[wip] Overload operator application to correctly apply operators with nonlinear behavior

[vpuri3]

Close #159. Detailed discussion in issue.

[codecov]

Codecov Report

Merging #166 (5affa9e) into master (9baa715) will increase coverage by 0.45%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master     #166      +/-   ##
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+ Coverage   67.40%   67.86%   +0.45%     
==========================================
  Files          10       10              
  Lines        1267     1282      +15     
==========================================
+ Hits          854      870      +16     
+ Misses        413      412       -1     

Impacted Files	Coverage Δ
src/basic.jl	73.95% <100.00%> (+1.32%)	⬆️

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[gaurav-arya]

I thought the conclusion was that this is not needed? If one really wanted to make a nonlinear op a SciMLOperator, then it should still do nothing on update_coefficients and do all its work in op(u,p,t). This interlacing of * and update_coefficients doesn't seem right?

(Perhaps I'm just not familiar with the use case here)

[gaurav-arya]

And in this design, if you were to write A * A * B, A would be updated two different times with different u's. So I still maintain that u should always be the same in update_coefficients

[vpuri3]

Fixed the name to reflect what is happening here. We are overloading L(u, p, t), L(du, u, p, t). update_coeffs isn't touched.

[vpuri3]

I have limited bandwidth during the week. So I'll get to this over the weekend or on some evening.

[vpuri3]

TODO

• preserve order of operations in scalaroperator constructor: ie A * λ vs λ * A and apply updatecoeffs accordingly. Also need to write L(u,p,t) method for ComposedScalarOperator.
• add L(u, p, t) for InvertedOperator as well.