-
-
Notifications
You must be signed in to change notification settings - Fork 52
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
Merge pull request #449 from SciML/ap/adjoint
Adjoints for Linear Solve
- Loading branch information
Showing
9 changed files
with
261 additions
and
21 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,93 @@ | ||
| # TODO: Preconditioners? Should Pl be transposed and made Pr and similar for Pr. | ||
|
|
||
| @doc doc""" | ||
| LinearSolveAdjoint(; linsolve = missing) | ||
| Given a Linear Problem ``A x = b`` computes the sensitivities for ``A`` and ``b`` as: | ||
| ```math | ||
| \begin{align} | ||
| A^T \lambda &= \partial x \\ | ||
| \partial A &= -\lambda x^T \\ | ||
| \partial b &= \lambda | ||
| \end{align} | ||
| ``` | ||
| For more details, check [these notes](https://math.mit.edu/~stevenj/18.336/adjoint.pdf). | ||
| ## Choice of Linear Solver | ||
| Note that in most cases, it makes sense to use the same linear solver for the adjoint as the | ||
| forward solve (this is done by keeping the linsolve as `missing`). For example, if the | ||
| forward solve was performed via a Factorization, then we can reuse the factorization for the | ||
| adjoint solve. However, for specific structured matrices if ``A^T`` is known to have a | ||
| specific structure distinct from ``A`` then passing in a `linsolve` will be more efficient. | ||
| """ | ||
| @kwdef struct LinearSolveAdjoint{L} <: | ||
| SciMLBase.AbstractSensitivityAlgorithm{0, false, :central} | ||
| linsolve::L = missing | ||
| end | ||
|
|
||
| function CRC.rrule(::typeof(SciMLBase.solve), prob::LinearProblem, | ||
| alg::SciMLLinearSolveAlgorithm, args...; alias_A = default_alias_A( | ||
| alg, prob.A, prob.b), kwargs...) | ||
| # sol = solve(prob, alg, args...; kwargs...) | ||
| cache = init(prob, alg, args...; kwargs...) | ||
| (; A, sensealg) = cache | ||
|
|
||
| @assert sensealg isa LinearSolveAdjoint "Currently only `LinearSolveAdjoint` is supported for adjoint sensitivity analysis." | ||
|
|
||
| # Decide if we need to cache `A` and `b` for the reverse pass | ||
| if sensealg.linsolve === missing | ||
| # We can reuse the factorization so no copy is needed | ||
| # Krylov Methods don't modify `A`, so it's safe to just reuse it | ||
| # No Copy is needed even for the default case | ||
| if !(alg isa AbstractFactorization || alg isa AbstractKrylovSubspaceMethod || | ||
| alg isa DefaultLinearSolver) | ||
| A_ = alias_A ? deepcopy(A) : A | ||
| end | ||
| else | ||
| A_ = deepcopy(A) | ||
| end | ||
|
|
||
| sol = solve!(cache) | ||
|
|
||
| function ∇linear_solve(∂sol) | ||
| ∂∅ = NoTangent() | ||
|
|
||
| ∂u = ∂sol.u | ||
| if sensealg.linsolve === missing | ||
| λ = if cache.cacheval isa Factorization | ||
| cache.cacheval' \ ∂u | ||
| elseif cache.cacheval isa Tuple && cache.cacheval[1] isa Factorization | ||
| first(cache.cacheval)' \ ∂u | ||
| elseif alg isa AbstractKrylovSubspaceMethod | ||
| invprob = LinearProblem(transpose(cache.A), ∂u) | ||
| solve(invprob, alg; cache.abstol, cache.reltol, cache.verbose).u | ||
| elseif alg isa DefaultLinearSolver | ||
| LinearSolve.defaultalg_adjoint_eval(cache, ∂u) | ||
| else | ||
| invprob = LinearProblem(transpose(A_), ∂u) # We cached `A` | ||
| solve(invprob, alg; cache.abstol, cache.reltol, cache.verbose).u | ||
| end | ||
| else | ||
| invprob = LinearProblem(transpose(A_), ∂u) # We cached `A` | ||
| λ = solve( | ||
| invprob, sensealg.linsolve; cache.abstol, cache.reltol, cache.verbose).u | ||
| end | ||
|
|
||
| ∂A = -λ * transpose(sol.u) | ||
| ∂b = λ | ||
| ∂prob = LinearProblem(∂A, ∂b, ∂∅) | ||
|
|
||
| return (∂∅, ∂prob, ∂∅, ntuple(_ -> ∂∅, length(args))...) | ||
| end | ||
|
|
||
| return sol, ∇linear_solve | ||
| end | ||
|
|
||
| function CRC.rrule(::Type{<:LinearProblem}, A, b, p; kwargs...) | ||
| prob = LinearProblem(A, b, p) | ||
| ∇prob(∂prob) = (NoTangent(), ∂prob.A, ∂prob.b, ∂prob.p) | ||
| return prob, ∇prob | ||
| end |
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Oops, something went wrong.