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Revision 2452 - (download) (annotate)
Sat Oct 5 00:43:58 2013 UTC (6 years ago) by cchiw
File size: 14459 byte(s)
normalize test
structure NormalizeEin = struct

    local

    structure E = Ein
    structure P=Printer

    in

      
(*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 *)
     end
        

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  0.0>c) then (3,[E.Const 0.0])
                else flatten(i,l')
         | flatten(i,[])=(i,[])
         | flatten (i,e::l') =  let val(a,b)=flatten(i,l') in (a,[e]@b) end
     val (change,a)=flatten(0,e)
     in if(change=3) then (1,E.Const(0.0))
        else case a
        of [] => (1,E.Const(0.0))
        | [e] => (1,e)
        | es => (change, E.Prod es)
        (* end case *)
         end
    
(*
                   
fun mkEps(e)= (case e
    of E.Apply(E.Partial [E.V a], E.Prod( e2::m ))=> (0,e)
     | E.Apply(E.Partial [E.V a,E.V 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 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*))
                   
   *)
                
                
fun rmEpsIndex(_,_,[])=[]
| rmEpsIndex([],[],cs)=cs
| rmEpsIndex([],m ,e1::cs)=[e1]@rmEpsIndex(m,[],cs)
| rmEpsIndex(i::ix,rest ,(E.V c)::cs)=
    if(i=c) then rmEpsIndex(rest@ix,[],cs)
    else rmEpsIndex(ix,rest@[i],(E.V c)::cs)
                
                   
(* Transform eps to deltas*)
fun epsToDels(E.Sum(count,E.Prod e))= let
    fun doubleEps((E.Epsilon (a,b,c))::(E.Epsilon(d,e,f))::es,eps,e3)=
        let

        (*Function is called when eps are being changed to deltas*)
        fun createDeltas(i,s,t,u,v, e3)= let

            (*remove index from original index list*)
            (*currrent, left, sumIndex*)
                   
            val s'= rmEpsIndex([i,s,t,u,v],[],count)
            val s''=[E.V s, E.V t ,E.V u, E.V v]
            val deltas= E.Sub(
                    E.Sum(s'',E.Prod([E.Delta(E.V s,E.V u), E.Delta(E.V t,E.V v)] @e3)),
                    E.Sum(s'',E.Prod([E.Delta(E.V s,E.V v), E.Delta(E.V t,E.V u)]@e3)))
                   
            in (case (eps,s')
                of ([],[]) =>(1,deltas)
                |([],_)=>(1,E.Sum(s',deltas))
                |(_,[])=>(1,E.Prod(eps@[deltas]))
                |(_,_) =>(1, E.Sum(s', E.Prod(eps@[deltas])))
                   )
             end 
                
        in if(a=d) then createDeltas(a,b,c,e,f, e3)
           else if(a=e) then createDeltas(a,b,c,f,d, e3)
           else if(a=f) then createDeltas(a,b,c,d,e, e3)
           else if(b=d) then createDeltas(b,c,a,e,f, e3)
           else if(b=e) then createDeltas(b,c,a,f,d,e3)
           else if(b=f) then createDeltas(b,c,a,d,e,e3)
           else if(c=d) then createDeltas(c,a,b,e,f,e3)
           else if(c=e) then createDeltas(c,a,b,f,d,e3)
           else if(c=f) then createDeltas(c,a,b,d,e,e3)
           else (0,E.Const 0.0)
        end 
    fun findeps(e,[])= (e,[])
      | findeps(e,(E.Epsilon eps)::es)=  findeps(e@[E.Epsilon eps],es)
      | findeps(e,es)= (e, es)
           
      
    fun dist([],eps,rest)=(0,eps,rest)
     | dist([e],eps,rest)=(0,eps@[e],rest)
     | dist(c1::current,eps,rest)=let
            val(i, exp)= doubleEps(c1::current,eps,rest)
        in  (case i of 1=>(i,[exp],[E.Const 2.0])
            |_=> dist(current, eps@[c1],rest))
        end               
        
    val (es,rest)=findeps([],e)
                   
    in
        dist(es,[],rest)
    end


fun rmIndex(_,_,[])=[]
    | rmIndex([],[],cs)=cs
    | rmIndex([],m ,e1::cs)=[e1]@rmIndex(m,[],cs)
    | rmIndex(i::ix,rest ,c::cs)=
        if(i=c) then rmIndex(rest@ix,[],cs)
        else rmIndex(ix,rest@[i],c::cs)
                
(* Apply deltas to tensors/fields*)
fun reduceDelta(E.Sum(c,E.Prod p))=let
            
    fun findDeltas(dels,rest,E.Delta d::es)= findDeltas(dels@[E.Delta d], rest, es)
    | findDeltas(dels,rest,E.Epsilon eps::es)=findDeltas(dels,rest@[E.Epsilon eps],es)
    | findDeltas(dels,rest,es)=  (dels,rest,es)


    fun distribute(change,d,dels,[],done)=(change,dels@d,done)
    | distribute(change,[],[],e,done)=(change,[],done@e)
    | distribute(change,E.Delta(i,j)::ds,dels,E.Tensor(id,[tx])::es,done)=
        if(j=tx) then distribute(change@[j],dels@ds,[] ,es ,done@[E.Tensor(id,[i])])
        else distribute(change,ds,dels@[E.Delta(i,j)],E.Tensor(id,[tx])::es,done)
    | distribute(change,E.Delta(i,j)::ds,dels,E.Field(id,[tx])::es,done)=
        if(j=tx) then distribute(change@[j],dels@ds,[] ,es ,done@[E.Field(id,[i])])
        else distribute(change,ds,dels@[E.Delta(i,j)],E.Field(id,[tx])::es,done)
    | distribute(change,d,dels,e::es,done)=distribute(change,dels@d,[],es,done@[e])
 
    val (dels,eps,es)=findDeltas([],[],p)
    val (change,dels',done)=distribute([],dels,[],es,[])
    val index=rmIndex(change,[],c)
    
  in
       (change, E.Sum(index,E.Prod (eps@dels'@done)))
  end

fun mkApply2(E.Apply(d,e))=(case e
    of E.Tensor(a,[])=>(1,E.Const 0.0)
    | 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.Tensor(a,[])::e2)=>(1,E.Prod[E.Tensor(a,[]),E.Apply(d,e)])
    | E.Prod [e1]=>(1,E.Apply(d,e1))
    | E.Prod es=> (let
        fun prod [e1] =E.Apply(d,e1)
        | 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)                
        in (1,prod es) end)
    |_=>(0,E.Apply(d,e))
    (* end case*))
 
fun mkSumApply2(E.Sum(c,E.Apply(E.Partial d,e)))=(case e
    of E.Const _=>(1,E.Const 0.0)
    | E.Add l => (1,E.Add(List.map (fn e => E.Sum(c,E.Apply(E.Partial d, e))) l))
    | E.Sub(e2, e3) =>(1, E.Sub(E.Sum(c,E.Apply(E.Partial d, e2)), E.Sum(c,E.Apply(E.Partial d, e3))))
    | E.Prod(E.Tensor(a,[])::e2)=>(1, E.Prod[E.Tensor(a,[]),E.Sum(c,E.Apply(E.Partial d,E.Prod e2))])
    | E.Prod [e1]=>(1,E.Sum(c,E.Apply(E.Partial d,e1)))
    | E.Prod es =>(let
        fun prod (change,rest, sum,partial,[]) = (change,E.Sum(sum,E.Apply(E.Partial partial,E.Prod rest)))
        | prod (change,rest, sum,partial,E.Epsilon(i,j,k)::ps)= let
            fun matchprod(2,_,_,_)= 1 (*matched 2*)
            | matchprod(num,_,_,[])=0
            | matchprod(0,_,_,[eps])=0
            | matchprod(num,[],rest,eps::epsx)=
                matchprod(num,rest,[],epsx)
            | matchprod(num,E.V p::px,rest,eps::epsx)=
                if(p=eps) then matchprod(num+1,px,rest,epsx)
                else matchprod(num,px,rest@[E.V p], eps::epsx)
            | matchprod(num,p::px,rest,eps)=
                matchprod(num,px,rest,eps)
                
            val change'= matchprod(0,d,[],[i,j,k])
            in (case change'
                of 1 => (1,E.Const 0.0)
                | _ =>prod(change,rest@[E.Epsilon(i,j,k)],sum,partial,ps))
            end
        | prod (change,rest, sum,partial,E.Delta(i,j)::ps)=let
            fun applyDelPartial([],_)=(0,[])
            | applyDelPartial(p::px,r)=
                if(j=p) then (1,r@[i]@px)
                else  applyDelPartial(px,r@[p])
                
            val (change',px)=applyDelPartial(d,[])
                
            in (case change'
                of 1 => (let val index=rmIndex([j],[],sum)
                    in prod(1,rest, index,px, ps) end )
                | _ => prod(change,rest@[E.Delta(i,j)], sum,partial, ps)
                (*end case*)) end
                
        | prod (change,rest,sum, partial,e::es)= prod(change,rest@[e],sum,partial,es)
                
        val (change,exp) = prod(0,[],c, d, es)
                
        in
            (change,exp)
        end)
    | _=>(0,E.Sum(c,E.Apply(E.Partial d,e)))
        (* end case*))
                
(*
E.Sum(c,Apply(d,e))
    try E.Sum(c,e)=> E.Sum(c',e')
    ==>    E.Sum(c',E.Apply(d,e'))
        E.Apply(d,e')=> E.Apply(d',e'')
    ==>E.Sum(c',E.Apply(d',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.Kernel _ =>body
              | E.Delta _ => body
              | E.Value _ =>body
              | E.Epsilon _=>body
            
              | E.Neg e => E.Neg(rewriteBody e)
              | E.Add es => let val (change,body')= mkAdd(List.map rewriteBody es)
                   in if (change=1) then ( changed:=true;body') else body' end
              | E.Sub (a,b)=>  E.Sub(rewriteBody a, rewriteBody b)
              | E.Div (a, b) => E.Div(rewriteBody a, rewriteBody b)     
              | E.Partial _=>body
              | E.Conv (V, alpha)=> E.Conv(rewriteBody V, alpha)
              | E.Probe(u,v)=>  E.Probe(rewriteBody u, rewriteBody v)
              | E.Image es => E.Image(List.map rewriteBody es)
                   
                (*Product*)
              | 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(f,deltas)]=>
                   (changed :=true;E.Conv(f,deltas@r1))
              | E.Prod (E.Partial r1::E.Conv(f,deltas)::ps)=>
                   (changed:=true;
                    let val (change,e)=mkProd([E.Conv(f,deltas@r1)]@ps)
                    in e end)
              | E.Prod[(E.Epsilon(e1,e2,e3)), E.Tensor(_,[E.V i1,E.V i2])]=>
                    if(e2=i1 andalso e3=i2) then (changed :=true;E.Const(0.0))
                    else body
                
             | E.Prod(E.Partial r1::E.Partial r2::p)=>
                   (changed:=true;E.Prod([E.Partial(r1@r2)]@p))
              | E.Prod(e::es)=>let
                    val e'=rewriteBody e
                    val e2=rewriteBody(E.Prod es)
                    val(a,b)=(case e2 of E.Prod p'=> mkProd([e']@p')
                        |_=>mkProd [e',e2])
                    in b 
                   end
                   
              (*Apply*)
              | E.Apply(E.Partial [],e)=> e
              | E.Apply(E.Partial p, e)=>let
                    val body'=E.Apply(E.Partial p, rewriteBody e)
                    val (c, e')=mkApply2(body')
                in (case c of 1=>(changed:=true;e')
                    | _ =>e') end
              | E.Apply(e1,e2)=>E.Apply(rewriteBody e1, rewriteBody e2)
                   
                   
                   
              (* Sum *)
              | E.Sum([],e)=> (changed:=true;rewriteBody e)
              | E.Sum(_,E.Const c)=>(changed:=true;E.Const c)
              | E.Sum(c,(E.Add l))=> (changed:=true;E.Add(List.map (fn e => E.Sum(c,e)) l))
              | E.Sum(c,E.Prod(E.Epsilon eps1::E.Epsilon eps2::ps))=>
                   let val (i,e,rest)=epsToDels(body)
                   in (case (i, e,rest)
                        of (1,[e1],_) =>(changed:=true;e1)
                        |(0,eps,[])=>body
                        |(0,eps,rest)=>(let
                            val p'=rewriteBody(E.Prod rest)
                            val p''= (case p' of E.Prod p=>p |e=>[e])
                            val(a,b)= mkProd (eps@p'')
                            in E.Sum(c,b) end
                            )
                        |_=>body)
                   end
              | E.Sum(c, E.Prod(E.Delta d::es))=>let
                    val (change,a)=reduceDelta(body)
                    val (change',body')=(case a
                        of E.Prod p=> mkProd p
                        |_=> (0,a))
                   in (case change of []=>body'|_=>(changed:=true;body')) end
              | E.Sum(c,E.Apply(d,e))=>let
                    val(c',e')=mkSumApply2(body)
                in (case c' of 1=>(changed:=true;e') |_=>e')
                end
              | E.Sum(c,e)=>E.Sum(c,rewriteBody e)

            (*end case*))

      fun loop body = let
            val body' = rewriteBody body
            in
              if !changed
                   then (changed := false; print " \n \t => \n \t ";print( P.printbody body');print "\n";loop body')
                else body'
            end
    val b = loop body
    in
    ((Ein.EIN{params=params, index=index, body=b}))
    end
end 


end (* local *)

root@smlnj-gforge.cs.uchicago.edu
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