Command line parameters parsing in Test, Gaussian elimination benchmarks.

[Federerer]

Hi. I've tested how memory layout of arrays affects performance of the Gaussian elimination method in the inner loop of the simulation lambda and here are the results:

BenchmarkDotNet=v0.13.1, OS=Windows 10.0.19043.1110 (21H1/May2021Update)
Intel Core i7-8550U CPU 1.80GHz (Kaby Lake R), 1 CPU, 8 logical and 4 physical cores
.NET SDK=6.0.100-preview.6.21355.2
  [Host]     : .NET 6.0.0 (6.0.21.35212), X64 RyuJIT
  Job-WMMCQC : .NET 6.0.0 (6.0.21.35212), X64 RyuJIT

InvocationCount=1  UnrollFactor=1  

Method	M	Mean	Error	StdDev	Ratio	RatioSD	CacheMisses/Op	BranchMispredictions/Op	BranchInstructions/Op	Gen 0	Allocated
CompactColumnMajor	12	168.1 ms	3.26 ms	3.62 ms	1.09	0.03	5,895,782	3,725,107	292,493,722	-	336 B
CompactRowMajor	12	170.8 ms	3.35 ms	4.47 ms	1.10	0.04	5,845,524	3,755,540	268,238,848	-	336 B
ArrayOfArrays	12	155.1 ms	3.09 ms	3.68 ms	1.00	0.00	6,609,769	3,571,795	257,758,787	-	336 B
ArrayOfArraysVectorized	12	135.8 ms	2.64 ms	4.10 ms	0.88	0.04	6,657,404	2,985,282	198,694,853	-	336 B
MathNetSolve	12	312.0 ms	6.08 ms	9.46 ms	2.02	0.09	10,237,689	4,685,561	467,613,872	49000.0000	210,400,336 B

I've checked also how well perform MathNet's LU factorization, and it's significantly slower. It might be superior in cases where A matrix is constant, which is unfortunately not our case. Looking at the results I've found, that only vectorized method performs about 10% better than current implementation. I would be happy to se how it performs on a different machine, because I'm currently testing it on my laptop and thermal throttling might skew the results a little bit ;) Sidenote: messing with the equation-order in MNA, seems to have bigger influence on the performance, and sometimes stability of the solution. I'm suspecting, that it might be related to some cache-misses, but this requires more investigation ;)

I've also managed to fix this little TODO: // TODO: Make these command line arguments. using fresh beta version of System.CommandLine package ;)

[Federerer]

Really nice work, thanks for this! I have a few suggestions on the benchmarks that might affect the results.

For one of the benchmarks, it would be nice to actually try calling

https://github.com/dsharlet/LiveSPICE/blob/0d59564ea4ab6dc64c0e7e9d16dadb2d050e4ae4/Circuit/Simulation/Simulation.cs#L453 so we see how the currently used method compares.

It's the one called 'ArrayOfArrays' with the ratio of 1.00 😉

[dsharlet]

Right, I understand it's the same implementation strategy, but it's hard to be sure it's actually the same :) (now and in the future).

[Federerer]

Right, I understand it's the same implementation strategy, but it's hard to be sure it's actually the same :) (now and in the future).

I think I've got it 😄 I've added current implementation.

BenchmarkDotNet=v0.13.1, OS=Windows 10.0.19043.1288 (21H1/May2021Update)
Intel Core i7-8550U CPU 1.80GHz (Kaby Lake R), 1 CPU, 8 logical and 4 physical cores
.NET SDK=6.0.100-rc.1.21458.32
  [Host]     : .NET 5.0.10 (5.0.1021.41214), X64 RyuJIT
  Job-IUEOEC : .NET 5.0.10 (5.0.1021.41214), X64 RyuJIT

InvocationCount=1  UnrollFactor=1  

Method	M	Mean	Error	StdDev	Ratio	RatioSD	BranchInstructions/Op	CacheMisses/Op	BranchMispredictions/Op	Gen 0	Allocated
CompactColumnMajor	12	161.7 ms	2.47 ms	2.19 ms	1.18	0.03	292,431,462	5,869,841	3,769,003	-	-
CompactRowMajor	12	147.2 ms	2.63 ms	2.33 ms	1.08	0.03	267,941,751	5,904,725	3,291,887	-	-
Current	12	135.6 ms	2.68 ms	3.58 ms	1.00	0.00	257,833,697	6,623,519	3,595,141	-	-
ArrayOfArrays	12	142.9 ms	2.80 ms	4.59 ms	1.06	0.04	257,580,038	6,666,079	3,448,328	-	-
ArrayOfArraysVectorized	12	116.2 ms	2.31 ms	3.09 ms	0.86	0.03	205,933,773	6,618,399	3,122,586	-	-
MathNetSolve	12	283.7 ms	5.58 ms	9.01 ms	2.08	0.09	466,561,477	9,956,233	4,458,830	49000.0000	210,400,000 B