FAQ

How can I save a solution every n steps, or at specific parameter values?

You can use the callback finaliseSolution in the function call continuation. For example, you can use something like this to save all steps

function mySave(u, tau, step, contResult, personaldata)
	push!(personaldata, u)
end

and pass it like continuation(F, J, u, p0, finaliseSolution = (z, tau, step, contResult) -> mySave(z, tau, step, contResult, myData))

The Fold / Hopf Continuation does not work, why?

This requires some precise computations. Have you tried passing the expression of the Jacobian instead of relying on finite differences.

What is the parameter theta about in ContinuationPar?

See the description of continuation on the page Library.

How can I change the preconditioner during computations?

The easiest way to achieve this is by using the callbacks provided by newton and continuation. See the documentation about these two methods. See also the example Complex Ginzburg-Landau 2d

How can I implement my own bifurcation detection method?

You can use the callback finaliseSolution but the best way is probably to use the Iterator Interface to inject your code anywhere in the continuation procedure.

How do I dissociate the computation of eigenvalues from the jacobian that I passed?

Sometimes, for example when implementing boundary conditions, you pass a jacobian J but the eigenvalues, and the bifurcation points are not simply related to J. One way to bypass this issue is to define a new eigensolver <: AbstractEigenSolver and pass it to the NewtonPar field eigsolver. This is done for example in example/SH2d-fronts-cuda.jl.

How can I print the eigenvalues during continuation?

You can print the eigenvalues using the following callback:

finaliseSolution = (z, tau, step, contResult) -> 
		(Base.display(contResult.eig[end].eigenvals) ;true)

How can I reject a Newton Step?

You can reject a newton step by passing to continuation the argument callbackN

function mycallback(x, f, J, res, iteration, itlinear, options; kwargs...)
	# stop Newton algo if residual too large
	if res > 1e2
		@warn "Reject Newton step!!"
		return false
	end
	return true
end

How do I stop continuation?

Using the argument finaliseSolution in continuation. Simply make this function finaliseSolution return false.