# Numeric Haskell: A Vector Tutorial

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## Revision as of 05:37, 16 February 2010

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-negativeThe 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.

## 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