-
-
Notifications
You must be signed in to change notification settings - Fork 213
/
Copy pathodesystem.jl
1726 lines (1477 loc) · 52.3 KB
/
odesystem.jl
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
using ModelingToolkit, StaticArrays, LinearAlgebra
using ModelingToolkit: get_metadata, MTKParameters
using SymbolicIndexingInterface
using OrdinaryDiffEq, Sundials
using DiffEqBase, SparseArrays
using StaticArrays
using Test
using SymbolicUtils: issym
using ForwardDiff
using ModelingToolkit: value
using ModelingToolkit: t_nounits as t, D_nounits as D
# Define some variables
@parameters σ ρ β
@constants κ = 1
@variables x(t) y(t) z(t)
@parameters k
# Define a differential equation
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
ModelingToolkit.toexpr.(eqs)[1]
@named de = ODESystem(eqs, t; defaults = Dict(x => 1))
subed = substitute(de, [σ => k])
ssort(eqs) = sort(eqs, by = string)
@test isequal(ssort(parameters(subed)), [k, β, ρ])
@test isequal(equations(subed),
[D(x) ~ k * (y - x)
D(y) ~ (ρ - z) * x - y
D(z) ~ x * y - β * κ * z])
@named des[1:3] = ODESystem(eqs, t)
@test length(unique(x -> ModelingToolkit.get_tag(x), des)) == 1
@test eval(toexpr(de)) == de
@test hash(deepcopy(de)) == hash(de)
generate_function(de)
function test_diffeq_inference(name, sys, iv, dvs, ps)
@testset "ODESystem construction: $name" begin
@test isequal(independent_variables(sys)[1], value(iv))
@test length(independent_variables(sys)) == 1
@test isempty(setdiff(Set(unknowns(sys)), Set(value.(dvs))))
@test isempty(setdiff(Set(parameters(sys)), Set(value.(ps))))
end
end
test_diffeq_inference("standard", de, t, [x, y, z], [ρ, σ, β])
generate_function(de, [x, y, z], [σ, ρ, β])
jac_expr = generate_jacobian(de)
jac = calculate_jacobian(de)
jacfun = eval(jac_expr[2])
de = complete(de)
for f in [
ODEFunction(de, [x, y, z], [σ, ρ, β], tgrad = true, jac = true),
eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], tgrad = true, jac = true))
]
# system
@test f.sys === de
# iip
du = zeros(3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == [4, 0, -16]
# oop
du = @SArray zeros(3)
u = SVector(1:3...)
p = ModelingToolkit.MTKParameters(de, SVector{3}([σ, ρ, β] .=> 4.0:6.0))
@test f.f(u, p, 0.1) === @SArray [4.0, 0.0, -16.0]
# iip vs oop
du = zeros(3)
g = similar(du)
J = zeros(3, 3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == f(u, p, 0.1)
f.tgrad(g, u, p, t)
@test g == f.tgrad(u, p, t)
f.jac(J, u, p, t)
@test J == f.jac(u, p, t)
end
#check iip_config
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], iip_config = (false, true)))
du = zeros(3)
u = collect(1:3)
p = ModelingToolkit.MTKParameters(de, [σ, ρ, β] .=> 4.0:6.0)
f.f(du, u, p, 0.1)
@test du == [4, 0, -16]
@test_throws ArgumentError f.f(u, p, 0.1)
#check iip
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β]))
f2 = ODEFunction(de, [x, y, z], [σ, ρ, β])
@test SciMLBase.isinplace(f) === SciMLBase.isinplace(f2)
@test SciMLBase.specialization(f) === SciMLBase.specialization(f2)
for iip in (true, false)
f = eval(ODEFunctionExpr{iip}(de, [x, y, z], [σ, ρ, β]))
f2 = ODEFunction{iip}(de, [x, y, z], [σ, ρ, β])
@test SciMLBase.isinplace(f) === SciMLBase.isinplace(f2) === iip
@test SciMLBase.specialization(f) === SciMLBase.specialization(f2)
for specialize in (SciMLBase.AutoSpecialize, SciMLBase.FullSpecialize)
f = eval(ODEFunctionExpr{iip, specialize}(de, [x, y, z], [σ, ρ, β]))
f2 = ODEFunction{iip, specialize}(de, [x, y, z], [σ, ρ, β])
@test SciMLBase.isinplace(f) === SciMLBase.isinplace(f2) === iip
@test SciMLBase.specialization(f) === SciMLBase.specialization(f2) === specialize
end
end
#check sparsity
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], sparsity = true))
@test f.sparsity == ModelingToolkit.jacobian_sparsity(de)
f = eval(ODEFunctionExpr(de, [x, y, z], [σ, ρ, β], sparsity = false))
@test isnothing(f.sparsity)
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y * t,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
de = complete(de)
ModelingToolkit.calculate_tgrad(de)
tgrad_oop, tgrad_iip = eval.(ModelingToolkit.generate_tgrad(de))
u = SVector(1:3...)
p = ModelingToolkit.MTKParameters(de, SVector{3}([σ, ρ, β] .=> 4.0:6.0))
@test tgrad_oop(u, p, t) == [0.0, -u[2], 0.0]
du = zeros(3)
tgrad_iip(du, u, p, t)
@test du == [0.0, -u[2], 0.0]
@parameters σ′(t - 1)
eqs = [D(x) ~ σ′ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
test_diffeq_inference("global iv-varying", de, t, (x, y, z), (σ′, ρ, β))
f = eval(generate_function(de, [x, y, z], [σ′, ρ, β])[2])
du = [0.0, 0.0, 0.0]
f(du, [1.0, 2.0, 3.0], [x -> x + 7, 2, 3], 5.0)
@test du ≈ [11, -3, -7]
@parameters σ(..)
eqs = [D(x) ~ σ(t - 1) * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
test_diffeq_inference("single internal iv-varying", de, t, (x, y, z), (σ, ρ, β))
f = eval(generate_function(de, [x, y, z], [σ, ρ, β])[2])
du = [0.0, 0.0, 0.0]
f(du, [1.0, 2.0, 3.0], [x -> x + 7, 2, 3], 5.0)
@test du ≈ [11, -3, -7]
eqs = [D(x) ~ x + 10σ(t - 1) + 100σ(t - 2) + 1000σ(t^2)]
@named de = ODESystem(eqs, t)
test_diffeq_inference("many internal iv-varying", de, t, (x,), (σ,))
f = eval(generate_function(de, [x], [σ])[2])
du = [0.0]
f(du, [1.0], [t -> t + 2], 5.0)
@test du ≈ [27561]
# Conversion to first-order ODEs #17
D3 = D^3
D2 = D^2
@variables u(t) uˍtt(t) uˍt(t) xˍt(t)
eqs = [D3(u) ~ 2(D2(u)) + D(u) + D(x) + 1
D2(x) ~ D(x) + 2]
@named de = ODESystem(eqs, t)
de1 = ode_order_lowering(de)
lowered_eqs = [D(uˍtt) ~ 2uˍtt + uˍt + xˍt + 1
D(xˍt) ~ xˍt + 2
D(uˍt) ~ uˍtt
D(u) ~ uˍt
D(x) ~ xˍt]
#@test de1 == ODESystem(lowered_eqs)
# issue #219
@test all(isequal.(
[ModelingToolkit.var_from_nested_derivative(eq.lhs)[1]
for eq in equations(de1)],
unknowns(@named lowered = ODESystem(lowered_eqs, t))))
test_diffeq_inference("first-order transform", de1, t, [uˍtt, xˍt, uˍt, u, x], [])
du = zeros(5)
ODEFunction(complete(de1), [uˍtt, xˍt, uˍt, u, x], [])(du, ones(5), nothing, 0.1)
@test du == [5.0, 3.0, 1.0, 1.0, 1.0]
# Internal calculations
@parameters σ
a = y - x
eqs = [D(x) ~ σ * a,
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z * κ]
@named de = ODESystem(eqs, t)
generate_function(de, [x, y, z], [σ, ρ, β])
jac = calculate_jacobian(de)
@test ModelingToolkit.jacobian_sparsity(de).colptr == sparse(jac).colptr
@test ModelingToolkit.jacobian_sparsity(de).rowval == sparse(jac).rowval
f = ODEFunction(complete(de), [x, y, z], [σ, ρ, β])
@parameters A B C
_x = y / C
eqs = [D(x) ~ -A * x,
D(y) ~ A * x - B * _x]
@named de = ODESystem(eqs, t)
@test begin
local f, du
f = eval(generate_function(de, [x, y], [A, B, C])[2])
du = [0.0, 0.0]
f(du, [1.0, 2.0], [1, 2, 3], 0.0)
du ≈ [-1, -1 / 3]
f = eval(generate_function(de, [x, y], [A, B, C])[1])
du ≈ f([1.0, 2.0], [1, 2, 3], 0.0)
end
function lotka(u, p, t)
x = u[1]
y = u[2]
[p[1] * x - p[2] * x * y,
-p[3] * y + p[4] * x * y]
end
prob = ODEProblem(ODEFunction{false}(lotka), [1.0, 1.0], (0.0, 1.0), [1.5, 1.0, 3.0, 1.0])
de = complete(modelingtoolkitize(prob))
ODEFunction(de)(similar(prob.u0), prob.u0, prob.p, 0.1)
function lotka(du, u, p, t)
x = u[1]
y = u[2]
du[1] = p[1] * x - p[2] * x * y
du[2] = -p[3] * y + p[4] * x * y
end
prob = ODEProblem(lotka, [1.0, 1.0], (0.0, 1.0), [1.5, 1.0, 3.0, 1.0])
de = complete(modelingtoolkitize(prob))
ODEFunction(de)(similar(prob.u0), prob.u0, prob.p, 0.1)
# automatic unknown detection for DAEs
@parameters k₁ k₂ k₃
@variables y₁(t) y₂(t) y₃(t)
# reorder the system just to be a little spicier
eqs = [D(y₁) ~ -k₁ * y₁ + k₃ * y₂ * y₃,
0 ~ y₁ + y₂ + y₃ - 1,
D(y₂) ~ k₁ * y₁ - k₂ * y₂^2 - k₃ * y₂ * y₃ * κ]
@named sys = ODESystem(eqs, t, defaults = [k₁ => 100, k₂ => 3e7, y₁ => 1.0])
sys = complete(sys)
u0 = Pair[]
push!(u0, y₂ => 0.0)
push!(u0, y₃ => 0.0)
p = [k₁ => 0.04,
k₃ => 1e4]
p2 = (k₁ => 0.04,
k₂ => 3e7,
k₃ => 1e4)
tspan = (0.0, 100000.0)
prob1 = ODEProblem(sys, u0, tspan, p)
@test prob1.f.sys == sys
prob12 = ODEProblem(sys, u0, tspan, [k₁ => 0.04, k₂ => 3e7, k₃ => 1e4])
prob13 = ODEProblem(sys, u0, tspan, (k₁ => 0.04, k₂ => 3e7, k₃ => 1e4))
prob14 = ODEProblem(sys, u0, tspan, p2)
for p in [prob1, prob14]
@test p.p isa MTKParameters
p.ps[k₁] ≈ 0.04
p.ps[k₂] ≈ 3e7
p.ps[k₃] ≈ 1e-4
@test Set(Num.(unknowns(sys)) .=> p.u0) == Set([y₁ => 1, y₂ => 0, y₃ => 0])
end
# test remake with symbols
p3 = [k₁ => 0.05,
k₂ => 2e7,
k₃ => 1.1e4]
u01 = [y₁ => 1, y₂ => 1, y₃ => 1]
prob_pmap = remake(prob14; p = p3, u0 = u01)
prob_dpmap = remake(prob14; p = Dict(p3), u0 = Dict(u01))
for p in [prob_pmap, prob_dpmap]
@test p.p isa MTKParameters
p.ps[k₁] ≈ 0.05
p.ps[k₂] ≈ 2e7
p.ps[k₃] ≈ 1.1e-4
@test Set(Num.(unknowns(sys)) .=> p.u0) == Set([y₁ => 1, y₂ => 1, y₃ => 1])
end
sol_pmap = solve(prob_pmap, Rodas5())
sol_dpmap = solve(prob_dpmap, Rodas5())
@test all(isequal(0.05), sol_pmap.(0:10:100, idxs = k₁))
@test sol_pmap.u ≈ sol_dpmap.u
@testset "symbolic remake with nested system" begin
function makesys(name)
@parameters a = 1.0
@variables x(t) = 0.0
ODESystem([D(x) ~ -a * x], t; name)
end
function makecombinedsys()
sys1 = makesys(:sys1)
sys2 = makesys(:sys2)
@parameters b = 1.0
complete(ODESystem(Equation[], t, [], [b]; systems = [sys1, sys2], name = :foo))
end
sys = makecombinedsys()
@unpack sys1, b = sys
prob = ODEProblem(sys, Pair[])
prob_new = SciMLBase.remake(prob, p = Dict(sys1.a => 3.0, b => 4.0),
u0 = Dict(sys1.x => 1.0))
@test prob_new.p isa MTKParameters
@test prob_new.ps[b] ≈ 4.0
@test prob_new.ps[sys1.a] ≈ 3.0
@test prob_new.ps[sys.sys2.a] ≈ 1.0
@test prob_new.u0 == [1.0, 0.0]
end
# test kwargs
prob2 = ODEProblem(sys, u0, tspan, p, jac = true)
prob3 = ODEProblem(sys, u0, tspan, p, jac = true, sparse = true) #SparseMatrixCSC need to handle
@test prob3.f.jac_prototype isa SparseMatrixCSC
prob3 = ODEProblem(sys, u0, tspan, p, jac = true, sparsity = true)
@test prob3.f.sparsity isa SparseMatrixCSC
@test_throws ArgumentError ODEProblem(sys, zeros(5), tspan, p)
for (prob, atol) in [(prob1, 1e-12), (prob2, 1e-12), (prob3, 1e-12)]
local sol
sol = solve(prob, Rodas5())
@test all(x -> ≈(sum(x), 1.0, atol = atol), sol.u)
end
du0 = [D(y₁) => -0.04
D(y₂) => 0.04
D(y₃) => 0.0]
prob4 = DAEProblem(sys, du0, u0, tspan, p2)
prob5 = eval(DAEProblemExpr(sys, du0, u0, tspan, p2))
for prob in [prob4, prob5]
local sol
@test prob.differential_vars == [true, true, false]
sol = solve(prob, IDA())
@test all(x -> ≈(sum(x), 1.0, atol = 1e-12), sol.u)
end
@parameters σ β
@variables x(t) y(t) z(t)
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x - β * y,
x + z ~ y]
@named sys = ODESystem(eqs, t)
@test all(isequal.(unknowns(sys), [x, y, z]))
@test all(isequal.(parameters(sys), [σ, β]))
@test equations(sys) == eqs
@test ModelingToolkit.isautonomous(sys)
# issue 701
using ModelingToolkit
@parameters a
@variables x(t)
@named sys = ODESystem([D(x) ~ a], t)
@test issym(equations(sys)[1].rhs)
# issue 708
@parameters a
@variables x(t) y(t) z(t)
@named sys = ODESystem([D(x) ~ y, 0 ~ x + z, 0 ~ x - y], t, [z, y, x], [])
asys = add_accumulations(sys)
@variables accumulation_x(t) accumulation_y(t) accumulation_z(t)
eqs = [0 ~ x + z
0 ~ x - y
D(accumulation_x) ~ x
D(accumulation_y) ~ y
D(accumulation_z) ~ z
D(x) ~ y]
@test ssort(equations(asys)) == ssort(eqs)
@variables ac(t)
asys = add_accumulations(sys, [ac => (x + y)^2])
eqs = [0 ~ x + z
0 ~ x - y
D(ac) ~ (x + y)^2
D(x) ~ y]
@test ssort(equations(asys)) == ssort(eqs)
sys2 = ode_order_lowering(sys)
M = ModelingToolkit.calculate_massmatrix(sys2)
@test M == Diagonal([1, 0, 0])
# issue #609
@variables x1(t) x2(t)
eqs = [
D(x1) ~ -x1,
0 ~ x1 - x2
]
@named sys = ODESystem(eqs, t)
@test isequal(ModelingToolkit.get_iv(sys), t)
@test isequal(unknowns(sys), [x1, x2])
@test isempty(parameters(sys))
# one equation ODESystem test
@parameters r
@variables x(t)
eq = D(x) ~ r * x
@named ode = ODESystem(eq, t)
@test equations(ode) == [eq]
# issue #808
@testset "Combined system name collisions" begin
function makesys(name)
@parameters a
@variables x(t) f(t)
ODESystem([D(x) ~ -a * x + f], t; name)
end
function issue808()
sys1 = makesys(:sys1)
sys2 = makesys(:sys1)
@test_throws ArgumentError ODESystem([sys2.f ~ sys1.x, D(sys1.f) ~ 0], t,
systems = [sys1, sys2], name = :foo)
end
issue808()
end
#Issue 998
pars = []
vars = @variables((u1,))
eqs = [
D(u1) ~ 1
]
@test_throws ArgumentError ODESystem(eqs, t, vars, pars, name = :foo)
#Issue 1063/998
pars = [t]
vars = @variables((u1(t),))
@test_throws ArgumentError ODESystem(eqs, t, vars, pars, name = :foo)
@parameters w
der = Differential(w)
eqs = [
der(u1) ~ t
]
@test_throws ArgumentError ModelingToolkit.ODESystem(eqs, t, vars, pars, name = :foo)
@variables x(t)
@parameters M b k
eqs = [D(D(x)) ~ -b / M * D(x) - k / M * x]
ps = [M, b, k]
default_u0 = [D(x) => 0.0, x => 10.0]
default_p = [M => 1.0, b => 1.0, k => 1.0]
@named sys = ODESystem(eqs, t, [x], ps; defaults = [default_u0; default_p], tspan)
sys = ode_order_lowering(sys)
sys = complete(sys)
prob = ODEProblem(sys)
sol = solve(prob, Tsit5())
@test sol.t[end] == tspan[end]
@test sum(abs, sol.u[end]) < 1
prob = ODEProblem{false}(sys; u0_constructor = x -> SVector(x...))
@test prob.u0 isa SVector
# check_eqs_u0 kwarg test
@variables x1(t) x2(t)
eqs = [D(x1) ~ -x1]
@named sys = ODESystem(eqs, t, [x1, x2], [])
sys = complete(sys)
@test_throws ArgumentError ODEProblem(sys, [1.0, 1.0], (0.0, 1.0))
@test_nowarn ODEProblem(sys, [1.0, 1.0], (0.0, 1.0), check_length = false)
# check inputs
let
@parameters f k d
@variables x(t) ẋ(t)
δ = D
eqs = [δ(x) ~ ẋ, δ(ẋ) ~ f - k * x - d * ẋ]
@named sys = ODESystem(eqs, t, [x, ẋ], [f, d, k]; controls = [f])
calculate_control_jacobian(sys)
@test isequal(calculate_control_jacobian(sys),
reshape(Num[0, 1], 2, 1))
end
# issue 1109
let
@variables x(t)[1:3, 1:3]
@named sys = ODESystem(D.(x) .~ x, t)
@test_nowarn structural_simplify(sys)
end
# Array vars
using Symbolics: unwrap, wrap
using LinearAlgebra
sts = @variables x(t)[1:3]=[1, 2, 3.0] y(t)=1.0
ps = @parameters p[1:3] = [1, 2, 3]
eqs = [collect(D.(x) .~ x)
D(y) ~ norm(collect(x)) * y - x[1]]
@named sys = ODESystem(eqs, t, sts, ps)
sys = structural_simplify(sys)
@test isequal(@nonamespace(sys.x), x)
@test isequal(@nonamespace(sys.y), y)
@test isequal(@nonamespace(sys.p), p)
@test_nowarn sys.x, sys.y, sys.p
@test all(x -> x isa Symbolics.Arr, (sys.x, sys.p))
@test all(x -> x isa Symbolics.Arr, @nonamespace (sys.x, sys.p))
@test ModelingToolkit.isvariable(Symbolics.unwrap(x[1]))
prob = ODEProblem(sys, [], (0, 1.0))
sol = solve(prob, Tsit5())
@test sol[2x[1] + 3x[3] + norm(x)] ≈
2sol[x[1]] + 3sol[x[3]] + sol[norm(x)]
@test sol[x .+ [y, 2y, 3y]] ≈ map((x...) -> [x...],
map((x, y) -> x[1] .+ y, sol[x], sol[y]),
map((x, y) -> x[2] .+ 2y, sol[x], sol[y]),
map((x, y) -> x[3] .+ 3y, sol[x], sol[y]))
using ModelingToolkit
function submodel(; name)
@variables y(t)
@parameters A[1:5]
A = collect(A)
ODESystem(D(y) ~ sum(A) * y, t; name = name)
end
# Build system
@named sys1 = submodel()
@named sys2 = submodel()
@named sys = ODESystem([0 ~ sys1.y + sys2.y], t; systems = [sys1, sys2])
# DelayDiffEq
using ModelingToolkit: hist
@variables x(t) y(t)
xₜ₋₁ = hist(x, t - 1)
eqs = [D(x) ~ x * y
D(y) ~ y * x - xₜ₋₁]
@named sys = ODESystem(eqs, t)
# register
using StaticArrays
using SymbolicUtils: term
using SymbolicUtils.Code
using Symbolics: unwrap, wrap, @register_symbolic
foo(a, ms::AbstractVector) = a + sum(ms)
@register_symbolic foo(a, ms::AbstractVector)
@variables x(t) ms(t)[1:3]
eqs = [D(x) ~ foo(x, ms); D(ms) ~ ones(3)]
@named sys = ODESystem(eqs, t, [x; ms], [])
@named emptysys = ODESystem(Equation[], t)
@mtkbuild outersys = compose(emptysys, sys)
prob = ODEProblem(
outersys, [outersys.sys.x => 1.0; collect(outersys.sys.ms .=> 1:3)], (0, 1.0))
@test_nowarn solve(prob, Tsit5())
# array equations
bar(x, p) = p * x
@register_array_symbolic bar(x::AbstractVector, p::AbstractMatrix) begin
size = size(x)
eltype = promote_type(eltype(x), eltype(p))
end
@parameters p[1:3, 1:3]
eqs = [D(x) ~ foo(x, ms); D(ms) ~ bar(ms, p)]
@named sys = ODESystem(eqs, t)
@named emptysys = ODESystem(Equation[], t)
@mtkbuild outersys = compose(emptysys, sys)
prob = ODEProblem(
outersys, [sys.x => 1.0, sys.ms => 1:3], (0.0, 1.0), [sys.p => ones(3, 3)])
@test_nowarn solve(prob, Tsit5())
obsfn = ModelingToolkit.build_explicit_observed_function(
outersys, bar(3outersys.sys.ms, 3outersys.sys.p))
@test_nowarn obsfn(sol.u[1], prob.p, sol.t[1])
# x/x
@variables x(t)
@named sys = ODESystem([D(x) ~ x / x], t)
@test equations(alias_elimination(sys)) == [D(x) ~ 1]
# observed variable handling
@variables x(t) RHS(t)
@parameters τ
@named fol = ODESystem([D(x) ~ (1 - x) / τ], t; observed = [RHS ~ (1 - x) / τ])
@test isequal(RHS, @nonamespace fol.RHS)
RHS2 = RHS
@unpack RHS = fol
@test isequal(RHS, RHS2)
#1413 and 1389
@parameters α β
@variables x(t) y(t) z(t)
eqs = [
D(x) ~ 0.1x + 0.9y,
D(y) ~ 0.5x + 0.5y,
z ~ α * x - β * y
]
@named sys = ODESystem(eqs, t, [x, y, z], [α, β])
sys = complete(sys)
@test_throws Any ODEFunction(sys)
eqs = copy(eqs)
eqs[end] = D(D(z)) ~ α * x - β * y
@named sys = ODESystem(eqs, t, [x, y, z], [α, β])
sys = complete(sys)
@test_throws Any ODEFunction(sys)
@testset "Preface tests" begin
using OrdinaryDiffEq
using Symbolics
using DiffEqBase: isinplace
using ModelingToolkit
using SymbolicUtils.Code
using SymbolicUtils: Sym
c = [0]
function f(c, du::AbstractVector{Float64}, u::AbstractVector{Float64}, p, t::Float64)
c .= [c[1] + 1]
du .= randn(length(u))
nothing
end
dummy_identity(x, _) = x
@register_symbolic dummy_identity(x, y)
u0 = ones(5)
p0 = Float64[]
syms = [Symbol(:a, i) for i in 1:5]
syms_p = Symbol[]
@assert isinplace(f, 5)
wf = let buffer = similar(u0), u = similar(u0), p = similar(p0), c = c
t -> (f(c, buffer, u, p, t); buffer)
end
num = hash(f) ⊻ length(u0) ⊻ length(p0)
buffername = Symbol(:fmi_buffer_, num)
D = Differential(t)
us = map(s -> (@variables $s(t))[1], syms)
ps = map(s -> (@variables $s(t))[1], syms_p)
buffer, = @variables $buffername[1:length(u0)]
dummy_var = Sym{Any}(:_) # this is safe because _ cannot be a rvalue in Julia
ss = Iterators.flatten((us, ps))
vv = Iterators.flatten((u0, p0))
defs = Dict{Any, Any}(s => v for (s, v) in zip(ss, vv))
preface = [Assignment(dummy_var, SetArray(true, term(getfield, wf, Meta.quot(:u)), us))
Assignment(dummy_var, SetArray(true, term(getfield, wf, Meta.quot(:p)), ps))
Assignment(buffer, term(wf, t))]
eqs = map(1:length(us)) do i
D(us[i]) ~ dummy_identity(buffer[i], us[i])
end
@named sys = ODESystem(eqs, t, us, ps; defaults = defs, preface = preface)
sys = complete(sys)
prob = ODEProblem(sys, [], (0.0, 1.0))
sol = solve(prob, Euler(); dt = 0.1)
@test c[1] == length(sol)
end
let
x = map(xx -> xx(t), Symbolics.variables(:x, 1:2, T = SymbolicUtils.FnType))
@variables y(t) = 0
@parameters k = 1
eqs = [D(x[1]) ~ x[2]
D(x[2]) ~ -x[1] - 0.5 * x[2] + k
y ~ 0.9 * x[1] + x[2]]
@named sys = ODESystem(eqs, t, vcat(x, [y]), [k], defaults = Dict(x .=> 0))
sys = structural_simplify(sys)
u0 = [0.5, 0]
du0 = 0 .* copy(u0)
prob = DAEProblem(sys, du0, u0, (0, 50))
@test prob.u0 ≈ u0
@test prob.du0 ≈ du0
@test prob.p isa MTKParameters
@test prob.ps[k] ≈ 1
sol = solve(prob, IDA())
@test sol[y] ≈ 0.9 * sol[x[1]] + sol[x[2]]
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
prob = DAEProblem(sys, [D(y) => 0, D(x[1]) => 0, D(x[2]) => 0], Pair[x[1] => 0.5],
(0, 50))
@test prob.u0 ≈ [0.5, 0]
@test prob.du0 ≈ [0, 0]
@test prob.p isa MTKParameters
@test prob.ps[k] ≈ 1
sol = solve(prob, IDA())
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
prob = DAEProblem(sys, [D(y) => 0, D(x[1]) => 0, D(x[2]) => 0], Pair[x[1] => 0.5],
(0, 50), [k => 2])
@test prob.u0 ≈ [0.5, 0]
@test prob.du0 ≈ [0, 0]
@test prob.p isa MTKParameters
@test prob.ps[k] ≈ 2
sol = solve(prob, IDA())
@test isapprox(sol[x[1]][end], 2, atol = 1e-3)
# no initial conditions for D(x[1]) and D(x[2]) provided
@test_throws ModelingToolkit.MissingVariablesError prob=DAEProblem(
sys, Pair[], Pair[], (0, 50))
prob = ODEProblem(sys, Pair[x[1] => 0], (0, 50))
sol = solve(prob, Rosenbrock23())
@test isapprox(sol[x[1]][end], 1, atol = 1e-3)
end
#issue 1475 (mixed numeric type for parameters)
let
@parameters k1 k2::Int
@variables A(t)
eqs = [D(A) ~ -k1 * k2 * A]
@named sys = ODESystem(eqs, t)
sys = complete(sys)
u0map = [A => 1.0]
pmap = (k1 => 1.0, k2 => 1)
tspan = (0.0, 1.0)
prob = ODEProblem(sys, u0map, tspan, pmap; tofloat = false)
@test prob.p isa MTKParameters
@test prob.ps[k1] ≈ 1.0
@test prob.ps[k2] == 1 && prob.ps[k2] isa Int
prob = ODEProblem(sys, u0map, tspan, pmap)
@test vcat(prob.p...) isa Vector{Float64}
pmap = [k1 => 1, k2 => 1]
tspan = (0.0, 1.0)
prob = ODEProblem(sys, u0map, tspan, pmap)
@test eltype(vcat(prob.p...)) === Float64
prob = ODEProblem(sys, u0map, tspan, pmap)
@test vcat(prob.p...) isa Vector{Float64}
# No longer supported, Tuple used instead
# pmap = Pair{Any, Union{Int, Float64}}[k1 => 1, k2 => 1.0]
# tspan = (0.0, 1.0)
# prob = ODEProblem(sys, u0map, tspan, pmap, use_union = true)
# @test eltype(prob.p) === Union{Float64, Int}
end
let
@parameters C L R
@variables q(t) p(t) F(t)
eqs = [D(q) ~ -p / L - F
D(p) ~ q / C
0 ~ q / C - R * F]
@named sys = ODESystem(eqs, t)
@test length(equations(structural_simplify(sys))) == 2
end
let
eq_to_lhs(eq) = eq.lhs - eq.rhs ~ 0
eqs_to_lhs(eqs) = eq_to_lhs.(eqs)
@parameters σ=10 ρ=28 β=8 / 3 sigma rho beta
@variables x(t)=1 y(t)=0 z(t)=0 x2(t)=1 y2(t)=0 z2(t)=0 u(t)[1:3]
eqs = [D(x) ~ σ * (y - x),
D(y) ~ x * (ρ - z) - y,
D(z) ~ x * y - β * z]
eqs2 = [
D(y2) ~ x2 * (rho - z2) - y2,
D(x2) ~ sigma * (y2 - x2),
D(z2) ~ x2 * y2 - beta * z2
]
# array u
eqs3 = [D(u[1]) ~ sigma * (u[2] - u[1]),
D(u[2]) ~ u[1] * (rho - u[3]) - u[2],
D(u[3]) ~ u[1] * u[2] - beta * u[3]]
eqs3 = eqs_to_lhs(eqs3)
eqs4 = [
D(y2) ~ x2 * (rho - z2) - y2,
D(x2) ~ sigma * (y2 - x2),
D(z2) ~ y2 - beta * z2 # missing x2 term
]
@named sys1 = ODESystem(eqs, t)
@named sys2 = ODESystem(eqs2, t)
@named sys3 = ODESystem(eqs3, t)
ssys3 = structural_simplify(sys3)
@named sys4 = ODESystem(eqs4, t)
@test ModelingToolkit.isisomorphic(sys1, sys2)
@test !ModelingToolkit.isisomorphic(sys1, sys3)
@test ModelingToolkit.isisomorphic(sys1, ssys3) # I don't call structural_simplify in isisomorphic
@test !ModelingToolkit.isisomorphic(sys1, sys4)
# 1281
iv2 = only(independent_variables(sys2))
@test isequal(only(independent_variables(convert_system(ODESystem, sys1, iv2))), iv2)
end
let
vars = @variables sP(t) spP(t) spm(t) sph(t)
pars = @parameters a b
eqs = [sP ~ 1
spP ~ sP
spm ~ a
sph ~ b
spm ~ 0
sph ~ a]
@named sys = ODESystem(eqs, t, vars, pars)
@test_throws ModelingToolkit.ExtraEquationsSystemException structural_simplify(sys)
end
# 1561
let
vars = @variables x y
arr = ModelingToolkit.varmap_to_vars([x => 0.0, y => [0.0, 1.0]], vars) #error
sol = Union{Float64, Vector{Float64}}[0.0, [0.0, 1.0]]
@test arr == sol
@test typeof(arr) == typeof(sol)
end
let
u = collect(first(@variables u(t)[1:4]))
Dt = D
eqs = [Differential(t)(u[2]) - 1.1u[1] ~ 0
Differential(t)(u[3]) - 1.1u[2] ~ 0
u[1] ~ 0.0
u[4] ~ 0.0]
ps = []
@named sys = ODESystem(eqs, t, u, ps)
@test_nowarn simpsys = structural_simplify(sys)
sys = structural_simplify(sys)
u0 = ModelingToolkit.missing_variable_defaults(sys)
u0_expected = Pair[s => 0.0 for s in unknowns(sys)]
@test string(u0) == string(u0_expected)
u0 = ModelingToolkit.missing_variable_defaults(sys, [1, 2])
u0_expected = Pair[s => i for (i, s) in enumerate(unknowns(sys))]
@test string(u0) == string(u0_expected)
@test_nowarn ODEProblem(sys, u0, (0, 1))
end
# https://github.com/SciML/ModelingToolkit.jl/issues/1583
let
@parameters k
@variables A(t)
eqs = [D(A) ~ -k * A]
@named osys = ODESystem(eqs, t)
osys = complete(osys)
oprob = ODEProblem(osys, [A => 1.0], (0.0, 10.0), [k => 1.0]; check_length = false)
@test_nowarn sol = solve(oprob, Tsit5())
end
let
function sys1(; name)
vars = @variables x(t)=0.0 dx(t)=0.0
ODESystem([D(x) ~ dx], t, vars, []; name, defaults = [D(x) => x])
end
function sys2(; name)
@named s1 = sys1()
ODESystem(Equation[], t, [], []; systems = [s1], name)
end
s1′ = sys1(; name = :s1)
@named s2 = sys2()
@unpack s1 = s2
@test isequal(s1, s1′)
defs = Dict(s1.dx => 0.0, D(s1.x) => s1.x, s1.x => 0.0)
@test isequal(ModelingToolkit.defaults(s2), defs)
end
# https://github.com/SciML/ModelingToolkit.jl/issues/1705
let
x0 = 0.0
v0 = 1.0
kx = -1.0
kv = -1.0
tf = 10.0
## controller
function pd_ctrl(; name)
@parameters kx kv
@variables u(t) x(t) v(t)
eqs = [u ~ kx * x + kv * v]
ODESystem(eqs, t; name)
end
@named ctrl = pd_ctrl()
## double integrator
function double_int(; name)
@variables u(t) x(t) v(t)
eqs = [D(x) ~ v, D(v) ~ u]
ODESystem(eqs, t; name)
end
@named sys = double_int()
## connections
connections = [sys.u ~ ctrl.u, ctrl.x ~ sys.x, ctrl.v ~ sys.v]
@named connected = ODESystem(connections, t)
@named sys_con = compose(connected, sys, ctrl)
sys_simp = structural_simplify(sys_con)
true_eqs = [D(sys.x) ~ sys.v
D(sys.v) ~ ctrl.kv * sys.v + ctrl.kx * sys.x]
@test isequal(full_equations(sys_simp), true_eqs)
end
let
@variables x(t) = 1
@variables y(t) = 1
@parameters pp = -1
@named sys4 = ODESystem([D(x) ~ -y; D(y) ~ 1 + pp * y + x], t)
sys4s = structural_simplify(sys4)
prob = ODEProblem(sys4s, [x => 1.0, D(x) => 1.0], (0, 1.0))
@test string.(unknowns(prob.f.sys)) == ["x(t)", "y(t)"]
@test string.(parameters(prob.f.sys)) == ["pp"]
@test string.(independent_variables(prob.f.sys)) == ["t"]
end
let
@parameters P(t) Q(t)
∂t = D
eqs = [∂t(Q) ~ 0.2P
∂t(P) ~ -80.0sin(Q)]
@test_throws ArgumentError @named sys = ODESystem(eqs, t)
end
@parameters C L R
@variables q(t) p(t) F(t)
eqs = [D(q) ~ -p / L - F
D(p) ~ q / C
0 ~ q / C - R * F]
testdict = Dict([:name => "test"])
@named sys = ODESystem(eqs, t, metadata = testdict)
@test get_metadata(sys) == testdict
@variables P(t)=NaN Q(t)=NaN
eqs = [D(Q) ~ 1 / sin(P), D(P) ~ log(-cos(Q))]
@named sys = ODESystem(eqs, t, [P, Q], [])
sys = complete(debug_system(sys))
prob = ODEProblem(sys, [], (0.0, 1.0))
@test_throws "log(-cos(Q(t))) errors" prob.f([1, 0], prob.p, 0.0)
@test_throws "/(1, sin(P(t))) output non-finite value" prob.f([0, 2], prob.p, 0.0)
let
@variables x(t) = 1
@variables y(t) = 1
@parameters pp = -1
der = Differential(t)
@named sys4 = ODESystem([der(x) ~ -y; der(y) ~ 1 + pp * y + x], t)
sys4s = structural_simplify(sys4)
prob = ODEProblem(sys4s, [x => 1.0, D(x) => 1.0], (0, 1.0))
@test !isnothing(prob.f.sys)
end
# SYS 1:
vars_sub1 = @variables s1(t)
@named sub = ODESystem(Equation[], t, vars_sub1, [])
vars1 = @variables x1(t)
@named sys1 = ODESystem(Equation[], t, vars1, [], systems = [sub])
@named sys2 = ODESystem(Equation[], t, vars1, [], systems = [sys1, sub])
# SYS 2: Extension to SYS 1
vars_sub2 = @variables s2(t)
@named partial_sub = ODESystem(Equation[], t, vars_sub2, [])
@named sub = extend(partial_sub, sub)
# no warnings for systems without events
new_sys2 = @test_nowarn complete(substitute(sys2, Dict(:sub => sub)))