Create SCCNonlinearSolve

[ChrisRackauckas]

Requires SciML/SciMLBase.jl#861

using NonlinearSolve, SCCNonlinearSolve

function f(du,u,p)
	du[1] = cos(u[2]) - u[1]
	du[2] = sin(u[1] + u[2]) + u[2]
	du[3] = 2u[4] + u[3] + 1.0
	du[4] = u[5]^2 + u[4]
	du[5] = u[3]^2 + u[5]
	du[6] = u[1] + u[2] + u[3] + u[4] + u[5]    + 2.0u[6] + 2.5u[7] + 1.5u[8]
	du[7] = u[1] + u[2] + u[3] + 2.0u[4] + u[5] + 4.0u[6] - 1.5u[7] + 1.5u[8]
	du[8] = u[1] + 2.0u[2] + 3.0u[3] + 5.0u[4] + 6.0u[5] + u[6] - u[7] - u[8]
end
prob = NonlinearProblem(f, zeros(8))
sol = solve(prob)

u0 = zeros(2)
p = zeros(3)

function f1(du,u,p)
	du[1] = cos(u[2]) - u[1]
	du[2] = sin(u[1] + u[2]) + u[2]
end
explicitfun1(p,sols) = nothing
prob1 = NonlinearProblem(NonlinearFunction{true, SciMLBase.NoSpecialize}(f1), zeros(2), p)
sol1 = solve(prob1, NewtonRaphson())

function f2(du,u,p)
	du[1] = 2u[2] + u[1] + 1.0
	du[2] = u[3]^2 + u[2]
	du[3] = u[1]^2 + u[3]
end
explicitfun2(p,sols) = nothing
prob2 = NonlinearProblem(NonlinearFunction{true, SciMLBase.NoSpecialize}(f2), zeros(3), p)
sol2 = solve(prob2, NewtonRaphson())

function f3(du,u,p)
	du[1] = p[1] + 2.0u[1] + 2.5u[2] + 1.5u[3]
	du[2] = p[2] + 4.0u[1] - 1.5u[2] + 1.5u[3]
	du[3] = p[3] + + u[1] - u[2] - u[3]
end
prob3 = NonlinearProblem(NonlinearFunction{true, SciMLBase.NoSpecialize}(f3), zeros(3), p)
function explicitfun3(p,sols)
	p[1] = sols[1][1] + sols[1][2] + sols[2][1] + sols[2][2] + sols[2][3]
	p[2] = sols[1][1] + sols[1][2] + sols[2][1] + 2.0sols[2][2] + sols[2][3]
	p[3] = sols[1][1] + 2.0sols[1][2] + 3.0sols[2][1] + 5.0sols[2][2] + 6.0sols[2][3]
end
explicitfun3(p,[sol1,sol2])
sol3 = solve(prob3, NewtonRaphson())
manualscc = [sol1; sol2; sol3]

sccprob = SciMLBase.SCCNonlinearProblem([prob1,prob2,prob3], SciMLBase.Void{Any}.([explicitfun1,explicitfun2,explicitfun3]))
scc_sol = solve(sccprob, NewtonRaphson())
sol ≈ manualscc ≈ scc_sol

Right now this just handles solve. I want to get a first version in, then the todos for next steps are:

• init
• step!
• Put appropriate trait calculations on this

[ChrisRackauckas]

Note the SciMLBase.Void{Any}.([explicitfun1,explicitfun2,explicitfun3]) can likely be done internally in the SCCNonlinearProblem constructor. This also requires SciMLBase.NoSpecialize which we are going to make the default after a few things from @oscardssmith first.

This will start as undocumented and experimental so we can work out the kinks.

It has a few allocations, I'm not worrying about those yet, correctness first.

[AayushSabharwal]

Looks really cool! Mostly just general readability/interface comments. I'm looking forward to targeting this with MTK, not so much figuring out how SII will have to interact with it 😅

[ChrisRackauckas]

@AayushSabharwal I see where the confusion was from yesterday: I didn't have the fully final version pushed to the package. This is now set to the parameter mutation form I mentioned.