Type-safe linear algebra library
================================
- General matrix types are implemented in native Haskell.
- The dimensions of matrices are statically typed.
- Provides bindings to high performance C++ linear algebra libraries such Eigen and Spectra.
Following GHC extensions may be needed:
- ScopedTypeVariables
- RankNTypes
- TypeFamilies
- DataKinds
Example
-------
```haskell
{-# LANGUAGE DataKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE GADTs #-}
{-# LANGUAGE TypeOperators #-}
import Data.Matrix.Static.LinearAlgebra
import qualified Data.Matrix.Static.Generic as G
import qualified Data.Matrix.Static.Dense as D
import qualified Data.Matrix.Static.Sparse as S
import Data.Singletons.Prelude hiding ((@@))
import Data.Singletons.TypeLits
import Data.Complex
import System.Random
import Control.Monad
import Data.Type.Equality
f :: (SingI n, (2 <= n - 2) ~ 'True)
=> Matrix n n Double -> Matrix n n (Complex Double)
f m = let (d, v) = eigS (sing :: Sing 2) m
in v @@ S.diag d @@ G.transpose v
main :: IO ()
main = do
n <- randomRIO (2, 6)
vals <- replicateM (n*n) $ randomRIO (-100,100) :: IO [Double]
withSomeSing (fromIntegral n) $ \sn@(SNat :: Sing n) ->
let s0 = SNat :: Sing 2
sn2 = sn %- s0
in case testEquality (s0 %<= sn2) STrue of
Just Refl -> do
let mat = G.fromList vals :: Matrix n n Double
print $ f mat
Nothing -> error $ "Requiring Matrix size >= 4, but got: " <> show n
```