Basic DAE Initialization

[kanav99]

https://cse.cs.ucsb.edu/sites/default/files/publications/SCE001495.pdf

Using NLsolve right now, I will try to remove that out

[ChrisRackauckas]

Needs a test.

[coveralls]

Coverage increased (+0.008%) to 77.406% when pulling 0398974 on daeinit into e96a97f on master.

[codecov]

Codecov Report

Merging #1037 into master will decrease coverage by 18.84%.
The diff coverage is 53.44%.

@@             Coverage Diff             @@
##           master    #1037       +/-   ##
===========================================
- Coverage   76.78%   57.93%   -18.85%     
===========================================
  Files          94       95        +1     
  Lines       30571    30252      -319     
===========================================
- Hits        23475    17528     -5947     
- Misses       7096    12724     +5628

Impacted Files	Coverage Δ
src/OrdinaryDiffEq.jl	100% <ø> (ø)	⬆️
src/caches/dae_caches.jl	86.2% <100%> (ø)	⬆️
src/solve.jl	89.24% <100%> (-2.64%)	⬇️
src/initialize_dae.jl	43.75% <43.75%> (ø)
src/tableaus/rkc_tableaus.jl	0% <0%> (-100%)	⬇️
src/caches/low_storage_rk_caches.jl	12.27% <0%> (-85.79%)	⬇️
src/caches/ssprk_caches.jl	13.38% <0%> (-81.4%)	⬇️
src/caches/rkc_caches.jl	22.5% <0%> (-74.28%)	⬇️
src/perform_step/rkc_perform_step.jl	15.2% <0%> (-70.4%)	⬇️
src/perform_step/low_storage_rk_perform_step.jl	23.79% <0%> (-68.47%)	⬇️
... and 40 more

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[kanav99]

Added some basic test. There is a failing test (non index 1 DAE), that means we know whats missing. I guess we need an interface to define what all is known to the user, and what all the user wants us to initialize

[ChrisRackauckas]

I guess we need an interface to define what all is known to the user, and what all the user wants us to initialize

That can come from the initialization method choice?

[ChrisRackauckas]

evaluate to see if initialization is required first? Or do that in initialize?