Numeric Haskell: A Vector Tutorial
From HaskellWiki
The vector library has an API similar to the famous Haskell list library, with many of the same names.
This tutorial is modelled on the NumPy tutorial.
1 Quick Tour
Here is a quick overview to get you started.
1.1 Importing the library
Download the vector package:
$ cabal install vector
and import it as, for boxed arrays:
import qualified Data.Vector as V
or:
import qualified Data.Vector.Unboxed as V
for unboxed arrays. The library needs to be imported qualified as it shares the same function names as list operations in the Prelude.
1.2 Generating Vectors
New vectors can be generated in many ways:
$ ghci GHCi, version 6.12.1: http://www.haskell.org/ghc/ :? for help Loading package ghc-prim ... linking ... done. Loading package integer-gmp ... linking ... done. Loading package base ... linking ... done. Loading package ffi-1.0 ... linking ... done. Prelude> :m + Data.Vector -- Generating a vector from a list: Prelude Data.Vector> let a = fromList [10, 20, 30, 40] Prelude Data.Vector> a fromList [10,20,30,40] :: Data.Vector.Vector -- Or filled from a sequence Prelude Data.Vector> enumFromStepN 10 10 4 fromList [10,20,30,40] :: Data.Vector.Vector -- A vector created from four consecutive values Prelude Data.Vector> enumFromN 10 4 fromList [10,11,12,13] :: Data.Vector.Vector
You can also build vectors using operations similar to lists:
-- The empty vector Prelude Data.Vector> empty fromList [] :: Data.Vector.Vector -- A vector of length one Prelude Data.Vector> singleton 2 fromList [2] :: Data.Vector.Vector -- A vector of length 10, filled with the value '2' -- Note that to disambiguate names, -- and avoid a clash with the Prelude, -- with use the full path to the Vector module Prelude Data.Vector> Data.Vector.replicate 10 2 fromList [2,2,2,2,2,2,2,2,2,2] :: Data.Vector.Vector
In general, you may construct new vectors by applying a function to the index space:
Prelude Data.Vector> generate 10 (^2) fromList [0,1,4,9,16,25,36,49,64,81] :: Data.Vector.Vector
Vectors may have more than one dimension:
-- Here we create a two dimensional vector, 10 columns, -- each row filled with the row index. Prelude Data.Vector> let x = generate 10 (\n -> Data.Vector.replicate 10 n) -- The type is "Vector of Vector of Ints" Prelude Data.Vector> :t x x :: Vector (Vector Int)
Vectors may be grown or shrunk arbitrarily:
Prelude Data.Vector> let y = Data.Vector.enumFromTo 0 11 Prelude Data.Vector> y fromList [0,1,2,3,4,5,6,7,8,9,10,11] :: Data.Vector.Vector -- Take the first 3 elements as a new vector Prelude Data.Vector> Data.Vector.take 3 y fromList [0,1,2] :: Data.Vector.Vector -- Duplicate and join the vector Prelude Data.Vector> y Data.Vector.++ y fromList [0,1,2,3,4,5,6,7,8,9,10,11,0,1,2,3,4,5,6,7,8,9,10,11] :: Data.Vector.Vector
1.3 Modifying vectors
Just as with lists, you can iterate (map) over arrays, reduce them (fold), filter them, or join them in various ways:
-- mapping a function over the elements of a vector Prelude Data.Vector> Data.Vector.map (^2) y fromList [0,1,4,9,16,25,36,49,64,81,100,121] :: Data.Vector.Vector -- Extract only the odd elements from a vector Prelude Data.Vector> Data.Vector.filter odd y fromList [1,3,5,7,9,11] :: Data.Vector.Vector -- Reduce a vector Prelude Data.Vector> Data.Vector.foldl (+) 0 y 66 -- Take a scan (partial results from a reduction): Prelude Data.Vector> Data.Vector.scanl (+) 0 y fromList [0,0,1,3,6,10,15,21,28,36,45,55,66] :: Data.Vector.Vector -- Zip two arrays pairwise, into an array of pairs Prelude Data.Vector> Data.Vector.zip y y fromList [(0,0),(1,1),(2,2),(3,3),(4,4),(5,5),(6,6),(7,7),(8,8),(9,9),(10,10),(11,11)] :: Data.Vector.Vector
1.4 Indexing vectors
And like all good arrays, you can index them in various ways:
-- Take the first element Prelude Data.Vector> Data.Vector.head y 0 -- Take the last element Prelude Data.Vector> Data.Vector.tail y fromList [1,2,3,4,5,6,7,8,9,10,11] :: Data.Vector.Vector -- Take an arbitrary element Prelude Data.Vector> y ! 4 4
2 The Tutorial
The vector package provides a several types of array. The most general interface is via Data.Vector, which provides for boxed arrays, holding any type.
There are also more specialized array types:
which provide unboxed arrays (i.e. no closures) and storable arrays (data that is pinned, and may be passed to and from C via a Ptr).
In all cases, the operations are subject to loop fusion. That is, if you compose two functions,
map f . map g
the compiler will rewrite it into a single traversal:
map (f . g)
saving time and space.
2.1 Simple example
You can create the arrays in many ways, for example, from a regular Haskell list:
let a = fromList [2,3,4] Prelude Data.Vector> a fromList [2,3,4] :: Data.Vector.Vector Prelude Data.Vector> :t a a :: Vector Integer
GHCi will print the contents of the vector as executable code.
To create a multidimensional array, you can use a nested list generator to fill it:
Prelude Data.Vector> let x = fromList [ fromList [1 .. x] | x <- [1..10] ] Prelude Data.Vector> :t x x :: Vector (Vector Integer)
-- XXX TODO need a better printing function for multidimensional arrays.
You can also just create arrays filled with zeroes:
Prelude Data.Vector> Data.Vector.replicate 10 0 fromList [0,0,0,0,0,0,0,0,0,0] :: Data.Vector.Vector
And you can fill arrays from a sequence generator:
Prelude Data.Vector> enumFromN 1 10 fromList [1,2,3,4,5,6,7,8,9,10] :: Data.Vector.Vector Prelude Data.Vector> enumFromStepN 0 10 10 fromList [0,10,20,30,40,50,60,70,80,90] :: Data.Vector.Vector
2.2 Array Types
2.2.1 Boxed Arrays
2.2.2 Unboxed Arrays
2.2.3 Pure Arrays
2.2.4 Impure Arrays
2.2.5 Some examples
The most important attributes of an array are available in O(1) time, such as the size (length),
-- how big is the array? Prelude Data.Vector> let a = fromList [1,2,3,4,5,6,7,8,9,10] Prelude Data.Vector> Data.Vector.length a 10 -- is the array empty? Prelude Data.Vector> Data.Vector.null a False
2.3 Array Creation
2.3.1 An example: filling a vector from a file
We often want to populate a vector using a external data file. The easiest way to do this is with bytestring IO, and Data.Vector.unfoldr (or the equivalent functions in Data.Vector.Unboxed or Data.Vector.Storable:
{-# LANGUAGE BangPatterns #-} import qualified Data.ByteString.Lazy.Char8 as L import qualified Data.Vector as U import System.Environment main = do [f] <- getArgs s <- L.readFile f print . U.sum . parse $ s -- Fill a new vector from a file containing a list of numbers. parse = U.unfoldr step where step !s = case L.readInt s of Nothing -> Nothing Just (!k, !t) -> Just (k, L.tail t)
Note the use of bang patterns to ensure the parsing accumulated state is produced strictly.
Create a data file filled with 1 million integers:
$ seq 1 1000000 > data
Compile with -Odph (enables special optimizations to help fusion):
$ ghc -Odph --make vector.hs
Run:
$ time ./vector data 500000500000 ./vector data 0.08s user 0.01s system 98% cpu 0.088 total
