required function not found' with '-var' option in ode_isol2po

Thank you, Jacob, for this question.

I am very happy to see that you are exploring COCO and attempting to reproduce existing results using independently developed code.

There are several parts to this that I will address below.
1. Even if the error you encountered hadn't been thrown, your code would not have executed, since the introduction of the variational problem added 9 to the dimensional deficit. To prevent this from happening, you would need to also introduce 9 constraints, e.g., using the following code:

[data, uidx] = coco_get_func_data(prob, 'po.orb.coll.var', 'data', 'uidx');
prob = coco_add_pars(prob, 'pars2', uidx(data.coll_var.v0_idx,:), ...
 {'s1' 's2' 's3' 's4' 's5' 's6' 's7' 's8' 's9'});

as is done in the coll/exampes/linode demo. This holds the initial values of the solution to the variational problem fixed and ensures a unique solution to the variational problem given the corresponding periodic orbit.

1. The error is thrown because the encoding of the ode_isol2coll constructor assumes that if you are embedding a linearization of the dynamical system with the continuation problem, then you will not want the toolbox to also define a monitor function that computes the solution to the variational problem and stores this for potential use during bifurcation analysis. This assumption was made to reduce redundant computations but is perhaps a flawed assumption in practice.

2. Two options come to mind: you either override this assumption by replacing

  [prob, data] = coll_add(prob, data, sol, '-no-var', '-cache-jac');

with

  [prob, data] = coll_add(prob, data, sol, '-cache-jac');

in ode_isol2coll.

Alternatively, you turn off the default bifurcation detection for the 'po' toolbox by invoking the command

prob = coco_set(prob, 'po', 'bifus', off);

before calling ode_isol2po. If you still want to perform bifurcation detection, you could now use the solution to the variational problem to define test functions that check for saddle-node, period-doubling, and Hopf bifurcations.

I ran your code with the second option (and with the fix described in 1.) but without implementing any further test functions, and everything seems to execute fine.

I hope that helps.

Harry

In case anyone from the future sees this, I've attached the example code with the fixes implemented.

Thank you, Jacob, also for the greetings!

Although option #2 provides a fix, the behavior you have identified should count as a bug, since a construction error is thrown for a syntactically correct construction. I will aim to encode a transparent and well-documented solution to this in a future COCO update.

Kind regards,

Harry