Proposing a callback mechanism for tracking bifurcation events in the path follower

[AndresFerCervell]

Following up on our recent work to handle fold bifurcations in the QRE logit tracer (related to Issue #492), we´re implementing a mechanism that applies a perturbation when the orientation of the curve changes, breaking the symmetry and allowing the tracer to proceed.

As discussed with @tturocy, it would be interesting to add a “perturbation applied event” as a callback to the tracer. So that users can record information about these events.

We are working now on a machinery that detects the path follower failing, not accepting the result as Nash, and returning the last iteration. However, the user does not know when a perturbation occurs and the algorithm solves by itself, nor the nature of the perturbation that "kills" the program.

Proposed Architecture:

A struct could be created to store the relevant data for the event.

struct TracerEventData {
    PathEvent type; // Is it already solved?? 
    double current_h;
    double current_lambda;
    double perturbation_value;
    double current_pert;  // The perturbation that is being currently applied
};

A new callback function could be defined in logit.cc that would print the info about the perturbation.

It would be called in path.cc when a new bifurcation happens (after omega_flip == -1.0), and when it finishes (if it does), after pert_countdown < 0.0.

Any thoughts or alternative approaches are highly welcome!