# Numeric Haskell: A Repa Tutorial

## Contents

# Numeric Haskell: A Repa Tutorial

Repa is a Haskell library for high performance, regular, multi-dimensional parallel arrays. All numeric data is stored unboxed. Functions written with the Repa combinators are automatically parallel provided you supply +RTS -Nwhatever on the command line when running the program.

See also the vector tutorial.

# Quick Tour

Repa (REgular PArallel arrays) is an advanced, multi-dimensional parallel arrays library for Haskell, with a number of distinct capabilities:

* The arrays are "regular" (i.e. dense and rectangular); and * Functions may be written that are polymorphic in the shape of the array; * Many operations on arrays are accomplished by changing only the shape of the array (without copying elements); * The library will automatically parallelize operations over arrays.

This is a quick start guide for the package.

## Importing the library

Download the `repa` package:

$ cabal install repa

and import it qualified:

import qualified Data.Array.Repa as R

The library needs to be imported qualified as it shares the same function names as list operations in the Prelude.

Note: Operations that involve writing new index types for Repa arrays will require the '-XTypeOperators' language extension.

For non-core functionality, a number of related packages are available:

* repa-bytestring * repa-io * repa-algorithms

and example algorithms in:

* repa-examples

## Index Types

Much like the classic 'array' library in Haskell, repa-based arrays are parameterized via a type which determines the dimension of the array, and the type of its index. However, while classic arrays take tuples to represent multiple dimensions, Repa arrays use a richer type language for array indices and shapes.

Index types consist of two parts:

* a dimension component; and * an index type

The most common dimensions are given by the shorthand names:

type DIM0 = Z type DIM1 = DIM0 :. Int type DIM2 = DIM1 :. Int type DIM3 = DIM2 :. Int type DIM4 = DIM3 :. Int type DIM5 = DIM4 :. Int

thus,

Array DIM2 Double

is a two-dimensional array of doubles, indexed via `Int` keys.

Many operations over arrays are polymorphic in the shape / dimension component. Others require operating on the shape itself, rather than the array.

To build values of `shape` type, we can use the `Z` and `:.` constructors:

> Z -- the zero-dimension Z

For arrays of non-zero dimension, we must give a size. A common error is to leave off the type of the size,

> :t Z :. 10 Z :. 10 :: Num head => Z :. head

For arrays of non-zero dimension, we must give a size. A common error is to leave off the type of the size,

> :t Z :. 10 Z :. 10 :: Num head => Z :. head

leading to annoying type errors about unresolved instances, such as:

No instance for (Shape (Z :. head0))

To select the correct instance, you will need to annotate the size literals with their concrete type:

> :t Z :. (10 :: Int) Z :. (10 :: Int) :: Z :. Int

is the shape of 1D arrays of length 10, indexed via Ints.

## Generating arrays

New repa arrays ("arrays" from here on) can be generated in many ways:

$ ghci GHCi, version 7.0.3: 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.Array.Repa

They may be constructed from lists:

A one dimensional array of length 10, here, given the shape `(Z :. 10)`:

> let x = fromList (Z :. (10::Int)) [1..10] > x [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0]

The type of `x` is inferred as:

> :t x x :: Array (Z :. Int) Double

which we can read as "an array of dimension 1, indexed via Int keys, holding elements of type Double"

We could also have written the type as:

x :: Array DIM1 Double

The same data may also be treated as a two dimensional array:

> let x = fromList (Z :. (5::Int) :. (2::Int)) [1..10] > x [1.0,2.0,3.0,4.0,5.0,6.0,7.0,8.0,9.0,10.0]

which would have the type:

x :: Array ((Z :. Int) :. Int) Double

or

x :: Array DIM2 Double

## Indexing arrays

To access elements in repa arrays, you provide an array and a shape, to access the element:

(!) :: (Shape sh, Elt a) => Array sh a -> sh -> a

## Modifying arrays

## Generating arrays

## Modifying arrays

## Indexing arrays

To access elements in repa arrays, you provide an array and a shape, to access the element:

(!) :: (Shape sh, Elt a) => Array sh a -> sh -> a

# Syntax

Repa arrays are instances of `Num`. This means that operations on numerical elements are lifted automagically onto arrays of such elements:

For example, `(+)` on two double values corresponds to zip-wise `(+)` on two arrays of doubles.