Numeric Haskell: A Vector Tutorial
Vector is a Haskell library for working with arrays, with an emphasis on raw performance, whilst retaining a rich interface. The main data types are boxed and unboxed arrays, and arrays may be immutable (pure), or mutable. Arrays are indexed by non-negative Int values.
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.
Quick Tour
Here is a quick overview to get you started.
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.
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
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
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
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.
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