, 5, 8 ] Array M Seq (Sz1 3) [ 3, 6, 9 ]>>>
stackInnerSlicesM columns :: IO (Matrix DL Int)
Array DL Seq (Sz (3 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] , [ 7, 8, 9 ] ]
Since: 0.5.4
:: (MonadThrow m, Extract r ix e)  
=> Dim  Dimension along which to split 
> Int  Index along the dimension to split at 
> Array r ix e  Source array 
> m (Array (R r) ix e, Array (R r) ix e) 
O(1)  Split an array into two at an index along a specified dimension.
Related: splitAt'
, splitExtractM
, sliceAt'
, sliceAtM
Exceptions: IndexDimensionException
, SizeSubregionException
Since: 0.3.0
splitAt' :: Extract r ix e => Dim > Int > Array r ix e > (Array (R r) ix e, Array (R r) ix e) Source #
O(1)  Split an array into two at an index along a specified dimension. Throws an error for a wrong dimension or incorrect indices.
Related: splitAtM
, splitExtractM
, sliceAt'
, sliceAtM
Examples
Since: 0.1.0
:: (MonadThrow m, Extract r ix e, Source (R r) ix e)  
=> Dim  Dimension along which to do the extraction 
> Ix1  Start index along the dimension that needs to be extracted 
> Sz Ix1  Size of the extracted array along the dimension that it will be extracted 
> Array r ix e  
> m (Array (R r) ix e, Array (R r) ix e, Array (R r) ix e) 
Split an array in three parts across some dimension
Since: 0.3.5
Upsample/Downsample
:: Load r ix e  
=> e  Element to use for filling the newly added cells 
> Stride ix  Fill cells according to this stride 
> Array r ix e  Array that will have cells added to 
> Array DL ix e 
Insert the same element into a Load
able array according to the supplied stride.
Examples
>>>
import Data.Massiv.Array as A
>>>
arr = iterateN (Sz2 3 2) succ (0 :: Int)
>>>
arr
Array DL Seq (Sz (3 :. 2)) [ [ 1, 2 ] , [ 3, 4 ] , [ 5, 6 ] ]>>>
upsample 0 (Stride (2 :. 3)) arr
Array DL Seq (Sz (6 :. 6)) [ [ 1, 0, 0, 2, 0, 0 ] , [ 0, 0, 0, 0, 0, 0 ] , [ 3, 0, 0, 4, 0, 0 ] , [ 0, 0, 0, 0, 0, 0 ] , [ 5, 0, 0, 6, 0, 0 ] , [ 0, 0, 0, 0, 0, 0 ] ]>>>
upsample 9 (Stride (1 :. 2)) arr
Array DL Seq (Sz (3 :. 4)) [ [ 1, 9, 2, 9 ] , [ 3, 9, 4, 9 ] , [ 5, 9, 6, 9 ] ]
Since: 0.3.0
downsample :: forall r ix e. Source r ix e => Stride ix > Array r ix e > Array DL ix e Source #
Discard elements from the source array according to the stride.
Since: 0.3.0
Zoom
Increaze the size of the array accoridng to the stride multiplier while replicating
the same element to fill the neighbors. It is exactly the same as zoomWithGrid
, but
without the grid.
Example
>>>
import Data.Massiv.Array as A
>>>
arr = resize' (Sz3 1 3 2) (Ix1 1 ... 6)
>>>
arr
Array D Seq (Sz (1 :> 3 :. 2)) [ [ [ 1, 2 ] , [ 3, 4 ] , [ 5, 6 ] ] ]>>>
zoom (Stride (2 :> 2 :. 3)) arr
Array DL Seq (Sz (2 :> 6 :. 6)) [ [ [ 1, 1, 1, 2, 2, 2 ] , [ 1, 1, 1, 2, 2, 2 ] , [ 3, 3, 3, 4, 4, 4 ] , [ 3, 3, 3, 4, 4, 4 ] , [ 5, 5, 5, 6, 6, 6 ] , [ 5, 5, 5, 6, 6, 6 ] ] , [ [ 1, 1, 1, 2, 2, 2 ] , [ 1, 1, 1, 2, 2, 2 ] , [ 3, 3, 3, 4, 4, 4 ] , [ 3, 3, 3, 4, 4, 4 ] , [ 5, 5, 5, 6, 6, 6 ] , [ 5, 5, 5, 6, 6, 6 ] ] ]
Since: 0.4.4
:: Source r ix e  
=> e  Value to use for the grid 
> Stride ix  Scaling factor 
> Array r ix e  Source array 
> Array DL ix e 
Replicate each element of the array by a factor in stride along each dimension and surround each such group with a box of supplied grid value. It will essentially zoom up an array and create a grid around each element from the original array. Very useful for zooming up images to inspect individual pixels.
Example
>>>
import Data.Massiv.Array as A
>>>
arr = resize' (Sz2 3 2) (Ix1 1 ... 6)
>>>
arr
Array D Seq (Sz (3 :. 2)) [ [ 1, 2 ] , [ 3, 4 ] , [ 5, 6 ] ]>>>
zoomWithGrid 0 (Stride (2 :. 3)) arr
Array DL Seq (Sz (10 :. 9)) [ [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 1, 1, 1, 0, 2, 2, 2, 0 ] , [ 0, 1, 1, 1, 0, 2, 2, 2, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 3, 3, 3, 0, 4, 4, 4, 0 ] , [ 0, 3, 3, 3, 0, 4, 4, 4, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 5, 5, 5, 0, 6, 6, 6, 0 ] , [ 0, 5, 5, 5, 0, 6, 6, 6, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0, 0 ] ]
Since: 0.3.1
Transform
transformM :: forall r ix e r' ix' e' a m. (Mutable r ix e, Source r' ix' e', MonadUnliftIO m, PrimMonad m, MonadThrow m) => (Sz ix' > m (Sz ix, a)) > (a > (ix' > m e') > ix > m e) > Array r' ix' e' > m (Array r ix e) Source #
General array transformation, that forces computation and produces a manifest array.
Since: 0.3.0
transform' :: (Source r' ix' e', Index ix) => (Sz ix' > (Sz ix, a)) > (a > (ix' > e') > ix > e) > Array r' ix' e' > Array D ix e Source #
General array transformation
Since: 0.3.0
transform2M :: (Mutable r ix e, Source r1 ix1 e1, Source r2 ix2 e2, MonadUnliftIO m, PrimMonad m, MonadThrow m) => (Sz ix1 > Sz ix2 > m (Sz ix, a)) > (a > (ix1 > m e1) > (ix2 > m e2) > ix > m e) > Array r1 ix1 e1 > Array r2 ix2 e2 > m (Array r ix e) Source #
Same as transformM
, but operates on two arrays
Since: 0.3.0
transform2' :: (Source r1 ix1 e1, Source r2 ix2 e2, Index ix) => (Sz ix1 > Sz ix2 > (Sz ix, a)) > (a > (ix1 > e1) > (ix2 > e2) > ix > e) > Array r1 ix1 e1 > Array r2 ix2 e2 > Array D ix e Source #
Same as transform'
, but operates on two arrays
Since: 0.3.0
Slicing
From the outside
(!>) :: OuterSlice r ix e => Array r ix e > Int > Elt r ix e infixl 4 Source #
O(1)  Slices the array from the outside. For 2dimensional array this will be equivalent of taking a row. Throws an error when index is out of bounds.
Examples
You could say that slicing from outside is synonymous to slicing from the end or slicing at the highermost dimension. For example with rank3 arrays outer slice would be equivalent to getting a page:
>>>
import Data.Massiv.Array
>>>
arr = makeArrayR U Seq (Sz (3 :> 2 :. 4)) fromIx3
>>>
arr
Array U Seq (Sz (3 :> 2 :. 4)) [ [ [ (0,0,0), (0,0,1), (0,0,2), (0,0,3) ] , [ (0,1,0), (0,1,1), (0,1,2), (0,1,3) ] ] , [ [ (1,0,0), (1,0,1), (1,0,2), (1,0,3) ] , [ (1,1,0), (1,1,1), (1,1,2), (1,1,3) ] ] , [ [ (2,0,0), (2,0,1), (2,0,2), (2,0,3) ] , [ (2,1,0), (2,1,1), (2,1,2), (2,1,3) ] ] ]>>>
arr !> 2
Array M Seq (Sz (2 :. 4)) [ [ (2,0,0), (2,0,1), (2,0,2), (2,0,3) ] , [ (2,1,0), (2,1,1), (2,1,2), (2,1,3) ] ]
There is nothing wrong with chaining, mixing and matching slicing operators, or even using them to index arrays:
>>>
arr !> 2 !> 0 !> 3
(2,0,3)>>>
arr !> 2 <! 3 ! 0
(2,0,3)>>>
(arr !> 2 !> 0 !> 3) == (arr ! 2 :> 0 :. 3)
True
Since: 0.1.0
(!?>) :: (MonadThrow m, OuterSlice r ix e) => Array r ix e > Int > m (Elt r ix e) infixl 4 Source #
(??>) :: (MonadThrow m, OuterSlice r ix e) => m (Array r ix e) > Int > m (Elt r ix e) infixl 4 Source #
O(1)  Safe slicing continuation from the outside. Similarly to (!>
) slices the array from
the outside, but takes Maybe
array as input and returns Nothing
when index is out of bounds.
Examples
>>>
import Data.Massiv.Array
>>>
arr = makeArrayR U Seq (Sz (3 :> 2 :. 4)) fromIx3
>>>
arr !?> 2 ??> 0 ??> 3 :: Maybe Ix3T
Just (2,0,3)>>>
arr !?> 2 ??> 0 ??> 1 :: Maybe Ix3T
Nothing>>>
arr !?> 2 ??> 10 ?? 1
*** Exception: IndexOutOfBoundsException: 10 is not safe for (Sz1 2)
Since: 0.1.0
From the inside
(<!) :: InnerSlice r ix e => Array r ix e > Int > Elt r ix e infixl 4 Source #
O(1)  Similarly to (!>
) slice an array from an opposite direction.
Since: 0.1.0
(<!?) :: (MonadThrow m, InnerSlice r ix e) => Array r ix e > Int > m (Elt r ix e) infixl 4 Source #
O(1)  Safe slice from the inside
Since: 0.1.0
(<??) :: (MonadThrow m, InnerSlice r ix e) => m (Array r ix e) > Int > m (Elt r ix e) infixl 4 Source #
O(1)  Safe slicing continuation from the inside
Since: 0.1.0
From within
(<!>) :: Slice r ix e => Array r ix e > (Dim, Int) > Elt r ix e infixl 4 Source #
O(1)  Slices the array in any available dimension. Throws an error when index is out of bounds or dimensions is invalid.
Since: 0.1.0
(<!?>) :: (MonadThrow m, Slice r ix e) => Array r ix e > (Dim, Int) > m (Elt r ix e) infixl 4 Source #
(<??>) :: (MonadThrow m, Slice r ix e) => m (Array r ix e) > (Dim, Int) > m (Elt r ix e) infixl 4 Source #
O(1)  Safe slicing continuation from within.
Since: 0.1.0
Many slices
outerSlices :: OuterSlice r ix e => Array r ix e > Array D Ix1 (Elt r ix e) Source #
Create a delayed array of outer slices.
Examples
>>>
import Data.Massiv.Array as A
>>>
A.mapM_ print $ outerSlices (0 ..: (3 :. 2))
Array D Seq (Sz1 2) [ 0 :. 0, 0 :. 1 ] Array D Seq (Sz1 2) [ 1 :. 0, 1 :. 1 ] Array D Seq (Sz1 2) [ 2 :. 0, 2 :. 1 ]
Since: 0.5.4
innerSlices :: InnerSlice r ix e => Array r ix e > Array D Ix1 (Elt r ix e) Source #
Create a delayed array of inner slices.
Examples
>>>
import Data.Massiv.Array as A
>>>
A.mapM_ print $ innerSlices (0 ..: (3 :. 2))
Array D Seq (Sz1 3) [ 0 :. 0, 1 :. 0, 2 :. 0 ] Array D Seq (Sz1 3) [ 0 :. 1, 1 :. 1, 2 :. 1 ]
Since: 0.5.4
withinSlices :: (IsIndexDimension ix n, Slice r ix e) => Dimension n > Array r ix e > Array D Ix1 (Elt r ix e) Source #
Create a delayed array of slices from within. Checks dimension at compile time.
Examples
>>>
import Data.Massiv.Array as A
>>>
arr = fromIx3 <$> (0 ..: (4 :> 3 :. 2))
>>>
print arr
Array D Seq (Sz (4 :> 3 :. 2)) [ [ [ (0,0,0), (0,0,1) ] , [ (0,1,0), (0,1,1) ] , [ (0,2,0), (0,2,1) ] ] , [ [ (1,0,0), (1,0,1) ] , [ (1,1,0), (1,1,1) ] , [ (1,2,0), (1,2,1) ] ] , [ [ (2,0,0), (2,0,1) ] , [ (2,1,0), (2,1,1) ] , [ (2,2,0), (2,2,1) ] ] , [ [ (3,0,0), (3,0,1) ] , [ (3,1,0), (3,1,1) ] , [ (3,2,0), (3,2,1) ] ] ]>>>
A.mapM_ print $ withinSlices Dim2 arr
Array D Seq (Sz (4 :. 2)) [ [ (0,0,0), (0,0,1) ] , [ (1,0,0), (1,0,1) ] , [ (2,0,0), (2,0,1) ] , [ (3,0,0), (3,0,1) ] ] Array D Seq (Sz (4 :. 2)) [ [ (0,1,0), (0,1,1) ] , [ (1,1,0), (1,1,1) ] , [ (2,1,0), (2,1,1) ] , [ (3,1,0), (3,1,1) ] ] Array D Seq (Sz (4 :. 2)) [ [ (0,2,0), (0,2,1) ] , [ (1,2,0), (1,2,1) ] , [ (2,2,0), (2,2,1) ] , [ (3,2,0), (3,2,1) ] ]
Since: 0.5.4
withinSlicesM :: (MonadThrow m, Slice r ix e) => Dim > Array r ix e > m (Array D Ix1 (Elt r ix e)) Source #
Create a delayed array of slices from within. Same as withinSlices
, but throws an
error on invalid dimension.
Throws Exceptions: IndexDimensionException
Since: 0.5.4
Algorithms
Sorting
quicksort :: (Mutable r Ix1 e, Ord e) => Array r Ix1 e > Array r Ix1 e Source #
This is an implementation of Quicksort, which is an efficient, but unstable sort that uses Medianofthree for pivot choosing, as such it performs very well not only for random values, but also for common edge cases like already sorted, reversed sorted and arrays with many duplicate elements. It will also respect the computation strategy and will result in a nice speed up for systems with multiple CPUs.
Since: 0.3.2
tally :: (Mutable r Ix1 e, Resize r ix, Load r ix e, Ord e) => Array r ix e > Array DS Ix1 (e, Int) Source #
Count how many occurance of each element there is in the array. Results will be sorted in ascending order of the element.
Example
>>>
import Data.Massiv.Array as A
>>>
xs = fromList Seq [2, 4, 3, 2, 4, 5, 2, 1] :: Array P Ix1 Int
>>>
xs
Array P Seq (Sz1 8) [ 2, 4, 3, 2, 4, 5, 2, 1 ]>>>
tally xs
Array DS Seq (Sz1 5) [ (1,1), (2,3), (3,1), (4,2), (5,1) ]
Since: 0.4.4
Iterations
:: (Load r' ix e, Mutable r ix e)  
=> (Int > Array r ix e > Array r ix e > Bool)  Convergence condition. Accepts current iteration counter, array at the previous state and at the current state. 
> (Int > Array r ix e > Array r' ix e)  A modifying function to apply at each iteration. The size of resulting array may differ if necessary 
> Array r ix e  Initial source array 
> Array r ix e 
Efficiently iterate a function until a convergence condition is satisfied. If the size of array doesn't change between iterations then no more than two new arrays will be allocated, regardless of the number of iterations. If the size does change from one iteration to another, an attempt will be made to grow/shrink the intermediate mutable array instead of allocating a new one.
Example
>>>
import Data.Massiv.Array
>>>
a = computeAs P $ makeLoadArrayS (Sz2 8 8) (0 :: Int) $ \ w > w (0 :. 0) 1 >> pure ()
>>>
a
Array P Seq (Sz (8 :. 8)) [ [ 1, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] , [ 0, 0, 0, 0, 0, 0, 0, 0 ] ]>>>
nextPascalRow cur above = if cur == 0 then above else cur
>>>
pascal = makeStencil (Sz2 2 2) 1 $ \ get > nextPascalRow <$> get (0 :. 0) <*> get (1 :. 1) + get (1 :. 0)
>>>
iterateUntil (\_ _ a > (a ! (7 :. 7)) /= 0) (\ _ > mapStencil (Fill 0) pascal) a
Array P Seq (Sz (8 :. 8)) [ [ 1, 0, 0, 0, 0, 0, 0, 0 ] , [ 1, 1, 0, 0, 0, 0, 0, 0 ] , [ 1, 2, 1, 0, 0, 0, 0, 0 ] , [ 1, 3, 3, 1, 0, 0, 0, 0 ] , [ 1, 4, 6, 4, 1, 0, 0, 0 ] , [ 1, 5, 10, 10, 5, 1, 0, 0 ] , [ 1, 6, 15, 20, 15, 6, 1, 0 ] , [ 1, 7, 21, 35, 35, 21, 7, 1 ] ]
Since: 0.3.6
Conversion
List
Convert a flat list into a vector
Since: 0.1.0
fromListsM :: forall r ix e m. (Nested LN ix e, Ragged L ix e, Mutable r ix e, MonadThrow m) => Comp > [ListItem ix e] > m (Array r ix e) Source #
O(n)  Convert a nested list into an array. Nested list must be of a rectangular shape, otherwise a runtime error will occur. Also, nestedness must match the rank of resulting array, which should be specified through an explicit type signature.
Examples
>>>
import Data.Massiv.Array as A
>>>
fromListsM Seq [[1,2,3],[4,5,6]] :: Maybe (Array U Ix2 Int)
Just (Array U Seq (Sz (2 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ] )
>>>
fromListsM Par [[[1,2,3]],[[4,5,6]]] :: Maybe (Array U Ix3 Int)
Just (Array U Par (Sz (2 :> 1 :. 3)) [ [ [ 1, 2, 3 ] ] , [ [ 4, 5, 6 ] ] ] )
Elements of a boxed array could be lists themselves if necessary, but cannot be ragged:
>>>
fromListsM Seq [[[1,2,3]],[[4,5]]] :: Maybe (Array B Ix2 [Int])
Just (Array B Seq (Sz (2 :. 1)) [ [ [1,2,3] ] , [ [4,5] ] ] )>>>
fromListsM Seq [[[1,2,3]],[[4,5]]] :: Maybe (Array B Ix3 Int)
Nothing>>>
fromListsM Seq [[[1,2,3]],[[4,5]]] :: IO (Array B Ix3 Int)
*** Exception: DimTooShortException: expected (Sz1 3), got (Sz1 2)
Since: 0.3.0
:: (Nested LN ix e, Ragged L ix e, Mutable r ix e)  
=> Comp  Computation startegy to use 
> [ListItem ix e]  Nested list 
> Array r ix e 
Same as fromListsM
, but will throw a pure error on irregular shaped lists.
Note: This function is the same as if you would turn on {# LANGUAGE OverloadedLists #}
extension. For that reason you can also use fromList
.
Examples
Convert a list of lists into a 2D Array
>>>
import Data.Massiv.Array as A
>>>
fromLists' Seq [[1,2,3],[4,5,6]] :: Array U Ix2 Int
Array U Seq (Sz (2 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ]
Above example implemented using GHC's OverloadedLists
extension:
>>>
:set XOverloadedLists
>>>
[[1,2,3],[4,5,6]] :: Array U Ix2 Int
Array U Seq (Sz (2 :. 3)) [ [ 1, 2, 3 ] , [ 4, 5, 6 ] ]
Example of failure on conversion of an irregular nested list.
>>>
fromLists' Seq [[1],[3,4]] :: Array U Ix2 Int
Array U *** Exception: DimTooLongException
Since: 0.1.0
toList :: Source r ix e => Array r ix e > [e] Source #
Convert any array to a flat list.
Examples
>>>
import Data.Massiv.Array
>>>
toList $ makeArrayR U Seq (Sz (2 :. 3)) fromIx2
[(0,0),(0,1),(0,2),(1,0),(1,1),(1,2)]
Since: 0.1.0
toLists :: (Nested LN ix e, Construct L ix e, Source r ix e) => Array r ix e > [ListItem ix e] Source #
O(n)  Convert an array into a nested list. Number of array dimensions and list nestedness
will always match, but you can use toList
, toLists2
, etc. if flattening of inner dimensions
is desired.
Note: This function is almost the same as toList
.
Examples
>>>
import Data.Massiv.Array
>>>
arr = makeArrayR U Seq (Sz (2 :> 1 :. 3)) id
>>>
arr
Array U Seq (Sz (2 :> 1 :. 3)) [ [ [ 0 :> 0 :. 0, 0 :> 0 :. 1, 0 :> 0 :. 2 ] ] , [ [ 1 :> 0 :. 0, 1 :> 0 :. 1, 1 :> 0 :. 2 ] ] ]>>>
toLists arr
[[[0 :> 0 :. 0,0 :> 0 :. 1,0 :> 0 :. 2]],[[1 :> 0 :. 0,1 :> 0 :. 1,1 :> 0 :. 2]]]
Since: 0.1.0
toLists2 :: (Source r ix e, Index (Lower ix)) => Array r ix e > [[e]] Source #
Convert an array with at least 2 dimensions into a list of lists. Inner dimensions will get flattened.
Examples
>>>
import Data.Massiv.Array
>>>
toLists2 $ makeArrayR U Seq (Sz2 2 3) fromIx2
[[(0,0),(0,1),(0,2)],[(1,0),(1,1),(1,2)]]>>>
toLists2 $ makeArrayR U Seq (Sz3 2 1 3) fromIx3
[[(0,0,0),(0,0,1),(0,0,2)],[(1,0,0),(1,0,1),(1,0,2)]]
Since: 0.1.0
toLists3 :: (Index (Lower (Lower ix)), Index (Lower ix), Source r ix e) => Array r ix e > [[[e]]] Source #
Convert an array with at least 3 dimensions into a 3 deep nested list. Inner dimensions will get flattened.
Since: 0.1.0
toLists4 :: (Index (Lower (Lower (Lower ix))), Index (Lower (Lower ix)), Index (Lower ix), Source r ix e) => Array r ix e > [[[[e]]]] Source #
Convert an array with at least 4 dimensions into a 4 deep nested list. Inner dimensions will get flattened.
Since: 0.1.0
Mutable
module Data.Massiv.Array.Mutable
Core
module Data.Massiv.Core
Representations
module Data.Massiv.Array.Delayed
module Data.Massiv.Array.Manifest
Stencil
module Data.Massiv.Array.Stencil
Numeric Operations
module Data.Massiv.Array.Numeric