DiffKrylov provides a differentiable API for Krylov.jl using ForwardDiff.jl and Enzyme.jl. This is a work in progress and eventually should enable numerical comparisons between discrete and continuous tangent and adjoint methods (see this report).

• Only supports gmres, cg, and bicgstab methods
• No support for linear operators

• How to set the options for the tangent/adjoint solve based on the options for the forward solve? For example bicgtab may return NaN for the tangents or adjoints.

] add DiffKrylov

Using ForwardDiff.jl, we can compute the Jacobian of x with respect to b using the ForwardDiff.jl API:

using ForwardDiff, DiffKrylov, Krylov, Random
A = rand(64,64)
b = rand(64)
J = ForwardDiff.jacobian(x -> gmres(A, x)[1], b)