numeric-libs-overview

An overview of different Haskell numeric libraries. This is intended to be a place to compare different numeric libraries by their ease of use, performance and more.

Libraries are categorised and you should compare the libraries in the same category with each other.

Pull requests are welcome if you want to add a library!

These overviews include:

• Benchmarks
• Example code
• Links to hackage, github and the homepage if available

Vector representation libraries

vector

An efficient implementation of Int-indexed arrays (both mutable and immutable), with a powerful loop optimisation framework.

Example code:

let x = fromList [0..5]

length x -- 6
null x -- False

-- Indexing
x ! 1 -- 1
head x -- 0
last x -- 5

-- Slicing
slice 2 3 x -- [2, 3, 4]
splitAt 2 x -- ([0, 1], [2, 3, 4, 5])

-- Prepending and Appending
cons (-1) x -- [-1, 0, 1, 2, 3, 4, 5]
snoc x 6 -- [0, 1, 2, 3, 4, 5, 6]

-- Concatenation
x ++ x -- [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]
concat [x, x] -- [0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5]

-- Update
x // [(0, 1), (2, 6)] -- [1, 1, 6, 3, 4, 5]

map (+2) x -- [2, 3, 4, 5, 6, 7]

Benchmarks

Links: Hackage . GitHub

Matrix representation libraries

hmatrix

hmatrix is a linear algebra library and matrix computations.

Example code:

-- Creating matrices
let x = (2><2) [0..3] :: Matrix Double

x -- [ 0.0, 1.0
  -- , 2.0, 3.0 ]

let y = fromLists [[0, 1], [2, 3]] :: Matrix Double

-- Random matrices

r <- randn 2 3
r -- [ 0.7764496757867578,    1.246311658930589,    -0.684233085372455
  -- , -2.540045307941425, -0.20975584071908912, -9.039537343065803e-3 ]

-- Matrix multiplication

x <> y -- [ 2.0,  3.0 
       -- , 6.0, 11.0 ]

-- Transpose

tr x -- [ 0.0, 2.0 
     -- , 1.0, 3.0 ]

-- Matrix slicing
r ?? (All, Take 2) -- [ 0.7764496757867578,    1.246311658930589
                   -- , -2.540045307941425, -0.20975584071908912 ]

-- Mapping over matrices

cmap ((+ 2) . (*2)) x -- [ 2.0, 4.0
                      -- , 6.0, 8.0 ]

-- Flatten

flatten x -- [0.0, 1.0, 2.0, 3.0]

Benchmarks

Notes:

• Uses the vector library under the hood (specifically, Data.Vector.Storable)

Links: Hackage . GitHub . Homepage

Linear algebra libraries

hmatrix

hmatrix is a linear algebra library and matrix computations.

Example code:

-- Creating matrices
r <- randn 2 2
r -- [  0.7668461757288327, 0.5573308002071669
  -- , -0.7412791132378888,  1.001032678483079 ]

-- SVD
(u, s, v) = svd r
(u, s, v) = thinSVD r

eigenvalues r

singularValues r

nullspace r
orthogonal r

determinant r

Benchmarks

Notes:

• Uses the vector library under the hood (specifically, Data.Vector.Storable)

Links: Hackage . GitHub . Homepage

Contribution

• Benchmarks are written using criterion
• Please try to write an example code that matches format of the others and presets the same set of functionalities if available