Created
May 20, 2020 09:33
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using PseudoArcLengthContinuation, LinearAlgebra, Plots, PyPlot, Optim | |
const PALC = PseudoArcLengthContinuation | |
using ForwardDiff | |
function f(x, alpha) | |
[alpha*x[1] + x[1]^3 ] | |
end | |
function Jf(x, alpha) | |
Jf = zeros(1, 1) | |
Jf[1] = alpha+3x[1]^2 | |
Jf | |
end | |
Fmit = f | |
D(f, x, p, dx) = ForwardDiff.derivative(t->f(x .+ t .* dx, p), 0.) | |
d1Fmit(x,p,dx1) = D((z, p0) -> Fmit(z, p0), x, p, dx1) | |
d2Fmit(x,p,dx1,dx2) = D((z, p0) -> d1Fmit(z, p0, dx1), x, p, dx2) | |
d3Fmit(x,p,dx1,dx2,dx3) = D((z, p0) -> d2Fmit(z, p0, dx1, dx2), x, p, dx3) | |
jet = (f, Jf, d2Fmit, d3Fmit) | |
opt_newton = PALC.NewtonPar(tol = 1e-8, verbose = true) | |
# options for continuation | |
alpha_min = -10. | |
alpha_max = 10. | |
alpha_start = 2. | |
opts_br = ContinuationPar(dsmin = 0.001, dsmax = 0.05, ds = -0.01, pMax = alpha_max, pMin = alpha_min, | |
detectBifurcation = 2, nev = 30, plotEveryNsteps = 10,maxSteps = 100, precisionStability = 1e-6, nInversion = 4, dsminBisection = 1e-7, maxBisectionSteps = 25) | |
optnewton = NewtonPar(verbose = true) | |
sol_start, _, _ = newton( x -> f(x, alpha_start), [1.], optnewton) | |
br, _ = continuation(f, sol_start, alpha_start, opts_br, plot = true, printSolution = (x,p) -> x[1], plotSolution = (x, p;kwargs...) -> (plot!(x; ylabel="solution",label="",kwargs...))) | |
br2, _ = continuation(jet..., br, 1, opts_br, plot = true, printSolution = (x,p) -> x[1], plotSolution = (x, p;kwargs...) -> (plot!(x; ylabel="solution",label="",kwargs...))) | |
Plots.plot([br,br2],plotfold=false) |
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