Make mex solve_algo=13 the default solve_algo=4

solve_algo=13 uses the block_trust_region MEX, which is essentially a MEX reimplementation of what is available under solve_algo=4.

After a Mattermost discussion on 2021-09-21/22, the consensus seems to be:

• verify that the two codes are really equivalent (in particular when moving in the complex domain)
• then change solve_algo=4 so that it calls the MEX file, and drop solve_algo=13
• the old MATLAB code for solve_algo=4 should be kept under missing/mex, ideally with an interface, in order to facilitate the debugging of models (which is easier in MATLAB than in Fortran)

changed milestone to %6.x

added decision label

mentioned in issue #1851 (closed)

changed title from Decide what to do with solve_algo=13 to Make mex solve_algo=13 the default solve_algo=4

removed decision label

added decision label

The mex-file requires jacobian_flag=true, which is not the case in general. This is a problem for the default algorithm as it will break e.g. Ramsey. A solution would be to not move the m-file to missing but rather use it if jacobian_flag=false.

Of course, another option is to add support for jacobian_flag=false to the MEX.

The question is whether that is feasible within the envisioned time frame and also in the context of calling external functions.

With 16eabbbc, the codebase has diverged even further. This suggests to keep the two options distinct. @sebastien What do you think?

I don’t think that the divergence between the two codebases is significant (do you think that under-determined blocks in the DM decomposition happen regularly?). So I’m still in favour of merging the two options, provided that the conditions set at the top of this issue are satisfied.

It's the combination of under-determined blocks that happens surprisingly often and the missing support for jacobian_flag.

Indeed, support for jacobian_flag needs to be implemented in block_trust_region MEX before we can consider switching.

I thought the problem is that this will not work with external functions.

removed milestone %6.x