add `tag` kwarg to JacVec, HesVec, HesVecGrad

[vpuri3]

This will fix errors in https://github.com/SciML/OrdinaryDiffEq.jl/pull/1917 by allowing OrdinaryDiffEq to pass the right ForwardDiff.tag to JacVec.

[codecov[bot]]

Codecov Report

Patch coverage: 100.00% and no project coverage change.

Comparison is base (c831947) 84.76% compared to head (e77e83f) 84.76%.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #241 +/- ## ======================================= Coverage 84.76% 84.76% ======================================= Files 14 14 Lines 952 952 ======================================= Hits 807 807 Misses 145 145 ``` | [Impacted Files](https://app.codecov.io/gh/JuliaDiff/SparseDiffTools.jl/pull/241?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaDiff) | Coverage Δ | | |---|---|---| | [ext/SparseDiffToolsZygote.jl](https://app.codecov.io/gh/JuliaDiff/SparseDiffTools.jl/pull/241?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaDiff#diff-ZXh0L1NwYXJzZURpZmZUb29sc1p5Z290ZS5qbA==) | `100.00% <100.00%> (ø)` | | | [src/differentiation/jaches\_products.jl](https://app.codecov.io/gh/JuliaDiff/SparseDiffTools.jl/pull/241?src=pr&el=tree&utm_medium=referral&utm_source=github&utm_content=comment&utm_campaign=pr+comments&utm_term=JuliaDiff#diff-c3JjL2RpZmZlcmVudGlhdGlvbi9qYWNoZXNfcHJvZHVjdHMuamw=) | `95.37% <100.00%> (ø)` | |

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[vpuri3]

@ChrisRackauckas

[vpuri3]

@Vaibhavdixit02 , @YingboMa can you review and merge this? It's blocking other PRs

[ChrisRackauckas]

This needs a test so it doesn't regress again.

[vpuri3]

added some tests here. After the ODE PR is merged, we can add ODE tests in this repo, as well as downstream tests to OrdinaryDiffEq in SparseDiffTools.

[vpuri3]

@ChrisRackauckas take a look. more comprehensive tests can be added only after ODE.jl supports sparsediff v2. Here's my todo list for sparsedifftools from https://github.com/SciML/SciMLOperators.jl/issues/142

SparseDiffTools.jl

• [ ] Add OrdinaryDiffEq.jl - InterfaceII to downstream tests. Same for SciMLSensitivity.jl when we get done with that.
• [ ] Add JacVec ODE tests
• [x] autodiff shouldn't be boolean logic but multi-valued logic through types choices, like AutoZygote(). change the autodiff choices to be non-boolean logic and Zygote an extension package in order to release.
• [x] release v2 Release v2 JuliaDiff/SparseDiffTools.jl#230

# JacVec OrdinaryDiffEq itnegration test

function lorenz(du, u, p, t)
    du[1] = 10.0(u[2] - u[1])
    du[2] = u[1] * (28.0 - u[3]) - u[2]
    du[3] = u[1] * u[2] - (8 / 3) * u[3]
end
u0 = [1.0; 0.0; 0.0]
tspan = (0.0, 100.0)

ff1 = ODEFunction(lorenz, jac_prototype = JacVec(lorenz, u0))
ff2 = ODEFunction(lorenz, jac_prototype = JacVec(lorenz, u0, autodiff=false))

for ff in [ff1, ff2]
    prob = ODEProblem(ff, u0, tspan)
    @test solve(prob, TRBDF2()).retcode == :Success
    @test solve(prob, TRBDF2(linsolve = KrylovJL_GMRES())).retcode == :Success
    @test solve(prob, Exprb32()).retcode == :Success
    @test solve(prob, Rosenbrock23()).retcode == :Success
    @test solve(prob, Rosenbrock23(linsolve = KrylovJL_GMRES())).retcode == :Success
end