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# View of /branches/charisee/src/compiler/ein/mkoperators.sml

Wed Feb 25 21:47:43 2015 UTC (4 years, 7 months ago) by cchiw
File size: 18764 byte(s)
added sqrt,pow, and examples
(* creates EIN operators
*
* COPYRIGHT (c) 2012 The Diderot Project (http://diderot-language.cs.uchicago.edu)
*)

structure mkOperators = struct

local

structure E = Ein
structure P=Printer
in

fun specialize(alpha,inc)=  List.tabulate(length(alpha), (fn(x)=>E.V (x+inc)))
fun sumIds(n,i)=List.tabulate(n, (fn v=>(E.V v, 0, i)))

(* Adding tensors : < X{\alpha} + Y_{\alpha}>_{\alpha} *)
val expindex= specialize(alpha,0)
in
E.EIN{
params = [E.TEN(1,alpha), E.TEN(1,alpha)],
index = alpha,
body = E.Add[E.Tensor(0, expindex), E.Tensor(1, expindex)]
}
end

fun createVec dim=
E.EIN{params = [E.TEN(1,[dim])], index = [dim], body = E.Tensor(0, [E.V 0])}

val zero=
E.EIN{params = [], index = [], body = E.Const(0)}

fun subTen alpha=let
val expindex= specialize(alpha,0)
in
E.EIN{
params = [E.TEN(1,alpha), E.TEN(1,alpha)],
index = alpha,
body = E.Sub(E.Tensor(0, expindex), E.Tensor(1, expindex))
}
end

fun divTen alpha =let
val expindex= specialize(alpha,0)
in
E.EIN{
params = [E.TEN(1,alpha), E.TEN(1,[])],
index = alpha,
body = E.Div(E.Tensor(0, expindex), E.Tensor(1,[]))
}
end

(* Trace: <M_{i, i}>  This one Sx represents both i's*)
fun trace dim = E.EIN{
params = [E.TEN(1,[dim,dim])],
index = [],
body = E.Sum([(E.V 0,0,dim-1)],E.Tensor(0, [E.V 0, E.V 0]))
}

fun negTen alpha=let
val  expindex= specialize(alpha,0)
in
E.EIN{
params = [E.TEN(1,alpha)],
index = alpha,
body = E.Neg(E.Tensor(0, expindex))
}
end

(* scalar times tensor product: <s * T_{\alpha}>_{\alpha} *)
fun scaleTen alpha = let
val expindex= specialize(alpha,0)
in
E.EIN{
params = [E.TEN(1,[]), E.TEN(1,alpha)],
index = alpha,
body = E.Prod[ E.Tensor(0, []),  E.Tensor(1, expindex)]
}
end

fun dot i =
E.EIN{
params = [E.TEN(1,[i]) ,E.TEN(1,[i])],
index = [],
body = E.Sum([(E.V 0,0,i-1)], E.Prod[E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 0])])
}

(* generic inner product: <T_{\alpha i} * T_{i \beta}>_{\alpha \beta} *)
fun innerProduct(shape1,i::beta) = let
val alpha= List.take(shape1,length(shape1)-1)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val s'=E.V(length(alpha)+ length(beta))
val s''=[(s',0,i-1)]
in
E.EIN{
params = [E.TEN(1,shape1) ,E.TEN(1,i::beta)],
index = alpha@beta,
body = E.Sum(s'', E.Prod[
E.Tensor(0, expindexA@[s']),   (* T_{\alpha i} *)
E.Tensor(1, [s']@expindexB )  (* T'_{i \beta} *)])
}
end
| innerProduct _ = raise Fail "Wrong shape for inner product"

(*<T_{\alpha i j} * B{i j \beta }>_\alpha \beta*)
fun doubleDot(shape1,i::j::beta) = let
val alpha= List.take(shape1,length(shape1)-2)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val sumi=length(alpha)+ length(beta)
val s'=[E.V sumi,E.V(sumi+1)]
val s''=[(E.V sumi,0,i-1),(E.V(sumi+1),0,j-1)]
in
E.EIN{
params = [E.TEN(1,shape1),E.TEN(1,i::j::beta)],
index = alpha@beta,
body = E.Sum(s'',E.Prod[ E.Tensor(0, expindexA@s'), E.Tensor(1,s'@expindexB)])
}
end
| doubleDot _ = raise Fail "Wrong shape for double dot "

(*Vector Examples : <T_i * T_j>_ij..t0⊗t1*)
fun outerProduct(dimA,dimB) =
E.EIN{
params = [E.TEN(1,[dimA]), E.TEN(1,[dimB])],
index= [dimA,dimB],
body= E.Prod[E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 1])]
}

fun transpose alpha =E.EIN{
params = [E.TEN(1,alpha)],
index= List.rev alpha,
body= E.Tensor(0, [E.V 1,E.V 0])
}

fun modulate dim =E.EIN{
params = [E.TEN(1,[dim]), E.TEN(1,[dim])],
index = [dim],
body = E.Prod[E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 0])]
}

(*get norm, but without the sqrt
* implemented as a summation over a modulate
*)
fun norm alpha =let
val i=List.hd alpha
val expindex= specialize(alpha,0)
val sx= sumIds(length(alpha),i-1)
in E.EIN{
params = [E.TEN(1,alpha), E.TEN(1,alpha)],
index = [],
body = E.Sum(sx,
E.Prod[E.Tensor(0, expindex), E.Tensor(1, expindex)])
}
end

fun norm2 dim =let
in E.EIN{
params = [ E.TEN(1,[]),E.TEN(1,[dim])],
index = [dim],
body =E.Prod[ E.Div(E.Const 1,E.Tensor(0, [])),E.Tensor(1, [E.V 0])]
}
end

(*crossProduct is on 3D vectors ..vec3 t8=t0 × t1; *)
val crossProduct = E.EIN{
params = [E.TEN(1,[3]), E.TEN(1,[3])],
index= [3],
body=E.Sum([(E. V 1,0,2),(E.V 2,0,2)],
E.Prod[ E.Epsilon(0, 1, 2), E.Tensor(0, [E.V 1]),  E.Tensor(1, [E.V 2 ]) ])
}

(*2-d cross product Eps_{ij}U_i V_j*)
val crossProduct2 = E.EIN{
params = [E.TEN(1,[2]), E.TEN(1,[2])],
index= [],
body=E.Sum([(E. V 0,0,1),(E.V 1,0,1)],
E.Prod[ E.Eps2(0, 1), E.Tensor(0, [E.V 0]),  E.Tensor(1, [E.V 1])])
}

(* Identiy: <\delta_{i j}>_{i j}  *)
fun identity dim =E.EIN{
params = [],index = [dim,dim], body = E.Delta(E.V(0), E.V(1))
}

(*Tensor and Fields*)
params = [E.TEN(1,[]),E.FLD(dim)],
index = [],
}

fun subTenField dim = E.EIN{
params = [E.TEN(1,[]),E.FLD(dim)],
index = [],
}

fun subFieldTen dim = E.EIN{
params = [E.TEN(1,[]),E.FLD(dim)],
index = [],
body = E.Sub(E.Field(1, []),E.Lift(E.Tensor(0, [])))
}

(* mkField functions*)
(*Adding Fields : < F{\alpha} + G_{\alpha}>_{\alpha} *)
val expindex= specialize(shape,0)
in E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = shape,
}
end

fun subField(dim,shape) =let
val expindex= specialize(shape,0)
in E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = shape,
body = E.Sub(E.Field(0, expindex),E.Field(1, expindex))
}
end

fun scaleField(dim,shape) =let
val  expindex= specialize(shape,0)
in E.EIN{
params = [E.TEN(1,[]),E.FLD(dim)],
index = shape,
body = E.Prod[E.Lift( E.Tensor(0,[])), E.Field(1,expindex)]
}
end

fun divideField(dim,shape) = let
val expindex= specialize(shape,0)
in E.EIN{
params = [E.FLD(dim),E.TEN(1,[])],
index = shape,
body = E.Div(E.Field(0, expindex),E.Lift(  E.Tensor(1, [])))
}
end

fun negField(dim,shape) = let
val expindex = specialize(shape,0)
in E.EIN{
params = [E.FLD(dim)],
index = shape,
body = E.Neg(E.Field(0, expindex))
}
end

(*< d F /  d_i>_i  *)
val a=List.hd(alpha)
val  expindex= specialize(alpha,0)
in E.EIN{
params = [E.FLD(a)],
index =alpha,
body = E.Apply(E.Partial(expindex),E.Field(0,[]))
}
end

(*< Sigma d F_alpha /  d x_i>ALpha  i CHANGE HERE *)
fun dotimes(dim,alpha)= let
val n=length(alpha)
fun expIndex(n,inc)=List.tabulate(n, (fn(x)=>E.V (x+inc)))
val i'=expIndex(n,0)
in E.EIN{
params = [E.FLD(dim)], index =alpha@[dim],
body = E.Apply(E.Partial [E.V n] ,E.Field(0,i'))
}
end

(*  <d F_i /d_i> *)

fun divergence(dim,alpha)=let
val  expindex= specialize(alpha,0)
val sumI=length(alpha)
val sumIndex=E.V(sumI)
val sumIndexL=[sumIndex]
val S=expindex@sumIndexL

in E.EIN{
params = [E.FLD(dim)],
index = alpha,
body = E.Sum([(sumIndex,0,dim-1)],E.Apply(E.Partial(sumIndexL),E.Field(0,S)))
}
end

(*FLD here is bounded to image field, and dimension of h*)
fun conv(dim,shape) =let
val expindex= specialize(shape,0)
in E.EIN{
params = [E.IMG(dim,shape),E.KRN],
index = shape,
body= E.Conv(0,expindex,1,[])
}
end

(* Probe: <F(x)>_{\alpha}   *)
fun probe(alpha,dim) = let
val  expindex= specialize(alpha,0)
in E.EIN{
params = [E.FLD(dim),E.TEN(0,[])],
index= alpha,
body= E.Probe(E.Field(0, expindex), E.Tensor(1,[]))
}
end

(*(F_y/dx - F_x/dy )k*)
(*val curl2d=E.EIN{
params = [E.FLD 2],
index = [],
body = E.Sub(E.Apply(E.Partial([E.C 0]), E.Field(0,[E.C 1])),
E.Apply(E.Partial([E.C 1]), E.Field(0,[E.C 0])))
}*)

(*\EinExp{\sum_{ij}\mathcal{E}_{ij} \frac{ F_j}{\partial x_i}*)
val curl2d=E.EIN{
params = [E.FLD 2],
index = [],
body = E.Sum([(E.V 0,0,1), (E.V 1,0,1)],
E.Prod[E.Eps2(0, 1),E.Apply( E.Partial([E.V 0]), E.Field(0,[E.V 1]))])
}

val curl3d=E.EIN{
params = [E.TEN(1,[3])],
index = [3],
body = E.Sum([(E.V 1,0,2), (E.V 2,0,2)],E.Prod[E.Epsilon(0, 1, 2),
E.Apply( E.Partial([E.V 1]), E.Field(0,[E.V 2]))])
}

(*Scalars*)
params = [E.TEN(1,[]), E.TEN(1,[])] ,
index = [],
body = E.Add[ E.Tensor(0, []), E.Tensor(1, [])]
}

(* Subtract Scalars*)
val subScalar = E.EIN{
params = [E.TEN(1,[]), E.TEN(1,[])],
index = [],
body = E.Sub( E.Tensor(0, []), E.Tensor(1, []))
}

(* Divide Scalars*)
val divScalar = E.EIN{
params = [E.TEN(1,[]), E.TEN(1,[])],
index = [],
body = E.Div( E.Tensor(0, []), E.Tensor(1, []))
}

(* Product Scalars*)
val prodScalar = E.EIN{
params =[E.TEN(1,[]), E.TEN(1,[])],
index = [],
body = E.Prod[ E.Tensor(0, []), E.Tensor(1, [])]
}

(*Transform M_ij x_j+T*)
fun transform(i, j) = E.EIN{
params = [E.TEN(1,[i,j]), E.TEN(1,[j]), E.TEN(1,[j])],
index = [i],
body = E.Add[E.Sum([(E.V 1, 0,j-1)],E.Prod[E.Tensor(0, [E.V 0, E.V 1]),
E.Tensor(1, [E.V 1])]), E.Tensor(2,[E.V 0])]
}

fun transformA(i, j) = E.EIN{
params = [E.TEN(1,[i,j]), E.TEN(1,[j])],
index = [i],
body = E.Sum([(E.V 1, 0,j-1)],E.Prod[E.Tensor(0, [E.V 0, E.V 1]), E.Tensor(1, [E.V 1])])
}

fun transformB i = E.EIN{
params = [E.TEN(1,[i]), E.TEN(1,[i])],
index = [i],
body = E.Add[E.Tensor(0, [E.V 0]), E.Tensor(1,[E.V 0])]
}

(*multiply scalar fields *)
fun mulFieldss dim = E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = [],
body = E.Prod[E.Field(0, []),E.Field(1, [])]
}

fun mulFieldsf(dim,shape) =let
val  expindex= specialize(shape,0)
in E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = shape,
body = E.Prod[E.Field(0, []),E.Field(1, expindex)]
}
end

fun divFieldss dim = E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = [],
body = E.Div(E.Field(0, []),E.Field(1, []))
}

fun divFieldfs(dim,shape) = let
val  expindex= specialize(shape,0)
in  E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = shape,
body = E.Prod[E.Field(0, expindex),E.Div(E.Const 1,E.Field(1, []))]
}
end

(*Assumes same dimension vector field *)
fun outerField dim =
E.EIN{
params = [E.FLD(dim),E.FLD(dim)],
index = [dim, dim],
body = E.Prod[E.Field(0, [E.V 0]),E.Field(1, [E.V 1])]
}

fun fs x=Int.toString(x)
fun f x=fs(length(x))

(* generic inner product: <T_{\alpha i} * T_{i \beta}>_{\alpha \beta} *)
fun innerProductField(shape1,dim,i::beta) = let
val alpha= List.take(shape1,length(shape1)-1)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val s'=E.V(length(alpha)+ length(beta))
val s''=[(s',0,i-1)]
in E.EIN{
params = [E.FLD(dim) ,E.FLD(dim)],              (* T and T' *)
index = alpha@beta,(* \alpha \beta, i *)
body = E.Sum(s'', E.Prod[
E.Field(0, expindexA@[s']),   (* F_{\alpha i} *)
E.Field(1, [s']@expindexB )  (* F'_{i \beta} *)
])}
end
| innerProductField _ = raise Fail "Wrong shape for innerProductField"

(*Field Cross Product*)
val crossProductField2d = E.EIN{
params = [E.FLD(2), E.FLD(2)],
index= [],
body=E.Sum([(E. V 0,0,1),(E.V 1,0,1)],
E.Prod[ E.Eps2(0, 1), E.Field(0, [E.V 0]),  E.Field(1, [E.V 1]) ])
}

(*Field Cross Product*)
val crossProductField3d = E.EIN{
params = [E.FLD(3), E.FLD(3)],
index= [3],
body=E.Sum([(E. V 1,0,2),(E.V 2,0,2)],
E.Prod[ E.Epsilon(0, 1, 2), E.Field(0, [E.V 1]),  E.Field(1, [E.V 2 ]) ])
}

(* Trace: <Sigma_i F_{\alpha i, i}>  This one Sx represents both i's*)
fun traceField(dim,alpha) =let
val expindex= specialize(alpha,0)
val s=E.V(length(alpha))
in
E.EIN{
params = [E.FLD(dim)],
index = alpha,
body = E.Sum([(s,0,dim-1)],E.Field(0, expindex@[s,s]))
}
end

(*Transpose Field F_{ji}*)
fun transposeField(dim,i,j) =E.EIN{
params = [E.FLD(dim)], index= [i,j],
body= E.Field(0, [E.V 1,E.V 0])
}

(*<F_{\alpha i j} * G{i j \beta }>_\alpha \beta*)
fun doubleDotField(shape1,i::j::beta) = let
val alpha= List.take(shape1,length(shape1)-2)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val sumi=length(alpha)+ length(beta)
val s'=[E.V sumi,E.V(sumi+1)]
val s''=[(E.V sumi,0,i-1),(E.V(sumi+1),0,j-1)]
in
E.EIN{
params = [E.TEN(1,shape1),E.TEN(1,i::j::beta)],
index = alpha@beta,
body = E.Sum(s'',E.Prod[E.Field(0, expindexA@s'), E.Field(1,s'@expindexB)])
}
end
| doubleDotField _ = raise Fail "Wrong shape for double dot "

fun iter ([],_,cnt)=[]
|iter(true::es,c::cs,cnt)=[E.C c]@iter(es,cs,cnt)
|iter(false::es,cs,cnt)=[E.V cnt]@iter(es,cs,cnt+1)
in
E.EIN{
params = [E.TEN(1,argTy)],
index = rstTy,
body = E.Tensor(0, ix)
}
end

fun magnitudeTenVec(i::beta) = let
val shape1=i::beta
val n=length(shape1)
val alpha= List.take(shape1,n-1)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val s'=E.V(length(alpha)+ length(beta))
val s''=[(s',0,i-1)]
in E.EIN{
params = [E.TEN(1,shape1),E.TEN(1,shape1)],
index = alpha@beta,
body = E.Sqrt(E.Sum(s'', E.Prod[
E.Tensor(0, expindexA@[s']),
E.Tensor(0, [s']@expindexB )
]))
}

end
fun magnitudeFldVec(dim,[]) =
E.EIN{
params = [E.FLD(dim)],
index = [],
body =  E.Field(0, [])
}
| magnitudeFldVec(dim,i::beta) = let
val shape1=i::beta
val alpha= List.take(shape1,length(shape1)-1)
val expindexA= specialize(alpha,0)
val expindexB= specialize(beta,(length(alpha)))
val s'=E.V(length(alpha)+ length(beta))
val s''=[(s',0,i-1)]
in E.EIN{
params = [E.FLD(dim) ,E.FLD(dim)],              (* T and T' *)
index = alpha@beta,(* \alpha \beta, i *)
body = E.Sqrt(E.Sum(s'', E.Prod[
E.Field(0, expindexA@[s']),   (* F_{\alpha i} *)
E.Field(1, [s']@expindexB )  (* F'_{i \beta} *)
]))
}
end

fun normalizeFldVec(dim,[]) =raise Fail"normalize of a scalar"
| normalizeFldVec(dim,[i]) = let
val sx=[(E.V 0,0,i-1)]
val f=E.Field(0, [E.V 0])
in E.EIN{
params = [E.FLD(dim) ,E.FLD(dim)],
index = [dim],
body = E.Prod[f,
E.Div(E.Const 1,
E.Sqrt(E.Sum(sx, E.Prod[f,f]))
)]
}
end

fun sqrt dim=
E.EIN{
params = [E.FLD(dim)],
index = [],
body = E.Sqrt(E.Field(0, []))
}

end; (* local *)

end (* local *)