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{-# LANGUAGE DataKinds #-}
{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE MultiParamTypeClasses #-}
{-# LANGUAGE FunctionalDependencies #-}
{-# LANGUAGE FlexibleContexts #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE EmptyDataDecls #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE FlexibleInstances #-}
{-# LANGUAGE TypeOperators #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE GADTs #-}
{- |
Module : Numeric.LinearAlgebra.Static
Copyright : (c) Alberto Ruiz 2006-14
License : BSD3
Stability : provisional
-}
module Numeric.LinearAlgebra.Static(
Dim(..),
R(..), C(..),
lift1F, lift2F,
vconcat, gvec2, gvec3, gvec4, gvect, gmat,
Sized(..),
singleV, singleM,GM
) where
import GHC.TypeLits
import Numeric.HMatrix as LA
import Data.Packed as D
import Data.Packed.ST
import Data.Proxy(Proxy)
import Foreign.Storable(Storable)
newtype R n = R (Dim n (Vector ℝ))
deriving (Num,Fractional)
newtype C n = C (Dim n (Vector ℂ))
deriving (Num,Fractional)
newtype Dim (n :: Nat) t = Dim t
deriving Show
lift1F
:: (c t -> c t)
-> Dim n (c t) -> Dim n (c t)
lift1F f (Dim v) = Dim (f v)
lift2F
:: (c t -> c t -> c t)
-> Dim n (c t) -> Dim n (c t) -> Dim n (c t)
lift2F f (Dim u) (Dim v) = Dim (f u v)
--------------------------------------------------------------------------------
instance forall n t . (Num (Vector t), Numeric t )=> Num (Dim n (Vector t))
where
(+) = lift2F (+)
(*) = lift2F (*)
(-) = lift2F (-)
abs = lift1F abs
signum = lift1F signum
negate = lift1F negate
fromInteger x = Dim (fromInteger x)
instance (Num (Vector t), Num (Matrix t), Numeric t) => Fractional (Dim n (Vector t))
where
fromRational x = Dim (fromRational x)
(/) = lift2F (/)
instance (Num (Matrix t), Numeric t) => Num (Dim m (Dim n (Matrix t)))
where
(+) = (lift2F . lift2F) (+)
(*) = (lift2F . lift2F) (*)
(-) = (lift2F . lift2F) (-)
abs = (lift1F . lift1F) abs
signum = (lift1F . lift1F) signum
negate = (lift1F . lift1F) negate
fromInteger x = Dim (Dim (fromInteger x))
instance (Num (Vector t), Num (Matrix t), Numeric t) => Fractional (Dim m (Dim n (Matrix t)))
where
fromRational x = Dim (Dim (fromRational x))
(/) = (lift2F.lift2F) (/)
--------------------------------------------------------------------------------
type V n t = Dim n (Vector t)
ud :: Dim n (Vector t) -> Vector t
ud (Dim v) = v
mkV :: forall (n :: Nat) t . t -> Dim n t
mkV = Dim
type GM m n t = Dim m (Dim n (Matrix t))
--ud2 :: Dim m (Dim n (Matrix t)) -> Matrix t
--ud2 (Dim (Dim m)) = m
mkM :: forall (m :: Nat) (n :: Nat) t . t -> Dim m (Dim n t)
mkM = Dim . Dim
vconcat :: forall n m t . (KnownNat n, KnownNat m, Numeric t)
=> V n t -> V m t -> V (n+m) t
(ud -> u) `vconcat` (ud -> v) = mkV (vjoin [u', v'])
where
du = fromIntegral . natVal $ (undefined :: Proxy n)
dv = fromIntegral . natVal $ (undefined :: Proxy m)
u' | du > 1 && size u == 1 = LA.konst (u D.@> 0) du
| otherwise = u
v' | dv > 1 && size v == 1 = LA.konst (v D.@> 0) dv
| otherwise = v
gvec2 :: Storable t => t -> t -> V 2 t
gvec2 a b = mkV $ runSTVector $ do
v <- newUndefinedVector 2
writeVector v 0 a
writeVector v 1 b
return v
gvec3 :: Storable t => t -> t -> t -> V 3 t
gvec3 a b c = mkV $ runSTVector $ do
v <- newUndefinedVector 3
writeVector v 0 a
writeVector v 1 b
writeVector v 2 c
return v
gvec4 :: Storable t => t -> t -> t -> t -> V 4 t
gvec4 a b c d = mkV $ runSTVector $ do
v <- newUndefinedVector 4
writeVector v 0 a
writeVector v 1 b
writeVector v 2 c
writeVector v 3 d
return v
gvect :: forall n t . (Show t, KnownNat n, Numeric t) => String -> [t] -> V n t
gvect st xs'
| ok = mkV v
| not (null rest) && null (tail rest) = abort (show xs')
| not (null rest) = abort (init (show (xs++take 1 rest))++", ... ]")
| otherwise = abort (show xs)
where
(xs,rest) = splitAt d xs'
ok = size v == d && null rest
v = LA.fromList xs
d = fromIntegral . natVal $ (undefined :: Proxy n)
abort info = error $ st++" "++show d++" can't be created from elements "++info
gmat :: forall m n t . (Show t, KnownNat m, KnownNat n, Numeric t) => String -> [t] -> GM m n t
gmat st xs'
| ok = mkM x
| not (null rest) && null (tail rest) = abort (show xs')
| not (null rest) = abort (init (show (xs++take 1 rest))++", ... ]")
| otherwise = abort (show xs)
where
(xs,rest) = splitAt (m'*n') xs'
v = LA.fromList xs
x = reshape n' v
ok = rem (size v) n' == 0 && size x == (m',n') && null rest
m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
abort info = error $ st ++" "++show m' ++ " " ++ show n'++" can't be created from elements " ++ info
class Num t => Sized t s d | s -> t, s -> d
where
konst :: t -> s
unwrap :: s -> d
fromList :: [t] -> s
extract :: s -> d
singleV v = size v == 1
singleM m = rows m == 1 && cols m == 1
|
