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* feat: add `PETScSNES` * feat: support automatic sparsity detection for PETSc * test: add PETScSNES to the wrapper tests * docs: add PETSc example * test: skip PETSc tests on windows * docs: print the benchmark results
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| # PETSc.jl | ||
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| This is a extension for importing solvers from PETSc.jl SNES into the SciML interface. Note | ||
| that these solvers do not come by default, and thus one needs to install the package before | ||
| using these solvers: | ||
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| ```julia | ||
| using Pkg | ||
| Pkg.add("PETSc") | ||
| using PETSc, NonlinearSolve | ||
| ``` | ||
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| ## Solver API | ||
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| ```@docs | ||
| PETScSNES | ||
| ``` |
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| # [PETSc SNES Example 2](@id snes_ex2) | ||
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| This implements `src/snes/examples/tutorials/ex2.c` from PETSc and `examples/SNES_ex2.jl` | ||
| from PETSc.jl using automatic sparsity detection and automatic differentiation using | ||
| `NonlinearSolve.jl`. | ||
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| This solves the equations sequentially. Newton method to solve | ||
| `u'' + u^{2} = f`, sequentially. | ||
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| ```@example snes_ex2 | ||
| using NonlinearSolve, PETSc, LinearAlgebra, SparseConnectivityTracer, BenchmarkTools | ||
| u0 = fill(0.5, 128) | ||
| function form_residual!(resid, x, _) | ||
| n = length(x) | ||
| xp = LinRange(0.0, 1.0, n) | ||
| F = 6xp .+ (xp .+ 1e-12) .^ 6 | ||
| dx = 1 / (n - 1) | ||
| resid[1] = x[1] | ||
| for i in 2:(n - 1) | ||
| resid[i] = (x[i - 1] - 2x[i] + x[i + 1]) / dx^2 + x[i] * x[i] - F[i] | ||
| end | ||
| resid[n] = x[n] - 1 | ||
| return | ||
| end | ||
| ``` | ||
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| To use automatic sparsity detection, we need to specify `sparsity` keyword argument to | ||
| `NonlinearFunction`. See [Automatic Sparsity Detection](@ref sparsity-detection) for more | ||
| details. | ||
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| ```@example snes_ex2 | ||
| nlfunc_dense = NonlinearFunction(form_residual!) | ||
| nlfunc_sparse = NonlinearFunction(form_residual!; sparsity = TracerSparsityDetector()) | ||
| nlprob_dense = NonlinearProblem(nlfunc_dense, u0) | ||
| nlprob_sparse = NonlinearProblem(nlfunc_sparse, u0) | ||
| ``` | ||
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| Now we can solve the problem using `PETScSNES` or with one of the native `NonlinearSolve.jl` | ||
| solvers. | ||
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| ```@example snes_ex2 | ||
| sol_dense_nr = solve(nlprob_dense, NewtonRaphson(); abstol = 1e-8) | ||
| sol_dense_snes = solve(nlprob_dense, PETScSNES(); abstol = 1e-8) | ||
| sol_dense_nr .- sol_dense_snes | ||
| ``` | ||
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| ```@example snes_ex2 | ||
| sol_sparse_nr = solve(nlprob_sparse, NewtonRaphson(); abstol = 1e-8) | ||
| sol_sparse_snes = solve(nlprob_sparse, PETScSNES(); abstol = 1e-8) | ||
| sol_sparse_nr .- sol_sparse_snes | ||
| ``` | ||
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| As expected the solutions are the same (upto floating point error). Now let's compare the | ||
| runtimes. | ||
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| ## Runtimes | ||
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| ### Dense Jacobian | ||
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| ```@example snes_ex2 | ||
| @benchmark solve($(nlprob_dense), $(NewtonRaphson()); abstol = 1e-8) | ||
| ``` | ||
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| ```@example snes_ex2 | ||
| @benchmark solve($(nlprob_dense), $(PETScSNES()); abstol = 1e-8) | ||
| ``` | ||
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| ### Sparse Jacobian | ||
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| ```@example snes_ex2 | ||
| @benchmark solve($(nlprob_sparse), $(NewtonRaphson()); abstol = 1e-8) | ||
| ``` | ||
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| ```@example snes_ex2 | ||
| @benchmark solve($(nlprob_sparse), $(PETScSNES()); abstol = 1e-8) | ||
| ``` |
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| module NonlinearSolvePETScExt | ||
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| using FastClosures: @closure | ||
| using MPI: MPI | ||
| using NonlinearSolveBase: NonlinearSolveBase, get_tolerance | ||
| using NonlinearSolve: NonlinearSolve, PETScSNES | ||
| using PETSc: PETSc | ||
| using SciMLBase: SciMLBase, NonlinearProblem, ReturnCode | ||
| using SparseArrays: AbstractSparseMatrix | ||
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| function SciMLBase.__solve( | ||
| prob::NonlinearProblem, alg::PETScSNES, args...; abstol = nothing, reltol = nothing, | ||
| maxiters = 1000, alias_u0::Bool = false, termination_condition = nothing, | ||
| show_trace::Val{ShT} = Val(false), kwargs...) where {ShT} | ||
| # XXX: https://petsc.org/release/manualpages/SNES/SNESSetConvergenceTest/ | ||
| termination_condition === nothing || | ||
| error("`PETScSNES` does not support termination conditions!") | ||
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| _f!, u0, resid = NonlinearSolve.__construct_extension_f(prob; alias_u0) | ||
| T = eltype(prob.u0) | ||
| @assert T ∈ PETSc.scalar_types | ||
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| if alg.petsclib === missing | ||
| petsclibidx = findfirst(PETSc.petsclibs) do petsclib | ||
| petsclib isa PETSc.PetscLibType{T} | ||
| end | ||
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| if petsclibidx === nothing | ||
| error("No compatible PETSc library found for element type $(T). Pass in a \ | ||
| custom `petsclib` via `PETScSNES(; petsclib = <petsclib>, ....)`.") | ||
| end | ||
| petsclib = PETSc.petsclibs[petsclibidx] | ||
| else | ||
| petsclib = alg.petsclib | ||
| end | ||
| PETSc.initialized(petsclib) || PETSc.initialize(petsclib) | ||
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| abstol = get_tolerance(abstol, T) | ||
| reltol = get_tolerance(reltol, T) | ||
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| nf = Ref{Int}(0) | ||
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| f! = @closure (cfx, cx, user_ctx) -> begin | ||
| nf[] += 1 | ||
| fx = cfx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cfx; read = false) : cfx | ||
| x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx | ||
| _f!(fx, x) | ||
| Base.finalize(fx) | ||
| Base.finalize(x) | ||
| return | ||
| end | ||
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| snes = PETSc.SNES{T}(petsclib, | ||
| alg.mpi_comm === missing ? MPI.COMM_SELF : alg.mpi_comm; | ||
| alg.snes_options..., snes_monitor = ShT, snes_rtol = reltol, | ||
| snes_atol = abstol, snes_max_it = maxiters) | ||
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| PETSc.setfunction!(snes, f!, PETSc.VecSeq(zero(u0))) | ||
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| if alg.autodiff === missing && prob.f.jac === nothing | ||
| _jac! = nothing | ||
| njac = Ref{Int}(-1) | ||
| else | ||
| autodiff = alg.autodiff === missing ? nothing : alg.autodiff | ||
| if prob.u0 isa Number | ||
| _jac! = NonlinearSolve.__construct_extension_jac( | ||
| prob, alg, prob.u0, prob.u0; autodiff) | ||
| J_init = zeros(T, 1, 1) | ||
| else | ||
| _jac!, J_init = NonlinearSolve.__construct_extension_jac( | ||
| prob, alg, u0, resid; autodiff, initial_jacobian = Val(true)) | ||
| end | ||
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| njac = Ref{Int}(0) | ||
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| if J_init isa AbstractSparseMatrix | ||
| PJ = PETSc.MatSeqAIJ(J_init) | ||
| jac! = @closure (cx, J, _, user_ctx) -> begin | ||
| njac[] += 1 | ||
| x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx | ||
| if J isa PETSc.AbstractMat | ||
| _jac!(user_ctx.jacobian, x) | ||
| copyto!(J, user_ctx.jacobian) | ||
| PETSc.assemble(J) | ||
| else | ||
| _jac!(J, x) | ||
| end | ||
| Base.finalize(x) | ||
| return | ||
| end | ||
| PETSc.setjacobian!(snes, jac!, PJ, PJ) | ||
| snes.user_ctx = (; jacobian = J_init) | ||
| else | ||
| PJ = PETSc.MatSeqDense(J_init) | ||
| jac! = @closure (cx, J, _, user_ctx) -> begin | ||
| njac[] += 1 | ||
| x = cx isa Ptr{Nothing} ? PETSc.unsafe_localarray(T, cx; write = false) : cx | ||
| _jac!(J, x) | ||
| Base.finalize(x) | ||
| J isa PETSc.AbstractMat && PETSc.assemble(J) | ||
| return | ||
| end | ||
| PETSc.setjacobian!(snes, jac!, PJ, PJ) | ||
| end | ||
| end | ||
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| res = PETSc.solve!(u0, snes) | ||
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| _f!(resid, res) | ||
| u_ = prob.u0 isa Number ? res[1] : res | ||
| resid_ = prob.u0 isa Number ? resid[1] : resid | ||
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| objective = maximum(abs, resid) | ||
| # XXX: Return Code from PETSc | ||
| retcode = ifelse(objective ≤ abstol, ReturnCode.Success, ReturnCode.Failure) | ||
| return SciMLBase.build_solution(prob, alg, u_, resid_; retcode, original = snes, | ||
| stats = SciMLBase.NLStats(nf[], njac[], -1, -1, -1)) | ||
| end | ||
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| end |
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