br.specialpoint[n].x different from getSolx(br, br.specialpoint[n].idx)

[dchang24]

Using the temperature model from the tutorial:

using BifurcationKit, Parameters, Setfield
const BK = BifurcationKit

Nop(x; a = 0.5, b = 0.01) = 1 + (x + a*x^2)/(1 + b*x^2)

function F_chan(x, p)
    α, a, b = p.α, p.a, p.b
    f = similar(x)
    n = length(x)
    f[1] = x[1] - b
    f[n] = x[n] - b
    for i=2:n-1
        f[i] = (x[i-1] - 2 * x[i] + x[i+1]) * (n-1)^2 + α * Nop(x[i], a=a, b=b)
    end
    return f
end

n = 101
sol0 = [(i-1)*(n-i)/n^2+0.1 for i=1:n]

par = (α = 3.3, a = 0.5, b = 0.01)

prob1 = BifurcationProblem(F_chan, sol0, par, (@lens _.α))

optcont1 = ContinuationPar(dsmin = 0.01, dsmax = 0.1, ds= 0.01, pMin = 0., pMax = 4.2,
    newtonOptions = NewtonPar(maxIter = 10, tol = 1e-9), saveSolEveryStep=1,
    detectEvent=0, detectBifurcation=0)

@time br1 = continuation(prob1, PALC(), optcont1)

I found that the solution x from br1.specialpoint[n].x and that returned from getSolx (or br1.sol[br1.specialpoint[n].idx].x) are different:

idx = br1.specialpoint[1].idx   # idx=15
all(br1.specialpoint[1].x .== getSolx(br1, idx))   # false
all(br1.specialpoint[1].x .== getSolx(br1, idx+1))   # false
all(br1.specialpoint[1].x .== getSolx(br1, idx+2))   # true

Is this intended or a bug? I thought both should be the same.

I also found that sometimes when I try to refine a fold point (using newton or as part of a codim2 continuation), it doesn't converge at the initial guess even though tol remains the same. I'm not sure if this is related to the above mentioned problem or something that is normal.

[rveltz]

It should be a bug and I am surprised I did not put a test for this.

Concerning Fold continuation, the best is to use startWithEigen=true. Open an issue if this does not converge