Remove Dict{Symbol, Any} for type stability in FunctionOperator

[albertomercurio]

The current implementation of FunctionOperator requires a Dict{Symbol,Any} to handle the keyword arguments. This leads to type instabilities and performance decreases, as in the following simple code:

using LinearAlgebra
using BenchmarkTools
using SciMLOperators

T = ComplexF64
N = 10

u = rand(T, N)
du = similar(u)
p = (A=rand(T, N, N),)

op = FunctionOperator((du, u, p, t) -> mul!(du, p.A, u), u, p = p, T=T, isinplace=Val(true), outofplace=Val(true), has_mul5=Val(true), isconstant=true)

op(du, u, p, 0.1)

@benchmark $op($du, $u, $p, 0.1)

master branch

BenchmarkTools.Trial: 10000 samples with 53 evaluations.
 Range (min … max):  864.434 ns … 104.262 μs  ┊ GC (min … max): 0.00% … 98.52%
 Time  (median):     947.340 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   996.750 ns ±   1.294 μs  ┊ GC (mean ± σ):  2.57% ±  2.17%

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  864 ns           Histogram: frequency by time         1.34 μs <

 Memory estimate: 560 bytes, allocs estimate: 7.

This PR branch

BenchmarkTools.Trial: 10000 samples with 989 evaluations.
 Range (min … max):  46.024 ns … 64.056 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     48.916 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   48.858 ns ±  1.040 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

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  ▇██████████████████████████████████████████████████████████ █
  46 ns        Histogram: log(frequency) by time      50.9 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

---

To manage to fix this issue, I used NamedTuple instead of Dict{Symbol, Any}. For this reason, the additional kwargs are required when accepted_kwargs is provided, in order to initialize the types inside the NamedTuple. In principle, the accepted_kwargs can be directly obtained from kwargs keys, but I left it for consistency with the other functions.

Furthermore, I've extended the methods of the get_filtered_kwargs, also supporting Val types for accepted_kwargs. In this way, the filtering is performed at compile time, otherwise the type of the NamedTuple cannot be inferred. Thus, all the other functions supporting accepted_kwargs would also support Val types, improving performance.

[albertomercurio]

I've also made the mul! function for the IdentityOperator, because the following example was allocating

T = Float64
N = 10

u = rand(T, N)
du = similar(u)

A = MatrixOperator(rand(T, N, N))

op = T(0.1) * A + T(0.2) * IdentityOperator(N)
# op = T(0.2) * IdentityOperator(N)
# op = T(0.1) * A

@benchmark mul!($du, $op, $u)

Master branch

BenchmarkTools.Trial: 10000 samples with 982 evaluations.
 Range (min … max):  57.484 ns …  14.506 μs  ┊ GC (min … max): 0.00% … 99.22%
 Time  (median):     67.768 ns               ┊ GC (median):    0.00%
 Time  (mean ± σ):   79.566 ns ± 198.549 ns  ┊ GC (mean ± σ):  6.26% ±  2.77%

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  ▂▁▂▂▃▃▅▇███████▆▄▃▃▂▂▂▂▃▂▂▃▄▅▅▄▃▃▂▂▂▂▂▃▃▄▄▄▄▅▇██▇▄▃▃▂▂▂▂▂▂▂▂ ▃
  57.5 ns         Histogram: frequency by time          101 ns <

 Memory estimate: 112 bytes, allocs estimate: 3.

This PR branch

BenchmarkTools.Trial: 10000 samples with 994 evaluations.
 Range (min … max):  31.203 ns … 42.741 ns  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     33.894 ns              ┊ GC (median):    0.00%
 Time  (mean ± σ):   33.676 ns ±  0.924 ns  ┊ GC (mean ± σ):  0.00% ± 0.00%

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  31.2 ns         Histogram: frequency by time        35.8 ns <

 Memory estimate: 0 bytes, allocs estimate: 0.

[ChrisRackauckas]

this repo needs quite a bit of work in order to v1.0. Seems like you're starting to get into it. If you're interested in helping, maybe we can find a time to chat. The core issue is that a lot of the operators do f(u,p,t)*u when it needs to generally be f(u,p,t)*v

[albertomercurio]

Yes, I'm starting to use it due to its dependence of my package QuantumToolbox.jl. I don't think I have so much time for directly helping this repo, but for sure I will make other PRs when I will need it. Btw, I'm happy to have a chat and discuss about this.