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View of /branches/charisee/src/compiler/ein/normalizeEin.sml

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Revision 2383 - (download) (annotate)
Thu Jun 13 01:57:34 2013 UTC (7 years, 11 months ago) by cchiw
File size: 17257 byte(s)
added ein
structure NormalizeEin = struct

    structure G = GenericEin
    structure E = Ein
    structure S = Specialize
    structure R = Rewrite


If changed is true then I know the expression will run through the funciton again.
However, if not, then I want to make sure that every expression in the Product is examined, and not just individually but as a group.
Prod[t1,t2,(t3+t4)] indivually=> same
Prod[t1] @ Prod[t2,(t3+t4)]=> Notice rule here
Prod[t1] @ Add(Prod (t2, t3), Prod (t2, t4))
=> Add( Prod[t1, Prod(t2,t3)]..)
=> Add (Prod[t1,t2,t3]) Flattened


(*Orders the expression correctly.*)
fun orderfn(Ein.EIN{params, index, body})= let 
   fun order(body)=
    (case body of E.Prod es=> let
        fun pattern(s,[],y,z,(E.Epsilon e1)::es)= pattern(s,[E.Epsilon e1],y,z,es)
            |pattern(s,x,y,z,(E.Epsilon e2)::es)=let 
                fun sorteps(left,[], eps)= pattern(s,left@[eps],y,z, es)
                | sorteps(left, E.Epsilon(i,j,k)::right, E.Epsilon(a,b,c))=
                    if(i>a) then pattern(s,left@[E.Epsilon(a,b,c)]@E.Epsilon(i,j,k)::right,y,z,es)
                    else sorteps(left@ [E.Epsilon(i,j,k)], right, E.Epsilon(a,b,c))
                in sorteps([],x, E.Epsilon e2) end

            |pattern(s,x,y,z,(E.Delta d1)::es)= pattern(s,x,y@ [E.Delta d1],z,es)
            |pattern(s, x, y, z, (E.Sum(1, esum)::es))= pattern(s, x, y, z@[E.Sum(1, order esum)], es)
            |pattern(s, x, y, z, (E.Sum(c, E.Prod p)::es))= pattern(s+c, x,y,z,p@es)
            |pattern(s, x, y, z, (E.Sum(c, esum)::es))=pattern(s+c, x, y, z, [esum]@es)
            |pattern(s,x,y,z,(E.Prod p1)::es)=
                let val(s2,x2,y2,z2,e2)=pattern(0,[],[],[],p1) in
                pattern(s+s2,x@x2,y@y2,z@z2@e2,es) end
            |pattern(s,x,y,z,[])= (s,x,y,z,[])
        val (s,x,y,z,e4)=pattern(0,[],[],[],es)
        in if (s=0) then  E.Prod (x@y@z@e4)
            else E.Sum(s, E.Prod (x@y@z@e4))
    | E.Add es =>    E.Add(List.map order es)
    | E.Sub (a,b)=>  E.Sub(order a, order b)
    | E.Sum(c, E.Sum(1,e))=>E.Sum(c, E.Sum(1, order e))
    | E.Sum(c, E.Prod((E.Sum(1, e))::p))=>  E.Sum(c, order(E.Prod((E.Sum(1, order e))::p)))
    | E.Sum(c, E.Sum(c',e))=> E.Sum(c+c', e)
    | E.Sum(c, E.Prod((E.Sum(c', e))::p))=>E.Sum(c+c', order(E.Prod([e]@p)))
    | E.Sum (c,es)=>     E.Sum(c, order es)
    | E.Apply(d,e)=> E.Apply(d, order e)
    | _=> body)
    val b=order(body)
   in (Ein.EIN{params=params, index=index, body=b}) end

(*Flattens Add constructor: change, expression *)
fun mkAdd [e]=(1,e)
    | mkAdd(e)=let
    fun flatten((i, (E.Add l)::l'))= flatten(1,l@l')
        |flatten(i,((E.Const c):: l'))=
            if (c>0.0 orelse c<0.0) then let
                    val(b,a)=flatten(i,l') in (b,[E.Const c]@a) end
            else flatten(1,l')
        | flatten(i,[])=(i,[])
        | flatten (i,e::l') =  let
                    val(b,a)=flatten(i,l') in (b,[e]@a) end
     val (b,a)=flatten(0,e)
    in case a
     of [] => (1,E.Const(1.0))
                | [e] => (1,e)
                | es => (b,E.Add es)
                (* end case *)
fun mkProd [e]=(1,e)
    | mkProd(e)=let
    fun flatten(i,((E.Prod l)::l'))= flatten(1,l@l')
        |flatten(i,((E.Const c):: l'))=
           if(c>0.0 orelse c<0.0) then
               if (c>1.0 orelse c<1.0) then let
                val(b,a)=flatten(i,l') in (b,[E.Const c]@a) end
               else flatten(1,l')
            else (3, [E.Const(0.0)])
         | flatten(i,[])=(i,[])
         | flatten (i,e::l') =  let
                    val(b,a)=flatten(i,l') in (b,[e]@a) end
     val ( b,a)=flatten(0,e)
     in if(b=3) then (1,E.Const(0.0))
        else case a
        of [] => (1,E.Const(0.0))
        | [e] => (1,e)
        | es => (b, E.Prod es)
        (* end case *)
fun mkEps(e)= (case e
    of E.Apply(E.Partial [a], E.Prod( e2::m ))=> (0,e)
     | E.Apply(E.Partial [a,b], E.Prod( (E.Epsilon(i,j,k))::m ))=>
        (if(a=i andalso b=j) then (1,E.Const(0.0))
        else if(a=i andalso b=k) then (1,E.Const(0.0))
        else if(a=j andalso b=i) then (1,E.Const(0.0))
        else if(a=j andalso b=k) then (1,E.Const(0.0))
        else if(a=k andalso b=j) then (1,E.Const(0.0))
        else if(a=k andalso b=i) then (1,E.Const(0.0))
        else (0,e))
    |_=> (0,e)
    (*end case*))
fun mkApply(E.Apply(d, e)) = (case e
    of E.Tensor(a,[])=> (0,E.Const(0.0))
     | E.Tensor _=> (0,E.Apply(d,e))
     | E.Const _=> (1,E.Const(0.0))
     | E.Add l => (1,E.Add(List.map (fn e => E.Apply(d, e)) l))
     | E.Sub(e2, e3) =>(1, E.Sub(E.Apply(d, e2), E.Apply(d, e3)))
     | E.Prod((E.Epsilon c)::e2)=> mkEps(E.Apply(d,e))
     | E.Prod[E.Tensor(a,[]), e2]=>  (0, E.Prod[ E.Tensor(a,[]), E.Apply(d, e2)]  )
     | E.Prod((E.Tensor(a,[]))::e2)=>  (0, E.Prod[E.Tensor(a,[]), E.Apply(d, E.Prod e2)] )
     | E.Prod es =>    (let
           fun prod [e] = (E.Apply(d, e))
              | prod(e1::e2)=(let val l= prod(e2) val m= E.Prod[e1,l]
                   val lr=e2 @[E.Apply(d,e1)]   val(b,a) =mkProd lr
                in ( E.Add[ a, m] )
             | prod _= (E.Const(1.0))
                in (1,prod es)
             | _=> (0,E.Apply(d,e))
             (*end case*))
fun mkSumApply(E.Sum(c,E.Apply(d, e))) = (case e
    of E.Tensor(a,[])=> (0,E.Const(0.0))
    | E.Tensor _=> (0,E.Sum(c,E.Apply(d,e)))
    | E.Field _ =>(0, E.Sum(c, E.Apply(d,e)))
    | E.Const _=> (1,E.Const(0.0))
    | E.Add l => (1,E.Add(List.map (fn e => E.Sum(c,E.Apply(d, e))) l))
    | E.Sub(e2, e3) =>(1, E.Sub(E.Sum(c,E.Apply(d, e2)), E.Sum(c,E.Apply(d, e3))))
    | E.Prod((E.Epsilon c)::e2)=> mkEps(E.Apply(d,e))
    | E.Prod[E.Tensor(a,[]), e2]=>  (0, E.Prod[ E.Tensor(a,[]), E.Sum(c,E.Apply(d, e2))]  )
    | E.Prod((E.Tensor(a,[]))::e2)=>  (0, E.Prod[E.Tensor(a,[]), E.Sum(c,E.Apply(d, E.Prod e2))] )
    | E.Prod es =>   (let
        fun prod [e] = (E.Apply(d, e))
        | prod(e1::e2)=(let val l= prod(e2) val m= E.Prod[e1,l]
            val lr=e2 @[E.Apply(d,e1)]   val(b,a) =mkProd lr
            in ( E.Add[ a, m] ) end)
        | prod _= (E.Const(1.0))
            in (1, E.Sum(c,prod es))  end)
    | _=> (0,E.Sum(c,E.Apply(d,e)))
    (*end case*))
(* Identity: (Epsilon ijk Epsilon ilm) e => (Delta jl Delta km - Delta jm Delta kl) e
    The epsToDels Function searches for Epsilons in the expression, checks for this identity in all adjacent Epsilons and if needed, does the transformation.
     The Function returns two separate list, 1 is the remaining list of Epsilons that have not be changed to deltas, and the second is the Product of the remaining expression.
  Ex:(Epsilon_ijk Epsilon_ilm) Epsilon_stu e =>([Epsilon_stu], [Delta_jl,Delta_km,e -Delta_jm Delta_kl, e] )
   This is useful since we can normalize the second list without having to normalize the epsilons again.*)
fun epsToDels(E.Sum(count,E.Prod e))= let
    fun doubleEps((E.Epsilon (a,b,c))::(E.Epsilon(d,e,f))::es,e3)=
        fun createDeltas(s,t,u,v, e3)=
            (1,  E.Sub(E.Sum(2,E.Prod([E.Delta(s,u), E.Delta(t,v)] @e3)),
                    E.Sum(2,E.Prod([E.Delta(s,v), E.Delta(t,u)]@e3))))
        in if(a=d) then createDeltas(b,c,e,f, e3)
           else if(a=e) then createDeltas(b,c,f,d, e3)
           else if(a=f) then createDeltas(b,c,d,e, e3)
           else if(b=d) then createDeltas(c,a,e,f, e3)
           else if(b=e) then createDeltas(c,a,f,d,e3)
           else if(b=f) then createDeltas(c,a,d,e,e3)
           else if(c=d) then createDeltas(a,b,e,f,e3)
           else if(c=e) then createDeltas(a,b,f,d,e3)
           else if(c=f) then createDeltas(a,b,d,e,e3)
           else (0,(E.Prod((E.Epsilon (a,b,c))::(E.Epsilon(d,e,f))::e3)))
    fun findeps(e,[])= (e,[])
      | findeps(e,(E.Epsilon eps)::es)=  findeps(e@[E.Epsilon eps],es)
      | findeps(e,es)= (e, es)
    fun distribute([], s)=(0, [],s)
      | distribute([e1], s)=(0, [e1], s)
      | distribute(e1::es, s)= let val(i, exp)=doubleEps(e1::es, s)
          in if(i=1) then (1, tl(es), [exp])
             else let val(a,b,c)= distribute(es, s)
                  in (a, [e1]@b, c) end
    val (change, eps,rest)= distribute(findeps([], e)) 
    in (change, eps,rest) end 

(*The Deltas then need to be distributed over to the tensors in the expression e.
Ex.:Delta ij ,Tensor_j, e=> Tensor_i,e. The mkDelts function compares every Delta in the expression to the tensors in the expressions while keeping the results in the correct order.
   This also returns a list of deltas and a list of the remaining expression.

fun mkDel(e) = let
    fun Del(i, [],x)= (i,[],x)
       | Del(i, d,[])=(i, d,[])
       | Del(i, (E.Delta(d1,d2))::d, (E.Tensor(id,[x]))::xs)=
            if(x=d2) then (let
               val(i',s,t)= Del(i+1,d, xs)
               in Del(i',s, [E.Tensor(id, [d1])] @t) end)
            else (let val (i',s,t)= Del(i,[E.Delta(d1,d2)],xs)
               val(i2,s2,t2)= Del(i',d,[E.Tensor(id,[x])]@t)
               in (i2,s@s2, t2) end )
       | Del(i, (E.Delta(d1,d2))::d, (E.Field(id,[x]))::xs)=
                   if(x=d2) then (let
                   val(i',s,t)= Del(i+1,d, xs)
                   in Del(i',s, [E.Field(id, [d1])] @t) end)
                   else (let val (i',s,t)= Del(i,[E.Delta(d1,d2)],xs)
                   val(i2,s2,t2)= Del(i',d,[E.Field(id,[x])]@t)
                   in (i2,s@s2, t2) end )
        | Del(i, d, t)= (i,d,t)
    fun findels(e,[])= (e,[])
       | findels(e,es)= let val del1= hd(es)
            in (case del1
               of E.Delta _=> findels(e@[del1],tl(es))
                |_=> (e, es))
    val(a,b)= findels([], e) 
      Del(0, a, b)

(*The Deltas are distributed over to the tensors in the expression e.
 This function checks for instances of the dotProduct.
Sum_2 (Delta_ij (A_i B_j D_k))=>Sum_1(A_i B_i) D_k 
   fun checkDot(E.Sum(s,E.Prod e))= let
       fun dot(i,d,r, (E.Tensor(ida,[a]))::(E.Tensor(idb,[b]))::ts)=
                   if (a=b) then
                        dot(i-1,d@[E.Sum(1,E.Prod[(E.Tensor(ida,[a])), (E.Tensor(idb,[b]))])], [],r@ts)
                   else dot(i,d, r@[E.Tensor(idb,[b])],(E.Tensor(ida,[a]))::ts)
          |dot(i, d,r, [t])=dot(i,d@[t], [], r)
          |dot(i,d, [],[])= (i,d, [],[])
          |dot(i,d, r, [])= dot(i,d, [], r)
          |dot(i, d, r, (E.Prod p)::t)= dot (i, d, r, p@t)
          |dot(i,d, r, e)= (i,d@r@e, [], [])
        val(i,d,r,c)= dot(s,[],[], e)
        val soln= (case d of [d1]=>d1
                   |_=> E.Prod d)
        in E.Sum(i,soln) end
      |checkDot(e)= (e)

(*Apply normalize to each term in product list
or Apply normalize to tail of each list*)
fun normalize (Ein.EIN{params, index, body}) = let
      val changed = ref false
      fun rewriteBody body = (case body
             of E.Const _=> body
              | E.Tensor _ =>body
              | E.Field _=> body
              | E.Delta _ => body
              | E.Epsilon _=>body
              | E.Conv _=> body
              | E.Partial _=>body
			  | E.Add es => let val (b,a)= mkAdd(List.map rewriteBody es)
                    in if (b=1) then ( changed:=true;a) else a end
              | E.Sub (a,b)=>  E.Sub(rewriteBody a, rewriteBody b)
              | E.Probe(u,v)=> (  E.Probe(rewriteBody u, v))
              | E.Sum(0, e)=>e
              | E.Sum(_, (E.Const c))=> E.Const c
              | E.Sum(c,(E.Add l))=> E.Add(List.map (fn e => E.Sum(c,e)) l)
              | E.Sum(c,E.Prod((E.Delta d)::es))=>(
                let val (i,dels, e)= mkDel((E.Delta d)::es)
                    val rest=(case e of [e1]=> rewriteBody e1
                            |_=> rewriteBody(E.Prod(e)))
                    val soln= (case rest of E.Prod r=> E.Sum(c-i, E.Prod(dels@r))
                        |_=>E.Sum(c-i, E.Prod(dels@[rest])))
                    val q= checkDot(soln)
                    in if (i=0) then q 
                   else (changed :=true;q)
                   end )

              | E.Sum(c,E.Prod((E.Epsilon e1 )::(E.Epsilon e2)::xs))=>
                   let val (i,eps, e)= epsToDels(body)
                   if (i=0) then let val e'=rewriteBody(E.Prod(e)) in (case e'
                        of E.Prod m=> let val (i2, p)= mkProd(eps @ m)
                                    in E.Sum(c, p) end
                        |_=>E.Sum(c, E.Prod(eps@ [e']))) end
                   else(let val [list]=e
                        val ans=rewriteBody(list)
                        val soln=(case ans
                            of E.Sub (E.Sum(c1,(E.Prod s1)),E.Sum(c2,(E.Prod s2))) =>
                                E.Sum(c-3+c1, E.Sub(E.Prod(eps@s1),E.Prod(eps@s2)))
                            | E.Sub (E.Sum(c1,s1),E.Sum(c2,s2)) =>
                                E.Sum(c-3+c1, E.Prod(eps@ [E.Sub(s1,s2)]))
                            |_=> E.Prod(eps@ [ans]))
                        in (changed :=true;soln) end
                   ) end
            | E.Sum(c, E.Apply(E.Partial p,   E.Prod((E.Delta(i,j))::e3 )))=> 
                let fun part([], e2, counter)=([], e2, counter)
                   | part(p1::ps, [E.Delta(i,j)],counter)=if (p1=j) then ([i]@ps,[],counter-1)
                        else (let val (a,b,counter)=part(ps, [E.Delta(i,j)],counter)
                        in ([p1]@a, b,counter )  end)
                val (e1,e2,counter)= part(p, [E.Delta(i,j)],c)
                   in   (E.Sum(counter, E.Apply(E.Partial e1, E.Prod(e2@e3)))) end
            | E.Sum(c, E.Apply(p, e))=>let
                   val e'= rewriteBody(E.Sum(c, e))
                   val p'= rewriteBody p
                   val (i, e2)= (case e'
                        of E.Sum(c',exp)=> mkSumApply(E.Sum(c', E.Apply(p', exp)))
                        |_=>mkApply( E.Apply(p', e')))
                   in if(i=1) then (changed :=true;e2) else e2 end
              | E.Sum(c, e)=> E.Sum(c, rewriteBody e)
              | E.Prod([e1])=>(rewriteBody e1 )
              | E.Prod(e1::(E.Add(e2))::e3)=>
                    (changed := true;
                    E.Add(List.map (fn e=> E.Prod([e1, e]@e3)) e2))
              | E.Prod(e1::(E.Sub(e2,e3))::e4)=>
                    ( changed :=true; E.Sub(E.Prod([e1, e2]@e4), E.Prod([e1,e3]@e4 )))
              | E.Prod[E.Partial r1,E. Conv(i, j, k, l)]=>
                    (changed:=true; ( let val j1=
					List.map (fn(x)=> (l,x))  r1 in E.Conv(i, j1@j, k, l) end ))
              | E.Prod((E.Partial r1)::(E.Partial r2)::e) =>
                    (changed := true; E.Prod([E.Partial (r1@r2)] @ e)  )
              | E.Prod[(E.Epsilon(e1,e2,e3)), E.Tensor(_,[i1,i2])]=>
                    if(e2=i1 andalso e3=i2) then (changed :=true;E.Const(0.0))
                    else body
              | E.Prod((E.Epsilon eps1)::es)=> (let
                   val rest=(case es of [e1] => rewriteBody e1
                   |_=> rewriteBody(E.Prod(es)))
                   val (i, solution)=(case rest
                        of E.Prod m=> mkProd ([E.Epsilon eps1] @m )
                            |_=>  mkProd([E.Epsilon eps1]@ [rest]))
                   in if (i=1) then (changed:=true;solution)
                   else solution end)

             | E.Prod (e::es) => (let val r=rewriteBody(E.Prod es)
                   val (i,solution)= (case r of E.Prod m => mkProd([e]@m )
                                    |_=> mkProd([e]@ [r]))
                   in if (i=1) then (changed:=true;solution)
                   else solution end)
              | E.Apply(E.Const _,_) => (E.Const(0.0))
              | E.Apply(E.Partial p, E.Prod((E.Delta(i,j))::e3))=>
                    let fun part([], e2)=([], e2)
                        | part(p1::ps, [E.Delta(i,j)])=if (p1=j) then ([i]@ps,[])
                                else (let val (a,b)=part(ps, [E.Delta(i,j)])
                                in ([p1]@a, b )  end)
                    val (e1,e2)= part(p, [E.Delta(i,j)])
                    in   E.Apply(E.Partial e1, E.Prod(e2@e3)) end

              | E.Apply(d,e)=> ( let val (t1,t2)= mkApply(E.Apply(rewriteBody d, rewriteBody e))
                    in if (t1=1) then (changed :=true;t2) else t2 end )
              |_=> body

            (*end case*))

      fun loop body = let
            val body' = rewriteBody body
              if !changed
                then (changed := false; loop body')
                else body'
    val b = loop body
    ((Ein.EIN{params=params, index=index, body=b}))

end (* local *)

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