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--{-# OPTIONS_GHC #-}
--module Main where
{-
import Data.Packed.Internal
import Data.Packed.Internal.Vector
import Data.Packed.Internal.Matrix
import Data.Packed.Tensor
import Data.Packed.Matrix
import GSL.Vector
import LAPACK
import Data.List(foldl')
import Complex
import Numeric(showGFloat)
import Foreign.Storable
-}
import GSL
import Data.List(foldl', foldl1')
import Data.Packed.Internal.Tensor
import Data.Packed.Tensor
import Complex
main = do
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)]
pru
t = T [IdxDesc 4 Covariant "p",IdxDesc 2 Covariant "q" ,IdxDesc 3 Contravariant "r"]
$ fromList [1..24::Double]
t1 = T [IdxDesc 4 Covariant "p",IdxDesc 4 Contravariant "q" ,IdxDesc 2 Covariant "r"]
$ fromList [1..32::Double]
t2 = T [IdxDesc 4 Covariant "p",IdxDesc 4 Contravariant "q"]
$ fromList [1..16::Double]
vector n v = tvector n (fromList v) :: Tensor Double
kron n = tensorFromMatrix (Contravariant,"k1") (Covariant,"k2") (ident n)
tensorFromTrans m = tensorFromMatrix (Contravariant,"1") (Covariant,"2") m
tam = (3><3) [1..9]
tbm = (3><3) [11..19]
ta = tensorFromMatrix (Contravariant,"a1") (Covariant,"a2") tam :: Tensor Double
tb = tensorFromMatrix (Contravariant,"b1") (Covariant,"b2") tbm :: Tensor Double
delta i j | i==j = 1
| otherwise = 0
e i n = fromList [ delta k i | k <- [1..n]]
diagl = diag.fromList
td = tensorFromMatrix (Contravariant,"i") (Covariant,"j") $ diagl [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 [IdxDesc 3 Covariant "p",IdxDesc 2 Covariant "q" ,IdxDesc 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) (possibleContractions 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)]
putStrLn "--------------------------------------------"
print $ flatten $ tam <> tbm
print $ contractions (ta <*> tb <*> kron 3) [("a2","k1'"),("b1'","k2'")]
print $ contraction ta "a2" tb "b1"
print $ normal $ contractions (ta <*> tb) [("a2","b1'")]
print $ normal $ contraction' ta "a2" tb "b1"
putStrLn "--------------------------------------------"
print $ raise $ dualMV $ raise $ dualMV (x1/\x2) /\ dualV [x3,x4]
putStrLn "--------------------------------------------"
print $ foldl' contractionF (leviCivita 4) [y1,y2]
print $ contractions (leviCivita 4 <*> (y1/\y2)) [("1","p'"),("2'","q''")] <*> (scalar (recip $ fact 2))
print $ foldl' contractionF (leviCivita 4) [y1,y2,y3,y5]
print $ contractions (leviCivita 4 <*> (y1/\y2/\y3/\y5)) [("1","p'"),("2'","q''"),("3'","r''"),("4'","t''")] <*> (scalar (recip $ fact 4))
print $ dim $ ten $ leviCivita 4 <*> (y1/\y2/\y3/\y5)
print $ innerAT (leviCivita 4) (y1/\y2/\y3/\y5)
y5 = vector "t" [0,1,-2,0]
u = vector "p" [1,1,0]
v = vector "q" [0,1,1]
w = vector "r" [1,0,1]
uv = u /\ v
uw = u /\ w
l1 = vector "p" [0,0,0,1]
l2 = vector "q" [1,0,0,1]
l3 = vector "r" [0,1,0,1]
dual1 = foldl' contractionF (leviCivita 3) [u,v]
dual2 = foldl' contractionF (leviCivita 3) [u,v,w]
dual1' = prod (foldl' contract1b ((leviCivita 3) <*> (u /\ v)) [("1","p'"),("2'","q''")]) (scalar (recip $ fact 2))
dual2' = prod (foldl' contract1b ((leviCivita 3) <*> (u /\ v /\ w)) [("1","p'"),("2'","q''"),("3'","r''")]) (scalar (recip $ fact 3))
x1 = vector "p" [0,0,1]
x2 = vector "q" [2,2,2]
x3 = vector "r" [-3,-1,-1]
x4 = vector "s" [12,0,3]
-- intersection of two lines :-)
-- > raise $ dualMV $ raise $ dualMV (x1/\x2) /\ dualV [x3,x4]
--(3'^[3]) [24.0,24.0,12.0]
y1 = vector "p" [0,0,0,1]
y2 = vector "q" [2,2,0,2]
y3 = vector "r" [-3,-1,0,-1]
y4 = vector "s" [12,0,0,3]
-- why not in R^4?
-- > raise $ dualMV $ raise $ dualMV (y1/\y2) /\ dualV [y3,y4]
-- scalar 0.0
-- it seems that the sum of ranks must be greater than n :(
z1 = vector "p" [0,0,0,1]
z2 = vector "q" [1,0,0,1]
z3 = vector "r" [0,1,0,1]
z4 = vector "s" [0,0,1,1]
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