-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathdae.mc
1489 lines (1397 loc) · 45.1 KB
/
dae.mc
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
include "these.mc"
include "mexpr/free-vars.mc"
include "mexpr/cse.mc"
include "peval/peval.mc"
include "./ast.mc"
include "./ad.mc"
include "./desugar.mc"
include "./daecore-structure.mc"
include "./lib/vec.mc"
let _daeIDMap = ref (mapEmpty (tupleCmp2 nameCmp subi))
let daeID : (Name, Int) -> Name
= lam id.
match id with (name, 0) then name
else
match id with (name, n) in
let daeIDMap = deref _daeIDMap in
if mapMem id daeIDMap then mapFindExn id daeIDMap
else
let name = nameSym (concat (nameGetStr name) (create n (lam. '\''))) in
modref _daeIDMap (mapInsert id name daeIDMap);
name
lang DAE = DAEAst + MExprFreeVars + PEval + PEvalLetInline + MExprCSE + AD
sem daeAnnotDVars : TmDAERec -> TmDAERec
sem daeAnnotDVars =| dae ->
let vars = mapFromSeq nameCmp dae.vars in
recursive let inner = lam t.
match t with TmVar r then
if mapMem r.ident vars then
TmDVar (tmDVarRecToTmVarRec 0 r)
else TmVar r
else smap_Expr_Expr inner t
in
match smap_Expr_Expr inner (TmDAE dae) with TmDAE dae then dae
else error "impossible"
sem daeStructure : TmDAERec -> [Set (Name, Int)]
sem daeStructure =| dae ->
map (lam eqn. dvars (peval (bind_ dae.bindings eqn))) dae.eqns
type DAEStructuralAnalysis = {
varOffset : [(Name, Int)],
eqnsOffset : [Int]
}
sem daeStructuralAnalysis : TmDAERec -> DAEStructuralAnalysis
sem daeStructuralAnalysis =| dae ->
-- Enumerate dependent variables
let varEnumMap =
mapFromSeq nameCmp (mapi (lam i. lam v. (v.0, i)) dae.vars)
in
-- Find equation structure
let eqnsStructure =
map
(lam vars. {
variables =
map
(lam x.
match x with (name, ord) in
(mapFindExn name varEnumMap, ord))
(setToSeq vars),
inputs = []
})
(daeStructure dae)
in
-- Perform the structural analysis
let analysis = consumeWarnErrsExn (structuralAnalysis eqnsStructure) in
let eqnsOffset = vecToSeq analysis.c in
let varOffset =
zipWith
(lam v. lam d. (v.0, d)) dae.vars (vecToSeq analysis.d)
in
{ varOffset = varOffset, eqnsOffset = eqnsOffset }
sem daeADExpr : Int -> Expr -> Expr
sem daeADExpr n =| t -> ad n (daeADRenameVarsExpr n t)
sem daeADRenameVarsExpr : Int -> Expr -> Expr
sem daeADRenameVarsExpr n =
| TmVar r -> TmVar { r with ident = daeID (r.ident, n) }
| TmLam r ->
smap_Expr_Expr
(daeADRenameVarsExpr n)
(TmLam { r with ident = daeID (r.ident, n) })
| TmLet r ->
smap_Expr_Expr
(daeADRenameVarsExpr n)
(TmLet { r with ident = daeID (r.ident, n) })
| TmRecLets r ->
let bindings =
map (lam b. { b with ident = daeID (b.ident, n) }) r.bindings
in
smap_Expr_Expr
(daeADRenameVarsExpr n)
(TmRecLets { r with bindings = bindings })
| TmMatch r ->
smap_Expr_Expr
(daeADRenameVarsExpr n)
(TmMatch { r with pat = daeADRenameVarsPat n r.pat })
| t -> smap_Expr_Expr (daeADRenameVarsExpr n) t
sem daeADRenameVarsPat : Int -> Pat -> Pat
sem daeADRenameVarsPat n =
| PatNamed (r & {ident = (PName ident)}) ->
PatNamed { r with ident = PName (daeID (ident, n)) }
| p -> smap_Pat_Pat (daeADRenameVarsPat n) p
sem daeCSE : TmDAERec -> TmDAERec
sem daeCSE =| dae ->
let bindings = cseGlobal dae.bindings in
let eqns = map cse dae.eqns in
let out = cse dae.out in
{ dae with bindings = bindings, eqns = eqns, out = out }
sem daeIndexReduce : [Int] -> TmDAERec -> TmDAERec
sem daeIndexReduce ns =| dae ->
let maxn = maxOrElse (lam. error "impossible") subi ns in
let bindings =
foldl1 bind_ (create (succ maxn) (lam n. daeADExpr n dae.bindings))
in
let eqns =
zipWith
(lam n. lam t.
let t = daeADExpr n t in
if neqi n 0 then tupleproj_ n t else t)
ns dae.eqns
in
{ dae with bindings = bindings, eqns = eqns }
sem daeJacADExpr : Name -> Name -> Expr -> Expr
sem daeJacADExpr y yp =| t ->
recursive let inner = lam t.
match t with
TmApp (appr1 & {
lhs =
TmApp (appr2 & {lhs = TmConst {val = CArrayGet _}, rhs = TmVar r}),
rhs = TmConst {val = CInt {val = i }},
info = info
})
then
let b = peadAstBuilder info in
if or (nameEq r.ident y) (nameEq r.ident yp) then
let ident = daeID (if nameEq r.ident y then y else yp, 1) in
let tp = if_ (eqi_ (nvar_ ident) (int_ i)) (float_ 1.) (float_ 0.) in
b.dualnum t tp
else t
else smap_Expr_Expr inner t
in
inner (ad 1 t)
type DAEFirstOrderState = {
ys : [These (Name, Int) (Name, Int)],
indexMap : Map (Name, Int) (These Int Int)
}
sem daeFirstOrderState : [(Name, Int)] -> DAEFirstOrderState
sem daeFirstOrderState =| ofs ->
let ys =
join
(map
(lam ofs.
switch ofs
case (name, 0) then [This ofs]
case (name, n) then
let vs = create (succ n) (lam n. (name, n)) in
zipWith (lam x. lam y. These (x, y)) (init vs) (tail vs)
end)
ofs)
in
let names =
mapi (lam i. theseBiMap (lam name. (name, i)) (lam name. (name, i))) ys
in
match thesePartition names with (xs, xps, xxps) in
let fthis =
lam acc. lam x.
mapUpdate x.0
(lam v.
switch v
case Some (That i) then Some (These (x.1, i))
case None _ then Some (This x.1)
case _ then error "impossible"
end)
acc
in
let fthat =
lam acc. lam x.
mapUpdate x.0
(lam v.
switch v
case Some (This i) then Some (These (i, x.1))
case None _ then Some (That x.1)
case _ then error "impossible"
end)
acc
in
let indexMap = foldl fthis (mapEmpty dvarCmp) xs in
let indexMap = foldl fthat indexMap xps in
let indexMap =
foldl (lam acc. lam x. fthat (fthis acc x.0) x.1) indexMap xxps
in
{ ys = ys, indexMap = indexMap }
sem daeIsDiffVars : DAEFirstOrderState -> [Bool]
sem daeIsDiffVars =| state ->
map (theseThese (lam. false) (lam. true) (lam. lam. true)) state.ys
sem daeOrderReduce : DAEFirstOrderState -> Name -> Name -> TmDAERec -> TmDAERec
sem daeOrderReduce state y yp =| dae ->
let gety_ = lam i. appf2_ (uconst_ (CArrayGet ())) (nvar_ y) (int_ i) in
let getyp_ = lam i. appf2_ (uconst_ (CArrayGet ())) (nvar_ yp) (int_ i) in
recursive let subs = lam t.
match t with TmDVar r then
theseThese
gety_ getyp_ (lam i. lam. gety_ i)
(mapFindExn (r.ident, r.order) state.indexMap)
else smap_Expr_Expr subs t
in
match subs (TmDAE dae) with TmDAE dae then
let vars = [(y, tyseq_ tyfloat_), (yp, tyseq_ tyfloat_)] in
let aliases = theseCatThese (mapValues state.indexMap) in
let eqns = map (lam a. subf_ (gety_ a.0) (getyp_ a.1)) aliases in
{ dae with vars = vars, eqns = concat dae.eqns eqns }
else error "impossible"
sem _daeErrMsg : String -> String -> Expr -> String
sem _daeErrMsg fname msg =| t ->
strJoin "\n" [strJoin ":" [fname, msg], expr2str t]
sem daeGenInitExpr : DAEFirstOrderState -> TmDAERec -> Expr
sem daeGenInitExpr state =| dae ->
let errMsg = _daeErrMsg "daeGenInitExpr" in
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
let errMsg = errMsg "Malformed initial equations" in
-- Construct assignments from the inital equations
let updateAssignment = lam i. lam ts1.
mapUpdate i
(optionMapOr (Some ts1)
(lam ts2.
Some(
switch (ts1,ts2)
case (This ts1, That ts2) | (That ts1, This ts2) then
These (ts1, ts2)
case (This ts1, This ts2) then This (concat ts1 ts2)
case (That ts1, That ts2) then That (concat ts1 ts2)
case (This ts1, These (ts2a, ts2b)) then
These (concat ts1 ts2a,ts2b)
case (That ts1, These (ts2a, ts2b)) then
These (ts2a,concat ts1 ts2b)
case _ then error "impossible"
end)))
in
let assignmentMap =
foldl
(lam acc. lam eqn.
match eqn with
TmApp {
lhs = TmApp {
lhs = TmConst {val = CSubf _},
rhs = TmApp {
lhs =
TmApp {lhs = TmConst {val = CArrayGet _}, rhs = TmVar r},
rhs = TmConst {val = CInt {val = i}}
}
},
rhs = t
}
then
if or (setMem y (freeVars t)) (setMem yp (freeVars t)) then
error (errMsg eqn)
else
let ts1 =
if nameEq r.ident y then This [t]
else if nameEq r.ident yp then That [t]
else error (errMsg eqn)
in
updateAssignment i ts1 acc
else error (errMsg eqn))
(mapEmpty subi)
dae.ieqns
in
-- If some state has been assigned multiple values we take the mean of
-- these.
-- TODO(oeriss, 2023-06-29): This should probably generate some warning.
let mean = lam ts.
match ts with [t] then t
else divf_ (foldl1 addf_ ts) (float_ (int2float (length ts)))
in
let assignmentMap = mapMap (theseBiMap mean mean) assignmentMap in
-- Go through aliases stemming from the order-reduction and propagate
-- assignments.
let assignmentMap =
mapFoldWithKey
(lam acc. lam.
theseThese (lam. acc) (lam. acc)
(lam i. lam j.
let lookup = lam i. mapLookup i acc in
switch
(optionBind (lookup i) theseGetHere,
optionBind (lookup j) theseGetThere)
case (None _, Some t1) then
mapUpdate i
(optionMapOr (Some (This t1))
(lam x.
Some(
switch x
case This t2 then
This (divf_ (addf_ t1 t2) (float_ 2.))
case That t2 then These (t1, t2)
case These (t2, t3) then
These (divf_ (addf_ t1 t2) (float_ 2.), t3)
end)))
acc
case (Some t1, None _) then
mapUpdate j
(optionMapOr (Some (This t1))
(lam x.
Some(
switch x
case This t2 then These (t2, t1)
case That t2 then
This (divf_ (addf_ t2 t1) (float_ 2.))
case These (t2, t3) then
These (t2, divf_ (addf_ t3 t1) (float_ 2.))
end)))
acc
case _ then acc
end))
assignmentMap
state.indexMap
in
-- Constucts inital values for all states from the assignements, defaults
-- to 0.
let initTms =
create (length state.ys)
(lam i. optionMapOr (float_ 0., float_ 0.)
(theseThese
(lam t. (t, float_ 0.))
(lam t. (float_ 0., t))
(lam t1. lam t2. (t1, t2)))
(mapLookup i assignmentMap))
in
match unzip initTms with (y0, yp0) in
bind_ dae.bindings (utuple_ [seq_ y0, seq_ yp0])
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem daeGenOutExpr : TmDAERec -> Expr
sem daeGenOutExpr =| dae ->
let errMsg = _daeErrMsg "daeGenOutExpr" in
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
let defaultPrint = print_ (str_ "Cannot print output") in
let genPrintWithCommaSep = lam ts.
if null ts then unit_
else
foldl1
semi_
(snoc
(map
(lam t. semi_ (print_ t) (print_ (str_ ",")))
(init ts))
(semi_ (print_ (last ts)) (print_ (str_ "\n"))))
in
let _r = nameSym "r" in
let body =
switch tyTm dae.out
case TyFloat _ then print_ dae.out
case TyRecord r then
let isFloatTy = lam ty. match ty with TyFloat _ then true else false in
match record2tuple r.fields with Some tys then
if forAll isFloatTy tys then
let inexpr =
genPrintWithCommaSep
(create (length tys)
(lam i. float2string_ (tupleproj_ i (nvar_ _r))))
in
bind_ (nulet_ _r dae.out) inexpr
else defaultPrint
else defaultPrint
case _ then defaultPrint
end
in
bind_ dae.bindings (nulams_ [y, yp] body)
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem daeGenResExpr : TmDAERec -> Expr
sem daeGenResExpr =| dae ->
let errMsg = _daeErrMsg "daeGenMutableResExpr" in
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
let r = nameSym "r" in
bind_
dae.bindings
(nulams_ [y, yp, r]
(bindall_
(snoc
(mapi
(lam i. lam e.
ulet_ "" (utensorLinearSetExn_ (nvar_ r) (int_ i) e))
dae.eqns)
unit_)))
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem daeJacStructure : TmDAERec -> ([[Int]], [[Int]])
sem daeJacStructure =| dae ->
let errMsg = _daeErrMsg "daeJacYStructure" in
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
-- partially evaluate to get a more accurate structure. We top-level
let eqns = map (lam eqn. peval (bind_ dae.bindings eqn)) dae.eqns in
recursive let inner = lam ident. lam acc. lam t.
match t with
TmApp {
lhs = TmApp {lhs = TmConst {val = CArrayGet _}, rhs = TmVar r},
rhs = TmConst {val = CInt {val = i}}
}
then
if nameEq ident r.ident then setInsert i acc else acc
else sfold_Expr_Expr (inner ident) acc t
in
let f = lam ident. lam eqn.
setToSeq (inner ident (setEmpty subi) eqn)
in
(map (f y) eqns, map (f yp) eqns)
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem daeJacStructureToIdxSeq : [[Int]] -> [(Int, [Int])]
sem daeJacStructureToIdxSeq =| structure ->
let js = create (length structure) (lam j. j) in
let is = mapi (lam i. lam eqn. (i, setOfSeq subi eqn)) structure in
foldl
(lam acc. lam j.
switch map (lam i. i.0) (filter (lam i. setMem j i.1) is)
case [] then acc
case is then snoc acc (j, is)
end)
[] js
sem daeGenJacY : TmDAERec -> Expr
sem daeGenJacY =| dae -> _daeGenJac true dae
sem daeGenJacYp : TmDAERec -> Expr
sem daeGenJacYp =| dae -> _daeGenJac false dae
sem _daeGenJac : Bool -> TmDAERec -> Expr
sem _daeGenJac jacY =| dae ->
let errMsg = _daeErrMsg "daeGenJacY" in
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
match
(if jacY then (y, yp) else (yp, y)) with (y, yp)
in
let n = length dae.eqns in
let _r = nameSym "r" in
let _idxs = nameSym "idxs" in
let _jis = nameSym "jis" in
let _j = tupleproj_ 0 (nvar_ _jis) in
let _is = tupleproj_ 1 (nvar_ _jis) in
let _i = nameSym "i" in
let _acc1 = nameSym "acc" in
let _acc2 = nameSym "acc" in
let daeJacADExpr = daeJacADExpr y yp in
let t = bindall_ [
nulet_ (daeID (yp, 1)) (int_ (negi 1)),
nulams_ (cons _idxs (unzip dae.vars).0)
(bind_
(nulet_ _r
(seq_
(map
(lam eqn.
-- NOTE(oerikss, 2023-07-03): We but each partial
-- derivative in a thunk to prevent the OCaml compiler
-- from trying to fit all of them in a single
-- stack-frame as this will make the OCaml compiler
-- fail when we have many large partial derivative
-- expressions.
nulams_ [daeID (y, 1), nameSym ""]
(tupleproj_ 1 (daeJacADExpr eqn)))
dae.eqns)))
(foldl_
(nulams_ [_acc1, _jis]
(bind_
(nulet_ (daeID (y, 1)) _j)
(foldl_
(nulams_ [_acc2, _i]
(cons_
(utuple_ [
utuple_ [nvar_ _i, _j],
app_
(get_ (nvar_ _r) (nvar_ _i))
(nvar_ (daeID (y, 1)))
])
(nvar_ _acc2)))
(nvar_ _acc1)
_is)))
(seq_ [])
(nvar_ _idxs)))
] in
bind_ (daeJacADExpr dae.bindings) t
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem _daeGenMixedJac : Bool -> Float -> TmDAERec -> Expr
sem _daeGenMixedJac jacY phi =| dae ->
let errMsg = _daeErrMsg "daeGenMixedJac" in
let logDebug = lam msg.
logMsg logLevel.debug
(lam.
strJoin "\n" [
join ["daeGenMixedJac", if jacY then "Y" else "Yp"],
msg ()
])
in
if or (ltf phi 0.) (gtf phi 1.) then
error
(join ["daeGenMixedJac:phi = ", float2string phi, " is outside [0, 1]"])
else
match dae.vars with
[(y, TySeq {ty = TyFloat _}), (yp, TySeq {ty = TyFloat _})]
then
let pevalInlineLets = pevalInlineLets (sideEffectEnvEmpty ()) in
let y = nameSetNewSym y in
let yp = nameSetNewSym yp in
let n = length dae.eqns in
let _idxs = nameSym "idxs" in
let idxs =
let s = daeJacStructure dae in
let s = if jacY then s.0 else s.1 in
daeJacStructureToIdxSeq s
in
let jact = _daeGenJac jacY dae in
let idxs_ = lam idxs.
seq_ (map (lam jis. utuple_ [int_ jis.0, seq_ (map int_ jis.1)]) idxs)
in
let yyp = (unzip dae.vars).0 in
let args = map nvar_ yyp in
switch
match
partition
(lam jis. leqf (int2float (length jis.1)) (mulf phi (int2float n)))
idxs
with (sIdxs, dIdxs)
in
logDebug (lam.
strJoin " " [int2string (length dIdxs), "AD derivatives"]);
logDebug (lam.
strJoin " "
[int2string (length sIdxs), "specialized partial derivatives"]);
(sIdxs, dIdxs)
case (sIdxs, []) then
nulams_ yyp
(utuple_ [
seq_ [],
pevalInlineLets
(peval (appSeq_ jact (cons (idxs_ sIdxs) args)))
])
case ([], dIdxs) then
nulams_ yyp
(utuple_ [
appSeq_ jact (cons (idxs_ dIdxs) args),
seq_ []
])
case (sIdxs, dIdxs) then
nulams_ yyp
(utuple_ [
appSeq_ jact (cons (idxs_ dIdxs) args),
pevalInlineLets
(peval (appSeq_ jact (cons (idxs_ sIdxs) args)))
])
end
else
error (errMsg "Not a first-order DAE" (TmDAE dae))
sem daeGenMixedJacY : Float -> TmDAERec -> Expr
sem daeGenMixedJacY phi =| dae -> _daeGenMixedJac true phi dae
sem daeGenMixedJacYp : Float -> TmDAERec -> Expr
sem daeGenMixedJacYp phi =| dae -> _daeGenMixedJac false phi dae
end
lang TestLang = DAE + DAEParseAnalysis + DAEParseDesugar end
mexpr
----------------
-- Test setup --
----------------
use TestLang in
let pevalInlineLets = pevalInlineLets (sideEffectEnvEmpty ()) in
let _parseExpr = lam prog.
(typeCheck (symbolize (parseDAEExprExn prog)))
in
let _parseAsTmDAE = lam prog.
TmDAE (_tmToTmDAERec ( _parseExpr prog))
in
let _parseDAEProg = lam prog.
let prog = daeParseExn "internal" prog in
logMsg logLevel.debug
(lam. strJoin "\n" ["Input program:", daeProgToString prog]);
match typeCheck (symbolize (TmDAE (daeDesugarProg prog))) with TmDAE r
then r else error "Impossible"
in
let _prepDVar = lam x. (nameGetStr x.0, x.1) in
let _prepDVars = lam vars. map _prepDVar (sort dvarCmp vars) in
-- let peval = pevalExpr { pevalCtxEmpty () with subsSingleLets = true } in
let utestToString = utestDefaultToString expr2str expr2str in
-------------------
-- Input program --
-------------------
let daer = _parseDAEProg "
let mul = lam x. lam y. x*y end
let pow2 = lam x. mul x x end
variables
x, y, h : Float
init
x = 1.;
x' = 2.;
y'' = 0. - 1.
equations
x'' = mul x h;
y'' = mul y h - 1.;
pow2 x + pow2 y = pow2 1.
output
{x, x', x''}
"
in
let daer2 = _parseDAEProg "
reclet pow = lam x. lam n.
if n < 1 then 1. else x * pow x (pred n)
end
variables
x, y, h, u: Float
init
x = 1.;
x' = 2.;
y'' = 0. - 1.
equations
x'' = x * h;
y'' = y * h - 1.;
x * x + pow y 2 = 1.;
u = pow x' 2 + pow y' 2
output
{x, y}
"
in
-------------------------
-- Test: daeAnnotDVars --
-------------------------
let expected = _parseAsTmDAE "
let mul = lam x. lam y. mulf x y in
let pow2 = lam x. mul x x in
lam x: Float. lam y: Float. lam h: Float. {
ieqns = (subf (prim 0 x) 1., subf (prim 1 x) 2., subf (prim 2 y) (subf 0. 1.)),
eqns = (subf (prim 2 x) (mul (prim 0 x) (prim 0 h)),
subf (prim 2 y) (subf (mul (prim 0 y) (prim 0 h)) 1.),
subf (addf (pow2 (prim 0 x)) (pow2 (prim 0 y))) (pow2 1.)),
out = (prim 0 x, prim 1 x, prim 2 x)
}
"
in
let daer = daeAnnotDVars daer in
let actual = TmDAE daer in
utest expected with actual using eqExpr in
let expected = _parseAsTmDAE "
recursive
let pow = lam x1. lam n.
match lti n 1 with true then 1.
else mulf x1 (pow x1 (subi n 1))
in
lam x: Float. lam y: Float. lam h: Float. lam u: Float. {
ieqns =
(subf (prim 0 x) 1.
,subf (prim 1 x) 2.
,subf (prim 2 y) (subf 0. 1.)),
eqns =
(subf (prim 2 x) (mulf (prim 0 x) (prim 0 h))
,subf (prim 2 y) (subf (mulf (prim 0 y) (prim 0 h)) 1.)
,subf (addf (mulf (prim 0 x) (prim 0 x)) (pow (prim 0 y) 2)) 1.
,subf (prim 0 u) (addf (pow (prim 1 x) 2) (pow (prim 1 y) 2))),
out = (prim 0 x, prim 0 y)
}
"
in
let daer2 = daeAnnotDVars daer2 in
let actual = TmDAE daer2 in
utest expected with actual using eqExpr in
------------------------
-- Test: daeStructure --
------------------------
let expected = [
[("x", 0), ("x", 2), ("h", 0)],
[("y", 0), ("y", 2), ("h", 0)],
[("x", 0), ("y", 0)]
] in
let actual =
map
(lam s. _prepDVars (setToSeq s))
(daeStructure daer)
in
utest actual with expected in
---------------------------------
-- Test: daeStructuralAnalysis --
---------------------------------
let expected = {
varOffset = [("x", 2), ("y", 2), ("h", 0)],
eqnsOffset = [0, 0, 2]
} in
let actual = daeStructuralAnalysis daer in
let ns = actual.eqnsOffset in
let varOffset = actual.varOffset in
utest _prepDVars varOffset with expected.varOffset in
utest ns with expected.eqnsOffset in
let expected = {
varOffset = [("x", 2), ("y", 2), ("h", 0), ("u", 0)],
eqnsOffset = [0, 0, 2, 0]
} in
let actual = daeStructuralAnalysis daer2 in
let ns2 = actual.eqnsOffset in
let varOffset2 = actual.varOffset in
utest _prepDVars varOffset2 with expected.varOffset in
utest ns2 with expected.eqnsOffset in
--------------------------
-- Test: daeIndexReduce --
--------------------------
let expected = _parseAsTmDAE "
let mul = lam x. lam y. mulf x y in
let pow2 = lam x. mul x x in
let mulp = lam xp. lam yp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0)))
xp yp
in
let pow2p = lam xp. mulp xp xp in
let mulpp = lam xpp. lam ypp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0),
addf
(addf (mulf x.0 y.2) (mulf 2. (mulf x.1 y.1)))
(mulf x.2 y.0)))
xpp ypp
in
let pow2pp = lam xpp. mulpp xpp xpp in
lam x: Float. lam y: Float. lam h:Float. {
ieqns = (subf (prim 0 x) 1., subf (prim 1 x) 2., subf (prim 2 y) (subf 0. 1.)),
eqns = (subf (prim 2 x) (mul (prim 0 x) (prim 0 h)),
subf (prim 2 y) (subf (mul (prim 0 y) (prim 0 h)) 1.),
((lam x. lam y. (subf x.0 y.0, subf x.1 y.1, subf x.2 y.2))
((lam x. lam y. (addf x.0 y.0, addf x.1 y.1, addf x.2 y.2))
(pow2pp (prim 0 x, prim 1 x, prim 2 x))
(pow2pp (prim 0 y, prim 1 y, prim 2 y)))
(pow2pp (1., 0., 0.))).2),
out = (prim 0 x, prim 1 x, prim 2 x)
}
"
in
let daer = daeIndexReduce ns daer in
let actual = TmDAE daer in
utest expected with actual using eqExpr in
let expected = _parseAsTmDAE "
recursive let pow = lam x. lam n.
match lti n 1 with true then 1.
else mulf x (pow x (subi n 1))
in
recursive let powp = lam xp. lam np.
match lti np 1 with true then (1., 0.)
else
(lam x. lam y.
(mulf x.0 y.0
,addf (mulf x.0 y.1) (mulf x.1 y.0)))
xp (powp xp (subi np 1))
in
recursive
let powpp = lam xpp. lam npp.
match lti npp 1 with true then (1., 0., 0.)
else
(lam x. lam y.
(mulf x.0 y.0
,addf (mulf x.0 y.1) (mulf x.1 y.0)
,addf
(addf (mulf x.0 y.2) (mulf 2. (mulf x.1 y.1)))
(mulf x.2 y.0)))
xpp (powpp xpp (subi npp 1))
in
lam x: Float. lam y: Float. lam h: Float. lam u: Float. {
ieqns =
(subf (prim 0 x) 1., subf (prim 1 x) 2., subf (prim 2 y) (subf 0. 1.)),
eqns =
(subf (prim 2 x) (mulf (prim 0 x) (prim 0 h)),
subf (prim 2 y) (subf (mulf (prim 0 y) (prim 0 h)) 1.)
,((lam x1. lam y1. (subf x1.0 y1.0, subf x1.1 y1.1, subf x1.2 y1.2))
((lam x2. lam y2. (addf x2.0 y2.0, addf x2.1 y2.1, addf x2.2 y2.2))
((lam x. lam y.
(mulf x.0 y.0
,addf (mulf x.0 y.1) (mulf x.1 y.0)
,addf (addf (mulf x.0 y.2) (mulf 2. (mulf x.1 y.1))) (mulf x.2 y.0)))
(prim 0 x, prim 1 x, prim 2 x) (prim 0 x, prim 1 x, prim 2 x))
(powpp (prim 0 y, prim 1 y, prim 2 y) 2))
(1., 0., 0.)).2
,subf (prim 0 u) (addf (pow (prim 1 x) 2) (pow (prim 1 y) 2))),
out = (prim 0 x, prim 0 y)
}
"
in
let daer2 = daeIndexReduce ns2 daer2 in
let actual = TmDAE daer2 in
utest expected with actual using eqExpr in
------------------------------
-- Test: daeFirstOrderState --
------------------------------
let expected = {
ys = [
These (("x", 0), ("x", 1)),
These (("x", 1), ("x", 2)),
These (("y", 0), ("y", 1)),
These (("y", 1), ("y", 2)),
This ("h", 0)
],
indexMap = [
(("x", 0), This 0),
(("x", 1), These (1, 0)),
(("x", 2), That 1),
(("y", 0), This 2),
(("y", 1), These (3, 2)),
(("y", 2), That 3),
(("h", 0), This 4)
] } in
let actual = daeFirstOrderState varOffset in
utest map (theseBiMap _prepDVar _prepDVar) actual.ys with expected.ys in
utest map (lam x. (_prepDVar x.0, x.1)) (mapBindings actual.indexMap)
with expected.indexMap
in
let state = actual in
let expected = {
ys = [
These (("x", 0), ("x", 1)),
These (("x", 1), ("x", 2)),
These (("y", 0), ("y", 1)),
These (("y", 1), ("y", 2)),
This ("h", 0),
This ("u", 0)
],
indexMap = [
(("x", 0), This 0),
(("x", 1), These (1, 0)),
(("x", 2), That 1),
(("y", 0), This 2),
(("y", 1), These (3, 2)),
(("y", 2), That 3),
(("h", 0), This 4),
(("u", 0), This 5)
] } in
let actual = daeFirstOrderState varOffset2 in
utest map (theseBiMap _prepDVar _prepDVar) actual.ys with expected.ys in
utest map (lam x. (_prepDVar x.0, x.1)) (mapBindings actual.indexMap)
with expected.indexMap
in
let state2 = actual in
-------------------------
-- Test: daeIsDiffVars --
-------------------------
let expected = [true, true, true, true, false] in
let actual = daeIsDiffVars state in
utest expected with actual in
let expected = [true, true, true, true, false, false] in
let actual = daeIsDiffVars state2 in
utest expected with actual in
--------------------------
-- Test: daeOrderReduce --
--------------------------
let expected = _parseAsTmDAE "
let mul = lam x. lam y. mulf x y in
let pow2 = lam x. mul x x in
let mulp = lam xp. lam yp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0)))
xp yp
in
let pow2p = lam xp. mulp xp xp in
let mulpp = lam xpp. lam ypp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0),
addf
(addf
(mulf x.0 y.2)
(mulf 2. (mulf x.1 y.1)))
(mulf x.2 y.0)))
xpp ypp
in
let pow2pp = lam xpp. mulpp xpp xpp in
lam y: [Float]. lam yp: [Float]. {
ieqns = (subf (arrayGet y 0) 1., subf (arrayGet y 1) 2., subf (arrayGet yp 3) (subf 0. 1.)),
eqns = (subf (arrayGet yp 1) (mul (arrayGet y 0) (arrayGet y 4)),
subf (arrayGet yp 3) (subf (mul (arrayGet y 2) (arrayGet y 4)) 1.),
((lam x. lam y. (subf x.0 y.0, subf x.1 y.1, subf x.2 y.2))
((lam x. lam y. (addf x.0 y.0, addf x.1 y.1, addf x.2 y.2))
(pow2pp (arrayGet y 0, arrayGet y 1, arrayGet yp 1))
(pow2pp (arrayGet y 2, arrayGet y 3, arrayGet yp 3)))
(pow2pp (1., 0., 0.))).2,
subf (arrayGet y 1) (arrayGet yp 0),
subf (arrayGet y 3) (arrayGet yp 2)),
out = (arrayGet y 0, arrayGet y 1, arrayGet yp 1)
}
"
in
let daer = daeOrderReduce state (nameSym "y") (nameSym "yp") daer in
utest expected with TmDAE daer using eqExpr in
--------------------------
-- Test: daeGenInitExpr --
--------------------------
let expected = _parseExpr "
let mul = lam x. lam y. mulf x y in
let pow2 = lam x. mul x x in
let mulp = lam xp. lam yp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0)))
xp yp
in
let pow2p = lam xp. mulp xp xp in
let mulpp = lam xpp. lam ypp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0),
addf
(addf
(mulf x.0 y.2)
(mulf 2. (mulf x.1 y.1)))
(mulf x.2 y.0)))
xpp ypp
in
let pow2pp = lam xpp. mulpp xpp xpp in
([ 1., 2., 0., 0., 0. ],
[ 2., 0., 0., subf 0. 1., 0. ])
"
in
let actual = daeGenInitExpr state daer in
let iexpr = actual in
utest expected with actual using eqExpr in
-------------------------
-- Test: daeGenOutExpr --
-------------------------
let expected = _parseExpr "
let mul = lam x. lam y. mulf x y in
let pow2 = lam x. mul x x in
let mulp = lam xp. lam yp.
(lam x. lam y.
(mulf x.0 y.0,
addf (mulf x.0 y.1) (mulf x.1 y.0)))