Data.Massiv.Array

Massiv is a library, that allows creation and manipulation of arrays in parallel and sequentially. Depending on the representation (r), an Array r ix e 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 (ix) 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).
• BN - Similar to B, it is also a boxed type, except its elements are always kept in a Normal Form (NF). This property is very useful for parallel processing, i.e. when calling compute you do want all of your elements to be fully evaluated.
• BL - Similar to B, it is also a boxed type, but lazy. Its elements are not evaluated when array is computed.
• 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 of Storable class. It is just as efficient as P and U arrays, except it is subject to fragmentation.
• U - Unboxed representation. Elements must be an instance of Unbox class.
• P - Array that can hold Haskell primitives, such as Int, Word, Double, etc. Any element must be an instance of Prim class.

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. Use computeAs in order to load array into Manifest 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. Use computeAs in order to load array into Manifest representation.
• DS - delayed stream vector representation that describes how to handle a vector with possibility of unknown length. Useful for filtering and unfolding. Use computeAs in order to load such vector into Manifest representation.
• DI - delayed interleaved array. Same as D, 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 fast Stencil computation.

Other Array types:

• L - this type isn't particularly useful on its own, but because it has unique ability to be converted to and from nested lists in constant time, it provides a perfect intermediary for conversion of nested lists into manifest arrays.

Most of the Manifest arrays are capable of in-place 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

Construct

With constant value

empty :: forall r ix e. Load r ix e => Array r ix e

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

singleton

Arguments

:: forall r ix e. Load r ix e

=> e

The only element

-> Array r ix e

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 :: Load r ix e => Comp -> Sz ix -> e -> Array r ix e

Construct an array of the specified size that contains the same element in all of the cells.

Since: 0.3.0

With a function

makeArray

Arguments

:: Load r ix e

=> Comp

Computation strategy. Useful constructors are Seq and Par

-> 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 :: Load r ix e => Comp -> Sz ix -> (Int -> e) -> Array r ix e

Same as makeArray, but produce elements using linear row-major 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 :: Load r ix e => r -> Comp -> Sz ix -> (ix -> e) -> Array r ix e

Just like makeArray but with ability to specify the result representation as an argument. Note the Unboxed 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 :: Load r ix e => r -> Comp -> Sz ix -> (Int -> e) -> Array r ix e

Same as makeArrayLinear, but with ability to supply resulting representation

Since: 0.3.0

makeVectorR :: Load r Ix1 e => r -> Comp -> Sz1 -> (Ix1 -> e) -> Vector r e

Same as makeArrayR, but restricted to 1-dimensional arrays.

Since: 0.1.0

Iterating

iterateN :: forall ix e. Index ix => Sz ix -> (e -> e) -> e -> Array DL ix e

Sequentially iterate over each cell in the array in the row-major 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

Same as iterateN, but with index aware function.

Since: 0.3.0

Unfolding

unfoldlS_ :: Index ix => Sz ix -> (a -> (a, e)) -> a -> Array DL ix e

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 achieve such effect.

Since: 0.3.0

iunfoldlS_ :: forall ix e a. Index ix => Sz ix -> (ix -> a -> (a, e)) -> a -> Array DL ix e

Unfold sequentially from the right with an index aware function.

Since: 0.3.0

unfoldrS_ :: forall ix e a. Index ix => Sz ix -> (a -> (e, a)) -> a -> Array DL ix e

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. Index ix => Sz ix -> (a -> ix -> (e, a)) -> a -> Array DL ix e

Right unfold of a delayed load array with index aware function

Since: 0.3.0

makeSplitSeedArray

Arguments

:: forall ix e g it. (Iterator it, Index ix)

=> it

Iterator

-> g

Initial seed

-> (g -> (g, g))

A function that can split a seed into two independent seeds. It will be called the same number of times as the number of jobs that will get scheduled during parallelization. Eg. only once for the sequential case.

-> Comp

Computation strategy.

-> Sz ix

Resulting size of the array.

-> (Ix1 -> ix -> g -> (e, g))

A function that produces a value and the next seed. It takes both versions of the index, in linear and in multi-dimensional forms, as well as the current seeding value.

-> Array DL ix e

Create a delayed array with an initial seed and a splitting function. It is somewhat similar to iunfoldlS_ function, but it is capable of parallelizing computation and iterating over the array accoriding to the supplied Iterator. Upon parallelization every job will get the second part of the result produced by the split function, while the first part will be used for subsequent splits. This function is similar to generateSplitSeedArray

Since: 1.0.2

Random

uniformArray

Arguments

:: forall ix e g. (Index ix, RandomGen g, Uniform e)

=> g

Initial random value generator.

-> Comp

Computation strategy.

-> Sz ix

Resulting size of the array.

-> Array DL ix e

Generate a random array where all elements are sampled from a uniform distribution.

Since: 1.0.0

uniformRangeArray

Arguments

:: forall ix e g. (Index ix, RandomGen g, UniformRange e)

=> g

Initial random value generator.

-> (e, e)

Inclusive range in which values will be generated in.

-> Comp

Computation strategy.

-> Sz ix

Resulting size of the array.

-> Array DL ix e

Same as uniformArray, but will generate values in a supplied range.

Since: 1.0.0

randomArray

Arguments

:: forall ix e g. Index ix

=> g

Initial random value generator

-> (g -> (g, g))

A function that can split a generator into two independent generators. It will only be called if supplied computation strategy needs more than one worker threads.

-> (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.

Note: Starting with massiv-1.1.0 this function will be deprecated in favor of a more general genSplitArray

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 Random
>>> gen = Random.mkStdGen 217
>>> randomArray gen Random.split Random.random (ParN 2) (Sz2 2 3) :: Array DL Ix2 Double
Array DL (ParN 2) (Sz (2 :. 3))
  [ [ 0.2616843941380331, 0.600959468331641, 0.4382415961606372 ]
  , [ 0.27812817813217605, 0.2993277194932741, 0.2774105268603957 ]
  ]

Since: 1.0.0

randomArrayS

Arguments

:: forall r ix e g. (Manifest r e, Index ix)

=> 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))
  [ [ 0.11217260506402493, 0.8870919238985904, 0.2616843941380331 ]
  , [ 0.600959468331641, 0.4382415961606372, 0.8375162573397977 ]
  ]

Since: 0.3.4

randomArrayWS

Arguments

:: forall r ix e g m. (Manifest r e, Index ix, MonadUnliftIO m, PrimMonad m)

=> WorkerStates g

Use initWorkerStates to initialize you per thread generators

-> 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 number generator from wmc-random, which is not thread safe, and safely parallelize it by giving each thread it's own generator. There is a caveat of course, statistical independence will depend on the entropy in your initial seeds, so do not use the example below verbatim, since initial seeds are sequential numbers.

>>> import Data.Massiv.Array as A
>>> import System.Random.MWC as MWC (initialize)
>>> import System.Random.Stateful (uniformRM)
>>> import Control.Scheduler (initWorkerStates, getWorkerId)
>>> :set -XTypeApplications
>>> gens <- initWorkerStates Par (MWC.initialize . A.toPrimitiveVector . A.singleton @P @Ix1 . fromIntegral . getWorkerId)
>>> randomArrayWS gens (Sz2 2 3) (uniformRM (0, 9)) :: IO (Matrix P Double)
Array P Par (Sz (2 :. 3))
  [ [ 8.999240522095299, 6.832223390653755, 3.065728078741671 ]
  , [ 7.242581103346686, 2.4565807301968623, 0.4514262066689775 ]
  ]
>>> randomArrayWS gens (Sz1 6) (uniformRM (0, 9)) :: IO (Vector P Int)
Array P Par (Sz1 6)
  [ 8, 8, 7, 1, 1, 2 ]

Since: 0.3.4

Applicative

makeArrayA :: forall r ix e f. (Manifest r e, Index ix, Applicative f) => Sz ix -> (ix -> f e) -> f (Array r ix e)

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. (Manifest r e, Index ix, Applicative f) => r -> Sz ix -> (ix -> f e) -> f (Array r ix e)

Same as makeArrayA, but with ability to supply result array representation.

Since: 0.2.6

makeArrayLinearA :: forall r ix e f. (Manifest r e, Index ix, Applicative f) => Sz ix -> (Int -> f e) -> f (Array r ix e)

Same as makeArrayA, but with linear index.

Since: 0.4.5

Enumeration

(...) :: Index ix => ix -> ix -> Array D ix ix infix 4

Handy synonym for rangeInclusive Seq. Similar to .. for list.

>>> Ix1 4 ... 10
Array D Seq (Sz1 7)
  [ 4, 5, 6, 7, 8, 9, 10 ]

Since: 0.3.0

(..:) :: Index ix => ix -> ix -> Array D ix ix infix 4

Handy synonym for range Seq

>>> Ix1 4 ..: 10
Array D Seq (Sz1 6)
  [ 4, 5, 6, 7, 8, 9 ]

Since: 0.3.0

range :: Index ix => Comp -> ix -> ix -> Array D ix ix

Create an array of indices with a range from start to finish (not-including), 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

rangeStepM

Arguments

:: forall ix m. (Index ix, MonadThrow m)

=> Comp

Computation strategy

-> ix

Start

-> ix

Step. Negative and positive values are ok, but 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' :: (HasCallStack, Index ix) => Comp -> ix -> ix -> ix -> Array D ix ix

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

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)

Just like rangeStepM, except the finish index is included.

Since: 0.3.0

rangeStepInclusive' :: (HasCallStack, Index ix) => Comp -> ix -> ix -> ix -> Array D ix ix

Just like range, except the finish index is included.

Since: 0.3.1

rangeSize

Arguments

:: Index ix

=> Comp

Computation strategy

-> ix

x - start value

-> Sz ix

sz - Size of resulting array

-> 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

rangeStepSize

Arguments

:: Index ix

=> Comp

Computation strategy

-> ix

x - start value

-> ix

delta - step value

-> Sz ix

sz - Size of resulting array

-> Array D ix ix

Same as rangeSize, but with ability to specify the step.

Since: 0.3.0

enumFromN

Arguments

:: Num e

=> Comp

-> e

x - start value

-> Sz1

n - length of resulting vector.

-> Vector D e

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 that enumFromN is faster, but it only works for Num and not for Enum elements

Data.Vector.Generic.enumFromN

Since: 0.1.0

enumFromStepN

Arguments

:: Num e

=> Comp

-> e

x - start number

-> e

dx - step number

-> Sz1

n - length of resulting vector

-> 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 that enumFromStepN is parallelizable and it only works for Num and not for Enum 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 n ix e r a. (IsIndexDimension ix n, Index (Lower ix), Manifest r a) => Dimension n -> Sz1 -> (a -> Ix1 -> e) -> Array r (Lower ix) a -> Array D ix e

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 Array r Ix1 a or Array r Ix2 a. Then you use expandWithin and a creation function a -> Int -> b to create an Array D Ix2 b or Array D Ix3 b respectfully.

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 :: forall r ix a b m. (Index ix, Index (Lower ix), Manifest r a, MonadThrow m) => Dim -> Sz1 -> (a -> Ix1 -> b) -> Array r (Lower ix) a -> m (Array D ix b)

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' :: forall r ix a b. (HasCallStack, Index ix, Index (Lower ix), Manifest r a) => Dim -> Sz1 -> (a -> Ix1 -> b) -> Array r (Lower ix) a -> Array D ix b

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 :: forall r ix a b. (Index ix, Index (Lower ix), Manifest r a) => Sz1 -> (a -> Ix1 -> b) -> Array r (Lower ix) a -> Array D ix b

Similar to expandWithin, except it uses the outermost dimension.

Since: 0.2.6

expandInner :: forall r ix a b. (Index ix, Index (Lower ix), Manifest r a) => Sz1 -> (a -> Ix1 -> b) -> Array r (Lower ix) a -> Array D ix b

Similar to expandWithin, except it uses the innermost dimension.

Since: 0.2.6

Compute

getComp :: Strategy r => Array r ix e -> Comp

Get computation strategy of this array

Since: 0.1.0

setComp :: Strategy r => Comp -> Array r ix e -> Array r ix e

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 ]

appComp :: Strategy r => Comp -> Array r ix e -> Array r ix e

Append computation strategy using Comp's Monoid instance.

Since: 0.6.0

compute :: forall r ix e r'. (Manifest r e, Load r' ix e) => Array r' ix e -> Array r ix e

Ensure that Array is computed, i.e. represented with concrete elements in memory, hence is the Mutable type class restriction. Use setComp if you'd like to change computation strategy before calling compute

Since: 0.1.0

computeS :: forall r ix e r'. (Manifest r e, Load r' ix e) => Array r' ix e -> Array r ix e

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'. (Manifest r e, Load r' ix e) => Array r' ix e -> Array r ix e

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. (Manifest r e, Load r' ix e, MonadIO m) => Array r' ix e -> m (Array r ix e)

Very similar to compute, but computes an array inside the IO monad. Despite being deterministic and referentially transparent, because this is an IO action it can be very useful for enforcing the order of evaluation. Should be a prefered way of computing an array during benchmarking.

Since: 0.4.5

computePrimM :: forall r ix e r' m. (Manifest r e, Load r' ix e, PrimMonad m) => Array r' ix e -> m (Array r ix e)

Compute an array in PrimMonad sequentially disregarding predefined computation strategy.

Since: 0.4.5

computeAs :: (Manifest r e, Load r' ix e) => r -> Array r' ix e -> Array r ix e

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 :: (Manifest r e, Load r' ix e) => proxy r -> Array r' ix e -> Array r ix e

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'. (Manifest r e, Source r' e, Index ix) => Array r' ix e -> Array r ix e

This is just like convert, but restricted to Source arrays. Will be a noop if resulting type is the same as the input.

Since: 0.1.0

computeWithStride :: forall r ix e r'. (Manifest r e, StrideLoad r' ix e) => Stride ix -> Array r' ix e -> Array r ix e

Same as compute, but with Stride.

O(n div k) - Where n is number of elements in the source array and k is number of elements in the stride.

Since: 0.3.0

computeWithStrideAs :: (Manifest r e, StrideLoad r' ix e) => r -> Stride ix -> Array r' ix e -> Array r ix e

Same as computeWithStride, but with ability to specify resulting array representation.

Since: 0.3.0

clone :: (Manifest r e, Index ix) => Array r ix e -> Array r ix e

O(n) - Make an exact immutable copy of an Array.

Since: 0.1.0

convert :: forall r ix e r'. (Manifest r e, Load r' ix e) => Array r' ix e -> Array r ix e

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 :: (Manifest r e, Load r' ix e) => r -> Array r' ix e -> Array r ix e

Same as convert, but let's you supply resulting representation type as an argument.

Since: 0.1.0

convertProxy :: (Manifest r e, Load r' ix e) => proxy r -> Array r' ix e -> Array r ix e

Same as convert and convertAs, but let's you supply resulting representation type as a proxy argument.

Since: 0.1.1

fromRaggedArrayM :: forall r ix e r' m. (Manifest r e, Ragged r' ix e, MonadThrow m) => Array r' ix e -> m (Array r ix e)

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'. (HasCallStack, Manifest r e, Ragged r' ix e) => Array r' ix e -> Array r ix e

Same as fromRaggedArrayM, but will throw an impure exception if its shape is not rectangular.

Since: 0.1.1

Vector

module Data.Massiv.Vector

Size

size :: Size r => Array r ix e -> Sz ix

O(1) - Get the exact size of an immutabe array. Most of the time will produce the size in constant time, except for DS representation, which could result in evaluation of the whole stream. See maxLinearSize and slength for more info.

Since: 0.1.0

elemsCount :: (Index ix, Size r) => Array r ix e -> Int

O(1) - Get the number of elements in the array.

Examples

>>> import Data.Massiv.Array
>>> elemsCount $ range Seq (Ix1 10) 15
5

Since: 0.1.0

isEmpty :: (Index ix, Size r) => Array r ix e -> Bool

O(1) - Check if array has elements.

Examples

>>> import Data.Massiv.Array
>>> isEmpty (singleton 1 :: Array D Ix2 Int)
False
>>> isEmpty (empty :: Array D Ix2 Int)
True

Since: 1.0.0

isNotEmpty :: (Index ix, Size r) => Array r ix e -> Bool

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: 1.0.0

isNull :: Shape r ix => Array r ix e -> Bool

O(1) - Check whether an array is empty or not.

Examples

>>> import Data.Massiv.Array
>>> isNull $ range Seq (Ix2 10 20) (11 :. 21)
False
>>> isNull $ range Seq (Ix2 10 20) (10 :. 21)
True
>>> isNull (empty :: Array D Ix5 Int)
True
>>> isNull $ sfromList []
True

Since: 1.0.0

isNotNull :: Shape r ix => Array r ix e -> Bool

O(1) - Check if array has elements.

Examples

>>> import Data.Massiv.Array
>>> isNotNull (singleton 1 :: Array D Ix2 Int)
True
>>> isNotNull (empty :: Array D Ix2 Int)
False

Since: 0.5.1

Indexing

(!?) :: forall r ix e m. (Index ix, Manifest r e, MonadThrow m) => Array r ix e -> ix -> m e infixl 4

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

(!) :: forall r ix e. (HasCallStack, Manifest r e, Index ix) => Array r ix e -> ix -> e infixl 4

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

Since: 0.1.0

(??) :: (Index ix, Manifest r e, MonadThrow m) => m (Array r ix e) -> ix -> m e infixl 4

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 U Seq (Sz (1 :. 3))
  [ [ 4, 5, 6 ]
  ]
)
>>> ma ??> 1 ?? 0 :. 2
Just 6
>>> ma ?? 1 :> 0 :. 2
Just 6

Since: 0.1.0

indexM :: (Index ix, Manifest r e, MonadThrow m) => Array r ix e -> ix -> m e

O(1) - Lookup an element in the array.

Exceptions: IndexOutOfBoundsException

Since: 0.3.0

index :: (Index ix, Manifest r e) => Array r ix e -> ix -> Maybe e

O(1) - Lookup an element in the array. Returns Nothing, when index is out of bounds and returns the element at the supplied index otherwise. Use indexM instead, since it is more general and it can just as well be used with Maybe.

Since: 0.1.0

index' :: (HasCallStack, Index ix, Manifest r e) => Array r ix e -> ix -> e

O(1) - Lookup an element in the array. This is a partial function and it will throw an error when index is out of bounds. It is safer to use indexM instead.

Examples

>>> import Data.Massiv.Array
>>> :set -XOverloadedLists
>>> xs = [0..100] :: Array U Ix1 Int
>>> index' xs 50
50

Since: 0.1.0

defaultIndex :: (Index ix, Manifest r e) => e -> Array r ix e -> ix -> e

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 :: (Index ix, Manifest r e) => Border e -> Array r ix e -> ix -> e

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 :: (Index ix, Source r e, MonadThrow m) => Array r ix e -> ix -> m e

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' :: (HasCallStack, Index ix, Source r e) => Array r ix e -> ix -> e

Similar to evaluateM, but will throw an error on out of bounds indices.

Examples

>>> import Data.Massiv.Array
>>> evaluate' (range Seq (Ix2 10 20) (100 :. 210)) 50
60 :. 70

Since: 0.3.0

Mapping

map :: (Index ix, Source r e') => (e' -> e) -> Array r ix e' -> Array D ix e

Map a function over an array

Since: 0.1.0

imap :: forall r ix e a. (Index ix, Source r e) => (ix -> e -> a) -> Array r ix e -> Array D ix a

Map an index aware function over an array

Since: 0.1.0

Traversing

Applicative

traverseA :: forall r ix e r' a f. (Source r' a, Manifest r e, Index ix, Applicative f) => (a -> f e) -> Array r' ix a -> f (Array r ix e)

Traverse with an Applicative action over an array sequentially.

Note - using traversePrim instead will always be significantly faster, roughly about 30 times faster in practice.

Since: 0.2.6

traverseA_ :: forall r ix e a f. (Index ix, Source r e, Applicative f) => (e -> f a) -> Array r ix e -> f ()

Traverse sequentially over a source array, while discarding the result.

Since: 0.3.0

itraverseA :: forall r ix e r' a f. (Source r' a, Manifest r e, Index ix, Applicative f) => (ix -> a -> f e) -> Array r' ix a -> f (Array r ix e)

Traverse with an Applicative index aware action over an array sequentially.

Since: 0.2.6

itraverseA_ :: forall r ix e a f. (Source r a, Index ix, Applicative f) => (ix -> a -> f e) -> Array r ix a -> f ()

Traverse with an Applicative index aware action over an array sequentially.

Since: 0.2.6

sequenceA :: forall r ix e r' f. (Source r' (f e), Manifest r e, Index ix, Applicative f) => Array r' ix (f e) -> f (Array r ix e)

Sequence actions in a source array.

Since: 0.3.0

sequenceA_ :: forall r ix e f. (Index ix, Source r (f e), Applicative f) => Array r ix (f e) -> f ()

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' a, Manifest r b, Index ix, PrimMonad m) => (a -> m b) -> Array r' ix a -> m (Array r ix b)

Traverse sequentially within PrimMonad over an array with an action.

Since: 0.3.0

itraversePrim :: forall r ix b r' a m. (Source r' a, Manifest r b, Index ix, PrimMonad m) => (ix -> a -> m b) -> Array r' ix a -> m (Array r ix b)

Same as traversePrim, but traverse with index aware action.

Since: 0.3.0

Monadic mapping

Sequential

mapM

Arguments

:: forall r ix b r' a m. (Source r' a, Manifest r b, Index ix, 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' a, Manifest r b, Index ix, Monad m) => Array r' ix a -> (a -> m b) -> m (Array r ix b)

Same as mapM except with arguments flipped.

Since: 0.2.6

imapM :: forall r ix b r' a m. (Source r' a, Manifest r b, Index ix, Monad m) => (ix -> a -> m b) -> Array r' ix a -> m (Array r ix b)

Map an index aware monadic action over an array sequentially.

Since: 0.2.6

iforM :: forall r ix b r' a m. (Source r' a, Manifest r b, Index ix, Monad m) => Array r' ix a -> (ix -> a -> m b) -> m (Array r ix b)

Same as forM, except with an index aware action.

Since: 0.5.1

mapM_ :: (Source r a, Index ix, Monad m) => (a -> m b) -> Array r ix a -> m ()

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 a, Index ix, Monad m) => Array r ix a -> (a -> m b) -> m ()

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_ :: (Index ix, Source r a, Monad m) => (ix -> a -> m b) -> Array r ix a -> m ()

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 a, Index ix, Monad m) => Array r ix a -> (ix -> a -> m b) -> m ()

Just like imapM_, except with flipped arguments.

Parallelizable

mapIO :: forall r ix b r' a m. (Size r', Load r' ix a, Manifest r b, MonadUnliftIO m) => (a -> m b) -> Array r' ix a -> m (Array r ix b)

Map an IO action over an Array. Underlying computation strategy is respected and will be parallelized when requested. Unfortunately no fusion is possible and new array will be create upon each call.

Since: 0.2.6

mapWS :: forall r ix b r' a s m. (Source r' a, Manifest r b, Index ix, MonadUnliftIO m, PrimMonad m) => WorkerStates s -> (a -> s -> m b) -> Array r' ix a -> m (Array r ix b)

Same as imapWS, but without the index.

Since: 0.3.4

mapIO_ :: forall r ix e a m. (Load r ix e, MonadUnliftIO m) => (e -> m a) -> Array r ix e -> m ()

Similar to mapIO, but ignores the result of mapping action and does not create a resulting array, therefore it is faster. Use this instead of mapIO when result is irrelevant. Most importantly it will follow the iteration logic outlined by the supplied array.

Since: 0.2.6

imapIO :: forall r ix b r' a m. (Size r', Load r' ix a, Manifest r b, MonadUnliftIO m) => (ix -> a -> m b) -> Array r' ix a -> m (Array r ix b)

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' a, Manifest r b, Index ix, MonadUnliftIO m, PrimMonad m) => WorkerStates s -> (ix -> a -> s -> m b) -> Array r' ix a -> m (Array r ix b)

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_ :: forall r ix e a m. (Load r ix e, MonadUnliftIO m) => (ix -> e -> m a) -> Array r ix e -> m ()

Same as mapIO_, but map an index aware action instead.

Since: 0.2.6

forIO :: forall r ix b r' a m. (Size r', Load r' ix a, Manifest r b, MonadUnliftIO m) => Array r' ix a -> (a -> m b) -> m (Array r ix b)

Same as mapIO but with arguments flipped.

Since: 0.2.6

forWS :: forall r ix b r' a s m. (Source r' a, Manifest r b, Index ix, MonadUnliftIO m, PrimMonad m) => WorkerStates s -> Array r' ix a -> (a -> s -> m b) -> m (Array r ix b)

Same as iforWS, but without the index.

Since: 0.3.4

forIO_ :: (Load r ix e, MonadUnliftIO m) => Array r ix e -> (e -> m a) -> m ()

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. (Size r', Load r' ix a, Manifest r b, MonadUnliftIO m) => Array r' ix a -> (ix -> a -> m b) -> m (Array r ix b)

Same as imapIO but with arguments flipped.

Since: 0.2.6

iforWS :: forall r ix b r' a s m. (Source r' a, Manifest r b, Index ix, MonadUnliftIO m, PrimMonad m) => WorkerStates s -> Array r' ix a -> (ix -> a -> s -> m b) -> m (Array r ix b)

Same as imapWS, but with source array and mapping action arguments flipped.

Since: 0.3.4

iforIO_ :: forall r ix e a m. (Load r ix e, MonadUnliftIO m) => Array r ix e -> (ix -> e -> m a) -> m ()

Same as imapIO_ but with arguments flipped.

Since: 0.2.6

imapSchedulerM_ :: (Index ix, Source r e, MonadPrimBase s m) => Scheduler s () -> (ix -> e -> m a) -> Array r ix e -> m ()

Same as imapM_, but will use the supplied scheduler.

Since: 0.3.1

iforSchedulerM_ :: (Index ix, Source r e, MonadPrimBase s m) => Scheduler s () -> Array r ix e -> (ix -> e -> m a) -> m ()

Same as imapM_, but will use the supplied scheduler.

Since: 0.3.1

iterArrayLinearM_

Arguments

:: forall r ix e m s. (Load r ix e, MonadPrimBase s m)

=> Scheduler s ()

-> Array r ix e

Array that is being loaded

-> (Int -> e -> m ())

Function that writes an element into target array

-> m ()

iterArrayLinearWithSetM_

Arguments

:: forall r ix e m s. (Load r ix e, MonadPrimBase s m)

=> Scheduler s ()

-> Array r ix e

Array that is being loaded

-> (Int -> e -> m ())

Function that writes an element into target array

-> (Ix1 -> Sz1 -> e -> m ())

Function that efficiently sets a region of an array to the supplied value target array

-> m ()

iterArrayLinearWithStrideM_

Arguments

:: forall r ix e m s. (StrideLoad r ix e, MonadPrimBase s m)

=> Scheduler s ()

-> Stride ix

Stride to use

-> Sz ix

Size of the target array affected by the stride.

-> Array r ix e

Array that is being loaded

-> (Int -> e -> m ())

Function that writes an element into target array

-> m ()

Zipping

zip :: (Index ix, Source r1 e1, Source r2 e2) => Array r1 ix e1 -> Array r2 ix e2 -> Array D ix (e1, e2)

Zip two arrays

Since: 0.1.0

zip3 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3) => Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> Array D ix (e1, e2, e3)

Zip three arrays

Since: 0.1.0

zip4 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3, Source r4 e4) => Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> Array r4 ix e4 -> Array D ix (e1, e2, e3, e4)

Zip four arrays

Since: 0.5.4

unzip :: (Index ix, Source r (e1, e2)) => Array r ix (e1, e2) -> (Array D ix e1, Array D ix e2)

Unzip two arrays

Since: 0.1.0

unzip3 :: (Index ix, Source r (e1, e2, e3)) => Array r ix (e1, e2, e3) -> (Array D ix e1, Array D ix e2, Array D ix e3)

Unzip three arrays

Since: 0.1.0

unzip4 :: (Index ix, Source r (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)

Unzip four arrays

Since: 0.5.4

zipWith :: (Index ix, Source r1 e1, Source r2 e2) => (e1 -> e2 -> e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array D ix e

Zip two arrays with a function. Resulting array will be an intersection of source arrays in case their dimensions do not match.

zipWith3 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3) => (e1 -> e2 -> e3 -> e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> Array D ix e

Just like zipWith, except zip three arrays with a function.

zipWith4 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3, Source r4 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

Just like zipWith, except zip four arrays with a function.

Since: 0.5.4

izipWith :: (Index ix, Source r1 e1, Source r2 e2) => (ix -> e1 -> e2 -> e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array D ix e

Just like zipWith, except with an index aware function.

izipWith3 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3) => (ix -> e1 -> e2 -> e3 -> e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> Array D ix e

Just like zipWith3, except with an index aware function.

izipWith4 :: (Index ix, Source r1 e1, Source r2 e2, Source r3 e3, Source r4 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

Just like zipWith4, except with an index aware function.

Since: 0.5.4

Applicative

zipWithA :: (Source r1 e1, Source r2 e2, Applicative f, Manifest r e, Index ix) => (e1 -> e2 -> f e) -> Array r1 ix e1 -> Array r2 ix e2 -> f (Array r ix e)

Similar to zipWith, except does it sequentially and using the Applicative. Note that resulting array has Manifest representation.

Since: 0.3.0

izipWithA :: (Source r1 e1, Source r2 e2, Applicative f, Manifest r e, Index ix) => (ix -> e1 -> e2 -> f e) -> Array r1 ix e1 -> Array r2 ix e2 -> f (Array r ix e)

Similar to zipWith, except does it sequentially and using the Applicative. Note that resulting array has Manifest representation.

Since: 0.3.0

zipWith3A :: (Source r1 e1, Source r2 e2, Source r3 e3, Applicative f, Manifest r e, Index ix) => (e1 -> e2 -> e3 -> f e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> f (Array r ix e)

Same as zipWithA, but for three arrays.

Since: 0.3.0

izipWith3A :: (Source r1 e1, Source r2 e2, Source r3 e3, Applicative f, Manifest r e, Index ix) => (ix -> e1 -> e2 -> e3 -> f e) -> Array r1 ix e1 -> Array r2 ix e2 -> Array r3 ix e3 -> f (Array r ix e)

Same as izipWithA, but for three arrays.

Since: 0.3.0

Folding

All folding is done in a row-major order.

Unstructured folds

Functions in this section will fold any Source array with respect to the inner Computation strategy setting.

fold

Arguments

:: (Monoid e, Index ix, Source r e)

=> Array r ix e

Source array

-> e

O(n) - Unstructured fold of an array.

Since: 0.3.0

ifoldMono

Arguments

:: (Index ix, Source r e, Monoid m)

=> (ix -> e -> m)

Convert each element of an array to an appropriate Monoid.

-> 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

foldMono

Arguments

:: (Index ix, Source r e, Monoid m)

=> (e -> m)

Convert each element of an array to an appropriate Monoid.

-> Array r ix e

Source array

-> m

O(n) - This is exactly like foldMap, but for arrays. Fold over an array, while converting each element into a Monoid. Also known as map-reduce. If elements of the array are already a Monoid you can use fold instead.

Since: 0.1.4

ifoldSemi

Arguments

:: (Index ix, Source r e, Semigroup m)

=> (ix -> e -> m)

Convert each element of an array to an appropriate Semigroup.

-> m

Initial element that must be neutral to the (<>) function.

-> Array r ix e

Source array

-> m

O(n) - Semigroup fold over an array with an index aware function.

Since: 0.2.4

foldSemi

Arguments

:: (Index ix, Source r e, Semigroup m)

=> (e -> m)

Convert each element of an array to an appropriate Semigroup.

-> m

Initial element that must be neutral to the (<>) function.

-> Array r ix e

Source array

-> m

O(n) - Semigroup fold over an array.

Since: 0.1.6

foldOuterSlice :: (Index ix, Index (Lower ix), Source r e, Monoid m) => (Array r (Lower ix) e -> m) -> Array r ix e -> m

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 :: (Index ix, Index (Lower ix), Source r e, Monoid m) => (Ix1 -> Array r (Lower ix) e -> m) -> Array r ix e -> m

Reduce each outer slice into a monoid with an index aware function and mappend results together

Since: 0.4.3

foldInnerSlice :: (Source r e, Index ix, Monoid m) => (Array D (Lower ix) e -> m) -> Array r ix e -> m

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 :: (Source r e, Index ix, Monoid m) => (Ix1 -> Array D (Lower ix) e -> m) -> Array r ix e -> m

Reduce each inner slice into a monoid with an index aware function and mappend results together

Since: 0.4.3

minimumM :: (MonadThrow m, Shape r ix, Source r e, Ord e) => Array r ix e -> m e

O(n) - Compute minimum of all elements.

Since: 0.3.0

minimum' :: forall r ix e. (HasCallStack, Shape r ix, Source r e, Ord e) => Array r ix e -> e

O(n) - Compute minimum of all elements.

Since: 0.3.0

maximumM :: (MonadThrow m, Shape r ix, Source r e, Ord e) => Array r ix e -> m e

O(n) - Compute maximum of all elements.

Since: 0.3.0

maximum' :: forall r ix e. (HasCallStack, Shape r ix, Source r e, Ord e) => Array r ix e -> e

O(n) - Compute maximum of all elements.

Since: 0.3.0

sum :: (Index ix, Source r e, Num e) => Array r ix e -> e

O(n) - Compute sum of all elements.

Since: 0.1.0

product :: (Index ix, Source r e, Num e) => Array r ix e -> e

O(n) - Compute product of all elements.

Since: 0.1.0

and :: (Index ix, Source r Bool) => Array r ix Bool -> Bool

O(n) - Compute conjunction of all elements.

Since: 0.1.0

or :: (Index ix, Source r Bool) => Array r ix Bool -> Bool

O(n) - Compute disjunction of all elements.

Since: 0.1.0

all :: (Index ix, Source r e) => (e -> Bool) -> Array r ix e -> Bool

O(n) - Determines whether all elements of the array satisfy a predicate.

Since: 0.1.0

any :: (Index ix, Source r e) => (e -> Bool) -> Array r ix e -> Bool

O(n) - Determines whether any element of the array satisfies a predicate.

Since: 0.1.0

elem :: (Eq e, Index ix, Source r e) => e -> Array r ix e -> Bool

O(n) - Determines whether an element is present in the array.

Since: 0.5.5

eqArrays :: (Index ix, Source r1 e1, Source r2 e2) => (e1 -> e2 -> Bool) -> Array r1 ix e1 -> Array r2 ix e2 -> Bool

Compute array equality by applying a comparing function to each element. Empty arrays are always equal, regardless of their size.

Since: 0.5.7

compareArrays :: (Index ix, Source r1 e1, Source r2 e2) => (e1 -> e2 -> Ordering) -> Array r1 ix e1 -> Array r2 ix e2 -> Ordering

Compute array ordering by applying a comparing function to each element. The exact ordering is unspecified so this is only intended for use in maps and the like where you need an ordering but do not care about which one is used.

Since: 0.5.7

Single dimension folds

Safe inner most

ifoldlInner :: (Index (Lower ix), Index ix, Source r e) => (ix -> a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Left fold over the inner most dimension with index aware function.

Since: 0.2.4

foldlInner :: (Index (Lower ix), Index ix, Source r e) => (a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Left fold over the inner most dimension.

Since: 0.2.4

ifoldrInner :: (Index (Lower ix), Index ix, Source r e) => (ix -> e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Right fold over the inner most dimension with index aware function.

Since: 0.2.4

foldrInner :: (Index (Lower ix), Index ix, Source r e) => (e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Right fold over the inner most dimension.

Since: 0.2.4

foldInner :: (Monoid e, Index (Lower ix), Index ix, Source r e) => Array r ix e -> Array D (Lower ix) e

Monoidal fold over the inner most dimension.

Since: 0.4.3

Type safe within

ifoldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r e) => Dimension n -> (ix -> a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Left fold along a specified dimension with an index aware function.

Since: 0.2.4

foldlWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r e) => Dimension n -> (a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

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 e) => Dimension n -> (ix -> e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Right fold along a specified dimension with an index aware function.

Since: 0.2.4

foldrWithin :: (Index (Lower ix), IsIndexDimension ix n, Source r e) => Dimension n -> (e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

Right fold along a specified dimension.

Since: 0.2.4

foldWithin :: (Source r a, Monoid a, Index (Lower ix), IsIndexDimension ix n) => Dimension n -> Array r ix a -> Array D (Lower ix) a

Monoidal fold over some internal dimension.

Since: 0.4.3

Partial within

ifoldlWithin' :: (HasCallStack, Index (Lower ix), Index ix, Source r e) => Dim -> (ix -> a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

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' :: (HasCallStack, Index (Lower ix), Index ix, Source r e) => Dim -> (a -> e -> a) -> a -> Array r ix e -> Array D (Lower ix) a

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' :: (HasCallStack, Index (Lower ix), Index ix, Source r e) => Dim -> (ix -> e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

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' :: (HasCallStack, Index (Lower ix), Index ix, Source r e) => Dim -> (e -> a -> a) -> a -> Array r ix e -> Array D (Lower ix) a

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' :: (HasCallStack, Index ix, Source r a, Monoid a, Index (Lower ix)) => Dim -> Array r ix a -> Array D (Lower ix) a

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 Computation strategy setting.

foldlS :: (Index ix, Source r e) => (a -> e -> a) -> a -> Array r ix e -> a

O(n) - Left fold, computed sequentially.

Since: 0.1.0

foldrS :: (Index ix, Source r e) => (e -> a -> a) -> a -> Array r ix e -> a

O(n) - Right fold, computed sequentially.

Since: 0.1.0

ifoldlS :: (Index ix, Source r e) => (a -> ix -> e -> a) -> a -> Array r ix e -> a

O(n) - Left fold with an index aware function, computed sequentially.

Since: 0.1.0

ifoldrS :: (Index ix, Source r e) => (ix -> e -> a -> a) -> a -> Array r ix e -> a

O(n) - Right fold with an index aware function, computed sequentially.

Since: 0.1.0

Monadic

foldlM :: (Index ix, Source r e, Monad m) => (a -> e -> m a) -> a -> Array r ix e -> m a

O(n) - Monadic left fold.

Since: 0.1.0

foldrM :: (Index ix, Source r e, Monad m) => (e -> a -> m a) -> a -> Array r ix e -> m a

O(n) - Monadic right fold.

Since: 0.1.0

foldlM_ :: (Index ix, Source r e, Monad m) => (a -> e -> m a) -> a -> Array r ix e -> m ()

O(n) - Monadic left fold, that discards the result.

Since: 0.1.0

foldrM_ :: (Index ix, Source r e, Monad m) => (e -> a -> m a) -> a -> Array r ix e -> m ()

O(n) - Monadic right fold, that discards the result.

Since: 0.1.0

ifoldlM :: (Index ix, Source r e, Monad m) => (a -> ix -> e -> m a) -> a -> Array r ix e -> m a

O(n) - Monadic left fold with an index aware function.

Since: 0.1.0

ifoldrM :: (Index ix, Source r e, Monad m) => (ix -> e -> a -> m a) -> a -> Array r ix e -> m a

O(n) - Monadic right fold with an index aware function.

Since: 0.1.0

ifoldlM_ :: (Index ix, Source r e, Monad m) => (a -> ix -> e -> m a) -> a -> Array r ix e -> m ()

O(n) - Monadic left fold with an index aware function, that discards the result.

Since: 0.1.0

ifoldrM_ :: (Index ix, Source r e, Monad m) => (ix -> e -> a -> m a) -> a -> Array r ix e -> m ()

O(n) - Monadic right fold with an index aware function, that discards the result.

Since: 0.1.0

Special folds

foldrFB :: (Index ix, Source r e) => (e -> b -> b) -> b -> Array r ix e -> b

Version of foldr that supports foldr/build list fusion implemented by GHC.

Since: 0.1.0

lazyFoldlS :: (Index ix, Source r e) => (a -> e -> a) -> a -> Array r ix e -> a

O(n) - Left fold, computed sequentially with lazy accumulator.

Since: 0.1.0

lazyFoldrS :: (Index ix, Source r e) => (e -> a -> a) -> a -> Array r ix e -> a

O(n) - Right fold, computed sequentially with lazy accumulator.

Since: 0.1.0

Parallel folds

Note It is important to compile with -threaded -with-rtsopts=-N flags, otherwise there will be no parallelization.

Functions in this section will fold any Source array in parallel, regardless of the inner Computation 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.

foldlP

Arguments

:: (MonadIO m, Index ix, Source r e)

=> (a -> e -> a)

Folding function g.

-> a

Accumulator. Will be applied to g multiple times, thus must be neutral.

-> (b -> a -> b)

Chunk results folding function f.

-> 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, Index ix, Source r e) => (e -> a -> a) -> a -> (a -> b -> b) -> b -> Array r ix e -> m b

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, Index ix, Source r e) => (a -> ix -> e -> a) -> a -> (b -> a -> b) -> b -> Array r ix e -> m b

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, Index ix, Source r e) => (ix -> e -> a -> a) -> a -> (a -> b -> b) -> b -> Array r ix e -> m b

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 row-major.

Since: 0.1.0

ifoldlIO

Arguments

:: (MonadUnliftIO m, Index ix, Source r 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, Index ix, Source r e) => (ix -> e -> a -> m a) -> a -> (a -> b -> m b) -> b -> Array r ix e -> m b

Similar to ifoldrP, except that folding functions themselves do live in IO

Since: 0.1.0

Transforming

Transpose

transpose :: forall r e. Source r e => Matrix r e -> Matrix D e

Transpose a 2-dimensional 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 :: forall r ix e. (Index (Lower ix), Index ix, Source r e) => Array r ix e -> Array D ix e

Transpose inner two dimensions of at least rank-2 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 :: forall r ix e. (Index (Lower ix), Index ix, Source r e) => Array r ix e -> Array D ix e

Transpose outer two dimensions of at least rank-2 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 :: forall n r ix e. (IsIndexDimension ix n, Index ix, Source r e) => Dimension n -> Array r ix e -> Array D ix e

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' :: forall r ix e. (HasCallStack, Index ix, Source r e) => Dim -> Array r ix e -> Array D ix e

Reverse an array along some dimension. Same as reverseM, but throws the IndexDimensionException from pure code.

Since: 0.4.1

reverseM :: forall r ix e m. (MonadThrow m, Index ix, Source r e) => Dim -> Array r ix e -> m (Array D ix e)

Similarly to reverse, flip an array along a particular dimension, but throws IndexDimensionException for an incorrect dimension.

Since: 0.4.1

Backpermute

backpermuteM

Arguments

:: forall r ix e r' ix' m. (Manifest r e, Index ix, Source r' e, Index ix', 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

backpermute'

Arguments

:: forall r ix ix' e. (HasCallStack, Source r e, Index ix, 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 :: forall r ix ix' e m. (MonadThrow m, Index ix', Index ix, Size r) => Sz ix' -> Array r ix e -> m (Array r ix' e)

O(1) - Change the size of an array. Throws SizeElementsMismatchException if total number of elements does not match the supplied array.

Since: 0.3.0

resize' :: forall r ix ix' e. (HasCallStack, Index ix', Index ix, Size r) => Sz ix' -> Array r ix e -> Array r ix' e

Same as resizeM, but will throw an error if supplied dimensions are incorrect.

Since: 0.1.0

flatten :: forall r ix e. (Index ix, Size r) => Array r ix e -> Vector r e

O(1) - Reduce a multi-dimensional array into a flat vector

Since: 0.3.1

Extract

extractM

Arguments

:: forall r ix e m. (MonadThrow m, Index ix, Source r e)

=> ix

Starting index

-> Sz ix

Size of the resulting array

-> Array r ix e

Source array

-> m (Array D ix e)

Extract a sub-array from within a larger source array. Array that is being extracted must be fully encapsulated in a source array, otherwise SizeSubregionException will be thrown.

Examples

>>> import Data.Massiv.Array as A
>>> m <- resizeM (Sz (3 :. 3)) $ Ix1 1 ... 9
>>> m
Array D Seq (Sz (3 :. 3))
  [ [ 1, 2, 3 ]
  , [ 4, 5, 6 ]
  , [ 7, 8, 9 ]
  ]
>>> extractM (0 :. 1) (Sz (2 :. 2)) m
Array D Seq (Sz (2 :. 2))
  [ [ 2, 3 ]
  , [ 5, 6 ]
  ]
>>> a <- resizeM (Sz (3 :> 2 :. 4)) $ Ix1 11 ... 34
>>> a
Array D Seq (Sz (3 :> 2 :. 4))
  [ [ [ 11, 12, 13, 14 ]
    , [ 15, 16, 17, 18 ]
    ]
  , [ [ 19, 20, 21, 22 ]
    , [ 23, 24, 25, 26 ]
    ]
  , [ [ 27, 28, 29, 30 ]
    , [ 31, 32, 33, 34 ]
    ]
  ]
>>> extractM (0 :> 1 :. 1) (Sz (3 :> 1 :. 2)) a
Array D Seq (Sz (3 :> 1 :. 2))
  [ [ [ 16, 17 ]
    ]
  , [ [ 24, 25 ]
    ]
  , [ [ 32, 33 ]
    ]
  ]

Since: 0.3.0

extract'

Arguments

:: forall r ix e. (HasCallStack, Index ix, Source r e)

=> ix

Starting index

-> Sz ix

Size of the resulting array

-> Array r ix e

Source array

-> Array D ix e

Same as extractM, but will throw a runtime exception from pure code if supplied dimensions are incorrect.

Since: 0.1.0

extractFromToM

Arguments

:: forall r ix e m. (MonadThrow m, Index ix, Source r e)

=> ix

Starting index

-> ix

Index up to which elements should be extracted.

-> Array r ix e

Source array.

-> m (Array D ix e)

Similar to extractM, except it takes starting and ending index. Result array will not include the ending index.

Examples

>>> a <- resizeM (Sz (3 :> 2 :. 4)) $ Ix1 11 ... 34
>>> a
Array D Seq (Sz (3 :> 2 :. 4))
  [ [ [ 11, 12, 13, 14 ]
    , [ 15, 16, 17, 18 ]
    ]
  , [ [ 19, 20, 21, 22 ]
    , [ 23, 24, 25, 26 ]
    ]
  , [ [ 27, 28, 29, 30 ]
    , [ 31, 32, 33, 34 ]
    ]
  ]
>>> extractFromToM (1 :> 0 :. 1) (3 :> 2 :. 4) a
Array D Seq (Sz (2 :> 2 :. 3))
  [ [ [ 20, 21, 22 ]
    , [ 24, 25, 26 ]
    ]
  , [ [ 28, 29, 30 ]
    , [ 32, 33, 34 ]
    ]
  ]

Since: 0.3.0

extractFromTo'

Arguments

:: forall r ix e. (HasCallStack, Index ix, Source r e)

=> ix

Starting index

-> ix

Index up to which elmenets should be extracted.

-> Array r ix e

Source array.

-> Array D ix e

Same as extractFromToM, but throws an error on invalid indices.

Since: 0.2.4

deleteRowsM :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => Ix1 -> Sz Ix1 -> Array r ix e -> m (Array DL ix e)

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 :: forall r ix e m. (MonadThrow m, Index ix, Source r e) => Ix1 -> Sz Ix1 -> Array r ix e -> m (Array DL ix e)

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

deleteRegionM

Arguments

:: forall r ix e m. (MonadThrow m, Index ix, Source r 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)

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, Index ix, Source r1 e, Source r2 e) => Dim -> Array r1 ix e -> Array r2 ix e -> m (Array DL ix e)

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' :: forall r1 r2 ix e. (HasCallStack, Index ix, Source r1 e, Source r2 e) => Dim -> Array r1 ix e -> Array r2 ix e -> Array DL ix e

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)

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, Index ix, Source r e) => Dim -> f (Array r ix e) -> m (Array DL ix e)

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' :: forall f r ix e. (HasCallStack, Foldable f, Index ix, Source r e) => Dim -> f (Array r ix e) -> Array DL ix e

Concat many arrays together along some dimension.

Since: 0.3.0

stackSlicesM :: forall r ix e f m. (Foldable f, MonadThrow m, Index (Lower ix), Source r e, Index ix) => Dim -> f (Array r (Lower ix) e) -> m (Array DL ix e)

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, Index (Lower ix), Source r e, Index ix) => f (Array r (Lower ix) e) -> m (Array DL ix e)

Specialized stackSlicesM 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 P Seq (Sz1 3)
  [ 1, 2, 3 ]
Array P Seq (Sz1 3)
  [ 4, 5, 6 ]
Array P 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, Index (Lower ix), Source r e, Index ix) => f (Array r (Lower ix) e) -> m (Array DL ix e)

Specialized stackSlicesM to handling stacking from the inside. It is the inverse of innerSlices.

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 D Seq (Sz1 3)
  [ 1, 4, 7 ]
Array D Seq (Sz1 3)
  [ 2, 5, 8 ]
Array D 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

splitAtM

Arguments

:: forall r ix e m. (MonadThrow m, Index ix, Source r e)

=> Dim

Dimension along which to split

-> Int

Index along the dimension to split at

-> Array r ix e

Source array

-> m (Array D ix e, Array D 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' :: forall r ix e. (HasCallStack, Index ix, Source r e) => Dim -> Int -> Array r ix e -> (Array D ix e, Array D ix e)

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

splitExtractM

Arguments

:: forall r ix e m. (MonadThrow m, Index ix, Source r 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 D ix e, Array D ix e, Array D ix e)

Split an array in three parts across some dimension

Since: 0.3.5

replaceSlice :: forall r r' ix e m. (MonadThrow m, Source r e, Source r' e, Index ix, Index (Lower ix)) => Dim -> Ix1 -> Array r' (Lower ix) e -> Array r ix e -> m (Array DL ix e)

Replace a slice of an array with another one

Example

>>> import Data.Massiv.Array
>>> arr = makeArrayR U Seq (Sz3 3 4 5) fromIx3
>>> arr' = makeArrayR U Seq (Sz3 3 4 5) (fromIx3 . liftIndex (* 100))
>>> replaceSlice 2 1 (arr' <!> (2, 3)) arr
Array DL Seq (Sz (3 :> 4 :. 5))
  [ [ [ (0,0,0), (0,0,1), (0,0,2), (0,0,3), (0,0,4) ]
    , [ (0,300,0), (0,300,100), (0,300,200), (0,300,300), (0,300,400) ]
    , [ (0,2,0), (0,2,1), (0,2,2), (0,2,3), (0,2,4) ]
    , [ (0,3,0), (0,3,1), (0,3,2), (0,3,3), (0,3,4) ]
    ]
  , [ [ (1,0,0), (1,0,1), (1,0,2), (1,0,3), (1,0,4) ]
    , [ (100,300,0), (100,300,100), (100,300,200), (100,300,300), (100,300,400) ]
    , [ (1,2,0), (1,2,1), (1,2,2), (1,2,3), (1,2,4) ]
    , [ (1,3,0), (1,3,1), (1,3,2), (1,3,3), (1,3,4) ]
    ]
  , [ [ (2,0,0), (2,0,1), (2,0,2), (2,0,3), (2,0,4) ]
    , [ (200,300,0), (200,300,100), (200,300,200), (200,300,300), (200,300,400) ]
    , [ (2,2,0), (2,2,1), (2,2,2), (2,2,3), (2,2,4) ]
    , [ (2,3,0), (2,3,1), (2,3,2), (2,3,3), (2,3,4) ]
    ]
  ]

Since: 0.6.1

replaceOuterSlice :: forall r ix e m. (MonadThrow m, Index ix, Source r e, Load r (Lower ix) e) => Ix1 -> Array r (Lower ix) e -> Array r ix e -> m (Array DL ix e)

Replace an outer slice of an array with another one

Example

>>> import Data.Massiv.Array
>>> arr = makeArrayR U Seq (Sz3 3 4 5) fromIx3
>>> arr' = makeArrayR U Seq (Sz3 3 4 5) (fromIx3 . liftIndex (* 100))
>>> replaceOuterSlice 1 (arr' !> 2) arr
Array DL Seq (Sz (3 :> 4 :. 5))
  [ [ [ (0,0,0), (0,0,1), (0,0,2), (0,0,3), (0,0,4) ]
    , [ (0,1,0), (0,1,1), (0,1,2), (0,1,3), (0,1,4) ]
    , [ (0,2,0), (0,2,1), (0,2,2), (0,2,3), (0,2,4) ]
    , [ (0,3,0), (0,3,1), (0,3,2), (0,3,3), (0,3,4) ]
    ]
  , [ [ (200,0,0), (200,0,100), (200,0,200), (200,0,300), (200,0,400) ]
    , [ (200,100,0), (200,100,100), (200,100,200), (200,100,300), (200,100,400) ]
    , [ (200,200,0), (200,200,100), (200,200,200), (200,200,300), (200,200,400) ]
    , [ (200,300,0), (200,300,100), (200,300,200), (200,300,300), (200,300,400) ]
    ]
  , [ [ (2,0,0), (2,0,1), (2,0,2), (2,0,3), (2,0,4) ]
    , [ (2,1,0), (2,1,1), (2,1,2), (2,1,3), (2,1,4) ]
    , [ (2,2,0), (2,2,1), (2,2,2), (2,2,3), (2,2,4) ]
    , [ (2,3,0), (2,3,1), (2,3,2), (2,3,3), (2,3,4) ]
    ]
  ]

Since: 0.6.1

Upsample/Downsample

upsample

Arguments

:: forall r ix e. 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 Loadable 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 e, Load r ix e) => Stride ix -> Array r ix e -> Array DL ix e

Discard elements from the source array according to the stride.

Since: 0.3.0

Zoom

zoom

Arguments

:: forall r ix e. (Index ix, Source r e)

=> Stride ix

Scaling factor

-> Array r ix e

Source array

-> Array DL ix e

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

zoomWithGrid

Arguments

:: forall r ix e. (Index ix, Source r 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. (Manifest r e, Index ix, Source r' e', Index ix', 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)

General array transformation, that forces computation and produces a manifest array.

Since: 0.3.0

transform' :: forall ix e r' ix' e' a. (HasCallStack, Source r' e', Index ix', Index ix) => (Sz ix' -> (Sz ix, a)) -> (a -> (ix' -> e') -> ix -> e) -> Array r' ix' e' -> Array D ix e

General array transformation

Since: 0.3.0

transform2M :: (Manifest r e, Index ix, Source r1 e1, Source r2 e2, Index ix1, Index ix2, 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)

Same as transformM, but operates on two arrays

Since: 0.3.0

transform2' :: (HasCallStack, Source r1 e1, Source r2 e2, Index ix, Index ix1, Index ix2) => (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

Same as transform', but operates on two arrays

Since: 0.3.0

Slicing

From the outside

(!>) :: forall r ix e. (HasCallStack, Index ix, Index (Lower ix), Source r e) => Array r ix e -> Int -> Array r (Lower ix) e infixl 4

O(1) - Slices the array from the outside. For 2-dimensional 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 rank-3 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 U 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:

>>> arr !> 2 !> 0 ! 3
(2,0,3)
>>> evaluateM (arr !> 2 <! 3) 0
(2,0,3)
>>> (arr !> 2 !> 0 ! 3) == (arr ! 2 :> 0 :. 3)
True

Since: 0.1.0

(!?>) :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => Array r ix e -> Int -> m (Array r (Lower ix) e) infixl 4

O(1) - Just like !> slices the array from the outside, but returns Nothing when index is out of bounds.

Since: 0.1.0

(??>) :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => m (Array r ix e) -> Int -> m (Array r (Lower ix) e) infixl 4

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

(<!) :: forall r ix e. (HasCallStack, Index ix, Source r e) => Array r ix e -> Int -> Array D (Lower ix) e infixl 4

O(1) - Similarly to (!>) slice an array from an opposite direction.

Since: 0.1.0

(<!?) :: forall r ix e m. (MonadThrow m, Index ix, Source r e) => Array r ix e -> Int -> m (Array D (Lower ix) e) infixl 4

O(1) - Safe slice from the inside

Since: 0.1.0

(<??) :: forall r ix e m. (MonadThrow m, Index ix, Source r e) => m (Array r ix e) -> Int -> m (Array D (Lower ix) e) infixl 4

O(1) - Safe slicing continuation from the inside

Since: 0.1.0

From within

(<!>) :: forall r ix e. (HasCallStack, Index ix, Index (Lower ix), Source r e) => Array r ix e -> (Dim, Int) -> Array D (Lower ix) e infixl 4

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

(<!?>) :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => Array r ix e -> (Dim, Int) -> m (Array D (Lower ix) e) infixl 4

O(1) - Same as (<!>), but fails gracefully with a Nothing, instead of an error

Since: 0.1.0

(<??>) :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => m (Array r ix e) -> (Dim, Int) -> m (Array D (Lower ix) e) infixl 4

O(1) - Safe slicing continuation from within.

Since: 0.1.0

Many slices

outerSlices :: forall r ix e. (Index ix, Index (Lower ix), Source r e) => Array r ix e -> Array D Ix1 (Array r (Lower ix) e)

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 :: forall r ix e. (Index ix, Source r e) => Array r ix e -> Array D Ix1 (Array D (Lower ix) e)

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 :: forall n r ix e. (IsIndexDimension ix n, Index (Lower ix), Source r e) => Dimension n -> Array r ix e -> Array D Ix1 (Array D (Lower ix) e)

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 :: forall r ix e m. (MonadThrow m, Index ix, Index (Lower ix), Source r e) => Dim -> Array r ix e -> m (Array D Ix1 (Array D (Lower ix) e))

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 :: (Manifest r e, Ord e) => Vector r e -> Vector r e

This is an implementation of Quicksort, which is an efficient, but unstable sort. This implementation uses Median-of-three 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

quicksortBy :: Manifest r e => (e -> e -> Ordering) -> Vector r e -> Vector r e

Same as quicksortBy, but instead of Ord constraint expects a custom Ordering.

Since: 0.6.1

quicksortByM :: (Manifest r e, MonadUnliftIO m) => (e -> e -> m Ordering) -> Vector r e -> m (Vector r e)

Same as quicksortBy, but instead of Ord constraint expects a custom Ordering.

Since: 0.6.1

tally :: (Manifest r e, Load r ix e, Ord e) => Array r ix e -> Vector DS (e, Int)

Count number of occurrences of each element 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

iterateUntil

Arguments

:: (Load r' ix e, Manifest r e, NFData (Array 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
>>> let arr = computeAs P $ makeLoadArrayS (Sz2 8 8) (0 :: Int) $ \ w -> () <$ w (0 :. 0) 1
>>> arr
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 ]
  ]
>>> let nextPascalRow cur above = if cur == 0 then above else cur
>>> let 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) arr
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

fromList

Arguments

:: forall r e. Manifest r e

=> Comp

Computation startegy to use

-> [e]

Flat list

-> Vector r e

Convert a flat list into a vector

Since: 0.1.0

fromListsM :: forall r ix e m. (Ragged L ix e, Manifest r e, MonadThrow m) => Comp -> [ListItem ix e] -> m (Array r ix e)

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 Integer)
Nothing
>>> fromListsM Seq [[[1,2,3]],[[4,5,6],[7,8,9]]] :: IO (Array B Ix3 Integer)
*** Exception: DimTooLongException for (Dim 2): expected (Sz1 1), got (Sz1 2)
>>> fromListsM Seq [[1,2,3,4],[5,6,7]] :: IO (Matrix B Integer)
*** Exception: DimTooShortException for (Dim 1): expected (Sz1 4), got (Sz1 3)

Since: 0.3.0

fromLists'

Arguments

:: forall r ix e. (HasCallStack, Ragged L ix e, Manifest r e)

=> Comp

Computation startegy to use

-> [ListItem ix e]

Nested list

-> Array r ix e

Same as fromListsM, but will throw an 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.

\xs -> fromLists' Seq xs == (fromList Seq xs :: Vector P Int)

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 ]
  ]

Since: 0.1.0

toList :: (Index ix, Source r e) => Array r ix e -> [e]

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

Arguments

:: (Ragged L ix e, Shape r ix, Source r e)

=> Array r ix e

Array to be converted to nested lists

-> [ListItem ix e]

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 e, Index ix, Index (Lower ix)) => Array r ix e -> [[e]]

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 :: (Source r e, Index ix, Index (Lower ix), Index (Lower (Lower ix))) => Array r ix e -> [[[e]]]

Convert an array with at least 3 dimensions into a 3 deep nested list. Inner dimensions will get flattened.

Since: 0.1.0

toLists4 :: (Source r e, Index ix, Index (Lower ix), Index (Lower (Lower ix)), Index (Lower (Lower (Lower ix)))) => Array r ix e -> [[[[e]]]]

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