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Mujoco_WASM/model/flex/asset/bag.obj
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Alessio 55d13aec5f Replace the flex metric factorization with a block preconditioner 
Every step, the flex block of the implicit effective metric M + K was
factorized by sparse Cholesky, because K depends on the configuration. On
model/flex/bag.xml, added here, that is roughly half the step, against a
comparable share for the constraint solve it exists to accelerate.

Keep only the metric's per-vertex 3x3 diagonal blocks, prefactored. Neither
consumer needs the exact inverse: the CG constraint solver only wants a
preconditioner, and qacc_smooth can come from an iterative solve using those
blocks. They are O(n) to build and to apply, but weaker, so CG runs about twice
the iterations and qacc_smooth becomes an iteration rather than a direct solve.
Net, the bag model steps roughly twice as fast.

The preconditioner, by metric state. Inactive, meaning no flex elasticity or an
explicit integrator: M^-1, unchanged. Bending only (nefmK == 0): M^-1 plus the
exact constant bending factor from mj_setConst on the dofs it covers,
unchanged; that factor is built at model compile time and costs nothing per
step. Per-step stiffness: M^-1 plus the 3x3 blocks, where before it was a
per-step sparse Cholesky, or, when M couples across the flex block, an inner
PCG of up to 50 iterations run once per outer CG iteration.

Only models carrying per-step stretch stiffness change in wall-clock. Both
ponchos hold their timing and take slightly fewer CG iterations than before,
because the preconditioner is now symmetric: it applies M^-1 and the covered
blocks to disjoint sets of dofs, where previously the two overlapped and the
operator was not symmetric, which PCG requires.

mjd_effSolve is the accurate solve of (M + K)x = b; what used to carry that
name only preconditions and is now mjd_effPrec. Its CG guarded the division by
pAp with mjMINVAL, an absolute floor on a quantity that scales with the square
of the right-hand side, so a small b aborted the solve while the curvature was
healthy: four flex models were quietly left short of tolerance. For an SPD
metric the guard is positivity, and with that the same solves converge. The qacc_smooth call site in
mj_fwdAcceleration is textually unchanged but now reaches the iterative solve,
which converges on opt.tolerance rather than a hardcoded threshold, floored in
mjUSESINGLE builds where the squared target is unreachable in float. Reaching
the iteration cap names the ill-conditioned flex stiffness and then reports it
through mjWARN_INERTIA, rather than returning an under-converged result.
Covered dofs are located by walking the covered rows of the stiffness matrix,
as they need not be 3-aligned from dof 0: any joint declared before a flexcomp
shifts them.

mjData.efm_L_rownnz, efm_L_rowadr and efm_L_colind described the sparsity of
the deleted factorization and are removed: left NULL with nonzero mjxmacro
extents they made the Python bindings hand back uninitialized arrays.
efm_active loses the value 2 for the same reason, nothing selects a solve path
on preconditioner exactness any more. Both are recorded under breaking changes.

model/flex/bag.xml is added because no shipped model carried per-step stretch
stiffness. The ponchos are bending-only and trampoline.xml uses an explicit
integrator, so the metric never activates there. It is excluded from
WriteReadCompareTest: stretch stiffness amplifies rest geometry that XML rounds
on save.
2026-07-29 14:36:15 +01:00

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# Blender 4.3.2
# www.blender.org
o Bag_latest
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s 1
f 50/1/50 295/2/295 824/3/820 464/4/464
f 295/2/295 63/5/63 466/6/466 824/3/820
f 824/3/820 466/6/466 149/7/149 469/8/469
f 464/4/464 824/3/820 469/8/469 148/9/148
f 63/5/63 294/10/294 825/11/821 466/6/466
f 294/10/294 36/12/36 436/13/436 825/11/821
f 825/11/821 436/13/436 134/14/134 467/15/467
f 466/6/466 825/11/821 467/15/467 149/7/149
f 149/16/149 467/17/467 826/18/822 468/19/468
f 467/17/467 134/20/134 437/21/437 826/18/822
f 826/18/822 437/21/437 17/22/17 377/23/377
f 468/19/468 826/18/822 377/23/377 104/24/104
f 148/25/148 469/26/469 827/27/823 465/28/465
f 469/26/469 149/16/149 468/19/468 827/27/823
f 827/27/823 468/19/468 104/24/104 376/29/376
f 465/28/465 827/27/823 376/29/376 8/30/8
f 2/31/2 281/32/281 828/33/824 462/34/462
f 281/32/281 56/35/56 470/36/470 828/33/824
f 828/33/824 470/36/470 150/37/150 473/38/473
f 462/34/462 828/33/824 473/38/473 147/39/147
f 56/35/56 280/40/280 829/41/825 470/36/470
f 280/40/280 46/42/46 439/43/439 829/41/825
f 829/41/825 439/43/439 135/44/135 471/45/471
f 470/36/470 829/41/825 471/45/471 150/37/150
f 150/37/150 471/45/471 830/46/826 472/47/472
f 471/45/471 135/44/135 438/48/438 830/46/826
f 830/46/826 438/48/438 37/49/37 427/50/427
f 472/47/472 830/46/826 427/50/427 129/51/129
f 147/39/147 473/38/473 831/52/827 463/53/463
f 473/38/473 150/37/150 472/47/472 831/52/827
f 831/52/827 472/47/472 129/51/129 426/54/426
f 463/53/463 831/52/827 426/54/426 52/55/52
f 38/56/38 423/57/423 832/58/828 425/59/425
f 423/57/423 127/60/127 474/61/474 832/58/828
f 832/58/828 474/61/474 151/62/151 477/63/477
f 425/59/425 832/58/828 477/63/477 128/64/128
f 127/60/127 422/65/422 833/66/829 474/61/474
f 422/65/422 51/67/51 442/68/442 833/66/829
f 833/66/829 442/68/442 137/69/137 475/70/475
f 474/61/474 833/66/829 475/70/475 151/62/151
f 151/62/151 475/70/475 834/71/830 476/72/476
f 475/70/475 137/69/137 443/73/443 834/71/830
f 834/71/830 443/73/443 52/55/52 426/54/426
f 476/72/476 834/71/830 426/54/426 129/51/129
f 128/64/128 477/63/477 835/74/831 424/75/424
f 477/63/477 151/62/151 476/72/476 835/74/831
f 835/74/831 476/72/476 129/51/129 427/50/427
f 424/75/424 835/74/831 427/50/427 37/49/37
f 6/76/6 293/77/293 836/78/832 460/79/460
f 293/77/293 62/80/62 478/81/478 836/78/832
f 836/78/832 478/81/478 152/82/152 481/83/481
f 460/79/460 836/78/832 481/83/481 146/84/146
f 62/80/62 292/85/292 837/86/833 478/81/478
f 292/85/292 16/87/16 434/88/434 837/86/833
f 837/86/833 434/88/434 133/89/133 479/90/479
f 478/81/478 837/86/833 479/90/479 152/82/152
f 152/82/152 479/90/479 838/91/834 480/92/480
f 479/90/479 133/89/133 435/93/435 838/91/834
f 838/91/834 435/93/435 27/94/27 395/95/395
f 480/92/480 838/91/834 395/95/395 113/96/113
f 146/84/146 481/83/481 839/97/835 461/98/461
f 481/83/481 152/82/152 480/92/480 839/97/835
f 839/97/835 480/92/480 113/96/113 394/99/394
f 461/98/461 839/97/835 394/99/394 3/100/3
f 5/101/5 289/102/289 840/103/836 458/104/458
f 289/102/289 60/105/60 482/106/482 840/103/836
f 840/103/836 482/106/482 153/107/153 485/108/485
f 458/104/458 840/103/836 485/108/485 145/109/145
f 60/105/60 288/110/288 841/111/837 482/106/482
f 288/110/288 26/112/26 441/113/441 841/111/837
f 841/111/837 441/113/441 136/114/136 483/115/483
f 482/106/482 841/111/837 483/115/483 153/107/153
f 153/116/153 483/117/483 842/118/838 484/119/484
f 483/117/483 136/120/136 440/121/440 842/118/838
f 842/118/838 440/121/440 47/122/47 411/123/411
f 484/119/484 842/118/838 411/123/411 121/124/121
f 145/125/145 485/126/485 843/127/839 459/128/459
f 485/126/485 153/116/153 484/119/484 843/127/839
f 843/127/839 484/119/484 121/124/121 410/129/410
f 459/128/459 843/127/839 410/129/410 49/130/49
f 9/131/9 300/132/300 844/133/840 299/134/299
f 300/132/300 66/135/66 486/136/486 844/133/840
f 844/133/840 486/136/486 154/137/154 489/138/489
f 299/134/299 844/133/840 489/138/489 65/139/65
f 66/135/66 301/140/301 845/141/841 486/136/486
f 301/140/301 12/142/12 302/143/302 845/141/841
f 845/141/841 302/143/302 67/144/67 487/145/487
f 486/136/486 845/141/841 487/145/487 154/137/154
f 154/137/154 487/145/487 846/146/842 488/147/488
f 487/145/487 67/144/67 303/148/303 846/146/842
f 846/146/842 303/148/303 13/149/13 304/150/304
f 488/147/488 846/146/842 304/150/304 68/151/68
f 65/139/65 489/138/489 847/152/843 298/153/298
f 489/138/489 154/137/154 488/147/488 847/152/843
f 847/152/843 488/147/488 68/151/68 305/154/305
f 298/153/298 847/152/843 305/154/305 15/155/15
f 10/156/10 308/157/308 848/158/844 307/159/307
f 308/157/308 70/160/70 490/161/490 848/158/844
f 848/158/844 490/161/490 155/162/155 493/163/493
f 307/159/307 848/158/844 493/163/493 69/164/69
f 70/160/70 309/165/309 849/166/845 490/161/490
f 309/165/309 14/167/14 310/168/310 849/166/845
f 849/166/845 310/168/310 71/169/71 491/170/491
f 490/161/490 849/166/845 491/170/491 155/162/155
f 155/162/155 491/170/491 850/171/846 492/172/492
f 491/170/491 71/169/71 311/173/311 850/171/846
f 850/171/846 311/173/311 13/149/13 303/148/303
f 492/172/492 850/171/846 303/148/303 67/144/67
f 69/164/69 493/163/493 851/174/847 306/175/306
f 493/163/493 155/162/155 492/172/492 851/174/847
f 851/174/847 492/172/492 67/144/67 302/143/302
f 306/175/306 851/174/847 302/143/302 12/142/12
f 11/176/11 314/177/314 852/178/848 313/179/313
f 314/177/314 73/180/73 494/181/494 852/178/848
f 852/178/848 494/181/494 156/182/156 497/183/497
f 313/179/313 852/178/848 497/183/497 72/184/72
f 73/180/73 315/185/315 853/186/849 494/181/494
f 315/185/315 15/155/15 305/154/305 853/186/849
f 853/186/849 305/154/305 68/151/68 495/187/495
f 494/181/494 853/186/849 495/187/495 156/182/156
f 156/182/156 495/187/495 854/188/850 496/189/496
f 495/187/495 68/151/68 304/150/304 854/188/850
f 854/188/850 304/150/304 13/149/13 311/173/311
f 496/189/496 854/188/850 311/173/311 71/169/71
f 72/184/72 497/183/497 855/190/851 312/191/312
f 497/183/497 156/182/156 496/189/496 855/190/851
f 855/190/851 496/189/496 71/169/71 310/168/310
f 312/191/312 855/190/851 310/168/310 14/167/14
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f 786/1181/782 211/783/211 656/802/656 1085/1183/1081
f 1085/1183/1081 656/802/656 204/801/204 787/1185/783
f 408/1184/408 1085/1183/1081 787/1185/783 47/1186/47
f 47/1186/47 787/1185/783 1086/1187/1082 440/1188/440
f 787/1185/783 204/801/204 668/841/668 1086/1187/1082
f 1086/1187/1082 668/841/668 217/840/217 788/1189/784
f 440/1188/440 1086/1187/1082 788/1189/784 136/1190/136
f 136/1191/136 788/1192/784 1087/1193/1083 441/1194/441
f 788/1192/784 217/811/217 669/808/669 1087/1193/1083
f 1087/1193/1083 669/808/669 197/807/197 789/1195/785
f 441/1194/441 1087/1193/1083 789/1195/785 26/1196/26
f 26/1196/26 789/1195/785 1088/1197/1084 387/1198/387
f 789/1195/785 197/807/197 651/947/651 1088/1197/1084
f 1088/1197/1084 651/947/651 208/946/208 790/1199/786
f 387/1198/387 1088/1197/1084 790/1199/786 109/1200/109
f 109/1200/109 790/1199/786 1089/1201/1085 386/1202/386
f 790/1199/786 208/946/208 650/1133/650 1089/1201/1085
f 1089/1201/1085 650/1133/650 199/879/199 791/1203/787
f 386/1202/386 1089/1201/1085 791/1203/787 28/1204/28
f 28/1204/28 791/1203/787 1090/1205/1086 393/1206/393
f 791/1203/787 199/879/199 653/876/653 1090/1205/1086
f 1090/1205/1086 653/876/653 209/875/209 792/1207/788
f 393/1206/393 1090/1205/1086 792/1207/788 112/1208/112
f 112/1208/112 792/1207/788 1091/1209/1087 392/1210/392
f 792/1207/788 209/875/209 652/908/652 1091/1209/1087
f 1091/1209/1087 652/908/652 198/907/198 793/1211/789
f 392/1210/392 1091/1209/1087 793/1211/789 27/1212/27
f 27/1212/27 793/1211/789 1092/1213/1088 435/1214/435
f 793/1211/789 198/907/198 663/1117/663 1092/1213/1088
f 1092/1213/1088 663/1117/663 214/868/214 794/1215/790
f 435/1214/435 1092/1213/1088 794/1215/790 133/1216/133
f 133/1216/133 794/1215/790 1093/1217/1089 434/1218/434
f 794/1215/790 214/868/214 662/865/662 1093/1217/1089
f 1093/1217/1089 662/865/662 194/864/194 795/1219/791
f 434/1218/434 1093/1217/1089 795/1219/791 16/1220/16
f 16/1220/16 795/1219/791 1094/1221/1090 383/1222/383
f 795/1219/791 194/864/194 649/1122/649 1094/1221/1090
f 1094/1221/1090 649/1122/649 207/1111/207 796/1223/792
f 383/1222/383 1094/1221/1090 796/1223/792 107/1224/107
f 107/1224/107 796/1223/792 1095/1225/1091 382/1226/382
f 796/1223/792 207/1111/207 648/1109/648 1095/1225/1091
f 1095/1225/1091 648/1109/648 196/1099/196 797/1227/793
f 382/1226/382 1095/1225/1091 797/1227/793 18/1228/18
f 18/1228/18 797/1227/793 1096/1229/1092 379/1230/379
f 797/1227/793 196/1099/196 647/1097/647 1096/1229/1092
f 1096/1229/1092 647/1097/647 206/1077/206 798/1231/794
f 379/1230/379 1096/1229/1092 798/1231/794 105/1232/105
f 105/1232/105 798/1231/794 1097/1233/1093 378/1234/378
f 798/1231/794 206/1077/206 646/1075/646 1097/1233/1093
f 1097/1233/1093 646/1075/646 195/923/195 799/1235/795
f 378/1234/378 1097/1233/1093 799/1235/795 17/1236/17
f 17/1236/17 799/1235/795 1098/1237/1094 437/1238/437
f 799/1235/795 195/923/195 665/920/665 1098/1237/1094
f 1098/1237/1094 665/920/665 215/919/215 776/1142/772
f 437/1238/437 1098/1237/1094 776/1142/772 134/1141/134
f 133/992/133 434/1239/434 1099/1240/1095 812/993/808
f 16/937/16 686/940/686 1099/1240/1095 434/1239/434
f 222/945/222 813/1114/809 1099/1240/1095 686/940/686
f 262/1113/262 800/1241/796 1099/1240/1095 813/1114/809
f 264/994/264 812/993/808 1099/1240/1095 800/1241/796
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