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{-# OPTIONS_GHC -fglasgow-exts -fth -fallow-overlapping-instances -fallow-undecidable-instances #-}
module Static where
import Language.Haskell.TH
import Numeric.LinearAlgebra
import Foreign
import Language.Haskell.TH.Syntax
instance Lift Double where
lift x = return (LitE (RationalL (toRational x)))
--instance (Lift a, Storable a) => Lift (Vector a ) where
tdim :: Int -> ExpQ
tdim 0 = [| Z |]
tdim n = [| S $(tdim (n-1)) |]
data Z = Z deriving Show
data S a = S a deriving Show
class Dim a
instance Dim Z
instance Dim a => Dim (S a)
class Sum a b c | a b -> c -- , a c -> b, b c -> a
instance Sum Z a a
instance Sum a Z a
instance Sum a b c => Sum a (S b) (S c)
newtype SVec d t = SVec (Vector t) deriving Show
newtype SMat r c t = SMat (Matrix t) deriving Show
createl :: d -> [Double] -> SVec d Double
createl d l = SVec (fromList l)
createv :: Storable t => d -> Vector t -> SVec d t
createv d v = SVec v
--vec'' v = [|createv ($(tdim (dim v))) v|]
vec' :: [Double] -> ExpQ
vec' d = [| createl ($(tdim (length d))) d |]
createml :: (Dim r, Dim c) => r -> c -> Int -> Int -> [Double] -> SMat r c Double
createml _ _ r c l = SMat ((r><c) l)
mat :: Int -> Int -> [Double] -> ExpQ
mat r c l = [| createml ($(tdim r)) ($(tdim c)) r c l |]
vec :: [Double] -> ExpQ
vec d = [|mat (length d) 1 d|]
covec :: [Double] -> ExpQ
covec d = mat 1 (length d) d
scalar :: SMat (S Z) (S Z) Double -> Double
scalar (SMat m) = flatten m @> 0
v = fromList [1..5] :: Vector Double
l = [1,1.5..5::Double]
k = [11..30::Int]
rawv (SVec v) = v
raw (SMat m) = m
liftStatic :: (Matrix a -> Matrix b -> Matrix c) -> SMat dr dc a -> SMat dr dc b -> SMat dr dc c
liftStatic f a b = SMat (f (raw a) (raw b))
a |+| b = liftStatic (+) a b
prod :: SMat r k Double -> SMat k c Double -> SMat r c Double
prod a b = SMat (raw a <> raw b)
strans :: SMat r c Double -> SMat c r Double
strans = SMat . trans . raw
sdot a b = scalar (prod a b)
jv :: (Field t, Sum r1 r2 r3) => SMat r1 c t -> SMat r2 c t -> SMat r3 c t
jv a b = SMat ((raw a) <-> (raw b))
-- curiously, we cannot easily fold jv because the matrics are not of the same type.
jh a b = strans (jv (strans a) (strans b))
homog :: (Field t) => SMat r c t -> SMat (S r) c t
homog m = SMat (raw m <-> constant 1 (cols (raw m)))
inhomog :: (Linear Vector t) => SMat (S (S r)) c t -> SMat r c t
inhomog (SMat m) = SMat (sm <> d) where
sm = takeRows r' m
d = diag $ 1 / (flatten $ dropRows r' m)
r' = rows m -1
ht t vs = inhomog (t `prod` homog vs)
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