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--{-# OPTIONS_GHC #-}
--module Main where
import Data.Packed.Internal.Vector
import Data.Packed.Internal.Matrix
import Data.Packed.Internal.Tensor
import Complex
import Numeric(showGFloat)
import Data.List(transpose,intersperse,sort)
import Foreign.Storable
r >< c = f where
f l | dim v == r*c = matrixFromVector RowMajor c v
| otherwise = error $ "inconsistent list size = "
++show (dim v) ++"in ("++show r++"><"++show c++")"
where v = fromList l
r >|< c = f where
f l | dim v == r*c = matrixFromVector ColumnMajor c v
| otherwise = error $ "inconsistent list size = "
++show (dim v) ++"in ("++show r++"><"++show c++")"
where v = fromList l
vr = fromList [1..15::Double]
vc = fromList (map (\x->x :+ (x+1)) [1..15::Double])
mi = (2 >< 3) [1 .. 6::Int]
mz = (2 >< 3) [1,2,3,4,5,6:+(1::Double)]
ac = (2><3) [1 .. 6::Double]
bc = (3><4) [7 .. 18::Double]
af = (2>|<3) [1,4,2,5,3,6::Double]
bf = (3>|<4) [7,11,15,8,12,16,9,13,17,10,14,18::Double]
a |=| b = rows a == rows b &&
cols a == cols b &&
toList (dat a) == toList (dat b)
mulC a b = multiply RowMajor a b
mulF a b = multiply ColumnMajor a b
cc = mulC ac bf
cf = mulF af bc
r = mulC cc (trans cf)
rd = (2><2)
[ 43492.0, 50572.0
, 102550.0, 119242.0 ]
main = do
print $ r |=| rd
print $ foldl part t [("p",1),("q",0),("r",2)]
print $ foldl part t [("p",1),("r",2),("q",0)]
print $ foldl part t $ reverse [("p",1),("r",2),("q",0)]
t = T [(4,(Covariant,"p")),(2,(Covariant,"q")),(3,(Contravariant,"r"))] $ fromList [1..24::Double]
t1 = T [(4,(Covariant,"p")),(4,(Contravariant,"q")),(2,(Covariant,"r"))] $ fromList [1..32::Double]
t2 = T [(4,(Covariant,"p")),(4,(Contravariant,"q"))] $ fromList [1..16::Double]
delta i j | i==j = 1
| otherwise = 0
e i n = fromList [ delta k i | k <- [1..n]]
ident n = fromRows [ e i n | i <- [1..n]]
diag l = reshape c $ fromList $ [ l!!(i-1) * delta k i | k <- [1..c], i <- [1..c]]
where c = length l
tensorFromVector idx v = T {dims = [(dim v,idx)], ten = v}
tensorFromMatrix idxr idxc m = T {dims = [(rows m,idxr),(cols m,idxc)], ten = cdat m}
td = tensorFromMatrix (Contravariant,"i") (Covariant,"j") $ diag [1..4] :: Tensor Double
tn = tensorFromMatrix (Contravariant,"i") (Covariant,"j") $ (2><3) [1..6] :: Tensor Double
tt = tensorFromMatrix (Contravariant,"i") (Covariant,"j") $ (2><3) [1..6] :: Tensor Double
tq = T [(3,(Covariant,"p")),(2,(Covariant,"q")),(2,(Covariant,"r"))] $ fromList [11 .. 22] :: Tensor Double
r1 = contraction tt "j" tq "p"
r1' = contraction' tt "j" tq "p"
pru = do
mapM_ (putStrLn.shdims.dims.normal) (contractions t1 t2)
let t1 = contraction tt "i" tq "q"
print $ normal t1
print $ foldl part t1 [("j",0),("p'",1),("r'",1)]
let t2 = contraction' tt "i" tq "q"
print $ normal t2
print $ foldl part t2 [("j",0),("p'",1),("r'",1)]
let t1 = contraction tq "q" tt "i"
print $ normal t1
print $ foldl part t1 [("j'",0),("p",1),("r",1)]
let t2 = contraction' tq "q" tt "i"
print $ normal t2
print $ foldl part t2 [("j'",0),("p",1),("r",1)]
names t = sort $ map (snd.snd) (dims t)
normal t = tridx (names t) t
contractions t1 t2 = [ contraction t1 n1 t2 n2 | n1 <- names t1, n2 <- names t2, compatIdx t1 n1 t2 n2 ]
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