Bad performance of tearing for large scale models

[Patrick Täuber]

The execution time for the postOptModule tearingSystem is quite bad for large scale models, e.g. from ScalableTestsuite.

The situation has been improved a lot by ​removing the loop check from differentiation.

The current times for tearing for the BreakerNetwork_N_XX models can be seen here:
#3816

The performance should be improved further. I will soon add some more times to compare.

[Patrick Täuber]

Current times of the entire tearing procedure (initDAE + simDAE) for the BreakerNetwork_N_XX models with the different heuristics (default: MC3):

N	MC1	MC2	MC11	MC21	MC12	MC22	MC13	MC23	MC231	MC3	MC4	omcTearing
320	3.864	2.067	3.733	1.9799	3.998	2.0087	3.859	2.0835	1.3303	1.8714	78.88	0.9606
640	27.04	13.378	29.14	12.523	28.43	12.745	29.1	13.685	7.279	10.524	671.9	6.017
1280	231.76	100.517	230.07	91.171	238.9	96.266	227.28	102.66	49.64	74.65	?	39.16

[Patrick Täuber]

Number of tearing variables altogether:

N	MC1	MC2	MC11	MC21	MC12	MC22	MC13	MC23	MC231	MC3	MC4	omcTearing
320	960	960	960	960	960	960	960	960	641	640	960	641
640	1920	1920	1920	1920	1920	1920	1920	1920	1281	1280	1920	1281
1280	3840	3840	3840	3840	3840	3840	3840	3840	2561	2560	?	2561

[Patrick Täuber]

By ​Speed up tearing matching a bit, ​Allow dividing by all globalKnownVars in initDAE and ​Speed up tearing the computation time of tearingSystem could be reduced.

The new times for BreakerNetwork_N_XX are the following:

N	MC1	MC2	MC11	MC21	MC12	MC22	MC13	MC23	MC231	MC3	MC4	omcTearing
320	0.5563	0.4898	0.5699	0.5022	0.5598	0.6282	0.5713	0.522	0.6635	0.6442	1.9331	0.8897
640	2.234	1.9099	2.347	2.019	2.347	2.047	2.384	2.111	2.724	2.612	7.632	5.897
1280	8.662	7.252	9.045	7.789	9.744	8.157	9.162	8.36	11.54	10.278	32.69	38.74

So this model now scales with O(n²).

[Patrick Täuber]

Here are some more times for a distribution model (DistributionSystemLinear_N_XX_M_XX):

Before:

	MC1	MC2	MC11	MC21	MC12	MC22	MC13	MC23	MC231	MC3	MC4	omcTearing
N_14_M_14	3.943	0.957	3.979	0.8367	4.084	0.9617	3.997	1.1681	1.7441	1.5703		2.2
N_20_M_20	29.84	5.793	28.88	4.247	29.02	4.969	29	6.216	9.914	8.989		15.553
N_28_M_28	195.77	37.4	199.51	23.54	200.92	24.8	194.64	39.39	67.4	55.91		113.01

After:

	MC1	MC2	MC11	MC21	MC12	MC22	MC13	MC23	MC231	MC3	MC4	omcTearing
N_14_M_14	0.671	0.5259	0.676	0.5373	0.74	0.6321	0.7345	0.7025	0.7934	0.612	2.318	2.099
N_20_M_20	2.092	1.9841	2.122	1.97	2.359	2.206	2.866	2.314	2.934	2.345	9.44	15.241
N_28_M_28	7.261	6.662	7.555	6.728	9.004	8.425	9.213	8.319	10.931	8.695	36.24	111.11