Adding an algorithm

The 2D deterministic inversion is built so that a new algorithm only has to say how it chooses a direction. The driver in Inv2D.jl does the rest: stopping tests, step capping, line search, history and file output.

Steps

1. Create src/Inv2D_<Name>.jl and include it after Inv2D.jl in src/MTGeophysics.jl. Inv2D_NLCG.jl is the smallest complete example.

2. Define a config type <: AbstractInversion2D.

3. Define these methods for it:

   • inv2d_tag

   • inv2d_init

   • inv2d_prepare!, which returns the gradient

   • inv2d_direction

   • inv2d_accept!

Optional methods have defaults:

• inv2d_reject! returns false, so a failed search ends the run.

• inv2d_info returns no extra history columns.

• inv2d_validate performs no checks.

Building blocks

Inv2D.jl provides:

• inv2d_frechet(problem, state): the weighted 2n_data × n_active Fréchet derivative

• inv2d_gradient(problem, state, G): Gᵗr + βRᵗ reg

• inv2d_gradient(problem, state): the same gradient from adjoint solves, for gradient-only methods

See 2D inversion theory for the objective these act on.