{-# OPTIONS_GHC -fno-warn-incomplete-uni-patterns #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE ConstraintKinds #-}
{-# LANGUAGE UndecidableInstances #-}
module Data.Tensor.Tensor where
import Control.DeepSeq
import Data.List (intercalate)
import Data.Proxy
import Data.Tensor.Type
import Data.Type.Bool hiding (If)
import qualified Data.Vector as V
import GHC.Exts (IsList (..))
import GHC.TypeLits
newtype Tensor (s :: [Nat]) n = Tensor { getValue :: Shape -> Index -> n }
type Scalar n = Tensor '[] n
type Vector s n = Tensor '[s] n
type Matrix a b n = Tensor '[a,b] n
type SimpleTensor (r :: Nat) (dim :: Nat) n = Tensor (Replicate r dim) n
instance Functor (Tensor s) where
fmap f t = Tensor $ \s i -> f (getValue t s i)
instance Applicative (Tensor s) where
pure n = Tensor $ \_ _ -> n
f <*> t = Tensor $ \s i -> getValue f s i (getValue t s i)
instance (HasShape s, Eq n) => Eq (Tensor s n) where
f == t = and $ (==) <$> f <*> t
instance HasShape s => Foldable (Tensor s) where
foldr f b t =
let s = shape t
r = toSize (Proxy :: Proxy s)
in foldr (f . gx t s) b ([0..r-1] :: [Int])
instance (HasShape s, NFData a) => NFData (Tensor s a) where
rnf = foldr (\_ -> rnf) ()
instance (HasShape s, Show n) => Show (Tensor s n) where
show (Tensor f) = let s = unShape (toShape :: SShape s) in go 0 [] s (f s)
where
{-# INLINE go #-}
go :: Int -> [Int] -> [Int] -> (Index -> n) -> String
go _ i [] fs = show $ fs (reverse i)
go z i [n] fs = g2 n z "," $ fmap (\x -> show (fs $ reverse (x:i))) [0..n-1]
go z i (n:ns) fs = g2 n z ",\n" $ fmap (\x -> go (z+1) (x:i) ns fs) [0..n-1]
{-# INLINE g2 #-}
g2 n z sep xs = let x = g3 n z xs in "[" ++ intercalate sep x ++ "]"
{-# INLINE g3 #-}
g3 n _ xs
| n > 9 = take 8 xs ++ [ "..", last xs]
| otherwise = xs
instance (HasShape s, Num n) => Num (Tensor s n) where
(+) = zipWithTensor (+)
(*) = zipWithTensor (*)
abs = fmap abs
signum = fmap signum
negate = fmap negate
fromInteger = pure . fromInteger
instance (HasShape s, Fractional n) => Fractional (Tensor s n) where
fromRational = pure . fromRational
(/) = zipWithTensor (/)
instance (HasShape s, Floating n) => Floating (Tensor s n) where
pi = pure pi
exp = fmap exp
log = fmap log
sqrt = fmap sqrt
logBase a b = logBase <$> a <*> b
sin = fmap sin
cos = fmap cos
tan = fmap tan
asin = fmap asin
acos = fmap acos
atan = fmap atan
sinh = fmap sinh
cosh = fmap cosh
tanh = fmap tanh
asinh = fmap asinh
acosh = fmap acosh
atanh = fmap atanh
{-# INLINE generateTensor #-}
generateTensor :: forall s n. HasShape s => (Index -> n) -> Tensor s n
generateTensor fn = case toSize (Proxy :: Proxy s) of
0 -> pure (fn [])
_ -> Tensor (const fn)
{-# INLINE transformTensor #-}
transformTensor
:: forall s s' n. HasShape s
=> (Shape -> (Shape, Index) -> Index)
-> Tensor s n
-> Tensor s' n
transformTensor go (Tensor fo) =
let s = unShape (toShape :: SShape s)
{-# INLINE g #-}
g = curry $ fo s . go s
in Tensor g
clone :: HasShape s => Tensor s n -> Tensor s n
clone t =
let s = shape t
v = V.generate (product s) (gx t s)
in Tensor $ \_ i -> v V.! tiTovi s i
{-# INLINE zipWithTensor #-}
zipWithTensor :: HasShape s => (n -> n -> n) -> Tensor s n -> Tensor s n -> Tensor s n
zipWithTensor f t1 t2 =
let s1 = shape t1
s2 = shape t2
in generateTensor (\i -> f (getValue t1 s1 i) (getValue t2 s2 i))
instance HasShape s => IsList (Tensor s n) where
type Item (Tensor s n) = n
fromList v =
let s = unShape (toShape :: SShape s)
l = product s
in if l /= length v
then error "length not match"
else let vv = V.fromList v in Tensor $ \s' i -> vv V.! tiTovi s' i
toList t =
let n = rank t - 1
s = unShape (toShape :: SShape s)
in fmap (gx t s) [0..n]
shape :: forall s n. HasShape s => Tensor s n -> [Int]
shape _ = unShape (toShape :: SShape s)
rank :: forall s n. HasShape s => Tensor s n -> Int
rank _ = toRank (Proxy :: Proxy s)
(!) :: HasShape s => Tensor s n -> TensorIndex s -> n
(!) t (TensorIndex i) = getValue t (shape t) i
gx :: HasShape s => Tensor s n -> Shape -> Int -> n
gx (Tensor t) s i = t s (viToti s i)
reshape :: (TensorSize s ~ TensorSize s', HasShape s) => Tensor s n -> Tensor s' n
reshape = transformTensor go
where
{-# INLINE go #-}
go s (s',i') = viToti s $ tiTovi s' i'
type Transpose (a :: [Nat]) = Reverse a '[]
transpose :: HasShape a => Tensor a n -> Tensor (Transpose a) n
transpose = transformTensor go
where
{-# INLINE go #-}
go _ (_, i') = reverse i'
type Swapaxes i j s = Take i s ++ (Dimension s j : (Drop i (Take j s))) ++ (Dimension s j : (Tail (Drop j s)))
swapaxes
:: (CheckIndices i j s
, HasShape s
, KnownNat i
, KnownNat j)
=> Proxy i
-> Proxy j
-> Tensor s n
-> Tensor (Swapaxes i j s) n
swapaxes px pj =
let i = toNat px
j = toNat pj
go _ (_,s) = take i s ++ [s !! j] ++ tail (drop i (take j s)) ++ [s!!i] ++ tail (drop j s)
in transformTensor go
identity :: forall s n . (HasShape s, Num n) => Tensor s n
identity = generateTensor go
where
go [] = 0
go [_] = 1
go (a:b:cs)
| a /= b = 0
| otherwise = go (b:cs)
dyad'
:: ( r ~ (s ++ t)
, HasShape s
, HasShape t
, HasShape r)
=> (n -> m -> o)
-> Tensor s n
-> Tensor t m
-> Tensor r o
dyad' f t1 t2 =
let l = rank t1
s1 = shape t1
s2 = shape t2
in generateTensor (\i -> let (ti1,ti2) = splitAt l i in f (getValue t1 s1 ti1) (getValue t2 s2 ti2))
dyad
:: ( r ~ (s ++ t)
, HasShape s
, HasShape t
, HasShape r
, Num n
, Eq n)
=> Tensor s n -> Tensor t n -> Tensor r n
dyad = dyad' mult
type DotTensor s1 s2 = Init s1 ++ Init s2
dot
:: ( Last s ~ Head s'
, r ~ DotTensor s s'
, HasShape s
, HasShape s'
, HasShape r
, Num n
, Eq n)
=> Tensor s n
-> Tensor s' n
-> Tensor r n
dot t1 t2 =
let s1 = shape t1
s2 = shape t2
n = last s1
b = length s1 - 1
f (!x,!y) = (getValue t1 s1 x) `mult` (getValue t2 s2 y)
in generateTensor (\i ->
let (ti1,ti2) = splitAt b i
in sum $ f <$> [(ti1++[x],x:ti2)| x <- [0..n-1]])
type Contraction s x y = DropIndex (DropIndex s y) x
type DropIndex s i = Take i s ++ Drop (i+1) s
contraction
:: forall x y s s' n.
( CheckIndices x y s
, s' ~ Contraction s x y
, Dimension s x ~ Dimension s y
, KnownNat x
, KnownNat y
, HasShape s
, HasShape s'
, KnownNat (Dimension s x)
, Num n)
=> (Proxy x, Proxy y)
-> Tensor s n
-> Tensor s' n
contraction (px, py) t@(Tensor f) =
let x = toNat px
y = toNat py
n = toNat (Proxy :: Proxy (Dimension s x))
s = shape t
in generateTensor (go x (y-x-1) n (f s) )
where
{-# INLINE go #-}
go a b n fs i =
let (r1,rt) = splitAt a i
(r3,r4) = splitAt b rt
in sum $ fmap fs [r1 ++ (j:r3) ++ (j:r4) | j <- [0..n-1]]
type CheckSelect dim i s = (CheckDimension dim s && IsIndex i (Dimension s dim)) ~ 'True
select
:: ( CheckSelect dim i s
, HasShape s
, KnownNat dim
, KnownNat i)
=> (Proxy dim, Proxy i)
-> Tensor s n
-> Tensor (DropIndex s dim) n
select (pd, pid) t=
let dim = toNat pd
ind = toNat pid
in transformTensor (go dim ind) t
where
{-# INLINE go #-}
go d i _ (_,i') = let (a,b) = splitAt d i' in a ++ (i:b)
type CheckSlice dim from to s = (CheckDimension dim s && IsIndices from to (Dimension s dim)) ~ 'True
type Slice dim from to s = Take dim s ++ ( to - from : Tail (Drop dim s))
slice
:: ( CheckSlice dim from to s
, s' ~ Slice dim from to s
, KnownNat dim
, KnownNat from
, KnownNat (to - from)
, HasShape s)
=> (Proxy dim, (Proxy from, Proxy to))
-> Tensor s n
-> Tensor s' n
slice (pd, (pa,_)) t =
let d = toNat pd
a = toNat pa
in transformTensor (\_ (_,i') -> let (x,y:ys) = splitAt d i' in x ++ (y+a:ys)) t
expand
:: (TensorRank s ~ TensorRank s'
, HasShape s)
=> Tensor s n
-> Tensor s' n
expand = transformTensor go
where
{-# INLINE go #-}
go s (_, i') = zipWith mod i' s
type CheckConcatenate i a b = (IsIndex i (TensorRank a)) ~ 'True
type Concatenate i a b = Take i a ++ (Dimension a i + Dimension b i : Drop (i+1) a)
concatenate
:: ( TensorRank a ~ TensorRank b
, DropIndex a i ~ DropIndex b i
, CheckConcatenate i a b
, Concatenate i a b ~ c
, HasShape a
, HasShape b
, KnownNat i)
=> Proxy i
-> Tensor a n
-> Tensor b n
-> Tensor c n
concatenate p ta@(Tensor a) tb@(Tensor b) =
let i = toNat p
sa = shape ta
sb = shape tb
n = sa !! i
in Tensor $ \_ ind -> let (ai,x:bi) = splitAt i ind in if x >= n then b sb (ai ++ (x-n):bi) else a sa ind
type CheckInsert dim i b = (CheckDimension dim b && IsIndex i (Dimension b dim)) ~ 'True
type Insert dim b = Take dim b ++ (Dimension b dim + 1 : Drop (dim + 1) b)
insert
:: ( DropIndex b dim ~ a
, CheckInsert dim i b
, KnownNat i
, KnownNat dim
, HasShape a
, HasShape b)
=> Proxy dim
-> Proxy i
-> Tensor a n
-> Tensor b n
-> Tensor (Insert dim b) n
insert pd px a@(Tensor ta) b@(Tensor tb) =
let d = toNat pd
i = toNat px
sa = shape a
sb = shape b
in Tensor $ \_ ci -> let (xs,n:ys) = splitAt d ci in if n == i then ta sa (xs++ys) else if n < i then tb sb ci else tb sb (xs ++ ((n-1):ys))
append
:: forall dim a b n.
( DropIndex b dim ~ a
, CheckInsert dim (Dimension b dim) b
, KnownNat (Dimension b dim)
, KnownNat dim
, HasShape a
, HasShape b)
=> Proxy dim
-> Tensor a n
-> Tensor b n
-> Tensor (Insert dim b) n
append pd = insert pd (Proxy :: Proxy (Dimension b dim))
runTensor :: HasShape s => Tensor s n -> Index -> n
runTensor t@(Tensor f) = f (shape t)