Diff of /branches/vis15/src/compiler/ein/mk-operators.sml

Parent Directory | Revision Log | Patch

	revision 3700, Mon Mar 28 23:12:00 2016 UTC	revision 3701, Wed Mar 30 19:59:51 2016 UTC
#	Line 124	Line 124
124	type dim = int	type dim = int
125	type shape = dim list	type shape = dim list
126	type ids = int list	type ids = int list
127	val subst_flag = false
128		(* controls whether tensor operations should be *)
129		val canSubst = true
130
131		(* A constructor function for tensor variables that (by default) can be substituted for;
132		* this behavior is controlled by the canSubst flag.
133		*)
134		fun mkTEN alpha = E.TEN(canSubst, alpha)
135
136		(* a constructor function for tensor parameters that should never be substituted for.  *)
137		fun mkNoSubstTEN alpha = E.TEN(false, alpha)
138
139	fun specialize (alpha, inc) = List.mapi (fn (i, _) => E.V(i + inc)) alpha	fun specialize (alpha, inc) = List.mapi (fn (i, _) => E.V(i + inc)) alpha
140
141	fun sumIds (n, inc, alpha) = let	fun sumIds (n, inc, alpha) = let
#	Line 142	Line 153
153	val expindex = specialize(alpha, 0)	val expindex = specialize(alpha, 0)
154	in	in
155	E.EIN{	E.EIN{
156	params = [E.TEN(subst_flag, alpha), E.TEN(subst_flag, alpha)],	params = [mkTEN alpha, mkTEN alpha],
157	index = alpha,	index = alpha,
158	body = E.Opn(E.Add, [E.Tensor(0, expindex), E.Tensor(1, expindex)])	body = E.Opn(E.Add, [E.Tensor(0, expindex), E.Tensor(1, expindex)])
159	}	}
#	Line 155	Line 166
166	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
167	in	in
168	E.EIN{	E.EIN{
169	params = [E.TEN(subst_flag, shape), E.FLD dim],	params = [mkTEN shape, E.FLD dim],
170	index = shape,	index = shape,
171	body = E.Opn(E.Add, [E.Lift(E.Tensor(0, expindex)), E.Field(1, expindex)])	body = E.Opn(E.Add, [E.Lift(E.Tensor(0, expindex)), E.Field(1, expindex)])
172	}	}
#	Line 178	Line 189
189	val expindex = specialize(alpha, 0)	val expindex = specialize(alpha, 0)
190	in	in
191	E.EIN{	E.EIN{
192	params = [E.TEN(subst_flag, alpha), E.TEN(subst_flag, alpha)],	params = [mkTEN alpha, mkTEN alpha],
193	index = alpha,	index = alpha,
194	body = E.Op2(E.Sub, E.Tensor(0, expindex), E.Tensor(1, expindex))	body = E.Op2(E.Sub, E.Tensor(0, expindex), E.Tensor(1, expindex))
195	}	}
#	Line 190	Line 201
201	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
202	in	in
203	E.EIN{	E.EIN{
204	params = [E.TEN(subst_flag, shape), E.FLD dim],	params = [mkTEN shape, E.FLD dim],
205	index = shape,	index = shape,
206	body = E.Opn(E.Add,	body = E.Opn(E.Add,
207	[E.Lift(E.Tensor(0, expindex)), E.Op1(E.Neg, E.Field(1, expindex))])	[E.Lift(E.Tensor(0, expindex)), E.Op1(E.Neg, E.Field(1, expindex))])
#	Line 201	Line 212
212	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
213	in	in
214	E.EIN{	E.EIN{
215	params = [E.TEN(subst_flag, shape), E.FLD dim],	params = [mkTEN shape, E.FLD dim],
216	index = shape,	index = shape,
217	body = E.Op2(E.Sub, E.Field(1, expindex), E.Lift(E.Tensor(0, expindex)))	body = E.Op2(E.Sub, E.Field(1, expindex), E.Lift(E.Tensor(0, expindex)))
218	}	}
#	Line 224	Line 235
235	val expindex = specialize(alpha, 0)	val expindex = specialize(alpha, 0)
236	in	in
237	E.EIN{	E.EIN{
238	params = [E.TEN(subst_flag, []), E.TEN(subst_flag,alpha)],	params = [mkTEN [], mkTEN alpha],
239	index = alpha,	index = alpha,
240	body = E.Opn(E.Prod, [E.Tensor(0, []),  E.Tensor(1, expindex)])	body = E.Opn(E.Prod, [E.Tensor(0, []),  E.Tensor(1, expindex)])
241	}	}
#	Line 236	Line 247
247	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
248	in	in
249	E.EIN{	E.EIN{
250	params = [E.TEN(subst_flag, []), E.FLD dim],	params = [mkTEN [], E.FLD dim],
251	index = shape,	index = shape,
252	body = E.Opn(E.Prod, [E.Lift( E.Tensor(0, [])), E.Field(1,expindex)])	body = E.Opn(E.Prod, [E.Lift( E.Tensor(0, [])), E.Field(1,expindex)])
253	}	}
#	Line 246	Line 257
257	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
258	in	in
259	E.EIN{	E.EIN{
260	params = [E.TEN(subst_flag,shape), E.FLD dim],	params = [mkTEN shape, E.FLD dim],
261	index = shape,	index = shape,
262	body = E.Opn(E.Prod, [E.Lift( E.Tensor(0,expindex)), E.Field(1, [])])	body = E.Opn(E.Prod, [E.Lift( E.Tensor(0,expindex)), E.Field(1, [])])
263	}	}
#	Line 273	Line 284
284	val expindex = specialize(alpha, 0)	val expindex = specialize(alpha, 0)
285	in	in
286	E.EIN{	E.EIN{
287	params = [E.TEN(subst_flag, alpha), E.TEN(subst_flag, [])],	params = [mkTEN alpha, mkTEN []],
288	index = alpha,	index = alpha,
289	body = E.Op2(E.Div, E.Tensor(0, expindex), E.Tensor(1, []))	body = E.Op2(E.Div, E.Tensor(0, expindex), E.Tensor(1, []))
290	}	}
#	Line 285	Line 296
296	val expindex = specialize(shape, 0)	val expindex = specialize(shape, 0)
297	in	in
298	E.EIN{	E.EIN{
299	params = [E.FLD dim, E.TEN(subst_flag, [])],	params = [E.FLD dim, mkTEN []],
300	index = shape,	index = shape,
301	body = E.Op2(E.Div, E.Field(0, expindex), E.Lift(E.Tensor(1, [])))	body = E.Op2(E.Div, E.Field(0, expindex), E.Lift(E.Tensor(1, [])))
302	}	}
#	Line 314	Line 325
325	(*changed tensor lift variable here *)	(*changed tensor lift variable here *)
326	in	in
327	E.EIN {	E.EIN {
328	params = [E.TEN(subst_flag, alpha)], index = alpha,	params = [mkTEN alpha], index = alpha,
329	body = E.Op1(E.Neg, E.Tensor(0, expindex))	body = E.Op1(E.Neg, E.Tensor(0, expindex))
330	}	}
331	end	end
#	Line 332	Line 343
343
344	(* 2-d cross product Eps_{ij}U_i V_j *)	(* 2-d cross product Eps_{ij}U_i V_j *)
345	val cross2TT = E.EIN{	val cross2TT = E.EIN{
346	params = [E.TEN(subst_flag, [2]), E.TEN(subst_flag, [2])],	params = [mkTEN [2], mkTEN [2]],
347	index = [],	index = [],
348	body = E.Sum([(E. V 0, 0, 1), (E.V 1, 0, 1)],	body = E.Sum([(E. V 0, 0, 1), (E.V 1, 0, 1)],
349	E.Opn(E.Prod, [E.Eps2(0, 1), E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 1])]))	E.Opn(E.Prod, [E.Eps2(0, 1), E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 1])]))
#	Line 340	Line 351
351
352	(* crossProduct is on 3D vectors ..vec3 t8=t0 × t1; *)	(* crossProduct is on 3D vectors ..vec3 t8=t0 × t1; *)
353	val cross3TT = E.EIN{	val cross3TT = E.EIN{
354	params = [E.TEN(subst_flag, [3]), E.TEN(subst_flag, [3])],	params = [mkTEN [3], mkTEN [3]],
355	index = [3],	index = [3],
356	body = E.Sum([(E.V 1, 0, 2), (E.V 2, 0, 2)],	body = E.Sum([(E.V 1, 0, 2), (E.V 2, 0, 2)],
357	E.Opn(E.Prod, [	E.Opn(E.Prod, [
#	Line 372	Line 383
383	val expIdxB = specialize (beta, length alpha)	val expIdxB = specialize (beta, length alpha)
384	in	in
385	E.EIN{	E.EIN{
386	params = [E.TEN(subst_flag, alpha), E.TEN(subst_flag, beta)],	params = [mkTEN alpha, mkTEN beta],
387	index = alpha@beta,	index = alpha@beta,
388	body = E.Opn(E.Prod, [E.Tensor(0, expIdxA), E.Tensor(1, expIdxB)])	body = E.Opn(E.Prod, [E.Tensor(0, expIdxA), E.Tensor(1, expIdxB)])
389	}	}
#	Line 395	Line 406
406	val expIdxB = specialize (beta, length alpha)	val expIdxB = specialize (beta, length alpha)
407	in	in
408	E.EIN{	E.EIN{
409	params = [E.TEN(subst_flag ,alpha), E.FLD dim],	params = [mkTEN alpha, E.FLD dim],
410	index = alpha@beta,	index = alpha@beta,
411	body = E.Opn(E.Prod, [E.Lift(E.Tensor(0, expIdxA)), E.Field(1, expIdxB)])	body = E.Opn(E.Prod, [E.Lift(E.Tensor(0, expIdxA)), E.Field(1, expIdxB)])
412	}	}
#	Line 406	Line 417
417	val expIdxB = specialize(beta, length alpha)	val expIdxB = specialize(beta, length alpha)
418	in	in
419	E.EIN{	E.EIN{
420	params = [E.FLD dim, E.TEN(subst_flag,alpha)],	params = [E.FLD dim, mkTEN alpha],
421	index = alpha@beta,	index = alpha@beta,
422	body = E.Opn(E.Prod, [E.Field(0, expIdxA), E.Lift(E.Tensor(1, expIdxB))])	body = E.Opn(E.Prod, [E.Field(0, expIdxA), E.Lift(E.Tensor(1, expIdxB))])
423	}	}
#	Line 422	Line 433
433	val s'' = [(s', 0, i-1)]	val s'' = [(s', 0, i-1)]
434	in	in
435	E.EIN{	E.EIN{
436	params = [E.TEN(subst_flag, shape1), E.TEN(subst_flag, i::beta)],	params = [mkTEN shape1, mkTEN i::beta],
437	index = alpha@beta,	index = alpha@beta,
438	body = E.Sum(s'', E.Opn(E.Prod, [	body = E.Sum(s'', E.Opn(E.Prod, [
439	E.Tensor(0, expindexA@[s']),   (* T_{\alpha i} *)	E.Tensor(0, expindexA@[s']),   (* T_{\alpha i} *)
#	Line 458	Line 469
469	val sid = E.V(length alpha + length beta)	val sid = E.V(length alpha + length beta)
470	in	in
471	E.EIN{	E.EIN{
472	params = [E.FLD dim, E.TEN(subst_flag, i::beta)],	params = [E.FLD dim, mkTEN i::beta],
473	index = alpha@beta,	index = alpha@beta,
474	body = E.Sum([(sid, 0, i-1)],	body = E.Sum([(sid, 0, i-1)],
475	E.Opn(E.Prod, [	E.Opn(E.Prod, [
#	Line 476	Line 487
487	val sid = E.V(length(alpha) + length beta)	val sid = E.V(length(alpha) + length beta)
488	in	in
489	E.EIN{	E.EIN{
490	params = [E.TEN(subst_flag,shape1), E.FLD dim],index = alpha@beta,	params = [mkTEN shape1, E.FLD dim], index = alpha@beta,
491	body = E.Sum([(sid, 0, i-1)],	body = E.Sum([(sid, 0, i-1)],
492	E.Opn(E.Prod, [	E.Opn(E.Prod, [
493	E.Lift(E.Tensor(0, expindexA@[sid])),   (* F_{\alpha i} *)	E.Lift(E.Tensor(0, expindexA@[sid])),   (* F_{\alpha i} *)
#	Line 499	Line 510
510	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]
511	in	in
512	E.EIN{	E.EIN{
513	params = [E.TEN(subst_flag, shape1), E.TEN(subst_flag, i::j::beta)],	params = [mkTEN shape1, mkTEN i::j::beta],
514	index = alpha@beta,	index = alpha@beta,
515	body = E.Sum(sx,	body = E.Sum(sx,
516	E.Opn(E.Prod, [E.Tensor(0, expindexA@s'), E.Tensor(1, s'@expindexB)]))	E.Opn(E.Prod, [E.Tensor(0, expindexA@s'), E.Tensor(1, s'@expindexB)]))
#	Line 536	Line 547
547	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]
548	in	in
549	E.EIN{	E.EIN{
550	params = [E.FLD dim, E.TEN(subst_flag,shape1)],	params = [E.FLD dim, mkTEN shape1],
551	index = alpha@beta,	index = alpha@beta,
552	body = E.Sum(sx,	body = E.Sum(sx,
553	E.Opn(E.Prod, [E.Field(0, expindexA@s'), E.Lift(E.Tensor(1, s'@expindexB))]))	E.Opn(E.Prod, [E.Field(0, expindexA@s'), E.Lift(E.Tensor(1, s'@expindexB))]))
#	Line 554	Line 565
565	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]	val sx = [(E.V sumi, 0, i-1), (E.V(sumi+1), 0, j-1)]
566	in	in
567	E.EIN{	E.EIN{
568	params = [E.TEN(subst_flag, i::j::beta), E.FLD dim],	params = [mkTEN i::j::beta, E.FLD dim],
569	index = alpha@beta,	index = alpha@beta,
570	body = E.Sum(sx,	body = E.Sum(sx,
571	E.Opn(E.Prod, [E.Lift(E.Tensor(0, expindexA@s')), E.Field(1, s'@expindexB)]))	E.Opn(E.Prod, [E.Lift(E.Tensor(0, expindexA@s')), E.Field(1, s'@expindexB)]))
#	Line 568	Line 579
579	val sx = sumIds(length alpha, 0, alpha)	val sx = sumIds(length alpha, 0, alpha)
580	in	in
581	E.EIN{	E.EIN{
582	params = [E.TEN(subst_flag, alpha)],	params = [mkTEN alpha],
583	index = [],	index = [],
584	body = E.Op1(E.Sqrt,	body = E.Op1(E.Sqrt,
585	E.Sum(sx, E.Opn(E.Prod, [E.Tensor(0, expIdx), E.Tensor(0, expIdx)])))	E.Sum(sx, E.Opn(E.Prod, [E.Tensor(0, expIdx), E.Tensor(0, expIdx)])))
#	Line 596	Line 607
607	val g = E.Tensor(1, expindexDot)	val g = E.Tensor(1, expindexDot)
608	in	in
609	E.EIN{	E.EIN{
610	params = [E.TEN(subst_flag, alpha), E.TEN(subst_flag, alpha)],	params = [mkTEN alpha, mkTEN alpha],
611	index = alpha,	index = alpha,
612	body = E.Opn(E.Prod, [	body = E.Opn(E.Prod, [
613	f, E.Op2(E.Div, E.Const 1, E.Op1(E.Sqrt, E.Sum(sx, E.Opn(E.Prod, [g, g]))))	f, E.Op2(E.Div, E.Const 1, E.Op1(E.Sqrt, E.Sum(sx, E.Opn(E.Prod, [g, g]))))
#	Line 625	Line 636
636
637	(* Trace: <M_{i, i}>  This one Sx represents both i's*)	(* Trace: <M_{i, i}>  This one Sx represents both i's*)
638	fun traceT dim = E.EIN{	fun traceT dim = E.EIN{
639	params = [E.TEN(subst_flag, [dim, dim])], index = [],	params = [mkTEN [dim, dim]], index = [],
640	body = E.Sum([(E.V 0, 0, dim-1)], E.Tensor(0, [E.V 0, E.V 0]))	body = E.Sum([(E.V 0, 0, dim-1)], E.Tensor(0, [E.V 0, E.V 0]))
641	}	}
642
#	Line 644	Line 655
655	(************************* tranpose *************************)	(************************* tranpose *************************)
656
657	fun transposeT alpha = E.EIN{	fun transposeT alpha = E.EIN{
658	params = [E.TEN(subst_flag, alpha)],	params = [mkTEN alpha],
659	index = List.rev alpha,	index = List.rev alpha,
660	body = E.Tensor(0, [E.V 1, E.V 0])	body = E.Tensor(0, [E.V 1, E.V 0])
661	}	}
#	Line 659	Line 670
670	(************************* determinant *************************)	(************************* determinant *************************)
671
672	val det2T = E.EIN{	val det2T = E.EIN{
673	params = [E.TEN(false, [2, 2])],	params = [mkNoSubstTEN [2, 2]],
674	index = [],	index = [],
675	body = E.Op2(E.Sub,	body = E.Op2(E.Sub,
676	E.Opn(E.Prod, [E.Tensor(0, [E.C 0, E.C 0]), E.Tensor(0, [E.C 1, E.C 1])]),	E.Opn(E.Prod, [E.Tensor(0, [E.C 0, E.C 0]), E.Tensor(0, [E.C 1, E.C 1])]),
#	Line 678	Line 689
689	val i = E.Tensor(0, [E.C 2, E.C 2])	val i = E.Tensor(0, [E.C 2, E.C 2])
690	in	in
691	E.EIN{	E.EIN{
692	params = [E.TEN(false, [3, 3])],	params = [mkNoSubstTEN [3, 3]],
693	index = [],	index = [],
694	body = E.Op2(E.Sub,	body = E.Op2(E.Sub,
695	E.Opn(E.Add, [	E.Opn(E.Add, [
#	Line 751	Line 762
762
763	(************************* Exponential **************************)	(************************* Exponential **************************)
764	fun expF dim = E.EIN{params = [E.FLD dim], index = [], body = E.Op1(E.Exp, E.Field(0, []))}	fun expF dim = E.EIN{params = [E.FLD dim], index = [], body = E.Op1(E.Exp, E.Field(0, []))}
765	val expT = E.EIN{params = [E.TEN(false, [])], index = [], body = E.Op1(E.Exp, E.Tensor(0, []))}	val expT = E.EIN{params = [mkNoSubstTEN []], index = [], body = E.Op1(E.Exp, E.Tensor(0, []))}
766
767	(************************* Lifted single-argument math functions *************************)	(************************* Lifted single-argument math functions *************************)
768	local	local
769	fun tensorFn rator = E.EIN{	fun tensorFn rator = E.EIN{
770	params = [E.TEN(false, [])],	params = [mkNoSubstTEN []],
771	index = [],	index = [],
772	body = E.Op1(rator, E.Field(0, []))	body = E.Op1(rator, E.Field(0, []))
773	}	}
#	Line 788	Line 799
799
800	(************************* other tensor ops *************************)	(************************* other tensor ops *************************)
801	fun modulate dim = E.EIN{	fun modulate dim = E.EIN{
802	params = [E.TEN(subst_flag, [dim]), E.TEN(subst_flag, [dim])],	params = [mkTEN [dim], mkTEN [dim]],
803	index = [dim],	index = [dim],
804	body = E.Opn(E.Prod, [E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 0])])	body = E.Opn(E.Prod, [E.Tensor(0, [E.V 0]), E.Tensor(1, [E.V 0])])
805	}	}
#	Line 812	Line 823
823	val ix = iter(mask, const, 0)	val ix = iter(mask, const, 0)
824	in	in
825	E.EIN{	E.EIN{
826	params = [E.TEN(subst_flag, argTy)],	params = [mkTEN argTy],
827	index = rstTy,	index = rstTy,
828	body = E.Tensor(0, ix)	body = E.Tensor(0, ix)
829	}	}
#	Line 836	Line 847
847	val expindex = specialize(alpha, 0)	val expindex = specialize(alpha, 0)
848	in	in
849	E.EIN{	E.EIN{
850	params = [E.FLD dim, E.TEN(false, [])], index = alpha,	params = [E.FLD dim, mkNoSubstTEN []], index = alpha,
851	body = E.Probe(E.Field(0, expindex), E.Tensor(1, []))	body = E.Probe(E.Field(0, expindex), E.Tensor(1, []))
852	}	}
853	end	end
#	Line 855	Line 866
866	}	}
867
868	val curl3d = E.EIN{	val curl3d = E.EIN{
869	params = [E.TEN(subst_flag, [3])],	params = [mkTEN [3]],
870	index = [3],	index = [3],
871	body = E.Sum([(E.V 1, 0, 2), (E.V 2, 0, 2)],	body = E.Sum([(E.V 1, 0, 2), (E.V 2, 0, 2)],
872	E.Opn(E.Prod, [	E.Opn(E.Prod, [

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