From e7c03c1ab4de85e7a700d2eafaebd37f4607c51f Mon Sep 17 00:00:00 2001
From: Alberto Ruiz <aruiz@um.es>
Date: Wed, 6 Jun 2007 17:40:09 +0000
Subject: working on tensor contractions

---
 examples/pru.hs | 76 ++++++++++++++++++++++++++++++++++-----------------------
 1 file changed, 46 insertions(+), 30 deletions(-)

(limited to 'examples')

diff --git a/examples/pru.hs b/examples/pru.hs
index bddc08f..a935d93 100644
--- a/examples/pru.hs
+++ b/examples/pru.hs
@@ -7,7 +7,7 @@ import Data.Packed.Internal.Tensor
 
 import Complex
 import Numeric(showGFloat)
-import Data.List(transpose,intersperse)
+import Data.List(transpose,intersperse,sort)
 import Foreign.Storable
 
 r >< c = f where
@@ -22,8 +22,6 @@ r >|< c = f where
                                  ++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])
 
@@ -62,38 +60,56 @@ main = do
 t = T [(4,(Covariant,"p")),(2,(Covariant,"q")),(3,(Contravariant,"r"))] $ fromList [1..24::Double]
 
 
-findIdx name t = ((d1,d2),m) where
-    (d1,d2) = span (\(_,(_,n)) -> n /=name) (dims t)
-    c = product (map fst d2)
-    m = matrixFromVector RowMajor c (ten t)
 
-putFirstIdx name t = (nd,m')
-    where ((d1,d2),m) = findIdx name t
-          m' = matrixFromVector RowMajor c $ cdat $ trans m
-          nd = d2++d1
-          c = dim (ten t) `div` (fst $ head d2)
+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]
 
-part t (name,k) = if k<0 || k>=l
-                    then error $ "part "++show (name,k)++" out of range in "++show t
-                    else T {dims = ds, ten = toRows m !! k}
-    where (d:ds,m) = putFirstIdx name t
-          (l,_) = d
 
-parts t name = map f (toRows m) 
-    where (d:ds,m) = putFirstIdx name t
-          (l,_) = d
-          f t = T {dims=ds, ten=t}
 
-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]
 
-contract1 t name1 name2 = map head $ zipWith drop [0..] (map (flip parts name2) (parts t name1))
 
-sumT ls = foldl (zipWith (+)) [0,0..] (map (toList.ten) ls)
 
-on f g = \x y -> f (g x) (g y)
+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
 
-contract t1 n1 t2 n2 = T (tail d1++tail d2) (cdat m)
-    where (d1,m1) = putFirstIdx n1 t1
-          (d2,m2) = putFirstIdx n2 t2
-          m = multiply RowMajor (trans m2) m1
\ No newline at end of file
+contractions t1 t2 = [ contraction t1 n1 t2 n2 | n1 <- names t1, n2 <- names t2, compatIdx t1 n1 t2 n2 ]
-- 
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