Automate solver

[azev77]

Hi Spencer and thanks for the awesome package!

When I took macro w/ Jesus FV we learned there are 3 broad approaches to solving econ models:

Method	Examples	Toolkits
Fixed Point Iteration	VFI, PFI, EE iteration	VFI toolkit, CLMM
Perturbation	Linearization, LQ ...	Dynare, SolveDSGE.jl, DSGE.jl
Projection	Chebyshev, Smolyak, PEA, FEM	SolveDSGE.jl, TaylorProjection.m

1 SolveDSGE.jl is the only package that allows both Perturbation and Projection (& their hybrids)
2 VFI toolkit originally planned a Julia version. It doesn't look like its coming soon.
3 Your package (CLMM) seems to be the best Julia option for FPI (allowing 7 methods!!!)

Is there any way CLMM can be automated into a toolkit?
I mean where the user creates:
ncgm: a set of parameters "ncgm"
u: a return function (flow utility)
g: a transition function for the state vector
And then something like:

solve_fpi(VFI(), ncgm, u, g, guess; maxiter=1000, verbose=false)
solve_fpi(VFI_EGM(), ncgm, u, g, guess; maxiter=1000, verbose=false)
solve_fpi(VFI_ECM(), ncgm, u, g, guess; maxiter=1000, verbose=false)
solve_fpi(dVFI_ECM(), ncgm, u, g, guess; maxiter=1000, verbose=false)

solve_fpi(PFI(), ncgm, u, g, guess; maxiter=1000, verbose=false)
solve_fpi(PFI_ECM(), ncgm, u, g, guess; maxiter=1000, verbose=false)
solve_fpi(EulEq(), ncgm, u, g, guess; maxiter=1000, verbose=false)

Science would be a lot better off if this were possible...
Thanks again for your awesome package