1 files changed, 422 insertions, 0 deletions

diff --git a/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
new file mode 100644
index 0000000..c9641d5
--- /dev/null
+++ b/packages/base/src/Numeric/LinearAlgebra/Static/Internal.hs
@@ -0,0 +1,422 @@
+{-# 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.Internal
+Copyright   :  (c) Alberto Ruiz 2006-14
+License     :  BSD3
+Stability   :  provisional
+
+-}
+
+module Numeric.LinearAlgebra.Static.Internal where
+
+
+import GHC.TypeLits
+import Numeric.LinearAlgebra.HMatrix as LA
+import Data.Packed as D
+import Data.Packed.ST
+import Data.Proxy(Proxy)
+import Foreign.Storable(Storable)
+import Text.Printf
+
+--------------------------------------------------------------------------------
+
+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)
+
+--------------------------------------------------------------------------------
+
+newtype R n = R (Dim n (Vector ℝ))
+  deriving (Num,Fractional)
+
+newtype C n = C (Dim n (Vector ℂ))
+  deriving (Num,Fractional)
+
+newtype L m n = L (Dim m (Dim n (Matrix ℝ)))
+
+newtype M m n = M (Dim m (Dim n (Matrix  ℂ)))
+
+
+mkR :: Vector ℝ -> R n
+mkR = R . Dim
+
+mkC :: Vector ℂ -> C n
+mkC = C . Dim
+
+mkL :: Matrix ℝ -> L m n
+mkL x = L (Dim (Dim x))
+
+mkM :: Matrix ℂ -> M m n
+mkM x = M (Dim (Dim x))
+
+--------------------------------------------------------------------------------
+
+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 
+
+
+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
+
+
+--------------------------------------------------------------------------------
+
+type GM m n t = Dim m (Dim n (Matrix t))
+
+
+gmat :: forall m n t . (Show t, KnownNat m, KnownNat n, Numeric t) => String -> [t] -> GM m n t
+gmat st xs'
+    | ok = Dim (Dim 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
+
+
+instance forall n. KnownNat n => Sized ℂ (C n) (Vector ℂ)
+  where
+    konst x = mkC (LA.scalar x)
+    unwrap (C (Dim v)) = v
+    fromList xs = C (gvect "C" xs)
+    extract (unwrap -> v)
+      | singleV v = LA.konst (v!0) d
+      | otherwise = v
+     where
+       d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+instance forall n. KnownNat n => Sized ℝ (R n) (Vector ℝ)
+  where
+    konst x = mkR (LA.scalar x)
+    unwrap (R (Dim v)) = v
+    fromList xs = R (gvect "R" xs)
+    extract (unwrap -> v)
+      | singleV v = LA.konst (v!0) d
+      | otherwise = v
+     where
+       d = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+
+instance forall m n . (KnownNat m, KnownNat n) => Sized ℝ (L m n) (Matrix ℝ)
+  where
+    konst x = mkL (LA.scalar x)
+    fromList xs = L (gmat "L" xs)
+    unwrap (L (Dim (Dim m))) = m
+    extract (isDiag -> Just (z,y,(m',n'))) = diagRect z y m' n'
+    extract (unwrap -> a)
+        | singleM a = LA.konst (a `atIndex` (0,0)) (m',n')
+        | otherwise = a
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+
+instance forall m n . (KnownNat m, KnownNat n) => Sized ℂ (M m n) (Matrix ℂ)
+  where
+    konst x = mkM (LA.scalar x)
+    fromList xs = M (gmat "M" xs)
+    unwrap (M (Dim (Dim m))) = m
+    extract (isDiagC -> Just (z,y,(m',n'))) = diagRect z y m' n'
+    extract (unwrap -> a)
+        | singleM a = LA.konst (a `atIndex` (0,0)) (m',n')
+        | otherwise = a
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m)
+        n' = fromIntegral . natVal $ (undefined :: Proxy n)
+
+--------------------------------------------------------------------------------
+
+instance (KnownNat n, KnownNat m) => Transposable (L m n) (L n m)
+  where
+    tr a@(isDiag -> Just _) = mkL (extract a)
+    tr (extract -> a) = mkL (tr a)
+
+instance (KnownNat n, KnownNat m) => Transposable (M m n) (M n m)
+  where
+    tr a@(isDiagC -> Just _) = mkM (extract a)
+    tr (extract -> a) = mkM (tr a)
+
+--------------------------------------------------------------------------------
+
+isDiag :: forall m n . (KnownNat m, KnownNat n) => L m n -> Maybe (ℝ, Vector ℝ, (Int,Int))
+isDiag (L x) = isDiagg x
+
+isDiagC :: forall m n . (KnownNat m, KnownNat n) => M m n -> Maybe (ℂ, Vector ℂ, (Int,Int))
+isDiagC (M x) = isDiagg x
+
+
+isDiagg :: forall m n t . (Numeric t, KnownNat m, KnownNat n) => GM m n t -> Maybe (t, Vector t, (Int,Int))
+isDiagg (Dim (Dim x))
+    | singleM x = Nothing
+    | rows x == 1 && m' > 1 || cols x == 1 && n' > 1 = Just (z,yz,(m',n'))
+    | otherwise = Nothing
+  where
+    m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+    n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+    v = flatten x
+    z = v `atIndex` 0
+    y = subVector 1 (size v-1) v
+    ny = size y
+    zeros = LA.konst 0 (max 0 (min m' n' - ny))
+    yz = vjoin [y,zeros]
+
+--------------------------------------------------------------------------------
+
+instance forall n . KnownNat n => Show (R n)
+  where
+    show (R (Dim v))
+      | singleV v = "("++show (v!0)++" :: R "++show d++")"
+      | otherwise   = "(vector"++ drop 8 (show v)++" :: R "++show d++")"
+      where
+        d = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+instance forall n . KnownNat n => Show (C n)
+  where
+    show (C (Dim v))
+      | singleV v = "("++show (v!0)++" :: C "++show d++")"
+      | otherwise   = "(vector"++ drop 8 (show v)++" :: C "++show d++")"
+      where
+        d = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+instance forall m n . (KnownNat m, KnownNat n) => Show (L m n)
+  where
+    show (isDiag -> Just (z,y,(m',n'))) = printf "(diag %s %s :: L %d %d)" (show z) (drop 9 $ show y) m' n'
+    show (L (Dim (Dim x)))
+       | singleM x = printf "(%s :: L %d %d)" (show (x `atIndex` (0,0))) m' n'
+       | otherwise = "(matrix"++ dropWhile (/='\n') (show x)++" :: L "++show m'++" "++show n'++")"
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+        n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+instance forall m n . (KnownNat m, KnownNat n) => Show (M m n)
+  where
+    show (isDiagC -> Just (z,y,(m',n'))) = printf "(diag %s %s :: M %d %d)" (show z) (drop 9 $ show y) m' n'
+    show (M (Dim (Dim x)))
+       | singleM x = printf "(%s :: M %d %d)" (show (x `atIndex` (0,0))) m' n'
+       | otherwise = "(matrix"++ dropWhile (/='\n') (show x)++" :: M "++show m'++" "++show n'++")"
+      where
+        m' = fromIntegral . natVal $ (undefined :: Proxy m) :: Int
+        n' = fromIntegral . natVal $ (undefined :: Proxy n) :: Int
+
+--------------------------------------------------------------------------------
+
+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) (/)
+
+--------------------------------------------------------------------------------
+
+
+adaptDiag f a@(isDiag -> Just _) b | isFull b = f (mkL (extract a)) b
+adaptDiag f a b@(isDiag -> Just _) | isFull a = f a (mkL (extract b))
+adaptDiag f a b = f a b
+
+isFull m = isDiag m == Nothing && not (singleM (unwrap m))
+
+
+lift1L f (L v) = L (f v)
+lift2L f (L a) (L b) = L (f a b)
+lift2LD f = adaptDiag (lift2L f)
+
+
+instance (KnownNat n, KnownNat m) =>  Num (L n m)
+  where
+    (+) = lift2LD (+)
+    (*) = lift2LD (*)
+    (-) = lift2LD (-)
+    abs = lift1L abs
+    signum = lift1L signum
+    negate = lift1L negate
+    fromInteger = L . Dim . Dim . fromInteger
+
+instance (KnownNat n, KnownNat m) => Fractional (L n m)
+  where
+    fromRational = L . Dim . Dim . fromRational
+    (/) = lift2LD (/)
+
+--------------------------------------------------------------------------------
+
+adaptDiagC f a@(isDiagC -> Just _) b | isFullC b = f (mkM (extract a)) b
+adaptDiagC f a b@(isDiagC -> Just _) | isFullC a = f a (mkM (extract b))
+adaptDiagC f a b = f a b
+
+isFullC m = isDiagC m == Nothing && not (singleM (unwrap m))
+
+lift1M f (M v) = M (f v)
+lift2M f (M a) (M b) = M (f a b)
+lift2MD f = adaptDiagC (lift2M f)
+
+instance (KnownNat n, KnownNat m) =>  Num (M n m)
+  where
+    (+) = lift2MD (+)
+    (*) = lift2MD (*)
+    (-) = lift2MD (-)
+    abs = lift1M abs
+    signum = lift1M signum
+    negate = lift1M negate
+    fromInteger = M . Dim . Dim . fromInteger
+
+instance (KnownNat n, KnownNat m) => Fractional (M n m)
+  where
+    fromRational = M . Dim . Dim . fromRational
+    (/) = lift2MD (/)
+
+--------------------------------------------------------------------------------
+
+
+class Disp t
+  where
+    disp :: Int -> t -> IO ()
+
+
+instance (KnownNat m, KnownNat n) => Disp (L m n)
+  where
+    disp n x = do
+        let a = extract x
+        let su = LA.dispf n a
+        printf "L %d %d" (rows a) (cols a) >> putStr (dropWhile (/='\n') $ su)
+
+instance (KnownNat m, KnownNat n) => Disp (M m n)
+  where
+    disp n x = do
+        let a = extract x
+        let su = LA.dispcf n a
+        printf "M %d %d" (rows a) (cols a) >> putStr (dropWhile (/='\n') $ su)
+
+
+instance KnownNat n => Disp (R n)
+  where
+    disp n v = do
+        let su = LA.dispf n (asRow $ extract v)
+        putStr "R " >> putStr (tail . dropWhile (/='x') $ su)
+
+instance KnownNat n => Disp (C n)
+  where
+    disp n v = do
+        let su = LA.dispcf n (asRow $ extract v)
+        putStr "C " >> putStr (tail . dropWhile (/='x') $ su)
+
+--------------------------------------------------------------------------------